CHc CHUNG CHENG HIGH SCHOOL YISHUN

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Preliminary Examination 2Secondary 4 Express/ 5 Normal Academic

Candidate

Name Register No

ELEMENTARY MATHEMATICS PAPER 1 Date: 23rd August 2012(4016/1) Duration: 2 h

READ THESE INSTRUCTIONS FIRST

Setter: Mrs Chan Wei Ling

This paper consists of 17 printed pages, INCLUDING the cover page.

Write your name, register number and class in the space provided above.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use paper clips, highlighters, glue or correction fluid / tape.

Answer all questions.If working is needed for any question, it must be shown with the answer.Omission of essential workings will result in loss of marks.

Calculators should be used where appropriate.

Answers are to be left in the simplest form.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer correct to three significant figures. Give answers in degrees to one decimal place. For p , use your calculator value or the value as stated in the question, unless the question requires the answer in terms of p .

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

Class

[TURN OVER

Mathematical Formulae

Compound interest

Total amount =

Mensuration

Curved surface area of a cone =

Surface area of a sphere =

Volume of a cone =

Volume of a sphere =

Area of triangle ABC =

Arc length = , where is in radians

Sector area = , where is in radians

Trigonometry

Statistics

Mean =

Standard deviation =

nr

P

1001

rl

24 r

hr 2

3

1

3

3

4r

Cabsin2

1

r

2

2

1r

C

c

B

b

A

a

sinsinsin

Acbcba cos))((2222

f

fx

22

f

fx

f

fx

1. (a) Estimate the value of

12 .033 . 95

correct to one significant figure.

(b) Hence, use your answer from part (a) to estimate the value of

12030 .395

, giving your answer correct to 1 significant figure. You must show your working.

Answer: (a) [1]

(b) [2]

2. A water tank is one-third full. After 48 litres of water are added in, the tank becomes

five-seventh full. Find the additional amount of water, in litres, needed to fill the tank

completely.

Answer: l [1]

3. (a) Solve the inequality

35

x− x−44

≤5.

(b) Hence, write down the greatest integer x such that

35

x− x−44

≤5.

Answer: (a) [2]

(b) [1]

4. A supercomputer has a memory capacity of 2 terabytes. (a) If a page of document takes up about 4.85 kilobytes, how many pages of

documents can be stored in the supercomputer? Give your answer correct to the nearest million.

(b) If Jimmy stored 20 video clips of 550 megabytes each in the supercomputer, what is the capacity left in the computer? Give your answer in standard form. (We assume that 1 kilobyte is 1000 bytes in this context.)

Answer: (a) pages [1]

(b) bytes [1]

5. (a) The reciprocal of 5−8

is 54n

. Find the value of n.

(b) Given that 7x=5 and 7

y=16 , find the value of 73 x−1

2y

.

Answer: (a) [1]

(b) [2]

6. Given that

34( x−2 y )=3 y−x

, find the ratio of x : y.

Answer: [2]

7. Given that M=( 2 1

−3 −1 ),

N=( 4 7−2 −3 )

, find

(a) M 2−N ,

(b) the matrix V such that 5 M+V=NI .

A

A

C B

B

B

C

C

Answer: (a) [1]

(b) [2]8. Three cylindrical cans, A, B and C, of the

same radii have heights 8 cm, 10 cm and 15 cm respectively. If all the cans are stacked to the same height as shown in the diagram, find the minimum height of the stacked cans.

Answer: cm [2]

9. (a) Simplify

(3 pq2 )2

3√8 r6÷15 p2 q

.

(b) Find the integer n such that 8n+8n+8n+8n=250

.

Answer: (a) [2]

(b) [2]

10. Factorise completely

(a) x2−2xy+ y2−1 ,

(b) 3 p2 q−54 a2 b−27 a2 q+6 p2 b .

Answer: (a) [2]

(b) [2]

11. Given that

x2=√ ay−b

y−c , express y in terms of a, b and c.

Answer: [3]

12. ε = {x : x is an integer such that 5≤x≤50}

A = {x : x is an odd number}

B = {x : x is a prime number}

C = {x : x is a perfect cube}

(a) On the Venn diagram below, label each circle with the appropriate letter. [1]

(b) List the element(s) of the set A∩C . (c) Find

(i) n(C ' ) (ii) n( A∪B)

Answer: (b) [1]

(c)(i) [1]

(c)(ii) [1]

13. y varies inversely as the cube root of x.

