mathematics 4016/01 paper 1 2 hours clementi town secondary school mathematics / paper 1 secondary 4...

Name : _________________________________ Register Number : ______ Class : ______

Clementi Town Secondary School Preliminary Examination 2011

Secondary 4 Express / 5 Normal Academic MATHEMATICS 4016/01

Paper 1 2 hours Candidates answer on the Question Paper.

CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL

READ THESE INSTRUCTIONS FIRST Do not open the booklets until you are told to do so. Write your name, register number and class on all the work you hand in. Write in dark blue or black pen on both sides of the answer paper. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. 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 number of marks for this paper is 80.

___________________________________________________________________________________

This question paper consists of 18 printed pages, including this cover page. [Turn over]

For Examiner’s Use

2 Clementi Town Secondary School

Mathematics / Paper 1 Secondary 4 Express / 5 Normal Academic Preliminary Examination 2011

Mathematical Formulae

Compound Interest

Total amount =

nr

P

1001

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere =24 r

Volume of a cone = hr 2

3

1

Volume of a sphere =3

3

4r

Area of triangle ABC = Cabsin2

1

Arc length = r , where is in radians

Sector area = 2

2

1r , where is in radians

Trigonometry

Abccba

C

c

B

b

A

a

cos2

sinsinsin222

Statistics

Mean =

f

fx

Standard deviation =

22

f

fx

f

fx

Clementi Town Secondary School 3 Preliminary Examination 2011 Secondary 4 Express / 5 Normal Academic Mathematics / Paper 1

[Turn over]

Answer all the questions.

1 (a) Find the middle number when the numbers below are arranged in ascending order:

,3

21 ,2.3 ,9.0 ,5.4

8

7.

(b) Ahmad scored 14 out of 26 in a test.

Express this mark as a percentage, correct to 2 decimal places.

Answer

(a) …………...…………… [1]

(b) ...…………………....% [1]

2 (i) Calculate

4

1978.56

1204.3

, showing all the figures on your calculator.

(ii) Give your answer correct to 4 significant figures.

Answer

(i) ………………………… [1]

(ii) ………………………... [1]



3 Weiming bought a handphone for $198.

He sold it to his friend and earned a profit of 150% of his cost.

Calculate the selling price.

Answer

$…………………………... [2]

4 Stanley invested $3000 in a bank.

The bank paid a half-yearly compound interest of 2% per annum.

Find the total interest he earned in 4 years.

Answer

$......………………………. [2]


[Turn over]

5 Solve 234 2793 xxx .

Answer

x = ………………………. [2]

6 At a fund-raising event, Bala wants to sell single-scoops of ice-cream in a cone.

Ice-cream cones are sold in boxes of 12.

Each tub of ice-cream can make 26 single scoops of ice-cream.

What is the minimum number of tubs of ice-cream he should get to ensure that there is no

cone or ice-cream remaining?

Answer

……...…….………………. [2]



7 The table below shows the distribution of number of children per household as interviewed

by Mary in Clementi Central.

Number of Children Number of household

0 10

1 23

2 35

3 27

4 4

5 1

(a) What is the modal number of children?

(b) What is the value of the angle representing households with no children, if the data

was represented in a pie chart?

Answer

(a) ………………..children [1]

(b) ………………………... [1]

8 Find the value of x in the figure on the right.

Answer

…..………………………... [2]

A

B C

D E

F

G


[Turn over]

9 The sequence of numbers, 1, 5, 11, 19, …, can also be expressed as

12 + 0, 22 + 1, 32 + 2, 42 + 3, …

(a) Find the 8th term of the sequence.

(b) Write down, in terms of n, an expression for the nth term.

Answer

(a) ………………………... [1]

(b) ………………………... [1]

10 (a) Express 198 as the product of its prime factors.

(b) Find the highest common factor of 198 and 66.

(c) Find the smallest integer value of h such that 198h is a perfect square.

Answer

(a) ………………………... [1]

(b) ………………………... [1]

(c) ………………………... [1]



11 (i) Express x2 – 4x – 7 in the form bax 2)( .

