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ST JOSEPH'S INSTITUTION

SECONDARY 4 PRELIMINARY EXAMINATION

MATHEMATICS 4016/1 PAPER 1

TUESDAY 17 AUGUST 2010 2 HOURS

(1030 1230)

NAME : ____________________________ ( ) CLASS : ________

INSTRUCTIONS TO CANDIDATES

1. Write your name, index number and class in the spaces provided above.

2. Answer ALL questions.

3. Write your answers in the spaces provided on the question paper.

4. If working is needed for any question, it must be shown in the space below that question.

5. Omission of essential working will result in loss of marks.

6. You are expected to use a scientific calculator to evaluate explicit numerical expressions.

7. 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.

8. For , use either your calculator value of 3.142, unless the question requires the answer in

terms of .

INFORMATION FOR CANDIDATES

1. The number of marks is given in brackets [ ] at the end of each question or part question.

2. The total of the marks for this paper is 80.

This question paper consists of 16 printed pages including the Cover Sheet.

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Mathematical Formulae

Compound Interest

Total amount = P

nr

1001

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere = 4r2

Volume of a cone = 3

1r2h

Volume of a sphere = 3

4r3

Area of triangle ABC = 2

1ab sin C

Arc length = r, where is in radians

Sector area = 2

1r

2, where is in radians

Trigonometry

C

c

B

b

A

a

sinsinsin

a2 = b

2 + c

2 2bc cos A

Statistics

Mean =

f

fx

Standard deviation =

22

f

fx

f

fx

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Answer all questions.

1(a) A number is 190 000 when rounded off to 2 significant figures. If the number is an integer, what

is the largest number it can be?

1(b) The number 723 600 has n significant figures. Find the possible values of n.

2 Given that 2 5p and 17 q , find

(a) the greatest possible value of p q ,

(b) the least possible value of 2 2p q .

Answer (a) ......... [1]

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

Answer (a) ......... [1]

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

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3 Bank A pays a compound interest of 2% p.a. compounded half-yearly. Charles will be making a

deposit of $10 000. Calculate how much interest Charles will earn after 3 years.

4 Find the sum, in kilobytes, of 5.3 megabytes and 7.4 gigabytes. Give your answer in standard

form, correct to 3 significant figures.

5 Given that y is inversely proportional to 2x and y is 10 when x takes a certain value. What is the

value of y when x is decreased by 75%?

Answer ......... [2]

Answer ......... [2]

Answer ......... [2]

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6 Simplify 2

3

2

3

3

2

2 16

ab

a

7 Given that axy 2 , express x in terms of a and y.

8 In the sequence 1, 3, 6, 10, 15 Write down the

(a) 7 th term,

(b) n th term.

Answer ......... [2]

Answer ......... [2]

Answer (a) ......... [1]

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

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9(a) Given that x = 517517517.0 , find the value of xx 1000 .

9(b) Hence express 517517517.0 in the form b

a where a and b are integers.

10(a) Express 126 as the product of its prime factors.

10(b) Find the smallest value of k such that k126 is a perfect square.

10(c) The lowest common multiple of 6, 9 and x is 126. Find the two smallest values of x which are odd

numbers.

Answer (a) ......... [1]

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

Answer (a) ......... [1]

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

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

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11 8 men took 5 hours to complete a certain job.

(a) How long will it take 5 men, working at the same rate to complete the same job?

(b) If 3 of the 5 men leave the job after working for 2 hours, how long will it take the remaining 2

men working at the same rate to complete the job?

12 Factorise completely

(a) ,)1(8122 xx

(b) .1842432 xyxyx

Answer (a) ......... [1]

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

Answer (a) ......... [1]

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

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13 In a game 2 fair dice are used. Die X has 2 red faces and 4 yellow faces. Die Y has 4 red faces and

2 orange faces. The 2 dice are thrown together. If both dice show red, the player wins a prize. If

just one die shows red, the player throws both dice again. He wins a prize if both show red this

time. Calculate the probability that the player wins a prize on

(a) the first throw,

(b) on the second throw.

