THE UNITED REPUBLIC OF TANZANIA

ORGANIZATION OF HEADS OF NON-GOVERNMENT SECONDARY SCHOOLS

(OHONGSS)
KIGOMA REGION

FORM FOUR MOCK EXAMINATION

041 BASIC MATHEMATICS

TIME: 3 HOURS YEAR: 2025

INSTRUCTIONS
1. This paper consists of two sections A and B with total of fourteen (14) questions
2. Answer all questions in both sections.
3. Show clearly the working and answers.
4. All writing must be in blue or black ink except drawing which must be in pencil
5. Any unauthorized materials are not allowed in the examination room.
6. Mathematical tables and calculators may be used in the examination room

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 SECTION A (60 Marks)
Answer all questions in this section.
1. (a). Mr. Medad is making small metal rods. He has three pieces of metals of the
lengths 432cm, 648cm, and 540cm. What is the longest length of the rod he can make
if the rods have the same length and no metal is wasted?
(b). A wire of length 80cm is cut from the right side 10% and from left side 30% of
its length at the same time. Find the remaining length of the wire.

√
2. (a). If
√
√ , find the value of a, b and c
(b). Given that ( ) , express y in terms of x

3. (a). In a certain class, a teacher displayed counting numbers less than 30. From the
displayed numbers, MARIAM mentioned all numbers divisible by 2 and NASRA
mentioned all numbers that were the multiples of 3.
i. Outline all numbers that were mentioned by MARIAM and NASRA in
common.
ii. How many numbers were mentioned by either MARIAM or NASRA?
(b). If some numbers were selected at random from the numbers displayed by
the teacher, what is the probability that the selected numbers were the multiples
of 3?
4. (a). Determine whether the triangular frame with vertices O(0, 0), A(-6, 8), and
B(-14, 2) is equilateral, isosceles or scalene.
(b). If = i + 2j, = i – 2j and = 5i + 14j; calculate:

i. unit vector in the direction of vector =3 - +

ii. direction of cosines of vector

5. (a). A rectangular frame ABCD measured 48cm by 55cm is made from. The
diagonals of the frame are also made from that wire. Calculate the length of the wire
used to make the frame and diagonals.
(b). Given the rectangle ABCD as shown below.
A B

D C

i. Name two triangles which are similar

ii. Prove your answer in (i) above.

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6. (a). A school cow produces 18litres of milk every day. How many cows of the same
type should the school keep to get 126litres of milk every day?
(b). One family from England travelled for holiday to France and exchange
450pounds for euros when the exchange rate was 1.41 euros to pound. They spent
500 euros and then exchange the remaining amount into pounds and by that time, the
exchange rate had become 1.46 euros to the pound. How much money remained in
terms of pound?

7. (a). The sides of a rectangular plot are in the ratio 3: 5. If the perimeter of the
rectangular plot is 800cm, find the dimensions of the rectangular plot.
(b). Assume that you are a businessman with the following transactions.
 Opening stock at 1st January, 2024 = Tsh.34,500/=
 Closing stock at 31st December, 2024 = Tsh.26,700/=
 Net purchases in a year = Tsh.219,300/=
 Gross profit made in a year = Tsh.138,550/=
 Expenses for the year = Tsh.45,800/=
Use the above information to find the cost of goods sold.

8. (a). A school hall has 32 rows of seats. If there are 26 seats in the first row, 30 seats
in the second row, 34 seats in the third row and so on, how many seats are there in
the hall?
(b). Mr. Said starts an employment with a monthly salary of Tsh.340,000/= and
receives an increment of Tsh.12,000/= every year.
i. What will be his salary in the fourteenth year of employment?
ii. After how long would he be earning Tsh.592,000/= per month?

9. (a). The following diagram shows the location of three houses A, B and C.

A 800m
C
800

700

B
How far is house C from house B?

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 (b). The hypotenuse of an isosceles right angled-triangle is 8cm. Is there enough
information to find the lengths of adjacent sides? If so find their lengths. If not,
explain why not.

10. (a). Asha is three years older than her brother Juma. Three years to come, the product
of their age will be 130 years.
i. Formulate the quadratic equation representing the information above.
ii. Use the quadratic formula to find the present age of Asha and Juma.
(b). The average of two numbers is 7 and three times the difference between them
is 18. Find the two numbers

SECTION B (40 Marks)

Answer all questions in this section
11. (a). The following are the marks obtained by 40 students in Mathematics test.
47 44 58 48 47 57 56 71 62 46 45 50
76 73 43 54 58 66 48 32 89 60 42 47
54 67 35 54 52 44 64 49 37 64 67 44
45 45 42 34

i. Prepare the frequency distribution table using the information: number of

classes = 6, size of each class =10 and the lower limit of the first class=32.
ii. Use the frequency distribution table prepared above to find the actual mean
when the assumed mean is 86.5
iii. Calculate the difference between the actual mean and the median of this
distribution.

(b). In the diagram below, XP is a tangent to the circle with centre O. OX cuts
the circle at Q. If P ̂ X = 280 ; find :

i. P ̂ O.
ii. X ̂Q

O
Q

280 X
P

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12. (a). A rectangular prism with top PQRS and base ABCD has ̅̅̅̅ = 12cm, ̅̅̅̅ = 5cm
and ̅̅̅̅ = 4cm. Calculate :
i. the length of AR.
ii. the angle that AR makes with base ABCD.
iii. the total surface area of the prism.
(b). A speed boat was travelling from Mwanza (30S, 330E) to Mara (10S, 330E)
using 30knots left Mwanza at 11:30 a.m. At what time did it reach Mara?

13. (a). One pair of opposite sides of a parallelogram is (4x + y) units and (3x + 5) units
while the other pair is (2x- y) units and 4 units. By using inverse matrix method, find
the values of x and y.

(b). Find the image of the values of point (x, y) obtained in (a) above when it is first
rotated through 900 anticlockwise about the origin and the followed by a reflection
about the line y + x = 0.

14. (a). Given the function f(x) = + 2, find (18).

(b). Two printers, N and T produces three different types of books. N produces 80
type I books per day, 10 type II books per day, and 20 type III books per day. T
produces 20 type I books per day, 10 type II books per day and 70 type III books per
day. The orders placed 1600 type I books, 500 type II books and 2100 type III books.
The daily operating cost for N is Tsh.10,000/= and for T is Tsh.20,000/=. How many
days should each printer operate to meet the orders at a minimum cost?

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