(ii) Hence solve the equation x2 – 4x – 7 = 0, leaving your answers in exact form.

Answer

(i) …………………….…... [1]

(ii) ………………………... [2]

12 The figure shows a circle with centre O and radius 7 cm.

Points A, B, C and D lie on the circumference and ABC 30.

Find

(a) the length of the major arc ABC.

(b) the area of segment ADC.

Answer

(a) ……………………..cm [1]

(b) ………………….…cm2 [2]

O A

B

C

7

30°

D


[Turn over]

13 The diagram shows three sides AB, BC and CD of a regular polygon.

Given that 12CDB , calculate the number of sides of the polygon.

Answer

…..………………………... [3]

14 Solve 32

xx

x

10

3

52.

Answer

…..………………………... [3]



15 Singapore has a population of 4.987 million and a total land area of 682.7 km2.

(a) Calculate the average number of people living per square kilometre in Singapore.

(b) If 23% of its total land area is made up of nature reserve, find the actual area of the

nature reserve in square metres.

Leave both your answers in standard form.

Answer

(a) …....…………………... [1]

(b) ....…….………….....m2 [2]

16 (a) Factorise babacc 5102 .

(b) Simplify )6(73 y .

(c) One of the solutions of 2x2 – px – 9 = 0 is x = 1.5.

Find

(i) the value of p,

(ii) the other solution of the equation.

Answer

(a) ………………………... [1]

(b) ………………………... [1]

(c) (i)……………………... [1]

(c) (ii) ……………………..[1]


[Turn over]

17 The diagram shows the speed-time graph of a lorry over a 10-second interval.

(a) Calculate the acceleration of the lorry during the first 3 seconds.

(b) Find

(i) the total distance covered by the lorry during the 10-second interval,

(ii) the average speed of the lorry during the 10-second interval.

Answer

(a) …………………… m/s2 [1]

(b) (i)…………………… m [2]

(b) (ii)………………… m/s [1]



18 In the diagram, S and T lie on the straight lines XY and XZ respectively.

XSZ = XTY = 90, XS = 4 cm, XT = 6 cm and SY = 8 cm.

(a) Show that XSZ is similar to XTY.

(b) Calculate the length of XZ.

Answer

(a) ............….…………………………………………………………………………………………

.....……………………………………………………………………………………………………

..…..……………………………………………………………………………………………… [2]

(b) ………………….…cm [2]

19 (a) 12 engineers worked together and completed 30 identical model cars in 6 days.

Assuming that all engineers worked at the same rate, how many days would 18

engineers need to complete 15 identical model cars?

(b) The kinetic energy of a moving object, E joules, is directly proportional to the

square of its speed, v m/s.

If the speed of the moving object is halved, the corresponding kinetic energy of the

object is p times its original kinetic energy.

Find the value of p.

.

Answer

(a) .......……………… days [2]

(b) .…….………………..... [2]

Y

S

X

Z

T

6 cm

8 cm

4 cm


[Turn over]

20 The diagram shows the cumulative frequency curves for the marks scored by

60 students in a Geography and a History test.

(a) Estimate how many more students scored more than 30 marks in the History test

than in the Geography test.

(b) Which of the two tests was more difficult for the students?

Justify your answer.

Answer

(a) ………………….…….. [2]

(b) ............……………………………………………………………………………………………

…..…………………………………………………………………………………………………[2]

10 20 30 40 50 O Marks

Cumulative

frequency

10

20

30

40

50

60

Geography

History



21 The diagram, drawn to scale, shows 2 sides of a quadrilateral PQRS.

(a) Given that S is 10 cm from R, PSR is acute and 120SPQ , complete the

quadrilateral.

(b) Construct the perpendicular bisector of PQ.

(c) A point X is equidistant from points P and Q and also equidistant from lines PQ

and QR.

Find and label the position of X.

Answer (a), (b) and (c)

[4]

P

Q R


[Turn over]

22 Two geometrically similar cups of Moi Bubble Tea drinks are shown below.

(a) Find, in the simplest form, the ratio of the total surface area of the smaller cup to

the total surface area of the larger cup.

(b) Which size of drink is a better buy?

