Maths T STPM 2014 Sem 1 Trial SMJK Jit Sin

954/2/2013 CONFIDENTIAL* 2014-1-PEN-JIT SIN Section A [45 marks] Answer all questions in this section. 2 + 9x − x 2 1. (a) Express as partial fractions. (1 + x )(1 − x )2 3 (b) Function f(x) = 4 x + 3 , x ∈ R , x ≥ − . 4 Find f −1 ( x ) . State its domain and range.

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3. (a) Solve the simultaneous equations log2 x − log4 y = 4 log 2 ( x − 2 y) = 5

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(b) Find the set of values of x that satisfies the inequality 4x − 1 > 3 − x .

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2. Express 3 cos θ + 3 sin θ in the form r cos(θ − α ) . Hence, (a) find its maximum and minimum values, (b) solve the equation 3 cos θ + 3 sin θ = 3 for 0 ≤ θ ≤ 2π .

4. Solve the inequality cos 2θ > 3 sin θ + 2 for the θ in the interval (−π, π).

954/2/2013 CONFIDENTIAL* find the set of values of k such that f(x) = 0 has at least 2 real distinct roots.

Section B [15 marks]

Answer any one question in this section.

6 − 8  −1 2 4   13     7. If A =  3 1 − 2  and B =  − 17 − 9 10  ,    6 − 7  1 4 5   11 find AB. Hence, solve the simultaneous equations. (a) −x + 2y + 4z = 8 3x + y − 2z = −1 x + 4y + 5z = 13 (b) 13p + 6q − 8r = −13 −17p − 9q + 10r = 20 11p + 6q − 7r = −14

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954/2/2013 *This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

8. (a) Solve the equation (3x +1 )(4 x + 2 ) = 52 x −1 . Give your answer correct to 4 significant figures. [4] (b) Let f(x) = 6x4 − 7x3 + ax2 + bx − 12, where a and b are independent of x. If (x − 1) is a factor of f(x) and when f(x) is divided by (x + 1), the remainder is −50, find the values of a and b. With these values of a and b, (i) find a factor of f(x) in the form x + k, where k is a positive integer, (ii) factorise f(x) completely, (iii) find the set of values for x so that f(x) > 0. [11]

6. (a) Show that x − y is a factor of x3 − y3. Find all real factors of x3 − y3 and x3 + y3. Hence, find all real factors of x6 − y6. [5] (b) Given that f(x) = (x − 2)(x2 + kx + 4), 954/2/2013 *This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

5. By transforming the augmented matrix into row-echelon form, solve the following system of equations. x + 2y + 3z = 3 2x + 3y + 8z = 4 3x + 2y + 17z = 1 [5]

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