14 Timothy bought 50 books, all at the same price. He sold 20 of them at a profit of 20% , 15 of them

at the cost price and the remainder at a loss of 8%. Calculate the profit, expressing it as a

percentage of the cost price.

Answer (a) ......... [1]

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

Answer ......... [3]

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15 A survey was conducted among a group of men on how many mugs of beer they drink each day.

The table below shows the results.

Number of mugs of beer 0 1 2 3

Number of men 6 9 5 x

(a) Write down the largest possible value of x given that the median is 2.

(b) Write down an inequality in x given that the mode is 3.

(c) If x is 4, calculate the standard deviation.

Answer (a) ......... [1]

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

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

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16 ABCDEF is a regular hexagon with centre O and A is due north of F.

(a) Calculate

(i) the size of an interior angle,

(ii) the obtuse AOC .

(b) Find the bearing of

(i) D from F,

(ii) D from A.

Answer (ai) ......... [1]

(aii) ........ [1]

(bi) ......... [1]

(bii) ........ [1]

A

B

D

E

F

C

.O

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17(a) Express 1082 2 xx in the form cbxa 2)( .

17(b) Sketch the graph of 1082 2 xxy [2]

x

y

Answer (a) ......... [2]

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18 It is given that A is the point )2,4( , B is the point )0,3( and

6

5BC . Find

(a) the equation of the line AB,

(b) the coordinates of the point C.

19 A model of a car has a scale of 1:25

(a) The painted surface of the model is 128 cm2 . Calculate the painted surface area of the car, giving

your answer in square meters.

(b) The size of the luggage space of the car is 0.25 m 3 . Calculate the size of the luggage space of the

model in cubic centimeters.

Answer (a) ......... [2]

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

Answer (a) ......... [2]

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

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20 In the diagram, ABCD is a quadrilateral with AB parallel to DC. AC and BD meet at E where

BE = 6 cm and DE = 9 cm. Find

(a) the ratio of area of triangle BCE : area of triangle ABE,

(b) the ratio of area of triangle BCE : area of triangle ADE.

21 In the diagram, PXR is a straight line, 90PRQ , 10PQ cm, 6QR cm and area of triangle

PXQ = 9 cm 2 . Calculate

(a) RX,

(b) tan QXP .

C B

9

6

E

A

Diagram is NOT drawn to scale

Answer (a) ......... [2]

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

Answer (a) ......... [2]

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

D

Diagram is NOT drawn to scale Q

R X P

6 cm 10 cm

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22(a) Find the smallest integer s such that .12225 s

22(b) Find the greatest prime number p for which 182

73 p

p

23 (a) The line cmxy 2 has gradient of 5 and passes through the point

1,

2

1. Find the values of m

and c.

23 (b) The curve 52 bxaxy passes through the point (3,4) and meets the x-axis at 1x . Find the

values of a and b.

Answer (a) ......... [2]

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

Answer (a) ......... [2]

(b) ......... [3]

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24 Construct PQR such that PQ = 8 cm, PQR = 50 and QR = 10 cm. [1]

(a) Construct the perpendicular bisector of P and Q. [1]

(b) By further construction, locate a point such that its distance from the vertices P, Q and

R are equal. Label the point O. [1]

(c) Construct the angle bisector of lines PQ and QR. A point A is equidistant from lines PQ and

QR and lies 3 cm from point Q. Label the point A. [2]

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25 The diagram is the speed-time graph for the first t seconds of a journey.

(a) Calculate the acceleration of the particle during the first 4 seconds.

(b) Calculate the distance travelled in the first 8 seconds.

(c) The particle decelerates to come to rest at time t seconds at a uniform rate of 4 m/s 2 . Find t.

THE END

10

0 t 8 4 Time (s)

Answer (a) ......... [1]

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

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

Speed (m/s)