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Legacy Girls’ College
2025 – 2026 AY MID-TERM EXAMINATION Date: October, 2025
Term 1 Year: 12W Duration: 𝟏 𝟏𝟔 𝒉𝒓𝒔
Name: …………………………………………… Class: …………………
MATHEMATICS (CORE)
Instructions
Answer all the questions
Mathematical tables may be used in any question.
The use of non-programmable, silent and cordless calculator is allowed.
Each question is followed by four options lettered A to D. Find the correct option for each question and shade in penci l, on your answer sheet, the answer space which bears the same letter as the option you have chosen.
Give only one answer to each question. An example is given below.
The ages, in years, of four boys are 10, 12, 14 and 18. What is the average age of the boys?
A. 12 years
B. 12
1 2 years C. 13 years
D. 13 12 years
The correct answer is 13 12 years, which is lettered D and therefore answer space D would be shaded.
Think carefully before you shade the answer spaces; erase completely any answer you wish to change.
Do all rough work on this question paper.
PAPER 1 OBJECTIVE TEST [30 marks]
- A cyclist covers 900 m in 5 minutes. What is his average speed in km/h? A. 10. B. 75. C. 108. D. 180.
- P varies directly as the cube root of Q. If P = 4 when Q = 8, find P when Q = 64. A. 16 B. 8 C. 4 D. 2
- If 2 −𝑛^ = 𝑥, 𝑓𝑖𝑛𝑑 2𝑛 A. – x B. (^1) 𝑥 C. x D. − (^1) 𝑥
- Factorise 12𝑥^2 − 3𝑦^2 completely A. 3(2𝑥 − 𝑦)^2 B. (4𝑥 − 𝑦)(𝑥 + 3𝑦) C. 3(4𝑥 − 𝑦)(𝑥 + 𝑦) D. 3(2𝑥 − 𝑦)(2𝑥 + 𝑦)
- A quantity z varies directly as x and inversely as the cube of y. If z = 2, x = 2 and y = 1, find the relation of z in terms of x and y. A. 𝑧 = (^) 3𝑦𝑥 B. 𝑧 = 𝑥𝑦^3 C. 𝑧 = (^) 𝑦𝑥 3 D. 𝑧 = (^) 𝑥𝑦 3
- A discount of $480.00 was given on an article marked $24,000.00. What was the percentage discount? A. 10% B. 5% C. 4% D. 2%
- The relation 𝑦 = 𝑥^2 + 2𝑥 + 𝑘 passes through the point (2, 0). Find the value of k. A. − B. −
- Find the semi-interquartile range of the data 2, 6, 4, 3, 3, 4, 5, 7 A. 1 B. 2 C. 3 D. 4
- Calculate the variance to 2 decimal places A. 2. B. 2. C. 2. D. 2.
- Evaluate 1001^2 – 1 A. 1002 B. 10020 C. 100200 D. 1002000
17. Given that (
1
𝑥+ 3
= 27 𝑥−^3. Find the value of x.
A. 35
B. 23
C. −
2 5 D. − (^35)
- Given that log 2 3 = 𝑚^2 and log 3 2 = 𝑛^2 Express log 2 81 − log 3 512 in terms of 𝑚 and 𝑛.
A. 4 𝑚^2 + 9𝑛^2 B. 9 𝑛^2 − 4 𝑚^2 C. (2𝑚 + 3𝑛)(2𝑚 − 3𝑛) D. (4𝑚 − 9𝑛)^2
- The graph of 𝑦 = 2𝑝𝑥^2 − 𝑝^2 𝑥 − 14 passes through the point (3, 10). Find the values of p. A. 2 and − B. −2 and 4 C. 2 and 4 D. −2 and −
- Solve the equation
A. −7 6 B. −3 2 C. −5 7 D. −
- Given that the gradient of the line joining the points (7, 𝑢 + 4) and (𝑢, 14) is. Calculate the value of 𝑢. A. −43 3 B.
43 3 C. 9 D. −
- If the mean of 2, 4, x, 5 and 8 is 6, what is the sum of 5, 8, x, 2, 12 and 4? A. 11 B. 31 C. 42 D. 30
- A man will be (𝑥 + 10) years old in 8 years’ time. If 2 years ago he was 63 years, find 𝑥. A. 67 B. 63 C. 57 D. 55
- P is a point 2m above the ground and 15m away from a tower. The angle of elevation of the tower from P is 65°. Calculate the height of the tower, correct to 2 decimal places. A. 8.33 m B. 15.59 m C. 15.17 m D. 34.17 m
- Given that cos(2𝑥 + 15°) = sin(𝑥 − 30°), where 0⁰ ≤ 𝑥 ≤ 90⁰. Find the value of 𝑥. A. 35⁰ B. 15⁰ C. 105⁰ D. 120⁰
- If 𝑝 ∶ 𝑞 = 𝑟 ∶ 𝑠, then (𝑝 + 𝑞) ∶ (𝑟 + 𝑠) is equal to A. 𝑝𝑠 ∶ 𝑞𝑟 B. 𝑝𝑞 – 𝑟𝑠 C. 𝑞 ∶ 𝑠 D. (𝑟 ∶ 𝑠) − (𝑝 ∶ 𝑞)
PAPER 2 ESSAY [20 Marks]
Instructions: Write clearly the number of each question you answer. You shall be penalised if you do not write the number accurately.
Answer all the questions in this section. All questions carry equal marks.
In each question, all necessary details of working, including rough work, must be shown with the answer.
Give answers as accurately as data and tables allow.
The use of non-programmable, silent and cordless calculator is allowed.
- (a) The cost, C of manning a household is partly constant and partly varies as the number of people, 𝒏, in the house. For 8 people, the cost is $70,000 and for 10 people, the cost is $90,000. Find i) an expression for C in terms of 𝒏 ii) the cost for 12 people.
(b) Two adjacent angles on a straight line are (𝑥 − 60)° and (𝑦 + 30)°. Find the value of (𝑥 + 𝑦).
- (a) Without using table or calculator evaluate:
log 10 (
) − 2 log 10 (
) + log 10 (
(b) Given that 25 𝑥^ = 1, find 𝑥.
END OF EXAM
