commentary on a/b level questions - understanding standards · solving equations and inequations...

$: Commentary on A/B level questions - Understanding Standards · Solving equations and inequations with fractional coefficients are treated as A/B Level. 2016: Paper 1, Question 8 (b)$
Commentary on A/B level questions

The table below illustrates examples of A/B questions or examples where A/B marks are found in existing questions.

A/B Level questions include those:

assessing more challenging aspects of some skills

assessing integration of some skills

set in more challenging contexts

Approximately 35% of the marks in the examination will be available for A/B Level responses.

Questions illustrated as A/B questions will not necessarily always perform as A/B questions. This may be because candidates’ performance in

these questions can improve over time because of increased exposure in past course assessments.

Level Example Commentary Source

Expansion of Brackets

A/B Level x x x 24 2 Expanding brackets in the form

2ax b cx dx e where

, , , anda b c d e are integers are A/B

Level.

2015: Paper1, Question 4

C Level (a) 2 5 3 1x x

(b) 2

2 5x

(a) 2014: Paper 1, Question 2

(b) Illustration

Factorising

A/B Level Factorise x x 22 5 3 Factorising trinomials with a non-

unitary 2x coefficient are generally

A/B Level except in cases such as

those shown in the example.

Illustration

National 5 Mathematics Question Paper Commentary on A/B level questions

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C Level Factorise

(a) 2 2 3x x

(b) 22 4 6x x

(c) 23 18x

(a) & (b) Illustrations

(c) 2016: Paper 2, Question 4

(modified)

Quadratic Equations

A/B Level Solve

2xx

x

A/B Level quadratic equations are

generally equations which:

require A/B Level factorising

are part of a problem

If the equation is in non-standard

form then the Level depends on the

complexity of the form.

Illustration

C Level Solve 2 8 2x x C Level quadratic equations are

generally equations which:

require C Level factorising

require use of the quadratic

formula (including non-unitary

coefficient)

Illustration


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Quadratic Equations (as part of a problem)

A/B Level The diagrams below show a rectangle and a triangle. All measurements are in centimetres.

(a) Find an expression for the area of the rectangle.

(b) Given that the area of the rectangle is equal to the area of

the triangle, show that 2 2 8 0x x .

(c) Hence find, algebraically, the length and breadth of the rectangle.

If the equation is part of a problem

then it is generally treated as A/B

Level.

2016: Paper 1, Question 12

Simplifying Algebraic Fractions

A/B Level Simplify

2

2

4

20

x x

x x

A/B level simplifying algebraic

fractions generally:

require A/B Level factorising

have no lead-in

Any part of the questions requiring

A/B level factorising is treated as

A/B Level.


C Level (a) Factorise 2 20x x

(b) Hence simplify 2

2

4

20

x x

x x

C level simplifying algebraic

fractions generally:

require C Level factorising

have a lead-in

2015: Paper 1, Question 12 (modified)


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Operations with Algebraic Fractions

A/B Level (a)

3 5

2 1x x

(b) 7 3

5x x

When performing operations on

algebraic fractions the Level

depends on the complexity of the

fractions.


(b) 2014: Paper 2, Question 9

C Level (a)

7 5

p q

(b) 2

5

2

t t

s s

(a) Illustration


Interpreting Graphs of Quadratic Functions

A/B Level The diagram below shows the path of a small rocket which is fired

into the air. The height, h metres, of the rocket after t seconds is

given by 216h t t t

(a) After how many seconds will the rocket first be at a height of

60 metres?

(b) Will the rocket reach a height of 70 metres? Justify your answer.

If the graph is part of a problem then

it is generally treated as A/B Level.



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C Level The diagram below shows part of the graph of 2y ax .

Find the value of a.

Quadratic graphs of the form 2y kx are treated as C Level.


C Level The graph below shows part of the parabola with equation of the

form 2

y x a b .

The minimum turning point (2,−4) is shown in the diagram.

(a) State the values of

(i) a

(ii) b

(b) Write down the equation of the axis of symmetry of the graph.

Quadratic graphs of the form

2

y x a b are treated as

C Level

2

y k x a b where k

(but 0, 1 ) are treated as A/B

Level.



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Sketching Graphs of Quadratic Functions

A/B Level (a) Sketch the graph of 2

3 1y x .

On your sketch, show clearly the coordinates of the turning

point and the point of intersection with the y-axis

(b) Sketch the graph of 2 1 1y x x

(c) Sketch the graph of 22 3 1y x x

When sketching a graph of a

quadratic function the Level

depends on the complexity of the

function.


(b) & (c) 2016: Paper 1,

Question 10 (modified)

C Level Sketch the graph of

(a) 2 1y x

(b) 2

3y x

(c) 1 3y x x

(a), (b) & (c) Illustrations

Equations and Inequations

A/B Level (a) Solve the equation

2 52

3 6

xx .

Give your answer in its simplest form.

(b) Solve 2

5 23

xx

(c) Solve 2 5 3

3 6 4

x

Solving equations and inequations

with fractional coefficients are

treated as

A/B Level.


