SEKOLAH MENENGAH KEBANGSAAN DATO’ JAAFARJOHOR BAHRU

MONTHLY TEST 1 (JULY 2012) DATE: 1/8/2012SUBJECT: MATHEMATICS T (954) DAY: WEDNESDAYCLASS: PRA-U-S1-BIO TIME: 10.30 – 12.00 pm

Answer all questions in Section A and any one question in Section B. Answer 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 Express in partial fractions. [5 marks]

2 Express in the form where R is a positive and is acute. Hence, solve the equation for . [6 marks]

3 Given that where , find x. [7 marks]

4 Find the set of values of x which satisfies . [7 marks]

5 By using the substitution and , where that , show that

. [3 marks]

Hence, or otherwise, by using the substitution , show that . [4 marks]

6 The polynomial , where a and b are real constants, is divisible by .(a) Find a and b. [5 marks](b) For these values a and b, factorise p(x) completely. [2 marks](c) Show that 2 is a zero of the polynomial . Hence, solve the equation

by using the polynomial p(x). [6 marks]

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

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7 Function f and g are defined by

and .

(a) State the domain and range of f and g. [2 marks](b) Sketch the graph of f and g. [2 marks](c) Find the composite function and its domain and range. [5 marks](d) Find the and . State also its domain and range for each function. [6 marks]

8 The polynomial has a factor and, when divided by , has remainder 60. Find the values of a and b, and factorise p(x) completely. Sketch the graph of p(x).

[12 marks]

Using the substitution , solve the equation . [3 marks]

END OF QUESTIONS

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