Name ( ) Class 4

Monday 17 Sep 2012 2 hours Paper 1 Candidates answer on the question paper. -------------------------------------------------------------------------------------------------------------------

READ THESE INSTRUCTIONS FIRST Write your answers in the spaces provided on the question paper. Write in dark blue or black pen in the spaces provided on the Question 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 below that question. Omission of essential working will result in loss of marks. You are expected to use a scientific calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give 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 of the marks for this section is 80.

This question paper consists of 16 printed pages.

ANGLICAN HIGH SCHOOL Preliminary Examination Three

Secondary Four MATHEMATICS (4016/01) 4017/01

Signature of Parent/Guardian & Date

Name of Parent/Guardian

For Examiners Use

80

2

[Turn Over

Mathematical Formulae

Compound interest

Total amount = nrP

+100

1

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere =

Volume of a cone =

Volume of a sphere = 334 r

Area of triangle ABC = Cab sin21

Arc length = r , where is in radians

Sector area = 221 r , where is in radians

Trigonometry

Cc

Bb

Aa

sinsinsin==

Abccba cos2222 +=

Statistics

Mean = ffx

Standard deviation = 22

ffx

ffx

24 r

hr 231

3

[Turn Over

Answer all the questions 1 Find the exact value of the following without using a calculator.

(a) 24 2-3 4!! ,

(b) 0.064! , giving your answer in fraction.

Answer (a) [2]

(b) [2]

_________________________________________________________________________________

2 Express, correct to 2 significant figures,

(a) 385.49,

(b) 0.029949.

Answer (a) [1]

(b) [1] _________________________________________________________________________________

4

[Turn Over

3 (a) Express the numbers 198 and 264 as a product of their prime factors.

(b) Find the largest integer which is both a factor of 198 and 264. (c) Find the smallest positive integer value of n for which 198n is a multiple of 264.

Answer (a) [1]

(b) [1]

(c) [1] _________________________________________________________________________________

4 Solve the inequality 23 < 3x 5 < 4.

Answer [2] _________________________________________________________________________________

5

[Turn Over

5 A map is drawn to the scale of 1: 2000. (a) The actual distance between Town A and Town B is 6.6 km. Calculate, in centimeters,

their distance apart on the map. (b) On the map, a lake in Town A has an area of 3.4 cm2. A lake in Town B has an area 50%

larger than that of the lake in Town A. Calculate, in square kilometers, the actual area of the lake in Town B.

Answer (a) cm [1]

(b) km2 [2] _________________________________________________________________________________

6 (a) Given that (m 1)2 = 64, find the possible values of m. (b) Given that x2 6x + p = (x q)2 , find the value of p.

Answer (a) or [2]

(b).. [2] _________________________________________________________________________________

6

[Turn Over

7 (a) Factorise completely (i) abc a2b c2 + ac

(ii) (12d 5)2 64

(b) Simplify !

!!!!!!!! !

!!!!!!!! .

(c) Given g = !!!

!!!!, make h the subject of the equation.

Answer (a) (i) [2]

(ii) [2]

(b) [3]

(c) [3]

_________________________________________________________________________________

7

[Turn Over

8 In the diagram, OAB is a quadrant of a circle, radius 21 cm. A semicircle is drawn with OB as diameter.

Leaving your answers in terms of , calculate

(a) the arc length AB, (b) the perimeter of the shaded area in the diagram.

Answer (a) cm [1]

(b) cm [2] _________________________________________________________________________________

B O

A

8

[Turn Over

9 (a) The point (t, 5t 7) lies on the line y = 2x 8. Calculate the value of t. (b) A line passes through the point (1,7) and is parallel to 2x + y = 12.

Find the equation of the line.

Answer (a) [2]

(b) [3] _________________________________________________________________________________

10 The rate of exchange between pounds () and dollars ($) was 1 = $2.80.

Calculate, (a) the number of dollars received in exchange for 198,

(b) the number of pounds received in exchange for $1845.20.

Answer (a) $ [1]

(b) [1]

_________________________________________________________________________________

9

[Turn Over

11 Timmy mixes Grade A tea ($32 per kg) with Grade B tea ($48 per kg) in the ratio 3 : 1 to obtain a mixture. He then sells the mixture at $45 per kg. Calculate the percentage profit.

Answer % [2] _________________________________________________________________________________

12 (a) In the diagram, AB is parallel to ED and EA is parallel to DC.

Find the value of (i) x,

(ii) y.

(b) A polygon has interior angles of 110 , 140 and the rest are 130 each.

Find the number of sides of the polygon.

Answer (a) (i) [1]

(ii) [1]

(b) [2] _________________________________________________________________________________

A B

C

D E

50

110

y

x

10

[Turn Over

13 (a) Sketch the graph of ( )( )23 += xxy

Answer (a)

[2]

(b) (i) Express 762 + xx in the form ( ) bax + 2 . (ii) Sketch the graph of 762 += xxy .

Answer (b) (i). [1]

Answer (b)(ii)

[2] _________________________________________________________________________________

0

y

x

0

y

x

11

[Turn Over

14

The diagram is the distance-time graph of a cars journey. The car started from rest. (a) Find the speed of the car when t = 20s. (b) The car moved with a constant acceleration for the first 15 seconds. Find this acceleration.

Answer (a) m/s [1]

(b) m/s2 [1]

(c) On the grid in the answer space below, draw the speed-time graph for the same journey.

[2]

_________________________________________________________________________________

Speed (m/s)

20

10

30

Time (s) 0 5 20 15 10 25

40

time/s 0 5 10 15 20 25

distance/m

100

200

300

400

500

600

12

[Turn Over

15 Two isosceles triangles are geometrically similar. The first triangle has dimensions 20 cm by 20cm by 24 cm as shown in the diagram.

The second triangle has one side of length 4 cm. (a) Find the two possible dimensions of the second triangle.

(b) Hence, find the two possible ratios of:

triangleondofareatrianglefirstofarea

sec.

Answer (a). or . [2]

(b) or [2] _________________________________________________________________________________

16 ABC is a right-angled triangle in which BC = 25 cm and AB = 7 cm.

AC is produced to D and AB is produced to E.

Express, as a fraction, the value of

(a) tan CBA ,

(b) cos EBC .

Answer (a) [1]

(b) [1]

_________________________________________________________________________________

20 cm

24 cm

25 7

A C D

E

B

13

[Turn Over

17 xx :{= is a positive integer and 15

14

[Turn Over

19 The pupils in two classes took the same Mathematics test. Information relating to the results is shown in the tables below.

Class A Marks 1 5 6 10 11 15 16 20 21 25 Frequency 3 5 8 10 x Class B Mean 12.5 Standard Deviation 5.20

(a) For Class A, calculate

(i) the value of x if the estimated mean is 6114 ,

(ii) the standard deviation.

(b) Comment on the results of the two classes.

Answer (a) (i) [2]

(ii) [2]

Answer (b)

[2]

________________________________________________________________________________

15

[Turn Over

20 In triangle PQR, angle QPR is 20 and sin21 =RQP .

The side PQ is drawn in the answer space below.

(a) Draw the two possible triangles PQR that are not congruent. (b) Construct a line which is equidistant from the lines PQ and PR.

[2] [1]

[2]

________________________________________________________________________________

Q

P

16

[Turn Over

21 A circle can be drawn such that ABCD lies on the circumference of the circle. (i) Construct this circle.

(ii) Prove that triangle CDM is similar to triangle BAM.

[2] Answer (ii)...

[2]

________________________________________________________________________________

--- THE END ---

C

A

M B D