anderson secondary school 2011 preliminary examination ... · 8 andss 4e5n prelim 2011...

This document consists of 18 printed pages.

ANDSS 4E5N Prelim 2011 4016/01 [Turn over

ANDERSON SECONDARY SCHOOL 2011 Preliminary Examination Secondary Four Express / Four Normal / Five Normal

CANDIDATE NAME

CENTRE NUMBER S INDEX

NUMBER

MATHEMATICS 4016/01 Paper 1 12 September 2011 Additional Material: Geometrical instruments 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, centre number and index number in the spaces at the top of this page and on all the work you hand in. Write in dark blue or black pen both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. If working is needed for any question it must be neatly and clearly shown in the space below the question. Omission of essential working will result in loss of marks. Calculators should be used where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

For Examiner's Use

80

ANDSS 4E5N Prelim 2011 4016/01/PE2011 [Turn over

Mathematical Formulae

Compound Interest

Total amount = nrP ⎟⎠⎞

⎜⎝⎛ +

1001

Mensuration

Curved surface area of a cone = rlπ

Surface area of a sphere = 24 rπ

Volume of a cone = hr 2

31π

Volume of a sphere = 3

34 rπ

Area of triangle ABC = Cabsin21

Arc length = θr , where θ is in radians

Sector area = θ2

21 r , where θ is in radians

Trigonometry

Cc

Bb

Aa

sinsinsin==

Abccba cos2222 −+=

Statistics

Mean = ffxΣΣ

Standard deviation = 22

⎟⎟⎠

⎞⎜⎜⎝

⎛ΣΣ

−ΣΣ

ffx

ffx

3


For Examiner's

Use

1 (a) Factorise completely 4348 p− .

(b) Solve 1632

241 −

+

=⎟⎠⎞

⎜⎝⎛ x

x

.

For Examiner's

Use

Answer (a) _____________________ [2]

(b) x = __________________ [2]

2 Express 2

0123

1 1−

−

−

⎟⎟⎠

⎞⎜⎜⎝

⎛×

yyxyxnn

n

in the form ba yx and find ba in terms of n.

Answer ba = ________________ [2]

4


For Examiner's

Use

3 (a) Express 84 as the product of its prime factors. (b) Find the smallest positive integer value of k for which 84k is a multiple of 18.

For Examiner's

Use

Answer (a) ____________________ [1]

(b) k = _________________ [2]

4 Lynn invested the $2440 in a bank which pays 2% per annum compound interest compounded every quarter of a year. Calculate the amount of money Lynn received at

the end of 211 years.

Answer $ ____________________ [2]

5 (a) Solve the inequality 32315 +≤−<− xx . Hence, illustrate your answer on a number line.

(b) Write down the smallest rational number that satisfies 32315 +≤−<− xx .

Answer (a) _____________________ [2]

(b) _____________________ [1]

5


For Examiner's

Use

6 A swimming pool is filled up with water by 8 taps. If an additional tap is used, the time taken to fill up the swimming pool is 15 minutes faster. Given that the time required to fill up the swimming pool is inversely proportional to the number of taps used, how many additional taps must be used in order for the swimming pool to be filled up 45 minutes faster.

For Examiner's

Use

Answer __________________ taps [3]

7 In the diagram, AB is parallel to CD. Calculate the value of x and of y.

Answer x = _________________ [1]

y = _________________ [1]

D

A

C

B

E x°

y° 112°75°

130°

F

6


For Examiner's

Use

8 A circle with centre O, passes through the points A, B, C, D and E. BD is the diameter of the circle and NT and LT are tangents to the circle at A and B respectively. Given o25ˆ =FAN and o53ˆ =FED , find (a) BOA ˆ

(b) BDA ˆ (c) ECB ˆ (d) BEA ˆ (e) BTA ˆ

For Examiner's

Use

Answer (a) BOA ˆ =__________________ ° [2]

(b) BDA ˆ =__________________ ° [1]

(c) ECB ˆ =__________________ ° [2]

(d) BEA ˆ =__________________ ° [1]

(e) BTA ˆ =__________________ ° [2]

A

B

C

D

E

O

T

25°

53°

N

L

F

7


For Examiner's

Use

9 POQΔ and XOYΔ are right-angled triangles such that PQ is parallel to XY.

It is given that OP = 4.5 cm, XY = 20 cm and 53ˆsin =OQP .