Find the percentage decrease in y when the value of x is increased by 26 times.

Answer: [2]

14. The diagram shows two geometrically similar popcorn buckets sold in Mr Tan’s shop.

The base area of the regular and large buckets are 160 cm2 and 360 cm2 respectively.

(a) If the height of the large bucket is 18 cm, find the height of the regular bucket.

(b) Both buckets are filled to the brim with popcorn. The regular bucket of popcorn

costs $5.20. Mr Tan used the ratio of the base areas given above to price the large

bucket of popcorn. Explain with working, why it is more value for money to buy

the large bucket of popcorn than the regular bucket.

Answer (b): [3]

Answer: (a) cm [1]

15. In the diagram, DB is parallel to FG and AB is parallel to EF and GH. Δ ABC

is an

equilateral triangle and Δ BCD

is a right-angled triangle. ∠BDC=32 °

and

∠DEF=130 °.

Calculate

(a)∠ ABD

,

(b)∠BDE

,

(c) reflex ∠FGH

.

Answer: (a) o [1]

(b) o [2]

(c) o [2]

16. The masses, in grams, of 20 crabs are measured and shown in the table below.

883 890 852 860 878

893 851 900 895 886

874 894 885 878 861

880 865 902 863 897

(a) Construct an ordered stem and leaf diagram to illustrate the above data in the answer space below. Indicate a legend for your answer.

(b) What is the median mass of the crabs?

(c) State the modal mass of the crabs.

(d) Two crabs are selected at random. Find the probability that one weighed more than 880 grams and the other weighed less than 860 grams.

Answer for (a): [2]

Answer: (b) grams [1]

(c) grams [1]

(d) [1]

17. The students in two secondary one classes were given the same Mathematics puzzle to

solve. The information relating to the time taken, in minutes, are given in the tables

below.

Class 1A Class 1B

Time (min) 11 – 15 16 – 20 21 – 25 26 – 30

Frequency 2 9 12 1

(a) Calculate the mean for class 1A.

(b) Calculate the standard deviation for class 1A.

(c) Compare, and comment briefly, on the time taken by the students to solve this puzzle.

Mean = 20.5 minutesStandard deviation = 4.8 min

A B

Answer: (a) min [1]

(b) min [2]

(c)

[1]

18. In the triangle ABC, AB = 10 cm, BC = 8 cm and .

The side AB is drawn in the answer space below.

Complete two possible triangles ABC that are of different sizes. [2]

(a) Construct

(i) the perpendicular bisector of AB, [1]

(ii) the angle bisector of . [1]

(b) Mark, with an X, the point that is equidistant from the points A and B, and

equidistant from the line AC and AB. [1]

(c) Hence, measure the length of BX.

Answer: (c) cm [1]

19. The diagram below shows the speed-time graph for T seconds of the motion of an object.

(a) Calculate

(i) the acceleration when t = 30,

(ii) the distance travelled in the first 100 seconds.

(b) The total distance travelled in the T seconds is 1850 m. Find the value of T.

(c) Find the retardation when t = 110.

(d) On the axes provided on the next page, sketch the distance-time graph for the

T seconds that the object is in motion.

Speed(metres per

second)

Time (t seconds)

0

800

400

1600

2000

1200

10040 T

Distance(metres)

Time (seconds)

Answer for (d): [2]

Answer: (a)(i) m/s2 [1]

(a)(ii) m [2]

(b) [2]

(c) m/s2 [1]

Time (seconds)

Distance (metres)

20. In the diagram, O⃗P

=

p~

and O⃗Q

=

q~

and O⃗R

= r~

. The point U is also marked.

(a) Mark and label on the grid, the point S such that

O⃗S=

−12 O⃗P

+ 2O⃗Q

- 3O⃗R

. [1]

(b) Given that O⃗T

= h

p~

and T⃗U

= k

q~

,

(i) mark and label the point T, [1]

(ii) find the value of h and the value of k.

Answer: (b)(ii) h = , k = [2]

21. The diagram shows the graph of y=( x−k )( x+3)

. The curve cuts the x-axis at the points P and Q and the straight line at the point (- 4, 9).

(a) Find the value of k.

(b) Find the coordinates of P and Q.

(c) Write down the equation of the line of symmetry of the curve.

(d) Calculate the area of the triangle PQR.

(e) Calculate the shortest distance from P to QR.

Answer: (a) [1]

(b) P = , Q = [2]

(c) [1]

(d) units2 [2]

(e) units [2]

END OF PAPER