mark scheme pure mathematics year 1 (as) unit test 1 ... · mark scheme pure mathematics year 1...

91
Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1 Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 1 Attempt to multiply the numerator and denominator by (8 3) k . For example, 63 4 8 3 8 3 8 3 M1 1.1b 3rd Rationalise the denominator of a fraction with a simple surd denominator Attempt to multiply out the numerator (at least 3 terms correct). 48 3 18 32 43 M1 1.1a Attempt to multiply out the denominator (for example, 3 terms correct but must be rational or 64 3 seen or implied). 64 83 83 3 M1 1.1b p and q stated or implied (condone if all over 61). 44 14 3 61 61 or 44 14 , 61 61 p q A1 1.1b (4 marks) Notes

Upload: others

Post on 25-Dec-2019

442 views

Category:

Documents


32 download

TRANSCRIPT

Page 1: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1 Attempt to multiply the numerator and denominator by

(8 3)k . For example,6 3 4 8 3

8 3 8 3

M1 1.1b 3rd

Rationalise the

denominator of a

fraction with a

simple surd

denominator

Attempt to multiply out the numerator (at least 3 terms

correct).

48 3 18 32 4 3

M1 1.1a

Attempt to multiply out the denominator (for example, 3 terms

correct but must be rational or 64 – 3 seen or implied).

64 8 3 8 3 3

M1 1.1b

p and q stated or implied (condone if all over 61).

44 143

61 61 or

44 14,

61 61p q

A1 1.1b

(4 marks)

Notes

Page 2: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2 2

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a Statement that discriminant is b2 – 4ac, and/or implied by

writing 2

8 4 1 8 1k k

M1 1.1a 4th

Understand and

use the

discriminant;

conditions for

real, repeated and

no real roots

Attempt to simplify the expression by multiplying out the

brackets. Condone sign errors and one algebraic error (but not

missing k term from squaring brackets and must have k2, k and

constant terms).

2 8 8 64 32 4k k k k o.e.

M1 1.1b

2 16 60k k A1 1.1b

(3)

2b Knowledge that two equal roots occur when the discriminant

is zero. This can be shown by writing b2 – 4ac = 0, or by

writing 2 16 60 0k k

M1 1.1b 5th

Solve problems

involving the

discriminant in

context and

construct simple

proofs involving

the discriminant

10, 6k k A1 1.1b

(2)

2c Correct substitution for k = 8: 2f( ) 16 65x x x B1 2.2a 3rd

Solve quadratic

equations by use

of formula

Attempt to complete the square for their expression of f(x).

2

f( ) 8 1x x

M1 1.1b

Statement (which can be purely algebraic) that f(x) > 0,

because, for example, a squared term is always greater than or

equal to zero, so one more than a square term must be greater

than zero or an appeal to a reasonable sketch of y = f(x).

A1 2.3

(3)

(8 marks)

Page 3: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3 3

Notes

2a

Not all steps have to be present to award full marks. For example, the second method mark can still be awarded

if the answer does not include that step.

2b

Award full marks for k = 6, k = 10 seen. Award full marks for valid and complete alternative method (e.g.

expanding (x – a)2 comparing coefficients and solving for k).

2c

An alternative method is acceptable. For example, students could differentiate to find that the turning point of

the graph of y = f(x) is at (8, 1), and then show that it is a minimum. The minimum can be shown by using

properties of quadratic curves or by finding the second differential. Students must explain (a sketch will suffice)

that this means that the graph lies above the x-axis and reach the appropriate conclusion.

Page 4: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4 4

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a 115 (m) is the height of the cliff (as this is the height of the

ball when t = 0). Accept answer that states 115 (m) is the

height of the cliff plus the height of the person who is ready to

throw the stone or similar sensible comment.

B1 3.2a 4th

Understand the

concepts of

domain and range

(1)

3b Attempt to factorise the – 4.9 out of the first two (or all)

terms.

2( ) 4.9 2.5 115h t t t or 2 5( ) 4.9 115

2h t t t

M1 3.1a 4th

Solve simple

quadratic

equations by

completing the

square

2 2( ) 4.9 1.25 ( 4.9) 1.25 115h t t

or

2 25 5

( ) 4.9 ( 4.9) 1154 4

h t t

M1 3.1a

2

( ) 122.65625 4.9 1.25h t t o.e.

(N.B. 122.65625 =3925

32)

Accept the first term written to 1, 2, 3 or 4 d.p. or the full

answer as shown.

A1 3.1a

(3)

3ci Statement that the stone will reach ground level when

h(t) = 0, or 24.9 12.25 115 0t t is seen.

M1 3.1a 4th

Form and solve

quadratic

equations in

context

Valid attempt to solve quadratic equation (could be using

completed square form from part b, calculator or formula). M1 3.1a

Clearly states that t = 6.25 s (accept t = 6.3 s) is the answer, or

circles that answer and crosses out the other answer, or

explains that t must be positive as you cannot have a negative

value for time.

A1 3.5a

(3)

Page 5: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5 5

3cii hmax = awrt 123

ft A from part b.

B1ft 3.1a 4th

Form and solve

quadratic

equations in

context

t =5

4or t = 1.25

ft C from part b.

B1ft 3.2a

(2)

(9 marks)

Notes

3c

Award 4 marks for correct final answer, with some working missing. If not correct B1 for each of A, B and C

correct.

If the student answered part b by completing the square, award full marks for part c, providing their answer to

their part b was fully correct.

Page 6: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6 6

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a Attempt to solve q(x) = 0 by completing the square or by using

the formula.

2

2

10 20 0

5 45 0

x x

x

or

10 100 4(1)( 20)

2(1)x

M1 1.1b 3rd

Solve quadratic

equations by use

of formula

5 3 5x and/or statement that says a = 5 and b = 5 A1 1.1b

(2)

4b Figure 1

q(0) = −20, so y = q(x)

intersects y-axis at (0, −20)

and x-intercepts labelled

(accept incorrect values from

part a).

B1ft 1.1b 3rd

Sketch graphs of

quadratic

functions

y = p(x) intersects y-axis

at (0, 3).

B1 1.1b

y = p(x) intersects x-axis

at (6, 0).

B1 1.1b

Graphs drawn as shown with

all axes intercepts labelled.

The two graphs should clearly

intersect at two points, one at

a negative value of x and one

at a positive value of x. These

points of intersection do not

need to be labelled.

B1 1.1b

(4)

Page 7: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7 7

4c Statement indicating that this is the point where p(x) = q(x)

or 2 110 20 3

2x x x seen.

M1 2.2a 4th

Solve more

complicated

simultaneous

equations where

one is linear and

one is quadratic

Their equation factorised, or attempt to solve their equation by

completing the square.

2x2 −19x – 46 = 0

(2x – 23)(x + 2) = 0

M1 1.1b

23 11,

2 4

A1 1.1b

2,4 A1 1.1b

(4)

4d x < – 2 or

23

2x o.e.

B1 2.2a 4th

Represent

solutions to

quadratic

inequalities using

set notation

{ : , 2} { : , 11.5}x x x x x x ¡ ¡

NB: Must see “or” or (if missing SC1 for just the correct

inequalities).

B1 2.2a

(2)

(12 marks)

Notes

4a

Equation can be solved by completing the square or by using the quadratic formula. Either method is acceptable.

4b

Answers with incorrect coordinates lose accuracy marks as appropriate. However, the graph accuracy marks can

be awarded for correctly labelling their coordinates, even if their coordinates are incorrect.

4c

If the student incorrectly writes the initial equation, award 1 method mark for an attempt to solve the incorrect

equation. Solving the correct equation by either factorising or completing the square is acceptable.

Page 8: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 8 8

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5 Figure 2

Asymptote drawn at x = 6

B1 1.1b 5th

Understand and

use properties of

asymptotes for

graphs of the

form y = a/x and y

= a/x2

Asymptote drawn at y = 5 B1 1.1b

Point13

0,3

labelled.

Condone 13

3clearly on y axis.

B1 1.1b

Point26

,05

labelled.

Condone26

5clearly on x axis.

B1 1.1b

Correctly shaped graph drawn

in the correct quadrants

formed by the asymptotes.

B1 1.1b

(5)

(5 marks)

Notes

Page 9: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 9 9

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6a Figure 3

Evidence of attempt to show

stretch of sf 1

2in x direction

(e.g. one correct set of

coordinates – not (0, –2)).

M1 1.1b 3rd

Transform graphs

using stretches

Fully complete graph with all

points labelled. A1 1.1b

(2)

Page 10: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 10 10

6b Figure 4

Evidence of attempt to show

reflection in y axis (e.g. one

correct set of coordinates – not

(0, –2)).

M1 1.1b 3rd

Transform graphs

using translations

Fully complete graph with all

points labelled. A1 1.1b

(2)

(4 marks)

Notes

Page 11: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 11 11

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7a Figure 5

Graph of y = 2x + 5 drawn.

B1

1.1b 4th

Represent linear

and quadratic

inequalities on

graphs

Graph of 2y + x = 6 drawn. B1 1.1b

Graph of y = 2 drawn onto the

coordinate grid and the

triangle correctly shaded.

B1 2.2a

(3)

7b Attempt to solve y = 2x + 5 and 2y + x = 6 simultaneously

for y. M1 2.2a 5th

Solve problems

involving linear

and quadratic

inequalities in

context

y = 3.4 A1 1.1b

Base of triangle = 3.5 B1 2.2a

Area of triangle = 1

2 (“3.4” – 2) 3.5

M1 2.2a

Area of triangle is 2.45 (units2). A1 1.1b

(5)

(8 marks)

Notes

7b

It is possible to find the area of triangle by realising that the two diagonal lines are perpendicular and therefore

finding the length of each line using Pythagoras’ theorem. Award full marks for a correct final answer using this

method.

In this case award the second and third accuracy marks for finding the lengths 2.45 and 9.8

Page 12: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a Use of the gradient formula to begin attempt to find k.

1 ( 2) 3

1 (3 4) 2

k

k

or

2 ( 1) 3

3 4 1 2

k

k

(i.e. correct

substitution into gradient formula and equating to 3

2 ).

M1 2.2a 1st

Assumed

knowledge.

