PSPM · Malaysia · Predicted papers

PSPM MathematicsSM015/SM025

2 papers200 marks4 h

What we predict comes up

From the syllabus weighting and how the papers are usually set. The papers below follow it.

Differentiation and its applications28%Differentiation closes SM015 with three questions and its applications (extrema, rates, optimisation) open SM025.
Conic sections and vectors16%A conics question and one or two vector questions on lines and planes end the Semester 2 paper.
Integration and its applications11%Integration by parts, partial fractions and substitution, then area and volume, are about 21 marks of SM025.
Functions, graphs and limits10%Inverse functions, asymptotes and limits with continuity at a point share about 20 marks of SM015.

SM015

2 h · 100 marks · Calculator allowed

120:00

This question paper consists of 10 questions.
Answer all questions.
The full marks for each question or part question are shown in brackets.
All steps must be shown clearly. Only non-programmable scientific calculators may be used.
Numerical answers may be given in the form of $π$ , $e$ , surds, fractions or correct to three significant figures, where appropriate, unless stated otherwise in the question.

Answer or mark a question and your score adds up here.

18 marks

(a)Express

w = \frac{2 + 3 i}{1 - i}

in the form

a + bi

, where

a, b \in R

. Hence, find

∣ w ∣

.[4]

(b)Find the real numbers

x

and

y

such that

(x + i y) (2 - i) = 7 + 4 i

.[4]

28 marks

(a)Solve the equation

4^{x} - 3 (2^{x + 1}) + 8 = 0

.[4]

(b)Solve the equation

2 lo g_{9} x = lo g_{3} (x + 6) - 1

.[4]

310 marks

(a)Find the solution set of the inequality

\frac{x + 3}{x - 1} \geq 2

.[3]

(b)Solve

∣2 x - 3∣ < x + 3

.[3]

(c)By squaring both sides, find the set of values of

x

that satisfies

∣ x - 2∣ \geq ∣2 x + 1∣

.[4]

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