(b) & (c) Illustrations

C Level Solve

(a) 11 2 1 3 39x

(b) 28 12x x x


(b) Illustration


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Changing the Subject of a Formula

A/B Level Change the subject of the formula

(a) 4L kt p to k

(b) 21

2s at to t

(c) 21

2s ut at to a

(d) at b ct to t

The Level depends on the

complexity of the formula. Where

one of the steps requires a square

or square root to be undone the

question is generally treated as A/B

Level.


(b) Illustration

(c) 2014: Paper 2, Question11

(d) Illustration

C Level Change the subject of the formula

21

2s at to a

Illustration

Equation of Straight Line

A/B Level A straight line has equation 4 3 12x y .

(a) Find the gradient of this line.

(b) Find the coordinates of the point where this line crosses the

x-axis.

Identifying the gradient and/or

intercepts with the axes from

equations in the form ax by c

and 0ax by c is often treated

as A/B level.

2014: Paper 1, Question11


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C Level A cattle farmer records the weight of some of his calves.

The scattergraph shows the relationship between the age, A

months and the weight, W kilograms of the calves.

A line of best fit is drawn.

Point D represents a 3 month old calf which weighs 100 kilograms. Point E represents a 15 month old calf which weighs 340 kilograms.

Find the equation of the line of best fit in terms of A and W.

Give the equation in its simplest form.

Determining the equation of straight

line given two points is generally

treated as C Level.



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Arcs, Sectors and Volume

A/B Level The pendulum of a clock swings along an arc of a circle, centre O.

The pendulum swings through an angle of 65°, travelling from A to B. The length of the arc AB is 28·4 centimetres.

Calculate the length of the pendulum.

Questions which require working

backwards are generally treated as

A/B Level.


C Level A carton is in the shape of a large cone with a small cone removed.

The large cone has diameter of 32 cm and height 24 cm. The small cone has diameter of 18 cm and height 13·5 cm.

Calculate the volume of the carton Give your answer correct to 2 significant figures.



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Perpendicular Bisector of a Chord

A/B Level The diagram below shows the circular cross-section of a milk tank.

The radius of the circle, centre O, is 1·2 metres. The width of the surface of the milk in the tank, represented by ML in the diagram, is 1·8 metres.

Calculate the depth of the milk in the tank.

Problems involving the

perpendicular bisector of a chord

and Pythagoras’ theorem are

generally treated as A/B Level.


Note: other questions of this

type are

2014: Paper 1, Question 12 and

2016: Paper 2, Question 15.

Trigonometric Identities

A/B Level Simplify tan cos2 2x x

Show your working.

Questions on this topic are generally

A/B Level.


Trigonometric Graphs

A/B Level Part of the graph of cosy x a is shown in the diagram.

Write down the value of a.

Interpreting or sketching graphs:

(a) involving phase angle or

(b) of the form siny a bx c

( , 1, 0a b c ) are generally A/B

Level.

Intermediate 2 2010: Paper 1,

Question 9


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C Level Part of the graph of siny a bx is shown in the diagram.

Write down the values of a and b.

Interpreting or sketching graphs of

the form siny a bx ,

siny a x c and siny a bx c

( , 1, 0a b c ) are generally C

Level.


Indices

A/B Level (a) Simplify ( )2 3 10n n . Give your answer with a positive

power.

(b) Express 42n with a positive power.

(c) Simplify 3

2n .

(d) Evaluate 5

38 .

Questions with two or more steps

with a maximum of one involving m n m na a a or

m n m na a a are

generally treated as A/B Level.


(b) & (c) Illustrations

(d) 2015: Paper 1, Question 14

C Level (a) Express 4n with a positive power.

(b) Simplify 5

2

10

2

n n

n

(a) Illustration



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Rationalising Denominator of Surd

A/B Level (a) The function f x is defined by

2, 0f x x

x .

Express 5f as a fraction with a rational denominator.

(b) Express 4

8 with a rational denominator.

Give the answer in its simplest form.

Questions with two or more steps

involved are generally A/B Level.



C Level Express

2

5 with a rational denominator.


(modified)

Contextualised Questions and/or Integration of Skills

A/B Level In the diagram below P, Q and R represent the positions of Portlee, Queenstown and Ruston respectively.

Portlee is 25 kilometres due South of Queenstown. From Portlee, the bearing of Rushton is 072°. From Queenstown, the bearing of Rushton is 128°.

Calculate the distance between Portlee and Rushton. Do not use a scale drawing.

Adding a context and/or integrating

two or more skills can increase the

level of difficulty.

2015: Paper 2 Question 13


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A/B Level In the diagram below

DE is perpendicular to AC.

AD = 4 centimetres.

DB = 6 centimetres.

AE = EC = 3 centimetres.

Calculate the length of BC. Give your answer correct to one decimal place.



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A/B Level The picture shows the entrance to a tunnel which is in the shape of part of a circle.

The diagram below represents the cross-section of the tunnel.

The centre of the circle is O.

MN is a chord of the circle.

Angle MON is 50°.

The radius of the circle is 7 metres.

Calculate the area of the cross-section of the tunnel.



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