2k + 6 = −15 + 9k

21 = 7k

k = 3* (must show sufficient, convincing and correct working).

A1* 1.1b

(2)

1b Student identifies the coordinates of either A or B. Can be seen

or implied, for example, in the subsequent step when student

attempts to find the equation of the line.

A(5, −2) or B(1, 4).

B1 1.1b 2nd

Find the equation

of a straight line

given the gradient

and a point on the

line. Correct substitution of their coordinates into y = mx + b or

y − y1 = m(x − x1) o.e. to find the equation of the line.

For example,

3

2 52

b

or 3

2 52

y x

or

3

4 12

b

or 3

4 12

y x

M1 1.1b

3 11

2 2y x or 3 2 11 0x y

A1 1.1b

(3)

Page 13: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2

1c Midpoint of AB is (3, 1) seen or implied. B1 2.2a 3rd

Find the equation

of a perpendicular

bisector.

Slope of line perpendicular to AB is2

3, seen or implied. B1 2.2a

Attempt to find the equation of the line (i.e. substituting their

midpoint and gradient into a correct equation). For example,

2

1 33

b

or 2

1 33

y x

M1 1.1b

2 3 3 0x y or 3 2 3 0y x . Also accept any multiple of

2 3 3 0x y providing a, b and c are still integers.

A1 1.1b

(4)

(9 marks)

Notes

Page 14: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

2a 11 ( 7) 18 9

6 4 10 5m

B1 1.1b 2nd

Find the equation

of a straight line

given two points. Correct substitution of (4, −7) or (−6, 11) and their gradient

into y = mx + b or y − y1 = m(x − x1) o.e. to find the equation

of the line. For example,

9

7 45

b

or 9

7 45

y x or

9

11 65

b

or 9

11 65

y x .

M1 1.1b

5y + 9x − 1 = 0 or −5y − 9x + 1 = 0 only A1 1.1b

(3)

2b 10,

9y x so

1,0

9A

. Award mark for 1

9x seen.

B1 1.1b 3rd

Solve problems

involving length

and area in the

context of straight

line graphs.

10,

5x y so

10,

5B

. Award mark for 1

5y seen.

B1 1.1b

Area = 1 1 1 1

2 5 9 90

B1 1.1b

(3)

(6 marks)

Notes

Page 15: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

3 y = mx − 2 seen or implied. M1 1.1b 4th

Use the

discriminant to

determine

conditions for the

intersection of

circles and

straight lines.

Substitutes their y = mx − 2 into 2 26 8 4x x y y

22 6 2 8( 2) 4x x mx mx o.e.

M1 3.1a

Rearranges to a 3 term quadratic in x

(condone one arithmetic error).

2 21 (6 12 ) 16 0m x m x

M1 1.1b

Uses 2 4 0b ac , 2 26 12 4 1 16 0m m

M1 3.1a

Rearranges to 220 36 7 0m m or any multiple of this. A1 1.1b

Attempts solution using valid method. For example,

236 36 4 20 7

2 20m

M1 2.2a

9 29

10 5m or

9 2 29

10m

o.e. (NB decimals A0).

A1 1.1b

(7)

(7 marks)

Notes

Elimination of x follows the same scheme.2y

xm

leading to

2

22 26 8 4

y yy y

m m

This leads to 2 2 2 2(1 ) (4 6 8 ) 4 12 4 0m y m m y m m

Use of 2 4 0b ac gives 2

2 2 24 6 8 4 1 4 12 4 0m m m m m which reduces to

2 24 20 36 7 0.m m m m cannot equal 0, so this must be discarded as a solution for the final A mark.

2 4 0b ac could be used implicitly within the quadratic equation formula.

Page 16: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

4a Student attempts to complete the square twice for the first

equation (condone sign errors).

2 2

2 2

5 25 6 36 3

5 6 64

x y

x y

M1 2.2a 4th

Find the centre

and radius of a

circle, given the

equation, by

completing the

square. Centre (−5, 6) A1 3.2a

Radius = 8 A1 3.2a

Student attempts to complete the square twice for the second

equation (condone sign errors).

2 2 2

2 2 2

3 9 9

3 18

x y q q

x y q q

M1 2.2a

Centre (3, q) A1 3.2a

Radius = 218 q A1 3.2a

(6)

4b Uses distance formula for their centres and 80 . For

example,

22 2

5 3 6 80q

M1 2.2a 5th

Solve coordinate

geometry

problems

involving circles

in context. Student simplifies to 3 term quadratic. For example, 2 12 20 0q q

M1 1.1b

Concludes that the possible values of q are 2 and 10 A1 1.1b

(3)

(9 marks)

Notes

Page 17: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

5a Student completes the square twice. Condone sign errors.

2 2

2 2

4 16 5 25 1 0

4 5 40

x y

x y

M1 1.1b 4th

Find the centre

and radius of a

circle, given the

equation, by

completing the

square.

So centre is (4, −5) A1 1.1b

and radius is 40 A1 1.1b

(3)

5b Substitutes x = 10 into equation (in either form).

2 210 8 10 10 1 0y y or 2 2

10 4 5 40y

M1 2.2a 5th

Solve coordinate

geometry

problems

involving circles

in context.

Rearranges to 3 term quadratic in y 2 10 21 0y y

(could be in completed square form 2

5 4y )

M1 1.1b

Obtains solutions y = −3, y = −7 (must give both). A1 1.1b

Rejects y = −7 giving suitable reason (e.g. −7 < −5) or ‘it

would be below the centre’ or ‘AQ must slope upwards’ o.e.

B1 2.3

(4)

5c 3 ( 5) 1=

10 4 3AQm

B1 1.1b 5th

Find the equation

of the tangent to a

given circle at a

specified point. 2

3lm (i.e. −1 over their AQm ) B1ft 2.2a

Substitutes their Q into a correct equation of a line. For

example,

3 3 10 b or 3 3 10y x

M1 1.1b

y = −3x + 27 A1 1.1b

(4)

Page 18: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7

5d 6

2AQ

uuur o.e. (could just be in coordinate form).

M1 3.1a 5th

Solve coordinate

geometry

problems

involving circles

in context.

2

6AP

uuuro.e. so student concludes that point P has

coordinates (2, 1).

M1 3.1a

Substitutes their P and their gradient 1

3 ( AQm from 5c) into a

correct equation of a line. For example,

1

1 23

b

or 1

1 23

y x

M1 2.2a

1 1

3 3y x

A1 1.1b

(4)

5e 40PA B1 3.1a 5th

Solve coordinate

geometry

problems

involving circles

in context.

Uses Pythagoras’ theorem to find 40

9EP .

B1 2.2a

Area of EPA = 1 40

402 9 (could be in two parts).

M1 1.1b

Area = 20

3

A1 1.1b

(4)

(19 marks)

Notes

Page 19: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1 Correctly shows that either

f(3) = 0, f(−2) = 0 or 1

f2

= 0

M1 3.1a 4th

Divide

polynomials by

linear expressions

with no

remainder Draws the conclusion that (x – 3), (x + 2) or (2x + 1) must

therefore be a factor. M1 2.2a

Either makes an attempt at long division by setting up the

long division, or makes an attempt to find the remaining

factors by matching coefficients. For example, stating

2 3 23 2 13 6x ax bx c x x x

or

2 3 22 2 13 6x rx px q x x x

or

2 3 22 1 2 13 6x ux vx w x x x

M1 1.1b

For the long division, correctly finds the the first two

coefficients.

For the matching coefficients method, correctly deduces that

a = 2 and c = 2 or correctly deduces that r = 2 and q = −3 or

correctly deduces that u = 1 and w = –6

A1 2.2a

For the long division, correctly completes all steps in the

division.

For the matching coefficients method, correctly deduces that

b = 5 or correctly deduces that p = −5 or correctly deduces

that v = –1

A1 1.1b

States a fully correct, fully factorised final answer:

(x – 3)(2x + 1)(x + 2)

A1 1.1b

(6 marks)

Page 20: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2 2

Notes

Other algebraic methods can be used to factorise h(x). For example, if (x – 3) is known to be a factor then

3 2 22 13 6 2 ( 3) 5 ( 3) 2( 3)x x x x x x x x by balancing (M1)

2(2 5 2)( 3)x x x by factorising (M1)

(2 1)( 2)( 3)x x x by factorising (A1)

Page 21: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3 3

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a States or implies the expansion of a binomial expression to

the 8th power, up to and including the x3 term.

8 8 8 8 7 8 6 2 8 5 30 1 2 3( ) ...a b C a C a b C a b C a b

or

8 8 7 6 2 5 3( ) 8 28 56 ...a b a a b a b a b

M1 1.1a 5th

Understand and

use the general

binomial

expansion for

positive integer n

Correctly substitutes 1 and 3x into the formula:

2 38 8 7 6 5(1 3 ) 1 8 1 3 28 1 3 56 1 3 ...x x x x

M1 1.1b

Makes an attempt to simplify the expression (2 correct

coefficients (other than 1) or both 9x2 and 27x3).

8 8 2 3(1 3 ) 1 24 28 9 56 27 ...x x x x

M1

dep

1.1b

States a fully correct answer:

8 2 3(1 3 ) 1 24 252 1512 ...x x x x

A1 1.1b

(4)

2b States x = 0.01 or implies this by attempting the substitution:

2 3

1 24 0.01 252 0.01 1512 0.01 ...

M1 2.2a 5th

Find

approximations

using the

binomial

expansion for

positive integer n

Attempts to simplify this expression (2 calculated terms

correct):

1 + 0.24 + 0.0252 + 0.001512

M1 1.1b

1.266712 = 1.2667 (5 s.f.) A1 1.1b

(3)

(7 marks)

Notes

Page 22: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4 4

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a States or implies the expansion of a binomial expression to

the 9th power, up to and including the x3 term.

9 9 9 9 8 9 7 2 9 6 30 1 2 3( ) ...a b C a C a b C a b C a b

or 9 9 8 7 2 6 3( ) 9 36 84 ...a b a a b a b a b

M1 1.1a 5th

Use the binomial

expansion to find

arbitrary terms

for positive

integer n

Correctly substitutes 2 and px into the formula.

