CONFIDENTIAL* 1

1.Given that .prove that

[6m]

2. Find the values of the constants and for which

in partial fractions.

[6m]

3. Solve the simultaneous equation

and

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4. If , find the set of values for where is defined.

Find the maximum value of the expression . Deduce the maximum value of

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5. By using a suitable substitution method, show that

Hence, find the value of .

[7m]

6. The function and are defined by

a) Find ,state the domain and range of

b) Determine whether is an odd or even function[5m]

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7. Prove that the sum of the first terms of a geometric progression with the first term and the common ratio is

Hence, state the sum to infinity.

By assuming that the repeating decimal is a geometric

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950/1,954/1(KELANTAN 2012)

*This question paper is CONFIDENTIAL until the examination is over CONFIDENTIAL*

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sequence, find the value of the decimal as a fraction in the lowest term.

8. The point has coordinates . The straight line cuts the at and the at . Find

a) The equation of the line through which is perpendicular to the line .

b) The perpendicular distance from to the line .

c) The area of the triangle .

[8m]

9. a) The polynomial is divisible by (2x-1). When divided by , the remainder is 120. Find the values of and .

Hence,factorise completely.

b) Find the range of given that is real.

[3m]

[3m]

[4m]

10.a) Given the matrices and , show

that , where is constant and the 3x3 identity matrix.

b) Three shops and sell three grades of trousers with the top grade providing a profit of a piece, and the moderate and low grades providing profits and a piece respectively. On a certain days, the numbers of trousers of the three grades sold and the total profit of each of the shops are shown in the table below

ShopGrades of trousers

ProfitTop Moderate Low

A 5 10 15 RM520

B 10 20 25 RM920

C 15 25 30 RM1140

Using the result in (a), find and .

[10m]

950/1,954/1(KELANTAN 2012)

*This question paper is CONFIDENTIAL until the examination is over CONFIDENTIAL*

CONFIDENTIAL* 3

11. Sketch on separate diagrams, the graph of and

. Show clearly the turning points and all asymptotes of the curve.

The line meets the curve at points and . Calculate the area of the finite region bounded by line and the arc of the curve between and . Give the answer correct to three significant figures.

[6m]

[6m]

12. a) Find the domain of the function

b) The function is defined as

Given that is a continuous function, find the value of constant .

c) The function is defined as

state the domain of

Hence, sketch the graph of .

[3m]

[3m]

[2m]

[4m]

END OF QUESTIONS PAPER

950/1,954/1(KELANTAN 2012)

*This question paper is CONFIDENTIAL until the examination is over CONFIDENTIAL*