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ZIMBABWE SCHOOL EXAMINATIONS COUNCILGeneral Certificate of Education Advanced Level
PURE MATHEMATICS 6042/2
PAPER 2
SPECIMEN PAPER 3 hours
Additional materials:
Answer paper
Graph paper
List of Formulae
Electronic calculator
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the answer
paper/answer booklet.
Answer all questions in Section A and any five questions from Section B
If a numerical answer cannot be given exactly, and the accuracy required is not specified in the
question, then in the case of an angle it should be given correct to the nearest degree, and in other
cases it should be given correct to 2 significant figures.
If a numerical value for g is necessary, take g = 9.81 ms-2.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 120.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
_______________________________________________________________________________
This question paper consists of 5 printed pages and 3 blank pages.
Copyright: Zimbabwe School Examinations Council, Specimen paper.
©ZIMSEC Specimen paper [Turn over
, 2
Section A (40).
Answer all questions in this section.
d2y æ dy ö
1 (i) If y = e x sin x , show that = 2 ç - y ÷. [3]
dx 2 è dx ø
(ii) Find the Maclaurin expansion of the function e x sin x as far as the term
in x 3 by further differentiation of the result in part (i), [4]
2 (i) Find the equation of a circle which has the points (-7; 3) and (1; 9)
as end points of its diameter. [3]
(ii) Hence or otherwise, find the equation of the tangent to the circle which
passes through the point (-7; 3) . [4]
3 Prove by induction that
𝑛
1 − 𝑝𝑛
∑ 𝑎𝑝𝑟 = 𝑎𝑝 [ ]
1−𝑝
𝑟−1
for all positive integral values of n, where a and p are constants. [8]
4 By using the substitution 𝑢 = 𝑠𝑖𝑛𝑥, show that
3𝑛
𝑐𝑜𝑠𝑥 1 1
∫02 𝑑𝑥 = 4 𝑙𝑛 3 [8]
3+𝑐𝑜𝑠2 𝑥
1 𝑦
5 Let H be the set of all matrices of the form ( ), where y ∈ 𝐼𝑅 .
0 1
Show that
(i) H does not form a group under matrix addition. [4]
(ii) H forms an abelian group under matrix multiplication.
[Assume associativity] [6]
6042/2 Specimen paper
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