9(2 )px

2 39 8 7 62 9 2 36 2 84 2 ...px px px

M1 1.1b

Makes an attempt to simplify the expression (at least one

power of 2 calculated and one bracket expanded correctly).

9 2 2 3 3(2 ) 512 9 256 36 128 84 64 ...px px p x p x

M1dep 1.1b

States a fully correct answer:

9 2 2 3 3(2 ) 512 2304 4608 5376 ...px px p x p x

A1 1.1b

(4)

3bi States that 35376 84p M1ft 2.2a 5th

Understand and

use the general

binomial

expansion for

positive integer n

Correctly solves for p:

3 1 1

64 4p p

A1ft 1.1b

3bii Correctly find the coefficient of the x term:

12304 576

4

B1ft 1.1b 5th

Understand and

use the general

binomial

expansion for

positive integer n

Correctly find the coefficient of the x2 term: 2

14608 288

4

B1ft 1.1b

(4)

(8 marks)

Page 23: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5 5

Notes

ft marks – pursues a correct method and obtains a correct answer or answers from their 5376 from part a.

Page 24: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6 6

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a Attempt is made at expanding 5.p q Accept seeing the

coefficients 1, 5, 10, 10, 5, 1 or seeing

5 5 5 5 4 5 3 2

0 1 2

5 2 3 5 4 5 53 4 5 o.e.

p q C p C p q C p q

C p q C pq C q

M1 1.1a 5th

Understand and

use the general

binomial

expansion for

positive integer n

Fully correct answer is stated:

5 5 4 3 2 2 3 4 55 10 10 5p q p p q p q p q pq q

A1 1.1b

(2)

4b States that p, or the probability of rolling a 4, is

1

4

B1 3.3 5th

Use the binomial

expansion to find

arbitrary terms

for positive

integer n

States that q, or the probability of not rolling a 4, is3

4

B1 3.3

States or implies that the sum of the first 3 terms (or 1 − the

sum of the last 3 terms) is the required probability.

For example,

5 4 3 25 10p p q p q or 1 − 2 3 4 5(10 5 )p q pq q

M1 2.2a

5 4 3 21 1 3 1 3

5 104 4 4 4 4

or 1 15 90

1024 1024 1024

or

2 3 4 51 3 1 3 3

1 10 54 4 4 4 4

or 270 405 243

11024 1024 1024

M1 1.1b

Either53

512o.e. or awrt 0.104

A1 1.1b

(5)

Page 25: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7 7

(7 marks)

Notes

Page 26: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 8 8

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a Makes an attempt to interpret the meaning of f(5) = 0.

For example, writing 125 + 25 + 5p + q = 0 M1 2.2a 5th

Solve non-linear

simultaneous

equations in

context

5p + q = −150 A1 1.1b

Makes an attempt to interpret the meaning of f(−3) = 8.

For example writing −27 + 9 – 3p + q = 8 M1 2.2a

−3p + q = 26 A1 1.1b

Makes an attempt to solve the simultaneous equations. M1ft 1.1a

Solves the simultaneous equations to find that p = −22 A1ft 1.1b

Substitutes their value for p to find that q = −40 A1ft 1.1b

(7)

5b Draws the conclusion that (x – 5) must be a factor. M1 2.2a 5th

Divide

polynomials by

linear expressions

with a remainder

Either makes an attempt at long division by setting up the

long division, or makes an attempt to find the remaining

factors by matching coefficients. For example, stating:

2 3 25 22 40x ax bx c x x x

(ft their −22 or −40)

M1ft 1.1b

For the long division, correctly finds the the first two

coefficients.

For the matching coefficients method, correctly deduces that

a = 1 and c = 8

A1 2.2a

For the long division, correctly completes all steps in the

division.

For the matching coefficients method, correctly deduces that

b = 6

A1 1.1b

States a fully correct, fully factorised final answer:

(x – 5)(x + 4)(x + 2)

A1 1.1b

(5)

Page 27: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 9 9

(12 marks)

Notes

Award ft through marks for correct attempt/answers to solving their simultaneous equations.

In part b other algebraic methods can be used to factorise:

x – 5 is a factor (M1)

3 2 222 40 ( 5) 6 ( 5) 8( 5)x x x x x x x x by balancing (M1)

2( 6 8)( 5)x x x by factorising (M1)

( 4)( 2)( 5)x x x by factorising (A1 A1) (i.e. A1 for each factor other than (x – 5))

Page 28: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 10 10

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6 Considers the expression 2 13

162

x x either on its own or as

part of an inequality/equation with 0 on the other side.

M1 3.1a 6th

Complete

algebraic proofs

in unfamiliar

contexts using

direct or

exhaustive

methods

Makes an attempt to complete the square.

For example, stating:

213 169 256

4 16 16x

(ignore any (in)equation)

M1 1.1b

States a fully correct answer:

213 87

4 16x

(ignore any (in)equation)

A1 1.1b

Interprets this solution as proving the inequality for all values

of x. Could, for example, state that

213

04

x

as a number

squared is always positive or zero, therefore 2

13 870

4 16x

. Must be logically connected with the

statement to be proved; this could be in the form of an

additional statement. So 2 16 18 2

2x x x (for all x) or by

a string of connectives which must be equivalent to “if and

only if”s.

A1 2.1

(4)

(4 marks)

Notes

Any correct and complete method (e.g. finding the discriminant and single value, finding the minimum point by

differentiation or completing the square and showing that it is both positive and a minimum, sketching the graph

supported with appropriate methodology etc) is acceptable for demonstrating that 2 1316 0

2x x for all x.

Page 29: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 3: Further Algebra

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 11 11

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7a Makes an attempt to expand the binomial expression

3

1 x (must be terms in x0, x1, x2, x3 and at least 2 correct).

M1 1.1a 6th

Solve problems

using the

binomial

expansion (for

positive integer n)

in unfamiliar

contexts

(including the link

to binomial

probabilities)

2 3 2 31 3 1 3 3x x x x x A1 1.1b

0 < 3x A1 1.1b

x > 0* as required. A1* 2.2a

(4)

7b Picks a number less than or equal to zero, e.g. x = −1, and

attempts a substitution into both sides. For example,

2 3 2 3

1 3 1 1 1 3 1 3 1 1

M1 1.1a 5th

Use the binomial

expansion to find

arbitrary terms for

positive integer n Correctly deduces for their choice of x that the inequaltity does

not hold. For example, 3 ≮ 0

A1 2.2a

(2)

(6 marks)

Notes

Page 30: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

1a 45A o seen or implied in later working. B1 1.1b 5th

Solve problems

involving surds in

context and

complete simple

proofs involving

surds

Makes an attempt to use the sine rule, for example, writing

sin120 sin 45

8 3 4 1x x

o o

M1 1.1b

States or implies that 3

sin1202

o and 2

sin 452

o A1 1.2

Makes an attempt to solve the equation for x.

Possible steps could include:

3 2

16 6 8 2x x

or

6 1

16 6 4 1x x

or

3 6

16 6 8 2x x

8 3 2 3 16 2 6 2x x or 4 6 6 16 6x x or

24 6 16 6 6 6x x

6 2 2 3 16 2 8 3x or 4 6 6 16 6x x or

12 3 8 6 3 6x x

M1ft 1.1b

6 2 2 3

16 2 8 3x

or

6 6

16 4 6x

or

3 6 3

8 6 12x

o.e.

A1ft 1.1b

Makes an attempt to rationalise the denominator by

multiplying top and bottom by the conjugate.

Possible steps could include:

3 2 3 8 2 4 3

8 2 4 3 8 2 4 3x

48 12 6 8 6 12

128 48x

36 4 6

80x

M1ft 1.1b

States the fully correct simplifed version for x. A1* 2.1

Page 31: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2

9 6

20x

*

(7)

1b States or implies that the formula for the area of a triangle is

1sin

2ab C or

1sin

2ac B or

1sin

2bc A

M1 1.1a 3rd

Understand and

use the general

formula for the

area of a triangle.

1 9 6 9 64 1 8 3 sin15 or 0.259

2 20 20awrt

or 1

1.29 1.58 sin15 or 0.2592

awrt awrt awrt .

M1 3.1a

Finds the correct answer to 2 decimal places. 0.26 A1 1.1b

(3)

(10 marks)

Notes

1a

Award ft marks for correct work following incorrect values for sin 120° and sin 45°

1b

Exact value of area is 124 11 6 6 2 .

200 If 0.26 not given, award M1M1A0 if exact value seen.

Page 32: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

2a States or implies that the angle at P is 74° B1 2.2a 4th

Solve triangle

problems in a

range of contexts

States or implies the use of the cosine rule. For example,

2 2 2 2 cosp q r qr P

M1 1.1a

Makes substitution into the cosine rule.

2 2 27 15 2 7 15cos74p o

M1ft 1.1b

Makes attempt to simplify, for example, stating 2 216.11...p M1ft 1.1b

States the correct final answer. QR = 14.7 km. A1 1.1b

(5)

2b States or implies use of the sine rule, for example, writing

sin sinQ P

q p

M1 3.1a 4th

Solve triangle

problems in a

range of contexts

Makes an attempt to substitute into the sine rule.

sin sin 74

15 14.7

Q

o

M1ft 1.1b

Solves to find Q = 78.77…° A1ft 1.1b

Makes an attempt to find the bearing, for example, writing

bearing = 180° – 78.77…° – 33°

M1ft 1.1b

States the correct 3 figure bearing as 068° A1ft 3.2a

(5)

(10 marks)

Notes

2a

Award ft marks for correct use of cosine rule using an incorrect initial angle.

2b

Award ft marks for a correct solution using their answer to part (a).

Page 33: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

3 States 2 2sin cos 1x x or implies this by making a

substitution.

28 7cos 6 1 cosx x

M1 2.1 5th

Solve more

complicated

trigonometric

equations in a

given interval

such as ones

requiring use the

tan identity

(degrees)

Simplifies the equation to form a quadratic in cos x.

26cos 7cos 2 0x x

M1 1.1b

Correctly factorises this equation.

3cos 2 2cos 1 0x x or uses equivalent method for

solving quadratic (can be implied by correct solutions).