You must show all your working clearly.

Answer

(a) ...……….. ………….... [2]

(b)

………………………………………………………………………………………………………..

………………………………………………………………………………………………………..

…………………………………………………………………………..………………………... [2]

BUBBLE

TEA

500 ml

Size X

$ 3.50

BUBBLE

TEA

256 ml

Size Y

$ 2.50

:



23

On the axes shown, P is (– 8, 8) and Q is (– 8, 4).

Find

(a) the equation of line PQ,

(b) the area of triangle OPQ,

(c) the coordinates of two possible points R on the y-axis such that triangle ORQ has

the same area as triangle OPQ.

Answer

(a) .........…………………... [1]

(b)……..…………… units2 [1]

(c) ...….…..………………. [1]

....…….……………….. [1]

y

O – 8 – 6 – 4 – 2 – 2

– 4

– 6

10

2

4

6

8

x

P

Q

( , )

( , )


[Turn over]

24 A container is made up of a cube and a right-angled triangular prism.

Each side of the cube is 10 cm and EB = EA.

Calculate

(a) (i) the area of trapezium ABCD,

(ii) the volume of the container.

(b) Water is poured in at a constant rate and

fills the container in 30 s, on the axes below,

sketch the graph showing how the depth

of the water varies with time.

Answer

(a) (i) ………………... cm2 [1]

(a) (ii) ..…………….... cm3 [1]

(b) depth (cm)

[2]

20

O 30

10

Time (s) 10 20

A

B

C D

E

10 cm



25 In the diagram, ABCD is a parallelogram and the point E on AD is such that ADAE4

1 .

The diagonal AC meets BE at O such that OCAO4

1 .

It is given that OB 4b and OC 4c.

(a) Show that OA c.

(b) Express, in terms of b and/or c,

(i) AB ,

(ii) AD ,

(iii) OE .

(c) Find

(i) COB

AOE

of area

of area,

(ii) ABC

AOE

of area

of area.

Answer

(a) ...…………………………..

………………………………..

………………………………..

…………………………… [1]

(b) (i)................................... [1]

(b) (ii).................................. [1]

(b) (iii)................................. [2]

(c) (i) .................................. [1]

(c) (ii) ................................. [2]

- End of paper -

A

B C

O

E D

1a.8

7

1b.53.85

2i. 0.1885125184

2ii. 0.1885

3. $495

4. $248.57

5. – 3

6. 6 tubs

7. 2, 36

8. 75

9a. 71

9b. 12 nn

10a. 1132 2

10b. 66

10c. 22

11i. 11)2( 2 x

11ii. 112x

12a. 36.7

12b. 44.4

13. 15

14. 78 x

15a. 7.30 x 103

15b. 81057021.1

16a. )12)(5( acb

16b. 7y – 39

16c 3p , 3x

17a. 2.5

17bi. 130

17bii. 13

18b. 8

19a. 2 days

19b. 4

1p

20a. 34

20b. The Geography test was probably more

difficult for the students as it has a lower

median score.

22a. 16 : 25

22b. Hence, size X is a better buy since it is

cheaper per ml.

23a. 8x

23b. Area = 842

1 = 16 units2

23c. )4,0( )4,0(

24a. 150 units2

24b. 1500 units3

24c.

25 bi. c 4b

25 bii. 4c 4b

25 biii. b

25 ci. 16

1

25cii. 20

1

20

O 30

10

Time (s) 10 20

CTSS PRELIM 2011

EMATH PAPER 1 ANSWER KEY

Name : _________________________________ Register Number : ______ Class : ______

Clementi Town Secondary School Preliminary Examination 2011

Secondary 4 Express/ 5 Normal Academic

Mathematics 4016/2 Paper 2 2 hours 30 minutes Additional Materials provided: Answer Paper (7 sheets)

Graph paper (1 sheet)

CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL CLEMENTI TOWN SECONDARY SCHOOL

READ THESE INSTRUCTIONS FIRST Do not open the booklets until you are told to do so. Write your name, register number and class on all the work you hand in. Write in dark blue or black pen on both sides of the answer paper. Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer all questions.