(a) Find the length of

(i) PQ, (ii) QY. (b) State the value of QPX ˆcos .

For Examiner's

Use

Answer (a)(i) PQ = ______________ cm [2]

(ii) QY = ______________ cm [2]

(b) QPX ˆcos = ______________ [1]

Q

20 cm

P

X

O

4.5 cm

Y

8


For Examiner's

Use

10 The diagram shows three points A (5, 6), B (2, 3) and C (−1, 3). The line AB, when produced, meets the x-axis at D. Line BC makes an angle θ with the line DA.

(a) Find the equation of the line passing through A and parallel to the x-axis.

(b) Calculate the length AB.

(c) (i) Calculate the area of triangle ABC.

(ii) Hence, calculate the perpendicular distance from B to the line AC.

(d) Calculate the exact value of sin CAB ˆ .

(e) State the value of tan θ.

For Examiner's

Use

Answer (a) _____________________ [1]

(b) AB = ____________ units [1]

(c) (i) _____________ units2 [1]

(ii) ______________ units [2]

(d) sin CAB ˆ = ____________ [2]

(e) tan θ = _______________ [1]

D x

θ • B (2, 3)

• A (5, 6)

(−1 , 3) C •

y

0

9


For Examiner's

Use

11 The diagram shows the graph of rqxpy ++= 2)( where its turning point is (−2, 3) and the graph cuts the y−axis at 5−=y .

(a) Find the value of p, of q and of r. (b) The graph of rqxpy ++= 2)( is reflected in the line y = 3. Write down the equation of the reflected graph in the same form.

For Examiner's

Use

Answer (a) p = ____ , q = ____ , r = ____ [3]

(b) ________________________ [1]

12 Given that A is (2, −1), B is (1, 3) and ⎟⎟⎠

⎞⎜⎜⎝

⎛=

kCD

2such that AB is parallel to CD ,

find (a) AB ,

(b) the value of k.

Answer (a) __________________units[2]

(b) k = ___________________ [1]

(−2, 3) •

• −5

O

y

x

10


For Examiner's

Use

13 A bag contains 3 red balls (R) and 5 blue balls (B). In a game, two players, X and Y, take turns to draw a ball from the bag at random, one at a time, without replacement.

The first person to draw a blue ball wins the game. Player X draws the first ball. (a) The diagram below shows part of a tree diagram. Complete the tree diagram. (b) Calculate the ratio of the probability that player X wins to player Y wins.

For Examiner's

Use

Player X Player Y ……

Answer (a) Answer in the space above [2]

(b) __________ : __________ [2]

85

83

B

R

B

R

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

11


For Examiner's

Use

14 ε = { x : x is a whole number and 500 <≤ x }. A, B and C are subsets of the universal set ε such that A = { x : x is a perfect square } B = { x : x is a factor of the number 50} C = { x : x is a prime number }

(a) Find )( BAn ∪ .

(b) List the elements of BA ∩' .

(c) List the elements of CB ∩ .

For Examiner's

Use

Answer (a) )( BAn ∪ = _________________ [1]

(b) BA ∩' = ___________________ [1]

(c) CB ∩ = ____________________ [1]

12


For Examiner's

Use

15 A survey was conducted on 100 customers on their purchases during the Great Singapore Sale 2010. The cumulative curve below shows the amount of money spent per customer during the Great Singapore Sale 2010.

(a) Use your graph to find an estimate for

(i) the number of customers who spent more than $440, (ii) the median amount of money spent and

(iii) the interquartile range.

(b) Two customers were randomly selected. Find the probability that one of them spent less than $300 and another spent $700 or more.

For Examiner's

Use

Answer (a)(i) __________________________ [1]

(ii) _________________________ [1]

(iii) ________________________ [1]

(b) ___________________________ [2]

13


For Examiner's

Use

16 In this question, all constructions must be done with the use of a ruler, a protractor, and/or a pair of compass only. All construction arcs must be shown. A triangular shaped paddy field PQR is such that Q is due west of P. R is 210° from P and 135° from Q. (a) Using a scale of 2 cm to represent 3 km, construct ΔPQR. [2] A water sprinkler is located at point X which is equidistant from P and Q and equidistant from PR and PQ.