M1 1.1b

Correct solution. cos x 2

3 or

1

2

A1 1.1b

Finds one correct solution for x. (48.2°,60°, 311.8° or 300°). A1 1.1b

Finds all other solutions to the equation. A1 1.1b

(6)

(6 marks)

Notes

Page 34: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

4a 2 3 or awrt −3.46 B1 1.1b 4th

Determine exact

values for

trigonometric

functions in all

four quadrants

(1)

4b Figure 1

Sine curve with

max 2 and min

−2

B1 2.2a 4th

Transform the

graphs of

trigonometric

functions using

stretches and

translations

Sine curve

translated 60° to

the right.

B1 2.2a

Sin curve cuts

x-axis at (−120°,

0) and

(60°, 0) and the

y-axis (0, − 3 ).

B1 2.2a

Asymptotes for

tan curve at x =

90° and

x = −90°

B1 1.1b

Tangent curve is

‘flipped’. B1 2.2a

Uses the value

of

−2 tan (−120°)

to deduce no

intersection in

3rd quadrant

(can be

implied).

B1 2.2a

Tangent curve

cuts x-axis at

(−180°, 0),

(0, 0) and

B1 1.1b

Page 35: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6

(180°, 0).

(7)

4c States that solutions to the equation 2sin( 60 ) tan 0x x o

will occur where the two curves intersect.

B1ft 3.1a 4th

Use intersection

points of graphs

to solve equations

4d States that there are two solutions in the given interval. A1 2.2a 4th

Use intersection

points of graphs

to solve equations

(2)

(10 marks)

Notes

4b

Ignore any portion of curve(s) outside −180° ⩽ x ⩽ 180°

4c

Award both marks for correctly stating that there are two solutions even if explanation is missing.

Page 36: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

5 Makes an attempt to begin solving the equation. For example,

states that

sin 3 20 4

4 3cos 3 20

o

o

M1 2.1 5th

Solve more

complicated

trigonometric

equations in a

given interval

such as ones

requiring use the

tan identity

(degrees)

Uses the identity sin

tancos

to write,

4 1

tan 3 204 3 3

o

M1 2.1

States or implies use of the inverse tangent. For example,

1 13 20 tan

3

o or 3 20 30 o o

M1 1.1b

Shows understanding that there will be further solutions in the

given range, by adding 180° to 30° at least once.

3 20 30 , 210 , 390 ,... o o o o (ignore any out of range

values).

M1 1.1b

Subtracts 20 and divides each answer by 3.

10 190 370, , ,...

3 3 3

o o o

(ignore any out of range values).

M1 1.1b

States the correct final answers to 1 decimal place.

3.3°, 63.3°, 123.3°cao

A1 1.1b

(6)

(6 marks)

Notes

Page 37: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 8

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

6a Any reasonable explanation.

For example, the student did not correctly find all values of 2x

which satisfy 3

cos22

x . Student should have subtracted

150° from 360° first, and then divided by 2.

N.B. If insufficient detail is given but location of error is

correct then mark can be awarded from working in part (b).

B1 2.3 4th

Solve simple

trigonometric

equations in a

given interval

(degrees)

(1)

6b x = 75° B1 2.2a 4th

Solve simple

trigonometric

equations in a

given interval

(degrees)

x = 105° B1 2.2a

(2)

(3 marks)

Notes

6a

Award the mark for a different explanation that is mathematically correct, provided that the explanation is clear

and not ambiguous.

Page 38: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 9

Q Scheme Marks AOs Pearson

Progression Step

and Progress

descriptor

7a Figure 2

Correct

shape of sine

curve

through

(0, 0).

B1 3.1a 4th

Transform the

graphs of

trigonometric

functions using

stretches and

translations Sine curve

has max

value of 1

2and min

value of 1

2

B1 3.1a

Sine curve

has a period

of 2 (can be

implied by 5

complete

cycles) and

passes

through

(1,0),

(2,0),...,

(10,0).

B1 3.1a

(3)

7b Student states that the buoy will be 0.4 m above the still water

level 10 times. B1 3.2a 7th

Use functions in

modelling

(including

critiquing)

(1)

Page 39: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Pure Mathematics Year 1 (AS) Unit Test 4: Trigonometry

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 10

7c Sensible and correct reason. For example:

A buoy would not move up and down at exactly the same rate

during each oscillation.

The period of oscillation is likely to change each oscillation.

The maximum (or minimum) height is likely to change with

time.

Waves in the sea are not uniform.

B1 3.2b 7th

Use functions in

modelling

(including

critiquing)

(1)

(5 marks)

Notes

7c

Award the mark for a different explanation that is mathematically correct. For example, stating that the buoy

would not move exactly vertically each time.

Page 40: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a Observation or measurement of every member of a population. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

1b Two from:

takes a long time/costly

difficult to ensure whole population surveyed

cannot be used if the measurement process destroys the

item

can be hard to manage and analyse all the data.

B1

B1

1.2

1.2

3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

(2)

1c The list of unique serial numbers. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

1d A circuit board. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

(5 marks)

Notes

Page 41: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a A complete collection of relevant individual people or items. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

2b Opportunity (convenience). B1 1.2 3rd

Understand quota

and opportunity

sampling.

(1)

2c Systematic. B1 1.2 3rd

Understand and

carry out

systematic

sampling.

(1)

2d Two from:

not random

electoral register may have errors

there may not be enough (500) households on the

register.

B1

B1

2.4

2.4

5th

Select and

critique a

sampling

technique in a

given context.

(2)

2e Either: random sampling – it avoids bias.

Or: quota sampling – no sampling frame required, continue until

all quotas filled.

B1 2.4 5th

Select and

critique a

sampling

technique in a

given context.

Either: Random sampling from people buying kitchen cleaners

in a large store, as this would reduce potential bias.

Or: Quota sampling from people based on a chosen set of ages

and genders who use kitchen cleaners, continuing until all quotas

are filled, as this would avoid the need for a sampling frame and

allow for a more clearly representative sample.

B1 2.4

(2)

(7 marks)

Page 42: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3

Notes

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a One of:

to obtain a representative sample

large number of students compared to staff so would be

unfair to take same numbers of both.

B1 2.4 5th

Select and

critique a

sampling

technique in a

given context.

(1)

3b A list of the names of staff and students. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

3c A member of staff or a student. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

3d Find proportions for different strata out of 60 (either explained

or some sensible calculation seen).

M1 3.1b 3rd

Understand and

carry out stratified

sampling.

250

280´ 60 » 54 students,

30

280´ 60 » 6 staff.

A1 1.1b

Select at random using a random number generator. B1 1.1b

(3)

Page 43: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4

3e One of:

absence on the day of the survey

sampling frame may contain errors.

B1 2.2b 5th

Select and

critique a

sampling

technique in a

given context.

(1)

(7 marks)

Notes

3d

Must be whole numbers for A1.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a All readers of the online newspaper. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

4b A list of readers who subscribe to the extra content. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

4c The subscribers. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

Page 44: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5

4d Advantage: accuracy of the data, unbiased. B1 1.2 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

Disadvantage: difficult to get a 100% response to a survey. B1 1.2

(2)

4e Natural variation in a small sample. B1 1.2 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

Bias. B1 1.2

(2)

(7 marks)

Notes

Page 45: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a Quota. B1 1.2 3rd

Understand quota

and opportunity

sampling.

(1)

5b Advantages – two from:

easy to get sample size

inexpensive

fast

can be stratified if required.

B1

B1

2.4

2.4

5th

Select and

critique a

sampling

technique in a

given context.

Disadvantages – one from:

not random

could be biased.

B1 2.4

(3)

5c Allocate each of the males a number from 1 to 300 B1 3.1b 3rd

Understand and

carry out simple

random sampling.

Use calculator or number generator to generate 50 different

random numbers from 1 to 300 inclusive. B1 1.1b

Select males corresponding to those numbers. B1 1.1b

(3)

5d 300 ÷ 50 = 6 B1 3.1b 3rd

Understand and

carry out simple

random sampling.

Use a random number generator to select the first name (or one

of the first 6 names on the list) as a starting point and then select

every 6th name thereafter to get 50 names.

B1 1.1b

(2)

(9 marks)

Notes

Page 46: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6a There are a very large number of bags. B1 2.4 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

Bags are tested to destruction – there would be no bags left. B1 2.4

(2)

6b One value is less than 12 kg B1 2.4 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

therefore claim is not reliable. B1 2.3

(2)

6c Different samples can lead to different conclusions due to

natural variations. B1 2.3 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

Only a small sample taken so unreliable. B1 2.3

(2)

6d Larger sample. B1 2.4 3rd

Comment on the

advantages and

disadvantages of

samples and

censuses.

(1)

(7 marks)

Notes

Page 47: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 1: Statistical Sampling

©Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 8

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7a (Quantitative) continuous. B1 1.2 1st

Understand the

difference

between

qualitative and

quantitative data.

(1)

7b A list of the first two digits of the date. B1 1.2 2nd

Understand the

vocabulary of

sampling.

(1)

7c Simple random sample B1 3.1b 5th

Select and

critique a

sampling

technique in a

given context.

using a random number generator to select five dates. B1 1.1b

(2)

7d Number ordered list of data. B1 3.1b 3rd

Understand and

carry out

systematic

sampling.

Use random number generator is choose first selected piece of

data. B1 3.1b

Then take every 6th value

187

30

æ

èçö

ø÷

B1 1.1b

(3)

7e Some data may be missing or erroneous. B1 3.2b 5th

Select and

critique a

sampling

technique in a

given context.

(1)

(8 marks)

Notes

Page 48: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a All points correctly plotted.

B2 1.1b 2nd

Draw and

interpret scatter

diagrams for

bivariate data.

(2)

1b The points lie reasonably close to a straight line (o.e.). B1 2.4 2nd

Draw and

interpret scatter

diagrams for

bivariate data.

(1)

1c f B1 1.2 2nd

Know and

understand the

language of

correlation and

regression.

(1)

1d Line of best fit plotted for at least 2.2 ⩽ x ⩽ 8 with D and F

above and B and C below.

M1 1.1a 4th

Make predictions

using the

regression line

within the range

of the data.

26 to 31 inclusive (must be correctly read from x = 7 from the

line of best fit). A1 1.1b

(2)

Page 49: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

1e It is reliable because it is interpolation (700 km is within the

range of values collected). B1 2.4 4th

Understand the

concepts of

interpolation and

extrapolation.

