Exercise Chapter 1 Function Maths T

Mathematics (T) (954)_________

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Masyati binti Karim

Chapter 1: Function Instruction to candidates: Answer all questions in Section A and any one question in Section B. Answers may be written in either English or Bahasa Malaysia. All necessary working should be shown clearly. Section A [45 marks] Answer all questions in this section. 1

The function of f and g are defined by f : x  x  2 and g : x  x 2  4 . Determine the domain and range of both f and g. Hence, explain why f  g does not exist. [4 marks] 2

2

1 Given that log a  3 x  4a   log a 3 x  log a  log a 1  2a  where 0  a  , find x. 2 2

3

Prove

sin   2 sin 2  sin 3    tan 2 . sin   2 sin 2  sin 3 2

marks] Hence, find the exact value of tan 2 15 in the form marks] 4

[4 pq r

where p, q and r are integers.

6

[4

Find the constants A, B, C and D such that 3x 2  5x A B C D     2 2 2 1  x 1  x  1  x 1  x 1  x  1  x  3

5

[7 marks]

[8 marks]

The polynomial p  x   x 4  ax 3  7 x 2  4ax  b has a factor x  3 and when divided by x  3 , has remainder 60. Find the values of a and b and factorise p(x) completely. [9 marks] Find the values of x if

y  3 x

and 4 y   x 2  9   24 .

[9 marks]

Section B [15 marks] Answer any one question in this section. 7

The polynomial p x   6 x 4  ax 3  bx 2  28 x  12 , where a and b are real constants, has factors  x  2 and  x  2  . (a) Find the values a and b, and hence, factorise p(x) completely. [7 marks] 3 x    2,10 .       p x  2 x  3 q x  41  3 x (b) Give that , find q(x), and determine its range when [8 marks]

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8

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