If working is needed for any question it must be shown with the answer. 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 , use either your calculator value or 3.142, unless the question requires the answer in

terms of .

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 number of marks for this paper is 100.

___________________________________________________________________________________

This question paper consists of 10 printed pages, including this cover page.

[Turn over

For Examiner’s Use

Clementi Town Secondary School 2 Preliminary Examination 2011 Secondary 4 Express/ 5 Normal Academic Mathematics / Paper 2

Mathematical Formulae

Compound Interest

Total amount =

nr

P

1001

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere =24 r

Volume of a cone = hr 2

3

1

Volume of a sphere =3

3

4r

Area of triangle ABC = Cabsin2

1

Arc length = r , where is in radians

Sector area = 2

2

1r , where is in radians

Trigonometry

Abccba

C

c

B

b

A

a

cos2

sinsinsin222

Statistics

Mean =

f

fx

Standard deviation =

22

f

fx

f

fx


Answer all the questions.

1 A shop manufactures mooncakes.

A mooncake contains flour, sugar and yam paste in the ratio .3:2:7

The mass of sugar in a mooncake is 28 grams.

(a) Calculate

(i) the mass of a mooncake, [1]

(ii) the percentage of flour in a mooncake. [1]

The mooncakes were sold in boxes.

In the year 2010, each box cost $48.60.

(b) Xinhui had $370 and bought as many boxes as possible.

(i) How many boxes did she buy? [1]

(ii) How much money did she have left? [1]

(c) In 2011, the price is 5% more than the price in 2010, calculate the new price. [1]

(d) The price in 2010 was an increase of 8% on the price in 2009, calculate the price in 2009.

[2]

2

In the diagram, O is centre of the hemisphere of radius 30 cm.

A and B are points on the circumference of the circular cross-section of radius r cm, centre C.

Angle 40AOB and angle .44ACB

(a) Calculate the length of the line segment AB. [2]

M is the midpoint of the line segment AB.

(b) (i) Explain why angle BMC is a right angle. [1]

(ii) Hence, or otherwise, find the value of r. [2]

A circle is drawn passing through A, C and O (not shown in the diagram).

(c) (i) Write down the angle which is a right angle in the triangle ACO. [1]

(ii) State, with reason, the radius of the circle passing A, C and O. [1]

[Turn over

B r cm

r cm

A

O

M

C

40

44

30 cm 30 cm


3

In the diagram, AD is a diameter of the circle BCT, centre O.

The tangent to the circle at T meets AD produced at P.

AB is parallel to TC.

110 Angle AOT and .15 angle PAC

Find (a) , angle OPT [2]

(b) , angle ACT [1]

(c) , angle BAT [3]

(d) , angle ABC [2]

(e) . angle CTP [1]

4 (a) (i) Factorise 39 xx completely. [2]

(ii) Simplify .9

623xx

x

[1]

(b) Express 3

3

32

42

xxx

x as a single fraction in its simplest form. [3]

(c) Given that ,111

21 ffF find

(i) the value of F when 151 f and ,202 f [2]

(ii) an expression for 1f in terms of F and .2f [2]

P T

110

15

D

C

B

A

O


5 (a) }101:integer { xx

}numbers prime{P

}4 of multiples{Q

(i) Draw a Venn diagram to illustrate this information. [1]

(ii) Simplify .QP [1]

(iii) Write down the value of ).'( QPn [1]

Each element of another set R is a product of any two negative integers.

(iv) Write down the elements in the possible smallest set of '.R [1]

(b) A distributor supplied rice in three different packages, type A (2 kg), type B (5 kg) and

C type (10 kg) at $6.20, $13.50 and $24.00 respectively.

A 13 matrix P is used to represent the above information about the weight of each type

and a 31 matrix Q is used to represent the respective prices.

(i) Write down

(a) the matrix P, [1]

(b) the matrix Q. [1]

The orders from three shops in July 2011 were as follows:

Tasty shop ordered 100 of type A, 50 of type B and 25 of type C.

Fragrant shop ordered 120 of type A, 60 of type B and 20 of type C.