(b) Construct the perpendicular bisector of PQ. [1] (c) Construct the angle bisector of RPQ ˆ . [1]

(d) Mark the point X where the water sprinkler is located. Measure and write down the distance PX, in km. (e) The scale of the drawing can be expressed in the form 1: n. Find the value of n.

For Examiner's

Use

Answer (a) – (c) Working shown in the space above [4]

(d) PX = ________________ km [2]

(e) n = _____________________[1]

Q

N

P

14


For Examiner's

Use

17

The diagram shows three containers A, B and C. Container A is a cylinder with an open top of height h cm and radius r cm.

Container B is geometrically similar to Container A such that its height is ⎟⎠⎞

⎜⎝⎛ h

21 cm.

Container C is a cone with an open top and has a height h cm and radius r cm. Water is to be poured into the three containers at the same constant rate until the containers are full. The graph in the answer space shows the height of the water plotted against time as Container A is being filled. It takes 24 seconds to fill up Container A.

(a) Write down the ratio of the volume of water in container A, container B and container C. (b) On the axes below, draw the corresponding graphs for Container B and C respectively. Label each graph clearly.

For Examiner's

Use

Answer (a) _______ : ______ : ______ [2]

(b) Answer in the space above [3]

h h

h21

r r

Container A Container B Container C

Time (seconds)

Height (cm)

0 4 8 12 16 20 24

h

Container A

15

ANDSS 4E5N Prelim 2011 4016/01/PE2011 [End of Paper

Time (t) in seconds

Speed in m/s

0

25

30

MRT Train

For Examiner's

Use

18 The diagram shows the speed-time graph of a MRT train travelling from Ang Mo Kio Station to Bishan Station which is 4.5 km apart. The train starts from rest at Ang Mo Kio Station and accelerates uniformly for 30 seconds until it attains a speed of 25 m/s. The train continues to travel at this constant speed for some time before decelerating uniformly in the last 625m, and stopping at Bishan Station.

(a) Express 25m/s in km/h. (b) Calculate the speed of the train at t = 24. (c) Calculate the retardation in the last 625m of the journey. (d) Find the total time taken by the train to travel from Ang Mo Kio Station to

Bishan Station. (e) Find the average speed of the train for the whole journey. (f) On the axes in the answer space below, sketch the distance-time graph of the MRT train. [2]

Answer (a) _________________ km/h [1]

(b) __________________ m/s [1]

(c) _________________ m/s2 [2]

(d) ____________________ s [2]

(e) __________________ m/s [1] (f)

For Examiner's

Use

Time (t) in seconds

Distance in meters

0

1000

2000

30

3000

4000

16

ANDSS 4E5N Prelim 2011 4016/01/PE2011 [Answer Scheme


MATHEMATICS 4016/01

ANSWER SCHEME

1(a) )2)(2)(4(3 2 ppp −++ 11(a) p = −2, 32 == rq 1(b)

21

−=x 11(b) 3)2(2 2 ++= xy

2 )1(2

12−+

nn

12(a) 4.12 units

3(a) 7322 ×× 12(b) 8−=k 3(b) 3 13(b) 5 : 2 4 $2514.12 14(a) 10 5(a) 2

52

<≤− x 14(b) {2, 5, 10}

5(b) 52

− 14(c) {2, 5}

6 4 15(ai) 66 7 x = 37, y = 50 15(aii) $480 8(a) 74° 15(aiii) $120 8(b) 37° 15(b)

82514

8(c) 62° 16(d) 6.45 − 6.75 km 8(d) 37° 16(e) 150000 8(e) 106° 17(a) 24 : 3 : 8 9(ai) 7.5 cm 18(a) 90 km/h 9(aii) 10 cm 18(b) 20 m/s 9(b)

53

− 18(c)

21 m/s2

10(a) 6=y 18(d) 220 s 10(b) 4.24 units 18(e)

11520 m/s

10(ci) 4½ square units 10(cii) 1.34 units 10(d)

101

10(e) 1

17


13 (a) Player X Player Y Player X Player Y 16

85

83

B

R

B

R

⎟⎠⎞

⎜⎝⎛

75

⎟⎠⎞

⎜⎝⎛

72

B

R

⎟⎠⎞

⎜⎝⎛

65

⎟⎠⎞

⎜⎝⎛

61

B

R

( )1

( )0

(b) B1

Q

N

P

(a) R

B1

(c) B1

B1 X

18


17 Height (cm)

18 (f) Distance in metres

Container C

h21 − Container B

4500

4000 3875

3000

2000

1000

375

0 30 170 220 Time (t) in seconds

This document consists of 120 printed pages.

