Uganda Advanced Certificate of Education
S.6 PURE MATHEMATICS TEST 2 2022
Paper 1
1 HOUR
Answer all the questions in this paper
Silent , non-programmable scientific calculator
1. Use binomial theorem to obtain the first four terms of the expansion (1 − 16𝑥)
1⁄
4.
4
By substituting = 0.0001 , find √39 correct to 4 significant figures
(05 marks)
2.
3.
𝜋
Show that 𝑒𝑐2𝑥 − 𝑡𝑎𝑛2𝑥 = 𝑡𝑎𝑛 ( − 𝑥) .
4
( 05marks)
4. Given that

and  are the roots of the equation
whose roots are
2
and
 2
5 x2  3 x  2  0 ,
2
.
 2
find the equation
(05 marks)
5. Find the equation of the tangent to the curve 𝑥 2 − 𝑦 2 = 9 at the point (5,4)
(05 marks)
1
1
3
2
6. If 𝑎3 + 𝑏3 = 6𝑎𝑏(𝑎 + 𝑏), show that log [ (𝑎 + 𝑏)] = (log 𝑎 + log 𝑏).
(05 marks)
7. A strip of wire of length 28𝑐𝑚 is cut into two pieces. One piece is bent to form a
square of side 𝑥 𝑐𝑚 and the other piece is bent to form a rectangle of width 3𝑐𝑚.
Prove that the minimum total area which can be enclosed in this way is 24𝑐𝑚2 .
(05 marks)
8. Prove that the circles x 2  y 2  6 x  12 y  40  0 and x 2  y 2  4 y  16 are orthogonal.
(5 marks)
@2020 MTC DEPARTMENT
@2020 MTC DEPARTMENT