(1)

1f No, it is not sensible since this would be extrapolation (as

180 km is outside the range of distances collected). B1 2.4 4th

Understand the

concepts of

interpolation and

extrapolation.

(1)

(8 marks)

Notes

1a

First B1 for at least 4 points correct, second B1 for all points correct.

1b

Do not accept ‘The points lie reasonably close to a line’. Linear or straight need to be noted.

1e

Also allow ‘It is reliable because the points lie reasonably close to a straight line’.

1f

Allow the answer ‘It is sensible since even though it is extrapolation it is not by much’ provided that the

answer contains both ideas (i.e. it IS extrapolation but by a small amount compared to the given range of

data).

Page 50: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a 19.5 +

60 2910

43

= 26.7093… (Accept awrt 26.7 miles)

M1

A1

1.1b

1.1b

3rd

Estimate median

values, quartiles

and percentiles

using linear

interpolation.

(2)

2b 3552.5

120x = 29.6041… o.e. (Accept awrt 29.6 miles)

B1 1.1b 4th

Calculate

variance and

standard deviation

from grouped data

and summary

statistics.

2138 043.13

120x

or

2 2138 043.13

120x

or

2120

119s

M1 1.1a

σ = 16.5515… (Accept awrt 16.6 miles)

(or s = 16.6208… = 16.6 miles)A1 1.1b

(3)

2c Any sensible reason linked to the shape of the distribution.

For example:

The distribution is (positively) skewed.

A few large distances (values) distort the mean.

B1 2.4 4th

Calculate means,

medians, quartiles

and standard

deviation.

(1)

Page 51: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

2d Comparison of the two means.

For example, the mean distance for London is smaller than for

Devon.

Sensible interpretation comparing a county to a city.

For example, distance to work into one city may not be as far

as travelling to different cities in a county.

For example, commuters need to travel further to the cities in

Devon for work.

Comparison of the two standard deviations:

For example, the standard deviation for London is larger than

for Devon.

Sensible interpretation relating to variability/consistency

For example, there is more variability (less consistency) in the

commute distances from the Greater London station than from

the Devon station.

B1

B1

B1

B1

1.1b

2.2b

1.1b

2.2b

4th

Compare data sets

using a range of

familiar

calculations and

diagrams.

(4)

(10 marks)

Notes

2a

Allow consistent use of n + 1 (i.e. for median 60.5th rather than 60th), median = 26.8

2c

Candidates must compare both the means and standard deviations with interpretations for full marks.

Page 52: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3ai 37 (minutes). B1 1.1b 2nd

Draw and

interpret box

plots.

(1)

3aii Upper quartile or Q3 or third quartile or 75th

percentile or P75 B1 1.2 2nd

Understand

quartiles and

percentiles.

(1)

3b Outliers.

Sensible interpretation:

For example:

Observation that are very different from the other

observations (and need to be treated with caution).

Possible errors.

These two children probably walked/took a lot longer.

B1

B1

1.2

2.4

3rd

Recognise

possible outliers

in data sets.

(2)

3c 50 + 1.5 × 20 = 80 or 30 − 1.5 × 20 =0

Maximum value =55 < 80 minimum value = 25 > 0

No outliers.

M1

A1

B1

1.1b

1.1b

1.1b

4th

Calculate outliers

in data sets and

clean data.

(3)

3d The scale must be the same as for school A.

Figure 1

B1 1.1b 2nd

Draw and

interpret box

plots.

Box & whiskers 30, 37, 50

B1 1.1b

25, 55 B1 1.1b

(3)

Page 53: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

3e Three comparisons in context.

Comment on comparing averages.

For example, children from school A took less time on

average.

B3 2.2b 4th

Compare data sets

using a range of

familiar

calculations and

diagrams. Comment comparing consistency of times.

For example, there is less variation in the times for school A

than school B.

Comment on comparing symmetry:

For example,both positive skew (or neither symmetrical or

median closer to LQ (o.e.) for both). (Most children took a

short time with a few taking longer.)

Comment on comparing outliers.

For example, school A has two children whose times are

outliers (or errors) where as school B has no outliers.

(3)

(13 marks)

Notes

3c

Allow horizontal line through box.

Page 54: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4 467

200y

= −2.335 (seen or implied)

= 2.5 + 755.0

= 749.1625 (Accept awrt 749)

σy =

= 6.3594…

σx = 2.5 × 6.3594…

= 15.8986… (Accept awrt 15.9)

B1

M1

M1

A1

M1

A1

A1

M1

A1

1.1b

3.1a

1.1b

1.1b

1.1b

1.1b

3.1a

1.1b

1.1b

5th

Calculate the

mean and

standard deviation

of coded data.

(9)

(9 marks)

Notes

0.7555.2 yx

200

467

2

200

467

200

9179

Page 55: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a Order the data.

125, 160, 169, 171, 175, 186, 210, 243, 250, 258, 390, 420

M1 1.1b 2nd

Understand

quartiles and

percentiles. Q3 = (250 + 258) = 254

A1 1.1b

(2)

5b Q3 +1.5(Q3 – Q1) = 254 + 1.5(254 – 170) M1 1.1b 4th

Calculate outliers

in data sets and

clean data.

= 380 A1 1.1b

Patients F (420) and B (390) are outliers (so may be suspected

by the doctor as smoking more than one packet of cigarettes

per day).

B1 3.2a

(3)

(5 marks)

Notes

2

1

Page 56: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 2: Data presentation and interpretation

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6 Three comparisons in context:

For example:

Very much warmer in Beijing than Perth.

Both consistent in the temperatures.

Less rainfall in Beijing.

Less likely to have high rainfall in Beijing.

Rainfall in Beijing is consistently less than in Perth.

Evidence of use of a statistic from the boxplots:

For example:

Medians

Measure of a difference in medians

Mention of a particular outlier

B3

B1

2.4

2.4

4th

Compare data sets

using a range of

familiar

calculations and

diagrams.

For accurately reading data from boxplots. B1 2.4

(5)

(5 marks)

Notes

Page 57: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a

2 + 3

total number of students=

5

30=

1

6or awrt 0.167

M1

A1

1.1b

1.1b

1st

Calculate

probabilities for

single events.

(2)

1b

4 + 2 + 5+ 3

total

M1 1.1b 3rd

Understand and

use Venn

diagrams for

multiple events. =

14

30 or

7

15 or awrt 0.467

A1 1.1b

(2)

1c 0 B1 1.1b 3rd

Understand and

use the definition

of mutually

exclusive in

probability

calculations.

No student reads both magazine A and magazine C. B1 1.1b

(2)

1d

P(C reads at least one magazine) =

6 + 3

20=

9

20

B1 1.1b 3rd

Understand and

use Venn

diagrams for

multiple events.

(1)

1e

P(B) =

10

30=

1

3, P(C) =

9

30=

3

10

B1 2.1 4th

Understand and

use the definition

of independence in

probability

calculations. P(B and C) =

3

30=

1

10, and

M1 2.2a

P(B) ´ P(C) =

1

3

10=

1

10= P(B and C)

So yes, they are independent.

A1 2.4

(3)

(10 marks)

Page 58: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Notes

1e

Allow alternative using formal conditional probability: P(B) = 13

(B1). Finding P(B|C) = 3 1(3 6) 3

and

comparing with P(B) (M1). Correct conclusion (A1).

Or P(C) = 310

(B1). Finding P(C|B) = 3 3(2 3 5) 10

and comparing with P(C) (M1). Correct conclusion (A1).

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a

For shape and labels: 3 branches followed by 3,2,2

with some R, B and G seen.

M1

3.1a

3rd

Draw and use tree

diagrams with

three branches

and/or three

levels.

First set of branches correct. A1 1.1b

Second set of branches correct. A1 1.1b

(3)

2b P(Blue bead and a green bead) =

1 1 1 1 2 1

4 3 4 3 12 6

.

M1

A1

3.4

1.1b

3rd

Draw and use tree

diagrams with

three branches

and/or three

levels.

(2)

(5 marks)

Page 59: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Notes

2a

Allow 3 branches followed by 3, 3, 3 if 0 properly placed on redundant branches.

R B G labels can be implied on second set but only if order is consistent and probabilities correct.

Further sets of branches max M1 A1 A0 (2/3).

2b

M1 for or …+

1

1

3

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a

Three closed curves and four in centre.

Evidence of subtraction (any one of 31, 36, 24, 41, 17 or 11).

Any three of 31, 36, 24, 41, 17 or 11 correct.

All correct.

Labels on sets, 16 and closed curve or box outside.

M1

M1

A1

A1

B1

3.1a

3.3

1.1b

1.1b

1.1b

3rd

Understand and

use Venn

diagrams for

multiple events.

(5)

3bi P(None of the 3 options)

=

16

180=

4

45or awrt 0.0889

B1 3.4 3rd

Understand and

use Venn

diagrams for

multiple events.

(1)

3bii P(Networking only)

=

17

180or awrt 0.0944

B1 3.4 3rd

Understand and

use Venn

diagrams for

multiple events.

(1)

Page 60: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

3c

P(Takes all three options takes S and N) =

4

40=

1

10or 0.1

M1

A1

3.4

1.1b

3rd

Understand and

use Venn

diagrams for

multiple events.

(2)

(9 marks)

Notes

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a

Correct tree structure.

All labels correct.

All probabilities correct.

B1

B1

B1

3.1a

1.1b

1.1b

3rd

Draw and use tree

diagrams with

three branches

and/or three

levels.

(3)

4bi

1

1

10=

1

30or equivalent.

M1

A1

3.4

1.1b

3rd

Draw and use tree

diagrams with

three branches

and/or three

levels.

(2)

Page 61: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

4bii Car NL + Bike NL + Foot NL

=1

4

5

æ

èçö

ø÷+

1

3

5

æ

èçö

ø÷+

1

9

10

æ

èçö

ø÷

M1 3.4 3rd

Draw and use tree

diagrams with

three branches

and/or three

levels. =

4

5or equivalent.

A1 1.1b

(2)

(7 marks)

Notes

4bii

ft from their tree diagram. Allow one error for M1.