ANDSS 4E5N Prelim 2011 4016/02 [Turn over


CANDIDATE NAME

CENTRE NUMBER S INDEX

NUMBER

MATHEMATICS 4016/02 Paper 2 13 September 2011 2 hours 30 minutes Additional Materials: Writing paper (10 sheets) Graph paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your name, centre number and index number on all the work you hand in. Write in dark blue or black pen both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. If working is needed for any question it must be neatly and clearly shown in the space below the question. Omission of essential working will result in loss of marks. Calculators should be used where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100.

Mathematical Formulae

Compound Interest

Total amount = nrP ⎟⎠⎞

⎜⎝⎛ +

1001

Mensuration

Curved surface area of a cone = rlπ

Surface area of a sphere = 24 rπ

Volume of a cone = hr 2

31π

Volume of a sphere = 3

34 rπ

Area of triangle ABC = Cabsin21

Arc length = θr , where θ is in radians

Sector area = θ2

21 r , where θ is in radians

Trigonometry

Cc

Bb

Aa

sinsinsin==

Abccba cos2222 −+=

Statistics

Mean = ffxΣΣ

Standard deviation = 22

⎟⎟⎠

⎞⎜⎜⎝

⎛ΣΣ

−ΣΣ

ffx

ffx

ANDSS 4E5N Prelim 2011 Math (4016/02) [Turn over


3

1 The original price of a bag was US$358. After a discount, the sale price of the bag became US$149.

(a) Calculate the percentage discount of the bag. [1]

On a particular day, there was a factory promotion that gave a further 30% discount

on the sale price for the bag.

(b) Calculate the new sale price of the bag. [1] (c) Calculate the total percentage discount for the bag. [1]

A tax of 8.75% was imposed on the new sale price of the bag.

(d) Calculate the amount of tax payable. [1] (e) Calculate the price of the bag in Singapore dollars, if the exchange rate

on that day is US$1=S$1.24. [1]

2 (a) Simplify 22

2

28326

nmnmnnmnm

−−−+−

. [4]

(b) Solve the equation 016

8212311

2

2

2 =−−

−−+−

xxx

xxx

. [4]

3 The diagram shows a paper weight in the form of a prism where ABCD, ABFE and

CDEF are rectangular faces and ADE and BCF are triangular faces. AB = 6.5 cm,

AD = (12 − 3x) cm , AE = (2x + 3.2) cm and . o30ˆ =EAD

(a) Given that the difference in the area between the rectangle ABCD and the

triangle ADE is 21.6 cm2.

Form an equation in x and show that it reduces to15x 2 − 231x + 468 = 0. [2]

(b) Solve the equation 0468 . [2] 23115 2 =+− xx

(c) Calculate the volume of the paper weight. [2]

(12 − 3x) cm

A

B

D

E

F 6.5 cm

(2x + 3.2) cm

30°

C


4

4 The diagrams below show the first three triangles in a sequence of triangles of increasing size.

Each triangle is formed by joining the neatly arranged dots such that the smaller right-angled triangles are exactly identical.

The table below shows the number of dots and the number of small right-angled triangles in each of the larger triangles.

Triangle Total number of dots Number of small right-angled triangles

1 4 2 2 9 8 3 16 18 4 a b

…

…

…

n y z

(a) Find the value of a and of b. [2]

(b) Find the total number of dots needed to form Triangle 16. [1]

(c) Find the number of small right-angled triangles in Triangle 6. [1]

(d) (i) Express y in terms of n. [1]

(ii) Express z in terms of n. [1]

(e) State the triangle which has 450 small right-angled triangles. [1]

5 In the diagram below, O is the centre of a semicircle and TC is a tangent to the

semicircle at C. Given that OC = 12 cm and BT = 25 cm, calculate

(a) COB ˆ in radians, [2]

(b) the area of the shaded region. [3]

• •

•

• ••

•

• •

•

•

•

•

• •

•

• •

•

•

•

• •

•

•

• •

•

•

•

•

•

•

•

• •

•

•

•

• •

Triangle 1 Triangle 2 Triangle 3

C

T A O B


5

6 The table below shows the average number of visitors per day in July 2011 (rounded

off to the nearest hundred) and the price of admission ticket for each adult and each

child in three theme parks, Alpha Land, Beta Land and Gamma Land respectively.