Unusual shop ordered 80 of type A, 70 of type B and 30 of type C.

(ii) Write down a 33 matrix R to represent this information. [1]

(iii) Calculate the matrix product RP. [1]

(iv) Given that SRP is a 11 matrix and its only element represents the total weight of rice

ordered from the three shops, write down the matrix S. [1]

(v) Given that the three elements in the matrix product

c

b

a

00

00

00

Q represent the prices

per kilogram of the three types of rice respectively, write down, in decimal form, the

value of a, of b and of c. [1]

[Turn over


6

In Diagram I, a sphere is placed in a hollow right circular cone for which the centre C of the

circular base of the cone is the same as that of the sphere.

The hollow part of the cone is fully filled with liquid.

The diameter AB of the circular base of the cone is 14 cm and its height VC is 24 cm.

(a) Find the length of the slant edge VA. [1]

(b) By considering the area of the triangle ACV, or otherwise, show that the radius of the sphere

is cm. 72.6 [2]

(c) Calculate, giving your answers in terms of , the area of the surface of

(i) the cone which is in contact with the liquid, [1]

(ii) the part of the sphere which is above the liquid level. [2]

(d) Show that the volume of the liquid in the cone is .cm 89.690368π1 3 [2]

The sphere is removed and a lid is used to cover the cone tightly.

The cone is then inverted as shown in Diagram II.

(e) Find the depth of the liquid in the cone. [3]

Diagram I Diagram II

A B

V

C

14 cm

24 cm

A B

V

C

14 cm


7

In the diagram, the rectangle OPQR represents a vertical wall in a firing range, where

m 70RQ and m. 6PQ

The bottom of the wall, OP, runs from West to East on the level ground.

A shooter is on the ground at S, where 102 angle OSP and .43 angle OPS

(a) Find the bearing of O from S. [1]

(b) Show that m, 05.41PS correct to 4 significant figures. [2]

(c) Calculate the area of the triangle OPS. [2]

(d) Calculate the shortest distance from the shooter to the wall. [2]

(e) A target is placed at M, the midpoint of OP, calculate the length of SM. [2]

A moving target, T (not shown in the diagram), moves along a horizontal line m 3 above the

ground and m 3 away from the wall.

(f) Calculate the greatest possible angle of elevation of T when viewed by the shooter. [2]

O P

Q R

S

70 m

6 m

M

102

43

[Turn over


8 Azizah planned to spend $28 buying fruit at $x per kilogram.

(a) Write down an expression in terms of x for the number of kilograms she expected to buy.

[1]

She found, however, that the price had increased by 28 cents per kilogram.

(b) Write down an expression in terms of x for the number of kilograms she actually bought for

$28. [1]

(c) Given that she actually bought 5 kg less than she expected, form an equation in x and show

that it reduces to .019635125 2 xx [4]

(d) Solve this equation and use your answer to find the number of kilograms she actually

bought. [3]

In the following week, Azizah spent the same amount of money and was able to buy 2.4 kg

more of the same fruit.

(e) Show that the price of the fruit per kilogram had fallen by 15 cents. [2]


9 Everyday for a month of June, Sarjit ran round a park and recorded his time to the nearest

seconds.

The table below shows the numbers of seconds by which his times exceeded minutes. 26

27 22 25 21 43 15 14 31 52 76

23 12 36 73 52 18 15 29 34 27

15 56 64 34 41 44 33 43 49 16

(a) Copy and complete the frequency table below. [2]

(b) Estimate the mean and the standard deviation of the data represented by this frequency

table. [4]

(c) State the mean time and the standard deviation of a run. [2]

(d) A recorded time was chosen randomly.

Show that the probability that it was better than the mean time was 0.6. [1]

(e) 2 records were chosen randomly from the 30 recorded times.

Find the probability that both of them were not better than his mean time, leaving your

answer in simplest fraction. [1]

Tamil, Sarjit’s friend, was running with him everyday and found that 9 of his recorded times for

the 30 days in June were better than his own mean time.

(f) 2 records were chosen randomly from Tamil’s recorded times.