Can also be found from

1-1

1

5

æ

èçö

ø÷+

1

2

5

æ

èçö

ø÷+

1

1

10

æ

èçö

ø÷æ

èç

ö

ø÷

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a

Tree (both sections) and labels

0.85, 0.15

0.03, 0.97, 0.06, 0.94

B1

B1

B1

3.1a

1.1b

1.1b

2nd

Draw and use

simple tree

diagrams with

two branches and

two levels.

(3)

5b P(Not faulty) = (0.85 × 0.97) + (0.15 × 0.94)

= 0.9655

M1

M1dep

A1

3.4

1.1b

1.1b

2nd

Draw and use

simple tree

diagrams with

two branches and

two levels.

(3)

Page 62: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

(6 marks)

Notes

5b

M1 for either 0.85 × 0.97 or 0.15 × 0.94 (ft from their tree diagram) and M1 (dep) for adding two such probabilities

(allow one error).

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6a Find total frequency = åwidth ´ frequency density

= (5 2) + (4 4) + (4 6) + (7 5) + (15 1) = 100

P(Takes longer than 18 mins) =

35+15

“100”=

50

100=

1

2 or

equivalent.

M1

A1

M1

A1

3.1a

1.1b

3.1a

1.1b

2nd

Calculate

probabilities from

relative frequency

tables and real

data.

(4)

6b

1

3´15 = 5

P(Takes less than 30 mins) =

10 +16 + 24 + 35+ 5

100=

90

100=

9

10

or equivalent.

M1

M1

A1

2.2b

1.1b

1.1b

2nd

Calculate

probabilities from

relative frequency

tables and real

data.

(3)

(7 marks)

Notes

6a

M1 for attempt to find total frequency by adding at least three “width frequency density” terms (which may

contain errors).Alternative: M1 for 2

15 103

. M1 for 1 −10

100

" ".

" " A1 for

9

10 o.e.

Page 63: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 3: Probability

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7a Total frequency = 120

P(Less than 17 cm) 52 5 57

120 120

or equivalent or 0.475

B1

M1

A1

3.1a

1.1b

1.1b

2nd

Calculate

probabilities from

relative frequency

tables and real

data.

(3)

7b P(Between 12 cm and 18 cm)

52 15 67

120 120

or awrt 0.558

Assumption: foot lengths between 17 and 19 are uniformly

distributed.

M1

A1

B1

2.2b

1.1b

3.5b

2nd

Calculate

probabilities from

relative frequency

tables and real

data.

(3)

(6 marks)

Notes

Page 64: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a k(16 – 9) + k(25 – 9) + k(36 – 9) (or 7k + 16k + 27k). M1 2.1 4th

Model simple

discrete random

variables as

probability

distributions.

= 1 M1 1.1b

Þ k =

1

50(answer given).

A1* 1.1b

(3)

1b

x 4 5 6

P(X = x)

7

50

16

50

27

50

Note: decimal values are 0.14, 0.32, 0.54 respectively.

B1

B1

2.5

1.1b

4th

Calculate

probabilities from

discrete

distributions.

(2)

(5 marks)

Notes

1b

Ignore any extra columns with 0 probability. Otherwise –1 for each. If 4, 5 or 6 missing B0B0.

Page 65: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a 0.15 + 0.15 + + + 0.1 + 0.1 = 2 + 0.5 = 1 M1 1.1b 4th

Calculate

probabilities from

discrete

distributions.

= 0.25 A1 1.1b

(2)

2b P(–1 ⩽X < 2) = P(–1) + P(0) + P(1) = 0.6 B1 1.1b 4th

Calculate

probabilities from

discrete

distributions.

(1)

2c P(X > −2.3) = P(−2) + P(−1) + P(0) + P(1) + P(2) = 0.85 B1 1.1b 4th

Calculate

probabilities from

discrete

distributions.

(1)

(4 marks)

Notes

Page 66: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a 2k + k + 0 + k = 1 M1 2.1 4th

Calculate

probabilities from

discrete

distributions.

Þ4k = 1, so k = 0.25 (answer given). A1* 1.1b

(2)

3b P(X1 + X2 = 5) = P(X1 = 3 and X2 = 2) + P(X1 = 2 and X2 = 3)

= 0 + 0 = 0 (answer given).

B1* 2.4 4th

Calculate

probabilities from

discrete

distributions.

(1)

3c

x1 + x2 0 1 2 3 4 5 6

P(X1 + X2) 0.25 0.25 0.0625 0.25 0.125 0 0.0625

M1

A1

A1

2.5

1.1b

1.1b

4th

Calculate

probabilities from

discrete

distributions.

(3)

3d P(1.3 ⩽ X1 + X2 ⩽ 3.2) = P(X1 + X2 = 2) + P(X1 + X2 = 3) M1 3.4 4th

Calculate

probabilities from

discrete

distributions. = 0.0625 + 0.25 = 0.3125 or

5

16

A1ft 1.1b

(2)

(8 marks)

Notes

3b

Must show that 5 can only be obtained from 2 and 3 or 3 and 2, and so must use P(X = 2) = 0 but condone

explanation in words.

3c

M1 for correct set of values for X1 + X2. Condone omission of 5 column.

A1 for correct probabilities for 0, 2 and 6. A1 for others. Equivalent fractions are 1 1 1 1 1 1, , , , ,4 4 16 4 8 16

Page 67: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a Let X be the random variable the number of games Amir loses.

X ~ B(9, 0.2)

P(X = 3) = 0.17616… = 0.176 to 3 sf from calculator

B1

B1

3.3

1.1b

5th

Calculate

binomial

probabilities.

(2)

4b P( 4) X „ M1 3.4 6th

Use statistical

tables and

calculators to find

cumulative

binomial

probabilities.

= awrt 0.980 from calculator A1 1.1b

(2)

(4 marks)

Notes

4a

P( 3) P ) ( 2X X„ „ = 0.9144 – 0.7382

or

9!

3!6!(0.2)3(0.8)6

or 9 C

3´ 0.23 ´ 0.86

or 84 ´ 0.23 ´ 0.86

4b

0.98 is M1A0

Page 68: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a X ~ B(20, 0.05)

B1 for binomial

B1 for 20 and 0.05

B1

B1

3.1b

3.1b

5th

Understand the

binomial

distribution (and

its notation) and

its use as a model.

(2)

5b P(X = 0) = 0.358 (awrt) B1

A1

3.4

1.1b

5th

Calculate

binomial

probabilities.

(2)

5c P(X > 4) = 1 – P( 4) X „

= 1 – 0.9974

M1 3.4 6th

Use statistical

tables and

calculators to find

cumulative

binomial

probabilities.

= 0.0026 (2 s.f.) (answer given) A1* 1.1b

(2)

(6 marks)

Notes

5b

P(X = 0) = 0.9520

Page 69: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6a X ~ B(15, 0.5)

B1 for binomial

B1 for 15 and 0.5

B1

B1

3.1b

3.1b

5th

Understand the

binomial

distribution (and

its notation) and

its use as a model.

(2)

6bi from calculator P(X = 8) = 0.19638… M1

A1

3.4

1.1b

5th

Calculate

binomial

probabilities.

(2)

6bii P(X …4) = 1 – P(X „ 3)

= 1 – 0.0176

M1 3.4 6th

Use statistical

tables and

calculators to find

cumulative

binomial

probabilities.

= awrt 0.982 or

503

512

A1 1.1b

(2)

(6 marks)

Notes

6bi

P(X = 8) = P(X … 8) – P(X „ 7) = 0.6964 – 0.5

or

15!

8!7!0.58(1- 0.5)7

or 15 C

8´ 0.58 ´ 0.57

or 6435´ 0.515

= awrt 0.196 or

6435

32768

Page 70: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7a Binomial (distribution). B1

1.2

5th

Understand the

binomial

distribution (and

its notation) and

its use as a model. Each plate is either blue or not blue, independently of each

other, with constant probability and there is a fixed number of

them.

B1 2.4

(2)

7b X ~ B(10, 0.06) (could be seen in part a) B1 2.5 5th

Calculate

binomial

probabilities.

P(X > 2) = 1 – P(X „

= 1 – 0.981162163… from calculator

M1 3.4

= awrt0.0188378… A1 1.1b

(3)

(5 marks)

Notes

7a

Ignore any parameter values given for the first B1. For second B1 all four points must be made with some context.

Page 71: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 4: Statistical Distributions

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

8a There is a fixed number of trials. B1 1.2 5th

Understand the

binomial

distribution (and

its notation) and

its use as a model.

Each trial results in 1 of 2 outcomes, ‘success’ and ‘failure’. B1 1.2

Probability of success on each trial is the same. B1 1.2

The trials are independent. B1 1.2

(4)

8bi P(X = 5) =

2

7; P(X 5) =

5

7

(either may be implied in either part)

B1

B1

3.3

1.1b

5th

Calculate

binomial

probabilities. Idea of five failures followed by a success (or 0 successes out of

five and then a success) seen or implied. M1 3.4

P(5 on sixth throw) =

55 2

7 7

M1 1.1b

= awrt 0.0531 A1 1.1b

(5)

8bii

B 8,2

7

æ

èçö

ø÷ – or

B 8,5

7

æ

èçö

ø÷– seen or implied.

M1 3.3 5th

Calculate

binomial

probabilities.

P(X = 3) = 0.24285… from calculator M1

A1

1.1b

1.1b

(3)

(12 marks)

Notes

8bii

P(exactly 3 fives in first eight throws) =

8!

5!3!

2

7

æ

èçö

ø÷

3

5

7

æ

èçö

ø÷

5

o.e.

Page 72: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a Two from:

Each bolt is either faulty or not faulty.

The probability of a bolt being faulty (or not) may be

assumed constant.

Whether one bolt is faulty (or not) may be assumed

to be independent (or does not affect the probability

of) whether another bolt is faulty (or not).

There is a fixed number (50) of bolts.

A random sample.

B2

1.2

1.2

5th

Understand the

binomial

distribution (and

its notation) and

its use as a model.

(2)

1b Let X represent the number of faulty bolts.