Average number of visitors per day in July 2011

Price of tickets (US$)

Theme Park

Adults Children Adults Children Alpha Land 10 200 6 800 80 74 Beta Land 8 500 4 200 85 79

Gamma Land 2 400 1 400 69 59

(a) Write down two matrices such that the elements of their product, under matrix

multiplication, will give the average total amount of ticket sales in each theme

park. Evaluate the product of these two matrices and label the matrix T. [2]

(b) Evaluate (1 1 1 13

)T. [1]

(c) State what the element in (1 1 1 13

)T represents. [1]

During the school holidays, each theme park reduced the price of an adult ticket by

10% and the child ticket by 15%.

(d) Using matrix multiplication, find the discounted price for each type of ticket

at each theme park. [2]

7 In the diagram, , AB = 16 cm, BC = 12 cm, BP = x cm and the point Q

on the line AC is the image point of B under the reflection in the line AP.

o90=∠ABC

Calculate, without the use of a calculator, the exact value of

(a) x, [5] (b) tan PAC ˆ . [1]

xB P 12

A

• Q

16

C


6

8 The distribution below shows the number of SMS messages 20 students sent in a particular month.

78 74 84 78 85 94 88 72 68 76 25 84 78 82 78 87 80 92 95 69

(a) Illustrate the data using a stem-and-leaf diagram. [2]

Using the stem-and-leaf diagram, calculate (b) (i) the mode, [1]

(ii) the mean, [1]

(ii) the standard deviation of the distribution. [1]

(c)

• •

25 95 x2 a x1

Number of SMS messages

The distribution is represented using a box-and-whisker diagram. (i) Find the value of a. [1] (ii) Calculate and explain what 12 xx − 12 xx − represents. [2]

(d) Another student sent p SMS messages in that same month. Write the range of values of p such that the median is 80. [1] 9 In the diagram, PQRS is a rhombus where QS is one of the diagonal.

RS is produced to point T such that S is the midpoint of RT. PS and QT intersect at O.

PQ

R S T

O

(a) (i) Show that triangle QRS and triangle PST are congruent. [3] (ii) Explain why PQST is a parallelogram. [2] (b) Show that triangle POQ is similar to triangle RQT. [2]


7

10 C

DO

b

a B

M A

In the diagram above, =OA a, =OB b and 34

=CA a − 31 b.

M is the midpoint of AB and AC cuts OB at D.

(a) Express, as simply as possible, in terms of a and b, (i) OM , [1] (ii) OC . [1]

(b) What can you conclude about OC and AB ? [1] (c) Find the numerical value of

(i) ABOC , [1]

(ii) ABDOCDΔΔ

ofareaofarea . [1]

(d) Express, as simply as possible, CD , in terms of a and b. [1] (e) Find the numerical value of

(i) OCAOCDΔΔ

ofareaofarea , [1]

(ii) OCBOAMΔΔ

ofareaofarea , [1]

(iii) OABC

BCDofareaofarea Δ . [1]


8

11

E F

• O D A • X C B The diagram above shows a playground in the shape of a regular hexagon ABCDEF

with centre O. A circular fountain with centre X lies in the hexagon such that it

touches AB and BC. It is given that AB = 50 m and BX = 12 m.

(a) Calculate

(i) ABC∠ , [1] (ii) the area of triangle AOB in kilometers square, leaving your answer

in standard form. [2] (iii) the radius of the fountain. [3]

(b) A boy walks directly from A to E. Calculate the distance he walks. [2]

(c) A lamp post of height 8 m stands vertically at O. A bird sits on top of the lamp post.

(i) Calculate the angle of elevation of the bird on top of the lamp post from A. [1]

(ii) The boy decides to walk directly back along EA until he reaches a point T from which the angle of depression of the boy from the bird

is the greatest. Calculate the distance OT. [2]


9

12 A closed container, A, of negligible thickness is made up of a cylinder of diameter

22 cm and height 2 cm, and a right cone of height 42 cm as shown.

