UCE Mathematics 2-1

456/2
MATHEMATICS
Paper 2
July/Aug. 2022
2 ½ Hours
AITEL JOINT MOCK EXAMINATIONS

Uganda Certificate of Education
MATHEMATICS
Paper 2
2 hours 30 minutes
INSTRUCTIONS TO CANDIDATES:
Answer all the questions in Section A and any five from Section B.
Any additional question(s) answered will B not be marked.
All necessary calculations must be shown clearly with the rest of the answer.
Silent, non-programmed scientific calculators and mathematical tables with a list of formulae may be
used.
Turn Over
© 2022 AITEL Mocks
SECTION A (40 MARKS)
1. Find the LCM and HCF of 78 and 54. (4 marks)
2. Solve for x , (0.2) x+2 = 625(1− x ) (4 marks)
3. Find the equation of a line through point p(5,1) which is parallel to the line whose
equation is y − 2 x = 6 . (4 marks)
5
4. Simplify: 2log   − log15 + log54 (4 marks)
 3
5. Given that n( A) = 35, n( B ) = 20 and n( A B) = 40, Find the;
(i) n( A B)
(ii) n( A B| ) (4 marks)
6. If point Q (30,1) and R (18,13) have mid-point at Q . find the;
(i) Co-ordinates of Q
(ii) | OQ | (4 marks)
7. Ann gives a commission of 10% on first sales of shs. 100,000 and 25% in excess of
shs. 100,000. Find the total commission for the total sales of shs. 280,000. (4 marks)
8. Given that f ( x) = x + 1 and fg ( x) = 5 x − 2 Find g ( x) hence g (1) (4 marks)
9. On the map, a swimming pool of an area 75km2 is represented by 12cm 2 . Find the
representative fraction of the map. (4 marks)
10. Two similar cones with height 15cm and 9cm. if the capacity of the bigger cone is
250cc . find the capacity of the smaller cone. (4 marks)
2
SECTION B (60 MARKS)
11. (a) A machine cost shs. 2.85millions and its value depreciates at a rate of 15% per
annum. Find the time it will take the machine to cost shs. 1.8millions.
(b) The tax structure of a certain school is as follows;
Taxable income (shs) Tax rate (%)
1- 100,000 5
100,001 – 250,000 10
250001 – 350,000 18
350,001 – 500,000 25
Above 500,000 35
Given that peter is a staff member of this school and he is entitled to the total monthly
allowances of shs. 250,000 and his gross monthly salary is shs. 850,000. Determine
peter’s monthly,
(i) Taxable income
(ii) Net pay
(12 Marks)
27
12. (a) Express in form of a − b c hence state the values of a, b , and c
2− 3
(06 Marks)
42.10.35
(b) Use a table to evaluate; (06 Marks)
0.0014
13. The figure below shows a cuboid ABCDEFGH with AB = 9cm, AC = 15cm and
CG = 8cm.
If N is the mid-point of BC. Find the;

(i) Length BC
(ii) Length NG and BH
3 Turn Over
(iii) Angle between line BH and plane ADHE
(iv) Volume of cuboid (12 Marks)
14. (a) Given that f ( x) = ax 2 − bx − 3 . If f (−2) = 3 and f (−3) = 12 . Find the values of ;
(i) a and b
(ii) x when f ( x) = 0 (06 Marks)
2x + 1
(b) Given that h( x) = and g ( x) = x 2 − 1. Find
x −3
(i) hg ( x)
(ii) The value of x when hg ( x) is meaningless. (06 Marks)
15. A group of S.4 students of a certain school, 20 passed biology, 18 passed

mathematics and 16 passed chemistry. 7 passed both biology and chemistry only, 5
passed biology and mathematics only, 2 passed mathematics and chemistry only.
Given that the number of students who passed mathematics only is equal to twice the
number of students who passed chemistry only. If 6 students didn’t pass any of the
three subjects.
(a) Represent the above information on the Venn diagram.
(b) From your Venn diagram, find the;
(i) Number of students who passed all the three subjects
(ii) Number of students who passed only one subject
(iii) Number of students in the class.
(c) If a student is picked at random from the class, find the probability that the
students picked passed at least two subjects.
(12 Marks)
16. In the table below, y is known to be partly constant and partly varies as the square
root of x .
x N 25 4 100
y 47 35 M 50
(a) Write down an expression connecting x and y

(b) Find the values of N and M.
(12 Marks)
4
17. In the figure below, OA = a , OB = b , OB : BC = 1:1 = 1:1 and AM : MB = 2 :1
a) Express the following vectors in terms of a and b
(i) AB
(ii) OM
(iii) MC
b) Given that N is a midpoint of OA , show that N , M and C are on the same
straight line.
(12 Marks)
END

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456/2

AITEL JOINT MOCK EXAMINATIONS

Any additional question(s) answered will B not be marked.

2. Solve for x , (0.2) x+2 = 625(1− x ) (4 marks)

5. Given that n( A) = 35, n( B ) = 20 and n( A B) = 40, Find the;

6. If point Q (30,1) and R (18,13) have mid-point at Q . find the;

8. Given that f ( x) = x + 1 and fg ( x) = 5 x − 2 Find g ( x) hence g (1) (4 marks)

representative fraction of the map. (4 marks)

250cc . find the capacity of the smaller cone. (4 marks)

If N is the mid-point of BC. Find the;

15. A group of S.4 students of a certain school, 20 passed biology, 18 passed

(a) Write down an expression connecting x and y

a) Express the following vectors in terms of a and b

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