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SULIT 3472/1

INFORMATION FOR CANDIDATES

1. This question paper consists of25 questions.

2. Answerallquestions.

3. Give onlyone answer for each question.

4. Write the answers clearly in the space provided in the question paper.

5. Show your working. It may help you to get marks.

6. If you wish to change your answer, cross out the work that you have done. Then write down the

new answer.

7. The diagrams provided are not drawn to scale unless stated.

8. The marks allocated for each question and sub-part of a question is shown in brackets.

9. A list of formulae is provided on page 2.

10. You may use a non-programmable scientific calculator.

11. This question paper must be handed in at the end of the examination.

The following formulae may be helpful in answering the questions. The symbols given are the ones

commonly used.

ALGEBRA

1.

a

acbbx

2

42 =

5. nmmn aaa logloglog +=

2. nmnm aaa += 6.nm

n

maaa

logloglog =

3. nmnm aaa = 7. mnm an

aloglog =

4. mnnm aa =)( 8.

a

bb

c

ca

log

loglog =

GEOMETRY

1. Distance between two points

= ( ) ( )2212

21 yyxx +

2. Midpoint of two points

( )

++=

22

2121 yy,xx

y,x

3. A point dividing a line segment

( )

+

+

+

+=

nm

nyny

,nm

mxnx

y,x2121

4.Area of triangle = ( ) ( )312312133221

2

1yxyxyxyxyxyx ++++

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SULIT 3472/1

1. Diagram 1 shows the relation between set P and set Q.

DIAGRAM 1

State(a) the codomain of the relation,

(b) the type of the relation.[2 marks]

Answer: (a)____________________

(b)____________________

For

Examiners

Use

2. Given function xxf 34: .

Find(a) f(2),

(b) the value ofx which maps onto itself.[3 marks]

Answer: (a)____________________

(b)x =_________________

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8Set P

Set Q

2

1

3

2

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For

Examiners

Use

3. The following information refers to the functionsfand g.

Find

(a) the value ofk,(b) fg(x).

[3 marks]

Answer: (a) k=_________________

(b)____________________

4. Given the functions 2,2

:

xx

hxg and 0,

12:1

+

xx

kxxg

where h and kare constants, find the value ofh and ofk.

[3 marks]

Answer: h =____________________

k=____________________

3472/1 SULIT

SULIT 3472/1

kx

x

xg

xxf

,

32

4:

1:

3

3

3

4

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5. Given the function 23: + xx and the composite function

xxfg 25: , find

(a) f-1

(7),(b) g(x).

[4 marks]

Answer: (a)____________________

(b)____________________

For

Examiners

Use

6. Form a quadratic equation with roots -2 and4

3

[2 marks]

Answer: ____________________

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7. Given that the quadratic equation 422 =++ hhxx has two equal roots.

Find the value ofh.

[3 marks]

Answer: h =__________________

8. The straight liney = 4x - kis a tangent to the curvey + 8 = x( 6 - x) .

Find the value of k.

[3 marks]

Answer: k=___________________

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9. Solve the quadratic equation )3)(2()5(2 += xxxx . Give your answers

correct to four significant figures.

[3 marks]

Answer:x =___________________

For

Examiners

Use

10. The roots of the quadratic equation 02

2=

qxx are the same as the roots ofthe quadratic equation 023 2 =++pxx . Find the value ofp and q.

[4 marks]

Answer:p =________ q =__________

11. Find the range of values of x for which ( 2) 3x x <

[3 marks]

Answer:____________________

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Use 12. Find the range of values of m if 2( ) 2f x x x m= + has no real root.[3 marks]

Answer:____________________

13. The quadratic equation 3 3c xx = has two distinct and real roots. Find therange of values of c .

[3 marks]

Answer:____________________

14. For the quadratic function 2( ) 2 3 2g x x x= + , find the equation of the axis ofsymmetry.

[3 marks]

Answer:____________________

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15. The graph of the function 2( ) 2( )f x p q x= has a maximum point

at

1 5

,2 2

. Find the value ofp and q.[3 marks]

Answer:p = __________________

q =___________________

For

Examiners

Use

16. Solve the equation 2 12

279

3

xx

x

+

+=

[3 marks]

Answer: ____________________

17. Given that the quadratic function ,763)( 2 += xxxf

(a) Expressf(x) in the formf(x)=a(x + p)2 + q(b) If the graphf(x) is reflected in thex-axis, write down the

function of the new graph. [3 marks ]

Answer: (a) __________________

(b)__________________

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18. Given that xxxf 32: 2 and = )5(1f . Find the values of .

[4 marks]

Answer: =__________________

19.

Diagram above shows graph of 3)(2)( 2 += pxxf has a minimum point (1, q).

State:

(a) the value ofp and q(b) the equation of axis of symmetry [3 marks]

Answer: (a)p =_______ q =_________

(b)____________________

20. Givenp and q are the roots of the quadratic equations 2x2

+ 7x = m 5,

wherepq = 3 and m is a constant. Calculate the values ofm,p and q.[4 marks]

Answer:_________________3472/1 SULIT

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3

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20

),1( qx

)(xf

0

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21. Find the maximum or the minimum value of the function 2223: xxxf + .

Hence, state the equation of the axis of symmetry for the above function graph.

[4 marks]

Answer: ____________________

For

Examiners

Use

22. Quadratic function graph 45)( 2 += kxkxxf touches thex-axis at one point.

Find the value ofk.[3 marks]

Answer: ____________________

23. Given function baxxf +: . If f(3) = 3 and f(1) = 5, find the value of a and

ofb.

[4 marks]

Answer: a =_______ b =___________

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24. Find the largest integer value of k if 0)72(2 =++ kxkkx has real roots.

[3 marks]

Answer: ____________________

25. Given that 3)( =pxxf and 5)( 2 +=xxg , find

(a) the value ofp if 2)5(1 =f

(b) the value offg(-3) [4 marks]

Answer: (a)p = _________________

(b)____________________

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::: END OF QUESTION PAPER :::

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