X~B(50, 0.25)

P(X ⩽ 6) = 0.0194

P(X ⩽ 7) = 0.0453

P(X ⩾ 19) = 0.0287

P(X ⩾ 20) = 0.0139

M1

M1dep

3.4

1.1b

5th

Find critical

values and critical

regions for a

binomial

distribution.

Critical Region is X ⩽ 6 X ⩾ 20 A2 1.1b

1.1b

(4)

(6 marks)

Notes

1a

Each comment must be in context for its mark.

Page 73: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a The set of values of the test statistic for which the null

hypothesis is rejected in a hypothesis test.

B2

1.2

1.2

5th

Understand the

language of

hypothesis

testing.

(2)

2b P(X ⩾ 15) = 1− 0.9831 = 0.0169

P (X ⩾ 16) = 1 – 09936 = 0.0064

M1 1.1b 5th

Find critical

values and critical

regions for a

binomial

distribution.

Critical region is 16 ⩽ X (⩽ 30) A1 1.1b

Probability of rejection is 0.0064 A1 1.1b

(3)

2c Not in critical region therefore insufficient evidence to

reject H0. B1 2.2b 6th

Interpret the

results of a

binomial

distribution test in

context.

There is insufficient evidence at the 1% level to suggest

that the value of p is bigger than 0.3. B1 3.2a

(2)

(7 marks)

Notes

2c

Conclusion must be in context (i.e. use p), mention the significance level and be non-assertive.

Page 74: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a P(X ⩽ 1) = 0.0076 and P (X ⩽ 2) = 0.0355 M1 1.1b 5th

Find critical values

and critical regions

for a binomial

distribution.

P(X ⩾ 10) = 1 – 0.9520 = 0.0480 and

P(X ⩾ 11) = 1 – 0.9829 = 0.0171

A1 1.1b

Critical region is X ⩽ 1 11 ⩽ X (⩽ 20) A1 1.1b

(3)

3b Significance level = 0.0076 + 0.0171

= 0.0247 or 2.47%

B1 1.1b 6th

Calculate actual

significance levels

for a binomial

distribution test.

(1)

3c Not in critical region therefore insufficient evidence to reject

H0. B1 2.2b 6th

Interpret the results

of a binomial

distribution test in

context.

There is insufficient evidence at the 5% level to suggest that the

value of p is not 0.3. B1 3.2a

(2)

(6 marks)

Notes

3c

Conclusion must contain context and non-assertive for first B1.

Page 75: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a X~B(28, 0.37) M1 3.4 5th

Find critical values

and critical regions

for a binomial

distribution

P(X ⩾ 15) = 1 – 0.9454 = 0.0546 and

P(X ⩾ 16) = 1 – 0.9762 = 0.0238

M1dep 1.1b

Critical region is X ⩾ 16 A1 1.1b

(3)

4b In critical region therefore sufficient evidence to reject H0 B1 2.2b 6th

Interpret the results

of a binomial

distribution test in

context.

There is sufficient evidence at the 5% level to suggest that the

value of p is bigger than 0.37. B1 3.2a

(2)

(5 marks)

Notes

4a

First M1 for correct distribution seen or implied. Second M1 (dependent on first) for evidence that correct

probabilities for either critical value examined.

4b

Conclusion must contain context and non-assertive for first B1.

Page 76: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a H0: p = 0.2

H1: p > 0.2

B1 2.5 5th

Carry out 1-tail

tests for the

binomial

distribution. Let X represent the number of times the taxi is late.

X~B(5, 0.2) seen or implied.

M1 3.3

Either

P(X ⩾ 3) = 1 – P(X ⩽ 2) = 1 – 0.9421

= 0.0579

0.0579 > 0.05

There is insufficient evidence at the 5% significance level that

there is an increase in the number of times the taxi/driver is

late.

Or

P(X ⩾ 3) = 1 – P(X ⩽ 2) = 0.0579

P(X ⩾ 4) = 1 – P(X ⩽ 3) = 0.0067

So critical region is X ⩾ 4

3 < 4 or 3 is not in the critical region

So there is insufficient evidence at the 5% significance level

that there is an increase in the number of times the taxi/driver is

late.

M1

A1

B1

B1

M1

A1

B1

B1

1.1b

1.1b

1.1b

3.2a

1.1b

1.1b

1.1b

3.2a

(6)

5b Two sensible reasons. For example,

Different time of the day Linda travels to work.

More traffic on different days (e.g. Monday morning,

Friday afternoon).

Weather conditions.

Road works.

B2

2.2b

2.2b

5th

Understand the

binomial

distribution (and

its notation) and

its use as a model.

(2)

(8 marks)

Notes

Conclusion must be non-assertive.

Page 77: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

6a Let X represent the number of bowls with minor defects

(seen or implied).

XB(25, 0.2) may be implied

P(X ⩽ l) = 0.0274

P(X = 0) = 0.0038

P(X ⩽ 8) = 0.9532 P(X ⩾ 9) = 0.0468

P(X ⩽ 9) = 0.9827 P(X ⩾ 10) = 0.0173

Critical region is X = 0 X ⩾ 10

M1

M1dep

A1

M1

A2

3.4

1.1b

1.1b

1.1b

1.1b

1.1b

5th

Find critical

values and critical

regions for a

binomial

distribution.

(6)

6b Significance level = 0.0038 + 0.0173

= 0.0211 or 2.11%

B1 1.2 6th

Calculate actual

significance

levels for a

binomial

distribution test.

(1)

6c H0: p = 0.2; H1: p < 0.2 B1 2.5 5th

Carry out 1-tail

tests for the

binomial

distribution.

Let Y represent number of bowls with minor defects

(Under H0) Y~B(20, 0.2) (may be implied)

M1 3.4

Either

P(Y ⩽ 2) = 0.2061

0.2061 > 0.1 (or 10%)

Insufficient evidence at the 10% level to suggest that the

proportion of defective bowls has decreased.

Or

P(Y ⩽ 2) = 0.2061

P(Y ⩽ 1) = 0.0692 so critical region is Y ⩽ 1

Insufficient evidence at the 10% level to suggest that the

proportion of defective bowls has decreased.

0.2061 > 0.10 or 0.7939 < 0.9

B1

M1

A1

B1

M1

A1

1.1b

1.1b

3.2b

1.1b

1.1b

3.2a

(5)

(12 marks)

Page 78: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Statistics Year 1 (AS) Unit Test 5: Statistical Hypothesis Testing

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free.

Notes

6a

M1 for examining probabilities for on both sides for either critical value, A1 for each correct pair.

6c

Conclusion must be non-assertive.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

7 H0: p = 0.25, H1: p> 0.25 B1 2.5 5th

Carry out 1-tail

tests for the

binomial

distribution.

Let X represent the number of seeds that germinate.

(Under H0) X~B(25, 0.25)

M1 3.4

P(X ⩾ 10) = 1 – P(X ⩽ 9) = 0.0713 M1 1.1b

> 0.05 A1 1.1b

10 is not in critical region therefore insufficient evidence to

reject H0. B1 2.2b

There is insufficient evidence at the 5% level to suggest that the

book has underestimated the probability. (o.e.) B1 3.2a

(6 marks)

Notes

Page 79: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a States correct answer: 5.3 (m s−1) B1 2.2a 4th

Understand the

difference

between a scalar

and a vector.

(1)

1b States correct answer: −4.8 (m s−1) B1 2.2a 4th

Understand the

difference

between a scalar

and a vector.

(1)

1c States correct answer: −30 (m) B1 2.2a 4th

Understand the

difference

between a scalar

and a vector.

(1)

(3 marks)

Notes

Page 80: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2ai States that x = 0 needs to be substituted or implies it by writing

2

1.7 0.18 0 0.01 0h

M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Correctly substitutes x = 0 to get h = 1.7 (m) A1 1.1b

(2)

2aii States that x = 7 needs to be substituted or implies it by writing

h = 1.7 + 0.18(7) – 0.01(7)2 M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Correctly substitutes x = 7 to get h = 2.47 (m)

Accept awrt 2.5 (m)

A1 1.1b

(2)

2b Understands that the ball will hit the ground when h = 0 or

writes 2

1.7 0.18 0.01 0x x

M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Realises that the quadratic formula is needed to solve the

quadratic. For example a = 0.01, b = 0.18, c = 1.7 seen, or

makes attempt to use the formula:

20.18 0.18 4 0.01 1.7

2 0.01x

M1 1.1b

Simplifies the 2 4b ac part to get 0.1004 or shows

0.18 0.1004

0.02x

M1 1.1b

Calculates x = 24.84… (m)

Accept awrt 24.8 (m)

Does not need to show that 6.84...x (m)

A1 1.1b

States that the ball will be called ‘in’, or says, for example, yes

as 24.84… < 25. B1 3.2a

(5)

Page 81: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3

2c 2 km 1000 m 1min

1min 1km 60sec

Award 1 method mark for multiplication by 1000 and 1

method mark for division by 60.

M2 1.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

33.3 (m s−1) or 33.3

(m s−1) A1 1.1b

(3)

(12 marks)

Notes

2ai

Award both marks for a correct final answer.

2aii

Award both marks for a correct final answer.

2b

0.01, 0.18, 1.7a b c is also acceptable.

2b

Award the third method mark even if this step is not seen, providing the final answer is correct.

Page 82: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a Understands that the pole vaulter will land when h = 0 or

writes 21125 12 0

60x x

M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Correctly factorises to get 125 12 0x x o.e. M1 1.1b

Solves to get 125

10.41...12

x (m)

Accept awrt 10.4 (m)

A1 1.1b

(3)

3b States that the greatest height will occur when x = 5.20…(m) M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Makes an attempt to substitute x = 5.20…into the equation for

h. For example, 21125 5.20... 12 5.20...

60h seen.

M1 1.1b

h = 5.42…(m)

Accept awrt 5.4 (m)

A1 ft 1.1b

(3)

3c States h = 4.9 or states that 21

125 12 4.960

x x M1 3.1b 3rd

Understand how

mechanics

problems can be

modelled

mathematically.

