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P425/1 Pure Mathematics Paper 1 Aug 2019 3hours

This document is the first paper of the Pure Mathematics examination for the Uganda Advanced Certificate of Education administered by the LASS Examinations Council in August 2019. It contains 12 questions testing various pure mathematics concepts and is divided into two sections. Candidates are instructed to answer all 8 questions in Section A and 5 questions from Section B, showing all necessary working. They are permitted to use scientific calculators and mathematical tables during the 3-hour exam.

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160 views3 pages

P425/1 Pure Mathematics Paper 1 Aug 2019 3hours

This document is the first paper of the Pure Mathematics examination for the Uganda Advanced Certificate of Education administered by the LASS Examinations Council in August 2019. It contains 12 questions testing various pure mathematics concepts and is divided into two sections. Candidates are instructed to answer all 8 questions in Section A and 5 questions from Section B, showing all necessary working. They are permitted to use scientific calculators and mathematical tables during the 3-hour exam.

Uploaded by

King Ezra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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P425/1

PURE MATHEMATICS
Paper 1
Aug 2019
3Hours

LIGHT AFRICA SECONDARY SCHOOL


TERM TWO TEST 2019
Uganda Advanced Certificate of Education
PURE MATHEMATICS
Paper 1
3 Hours

INSTRUCTIONS TO CANDIDATES
Answer all the eight questions in section A and any five from section B

Any addition question(s) answered will not be marked

All necessary working must be clearly shown

Begin each answer on a fresh sheet of paper

Silent, non – programmable scientific calculators and mathematical tables

with a list of formulae may be used.

LASS Examinations Council 2019 Page 1


SECTION A (40 marks).
1. Solve the simultaneous equations
5
𝑙𝑜𝑔27 (𝑥𝑦) =
3
𝑙𝑜𝑔9 𝑥 = 2𝑙𝑜𝑔3 𝑦 (5 marks)

2. Solve 5𝑐𝑜𝑠𝜃 − 3𝑠𝑖𝑛𝜃 = 4 𝑓𝑜𝑟 0𝑜 ≤ 𝜃 ≤ 360𝑜 (5 marks)

3. The first, second, third and n th terms of a series are 4, -3, -16 and (an 2  bn  c)
respectively. Find the values a, b and c
4. (a)Given that x3 + 5x2 + ax + b is divisible by x2 +x – 2,

find (i) the values of a and b.


(ii) the linear factor of the polynomial.

5. Find the equation of a circle with diameter AB where A(-1, 6) and B(1,
12). (5 marks)
1 1
6. If 𝑥 2 + 𝑦 2 = 7𝑥𝑦, prove that log(𝑥 + 𝑦) = log 3 + 2 log 𝑥 + 2 log 𝑦

7. (b) The 5th term of an arithmetic progression is 12 and the sum of the first five
terms is 100. Determine the first term and the common difference

8. (c) Use a substitution t  tan to solve the equation 3 cos   5 sin    1 , for
2
0 o  x  360 o .

 
n
(d) Prove by induction that  2r  1 
n
4n 2  1 .
2
9.
r 1 3
10. (b) Solve the equation 𝒔𝒊𝒏 𝟐𝜽 + 𝒄𝒐𝒔 𝟐𝜽 = 𝟏, for 00 ≤ 𝜃 ≤ 3600

11. (a.) The first term of an arithmetic progression is – 11, the last term
is 44 and the sum of the terms of the progression is 198. Find;
(i.) The number of terms in the progression
(ii.) The common difference. (6mark)
2
12. (a.) Using binomial expansion, find the first 4 terms of (𝑥 − 3𝑥)5 .

(4marks)

LASS Examinations Council 2019 Page 2


(b.) Expand (1 − 2𝑥)6 up to the term in x3 . Hence evaluate
(i.) (25)6 ,
(ii.) (28)6 correct to 4 decimal places. (8marks)

(c) Prove that 𝑐𝑜𝑠3𝐴 = 𝑐𝑜𝑠𝐴(2𝑐𝑜𝑠2𝐴 − 1) (3marks)

End -

LASS Examinations Council 2019 Page 3

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