Find, as a fraction in its lowest terms, the probability that at least one of them is better than

his mean time. [2]

Number of seconds (x) Midpoint Tally Marks Frequency

200 x 10 7

4020 x 30

6040 x

8060 x

[Turn over


10 Answer the whole of this question on a sheet of graph paper.

The variables x and y are connected by the equation .1725

42

xxy

Some corresponding values of x and y, correct to 2 decimal places, are given in the table below.

(a) Calculate the value of p. [1]

(b) Using a scale of cm 2 to represent unit 1 on the x-axis and cm 2 to represent units 2 on the

y-axis, draw a horizontal x-axis for 71 x and a vertical y-axis for .146 y

On your axes, plot the points given in the table and join them by a smooth curve. [3]

(c) Use your graph to find

(i) the smallest value of y, [1]

(ii) the values of x for which .2025

42

xx [2]

(d) By drawing a tangent, find the gradient of the curve at the point (5, 4.00). [2]

(e) (i) On the same axes, draw the graph of .82

5 xy [1]

(ii) Write down the x-coordinates of the points at which the two graphs intersect. [1]

(iii) Find the equation, in the form ,03 23 rqxpxx which is satisfied by the values

of x found in part (e) (ii). [1]

– End of Paper –

x 1 1.2 1.5 2 3 5 7

y 12.00 5.16 0.11 -2.75 p 4.00 11.51

Clementi Town Secondary School

Preliminary Exam 2011

Sec 5N/Sec 4E Mathematics

Paper 2 Answers

1. (a) (i) g 168

(ii) %3

158

(b) (i) 7 boxes

(ii) $29.80

(c) 03.51$

(d) 00.45$

2. (a) 20.5 cm

(b) (i) the line joining the vertex

and the midpoint of the base

of an isos. is to the base

(ii) 4.27r

(c) (i) OCA is a right angle

(ii) 15 cm (converse of in a

semicircle)

3. (a) 20

(b) 55

(c) 105

(d) 105

(e) 50

4. (a) (i) )3)(3( xxx

(ii) )3(

2

xx

(b) 1

1

x

(c) (i) 60F

(ii) Ff

Fff

2

21

5. (a) (i)

(ii)

(iii) 10

(iv) 0} ,1{' R

(b) (i)

10

5

2

P

00.2450.1320.6Q

(ii)

307080

2060120

2550100

R

(iii)

810

740

600

(iv) 111S

(v) ,5.0a ,2.0b 1.0c

6. (a) cm 25

(b) 84)25)((2

1r 72.6 r

the radius is 6.72 cm [shown]

(c) (i) 2cm π175

(ii) 2cm π3168.90

(d) Volume of liquid

372.6π3

2π392

3cm π690368.189 [shown]

(e) cm 75.4

7. (a) 305

(b)

35sin102sin

70PS

047.41 m 05.41 [shown]

(c) 2m 980

(d) m 0.28

(e) m 4.28

(f) 8.6

8. (a) x

28

(b) 28.0

28

x

(c) 528.0

2828

xx

019635125 2 xx [shown]

(d) 20

(e) The new price is

25.1$40.220

28

the price has fallen by

cents 15125140 [shown]

9. (a)

midpt T mark Freq

200 x 10 //// // 7

4020 x 30 //// //// // 12

6040 x 50 //// /// 8

8060 x 70 /// 3

(b) mean = 34.7 s SD = s 4.18

(c) the mean time is 26 min 34.7 s

and the standard deviation is 18.4 s

(d) Prob(better than mean time) = 30

18

= 0.6 [shown]

(e) 145

22

(f) 29

15

10. (a) 22.2

(c) (i) 07.3

(ii) 7.4or 3.1x

(d) 3.6

(e) (ii) 45.5or 05.2x

(iii) 050183 23 xx

1725

42

xxy

82

5 xy

y = 3

x

y

(3, –3.2)

(7, 11.2)

–3

3

6

9

12

6 7 5 4 3 2 0 1

4 8

2 3

5 7

6 1 6

9

10 –1

0 P Q

mathematics 4016/01 paper 1 2 hours clementi town secondary school mathematics / paper 1 secondary 4...

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