42

22

2

Container A (a) Calculate

(i) the volume of Container A, leaving your answer in terms of π. [2] (ii) the surface area of Container A, giving your answer to 2 decimal place. [2]

2

42

Container B

A closed hollow Container B which has the same volume as Container A, is made up

of a right pyramid of height 42 cm and a cuboid of height 2 cm. Both the pyramid and

the cuboid have the same square base.

(b) Show that the length of the square base, correct to 1 decimal place, is 19.5 cm.[2]

(c) If Container B is filled with water up to 43 of its volume, find the depth of water

in the container. [4]

Container B

ANDSS 4E5N Prelim 2011 Math (4016/02) [End Of Paper

10

3

13 Answer the whole of this question on a sheet of graph paper. The table below gives the x- and y-coordinates of some points which lie on a curve . 523 +++−= xxxy

x −3 −2 −1 0 1 2 3 4

y 24 5 0 3 8 9 0 −25

(a) Using a scale of 2 cm to represent 1 unit on a horizontal axis for

and 2 cm to represent 5 units on a vertical axis for

43 ≤≤− x

2525 ≤≤− y , plot the points

given in the table and join them with a smooth curve. [2]

(b) Using your graph, solve the equation . [2] 08523 =+++− xxx

(c) By drawing a suitable tangent, find the gradient of the curve at the point where

x = 1. [2]

(d) The x-coordinates of the points where the line 33 +−= xy intersects the curve

are the solutions to the equation . 023 =+++− baxxx

Find the value of a and of b. [2]

(e) Using the same axes, draw the line 33 +−= xy . From your graphs, determine

the range of values of x for 43 ≤≤− x for which .

[2]

333523 +−>+++− xxxx

(f) The line kxy +−=25 intersects the curve at least two

points. Find the largest value of k. [1]

3523 +++−= xxxy


MATHEMATICS 4016/02

ANSWER SCHEME

1(a) 58.4%

6(a) ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

20024830010542001319

1(b) $104.30 6(b) ( )900873

1(c) 70.9%

6(c)

The element represents the mean ticket sales collected from the three theme parks in July.

1(d) $9.13

6(d) ⎟⎟⎠

⎞⎜⎜⎝

⎛15.5015.679.621.625.7672

1(e) $140.65

The discounted price for adult ticket and children ticket at Alpha Land is $72 and $62.90 respectively, and at Beta Land, $76.50 and $67.15 respectively and at Gamma Land, $62.10 and $50.15 respectively.

2(a) nm

n+−

43

7(a) 315=x

2(b) 21

=x

7(b) 31

3(b) 13=x or 4.2=x 8(b)(i) 78 3(c) 62.4 cm3

8(b)(ii) 78.35 4(a) a = 25 b = 32 8(b)(iii) 14.3 4(b) 289 8(c)(i) 79 4(c) 72 8(c)(ii) 11

4(d)(i) ( )21+= ny

8(c)(iii) 12 xx − represents interquartile range of the distribution.

4(d)(ii) 22nz = 8(d) 80≥p 4(e) Triangle 15 5(a) 2.75 radians 5(b) 172 cm2

ANDSS 4E5N Prelim 2011 Math (4016/02) [Answer Scheme

10(a)(i) 21 (a + b) 12(a)(i) 1936π cm3

10(a)(ii) 31 (a − b) 12(a)(ii) 2018.73 cm2

10(b) AB is parallel to OC . 12(c) 16.3 cm 10(c)(i)

31

=ABOC 13(b) x = 3.3

10(c)(ii) 91

ofareaofarea

=ΔΔ

ABDOCD 13(c) 4

10(d) 121 (4a − b) 13(d) a = 8, b = 0

10(e)(i) 41

ofareaofarea

=ΔΔ

OCAOCD 13(e) 4.23 −<≤− x , 3.30 << x

10(e)(ii) 23

13(f) k = 14

10(e)(iii) 163

ofareaofarea

=ΔΔOABCBCD

11(a)(i) 120° 11(a)(ii) 31008.1 −× km2 11(a)(iii) 10.4 m 11(b) 86.6 m 11(c)(i) 25m 11(c)(ii) 10.5°

13(a)

ANDSS 4E5N Prelim 2011 Math (4016/02) [Answer Scheme

anderson secondary school 2011 preliminary examination ... · 8 andss 4e5n prelim 2011...

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