Simplifies this to reach 2

12 125 294 0x x o.e. M1 1.1b

Realises that the quadratic formula is needed to solve the

quadratic. For example 12, 125, 294a b c seen, or

makes attempt to use the formula:

2125 125 4 12 294

2 12x

M1 1.1b

Simplifies the 2

4b ac part to get 1513 or shows

125 1513

24x

M1 1.1b

x = 6.82…(m)

Accept awrt 6.8 (m)

A1 1.1b

x = 3.58… (m)

Accept awrt 3.6 (m)

A1 1.1b

The pole vaulter can leave the ground between 3.6 m and

6.8 m from the bar. B1 3.2a

(7)

Page 83: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5

3di Allows the person to be treated as a single mass and allows the

effects of rotational forces to be ignored. B1 3.4 3rd

Understand

assumptions

common in

mathematical

modelling.

(1)

3dii The effects of air resistance can be ignored. B1 3.4 3rd

Understand

assumptions

common in

mathematical

modelling.

(1)

(15 marks)

Notes

3b

For the first method mark, accept their answer to part a divided by 2. Continue to award marks for a correct answer

using their initial incorrect value.

3c

Accept 3.6 ⩽ x ⩽ 6.8

Page 84: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a Makes an attempt to find the distance from A to B. For

example, 2 2

28 80 is seen.

M1 3.1b 4th

Find the

magnitude and

direction of a

vector quantity. Makes an attempt to find the distance from B to C. For

example, 2 2

130 15 is seen.

M1 3.1b

Demonstrates an understanding that these two values need to

be added. For example, 84.75… + 130.86… is seen. M1 1.1b

215.62… (m)

Accept anything which rounds to 216 (m)

A1 1.1b

(4)

4b States that 102 95AC i juuur

(m)

Award one point for each value.

B2 3.1b 4th

Find the

magnitude and

direction of a

vector quantity. States or implies that 95

tan102

M1 1.1b

Finds 42.96...

Accept awrt 43.0°

A1 1.1b

(4)

(8 marks)

Notes

Page 85: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 6: Quantities and Units in Mechanics

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 7

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a Makes an attempt to find the absolute value. For example,

2 2

14 22 is seen.

M1 3.1b 4th

Find the

magnitude and

direction of a

vector quantity. Simplifies to 680 M1 1.1b

Finds speed = 26.07… (ms−1)

Accept awrt 26.1 (ms−1)

A1 1.1b

(3)

5b States that

22tan

14

M1 1.1b 4th

Find the

magnitude and

direction of a

vector quantity.

Finds the value of θ, θ = 57.52… A1 1.1b

Demonstrates that the angle with the unit j vector is

90 – 57.52… M1 1.1b

Finds 32.47… (°)

Accept awrt 32.5(°)

A1 1.1b

(4)

5c Ignore the value of friction between the hockey puck and the

ice. B1 3.4 3rd

Understand

assumptions

common in

mathematical

modelling.

(1)

5d

3

1.4 g 1kg 100cm 100cm 100cm1000g 1m 1m 1m1cm

Award 1 method mark for division by 1000 and 1 method

mark for multiplication by 100 only once and the final method

mark for multiplication by 100 three times.

M3 1.1b 4th

Know derived

quantities and SI

units.

1400 kg m−3 A1 1.1b

(4)

(12 marks)

Notes

5b

Award all 4 marks for a correct final answer. Award 2 marks for a student stating 14

tan22

, and then either

making a mistake with the inverse or subtracting that answer from 90.

Page 86: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

1a Figure 1

General shape of the

graph is correct. i.e.

horizontal line,

followed by negative

gradient, followed by

a positive gradient.

M1 3.3 4th

Use and interpret

graphs of velocity

against time.

Vertical axis labelled

correctly. A1 1.1b

Horizontal axis

labelled correctly. A1 1.1b

(3)

1b Makes an attempt to find the area of trapezoidal section where

the car is decelerating. For example, 15 104

T is seen.

M1 1.1b 4th

Calculate and

interpret areas

under velocity–

time graphs. Makes an attempt to find the area of the trapezoidal section

where the car is accelerating. For example, 3

10 204

T is

seen.

M1 1.1b

States that 25 90

15 1312.54 4

T TT

M1 1.1b

Solves to find the value of T: T = 30 (s). A1 1.1b

(4)

(7 marks)

Notes

1a

Accept the horizontal axis labelled with the correct intervals.

1b

Award full marks for correct final answer, even if some work is missing.

Page 87: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 2

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

2a Velocity = acceleration × time seen or implied. M1 3.1b 4th

Use and interpret

graphs of velocity

against time.

Velocity = 11 × 8 = 88 m s−1 A1 1.1b

Figure 2

General shape of the

graph is correct. i.e.

positive gradient,

followed by horizontal

line, followed by

negative gradient not

returning to zero.

M1 3.3

Vertical axis labelled

correctly. A1 1.1b

Horizontal axis labelled

correctly. A1 1.1b

(5)

2b Makes an attempt to find the area of the trapezoidal section.

For example, 1

2 88 402

is seen.

M1 1.1b 4th

Calculate and

interpret areas

under velocity–

time graphs. Demonstrates an understanding that the three areas must total

1404. For example, 1 1

8 88 88 2 88 40 14042 2

T or

352 88 128 1404T is seen.

M1 2.1

Correctly solves to find T = 10.5 (s). A1 1.1b

(3)

(8 marks)

Notes

2a

Accept the horizontal axis labelled with the correct intervals.

2b

Award full marks for correct final answer, even if some work is missing.

Page 88: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 3

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

3a v ua

t

seen or implied.

M1 3.1b 5th

Use equations of

motion to solve

problems in

familiar contexts. Finds the value of a:

20 6 140.4

35 35a

m s−2

A1 1.1b

(2)

3b Use the fact that 1

2

4

3

t

t to write 3t1 = 4t2 or 3t1 − 4t2 = 0 or

equivalent.

M1 1.1b 5th

Use equations of

motion to solve

problems in

familiar contexts. States or implies that t1 + t2 = 35 M1 3.1b

Solves to find t1 = 20 or t2 = 15. Could use substitution or

simultaneous equations. Does not need to find both values for

mark to be awarded as either value can be used going forward.

A1 1.1b

Use v = u + at to write either x = 6 + 0.4(20)

or 20 = x + 0.4(15) M1 2.2a

Finds x = 14 (m s−1). A1ft 1.1b

(5)

3c States or implies that

2

u vs t

M1 2.2a 5th

Use equations of

motion to solve

problems in

familiar contexts. Finds the value of s: 6 20

35 4552

s

(m). A1 1.1b

(2)

(9 marks)

Notes

3b

Award ft marks for a correct answer using their value from part a.

Page 89: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 4

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

4a Demonstrates an understanding of the need to use

21

2s ut at

This can implied by using the equation in the next step(s).

M1 3.1b 5th

Use equations of

motion to solve

problems in

familiar contexts. Demonstrates the need to use (t – 3) when finding the

displacement of Q from A (or use (t + 3) when finding the

displacement of P from A). Can be implied in either of the

following steps.

M1 3.1b

Displacement of P: 22.8 0.06s t t A1 1.1b

Displacement of Q: 2

2.4 3 0.1 3s t t A1 1.1b

(4)

4b Writes 222.8 0.06 2.4 3 0.1 3t t t t M1 3.1b 5th

Use equations of

motion to solve

problems in

familiar contexts.

Makes an attempt to simplify this equation. For example,

2 22.8 0.06 2.4 7.2 0.1 6 9t t t t t

2 22.8 0.06 2.4 7.2 0.1 0.6 0.9t t t t t

20.04 6.3 0t t

M1 1.1b

Simplifies this expression to 22 50 315 0t t A1 1.1b

(3)

4c Makes an attempt to use the quadratic formula:

250 50 4 2 315

2 2t

M1 2.2a 5th

Use equations of

motion to solve

problems in

familiar contexts. Solves to find t = 30.21... (s).

Could also show that 5.21...t  (s).

A1 1.1b

States or implies 21

2s ut at

M1 3.1b

Makes a substitution using their 30.21… into the formula:

21

2.8 30.2... 0.12 30.2...2

s

M1 1.1b

Finds s = 139.36... (m). Accept awrt 139 (m). A1 ft 1.1b

(5)

(12 marks)

Page 90: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 5

Notes

4a

Award both accuracy marks if the following is seen:

Displacement of P from A: 2

2.8 3 0.06 3s t t

Displacement of Q from A: 22.4 0.1s t t

4c

Award ft marks for a correct answer using their ‘30.2’. They will have previously lost the first accuracy mark.

Q Scheme Marks AOs

Pearson

Progression Step

and Progress

descriptor

5a States or implies that s = −80 B1 3.1b 5th

Use equations of

motion to solve

problems

involving vertical

motion.

States or implies that a = −9.8 B1 3.1b

Writes 2 2 2v u as or makes a substitution

22 16 2 9.8 80v

M1 3.1b

Finds v = 42.70... (m s−1). Accept awrt 42.7 (m s−1). A1 1.1b

(4)

5b States or implies that s = 5 m. B1 3.1b 5th

Use equations of

motion to solve

problems

involving vertical

motion.

Simplifies 25 16 4.9t t to obtain 24.9 16 5 0t t M1 1.1b

Makes an attempt to use the quadratic formula:

216 16 4 4.9 5

2 4.9t

M1 1.1b

Solves to find t = 0.35… (s). Accept awrt 0.35 (s). A1 1.1b

Solves to find t = 2.91… (s). Accept awrt 2.92 (s). A1 1.1b

States that the ball is above 85 m for 2.56… (s). Accept awrt

2.6 (s). B1 3.2a

(6)

Page 91: Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1 ... · Mark scheme Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions © Pearson Education Ltd 2017. Copying permitted

Mark scheme Mechanics Year 1 (AS) Unit Test 7: Kinematics 1 (constant acceleration)

© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 6

5c States or implies that at the greatest height v = 0 B1 3.1b 5th

Use equations of

motion to solve

problems

involving vertical

motion.

Finds the value of u: 1

42.7... 8.54...5

u  (m s−1). Accept

awrt 8.5 (m s−1).

M1 3.1b

Writes 2 2 2v u as or makes a substitution

2 2

0 8.54... 2 9.8 s

M1 3.1b

Finds s = 3.72...(m). Accept awrt 3.7 (m). A1 ft 1.1b

(4)

(14 marks)

Notes

5c

Award ft marks for a correct answer using their answer from part a.