Form 4 Mathematics national exam 2024 with answers
The 2024 Form 4 national exam paper for Form 4 Mathematics, question by question. Take it timed like the real exam, then see the answer and explanation to every question.
- 34 questions, 100 marks
- 120 minutes
Take this paper
120 minutes, 100 marks. Multiple choice is marked for you; you mark your written answers against the marking points.
A free account is needed to start, so your answers and results are saved.
Instructions to candidates
Answer all questions in the ANSWER BOOKLET.
PART ONE: MULTIPLE CHOICE QUESTIONS (20 × 2 = 40 MARKS)
- 12 marks
The algebraic expression for half of x is
- A.x+2
- B.x-2
- C.2x
- D.x/2
- 22 marks
cot x · sin 2x · sec^2 x =
- A.0
- B.1
- C.2
- D.4
- 32 marks
The value of angle C in the figure below (figure 1) is (right angle at B, angle A = 30°)
- A.50°
- B.40°
- C.60°
- D.70°
- 42 marks
The expression cuberoot(16) × cuberoot(4) is equal
- A.16
- B.4
- C.3
- D.12
- 52 marks
The number 20.003 has _____ significant digits
- A.2
- B.3
- C.4
- D.5
- 62 marks
A Group of 250 students took a test. If 76% of them passed the test. How many students passed the exam?
- A.100
- B.190
- C.200
- D.60
- 72 marks
If A = (2 3; 3 4) (a 2 by 2 matrix with first row 2, 3 and second row 3, 4), then det(A) =
- A.1
- B.9
- C.-1
- D.8
- 82 marks
Find the area of the rectangle below (Fig. 2), whose sides are (3+√2) cm and (3-√2) cm.
- A.9 cm^2
- B.2 cm^2
- C.7 cm^2
- D.5 cm^2
- 92 marks
The factorization of a^3 - 8 is:
- A.(a+2)(a^2-2a+4)
- B.(a+2)(a^2+4a+4)
- C.(a-2)(a^2-2a+4)
- D.(a-2)(a^2+2a+4)
- 102 marks
The Mean of four numbers is 7, three of the numbers are 4,6 and 10. The fourth number is:
- A.10
- B.4
- C.6
- D.8
- 112 marks
integral of 2/x dx =
- A.ln x + c
- B.2 ln x + c
- C.ln 2x + c
- D.ln(2/x) + c
- 122 marks
If z = 3 + 4i then the magnitude of z, |z| =
- A.3
- B.4
- C.5
- D.7
- 132 marks
The lim as x→-1 of x^3 + x^2 + x + 1 =
- A.0
- B.1
- C.2
- D.3
- 142 marks
The derivative of y = x cos x is
- A.y' = cos x - x sin x
- B.y' = x cos x
- C.y' = x sin x
- D.y' = cos x + x sin x
- 152 marks
The 6th term of a Geometric series is 486 and the 7th term is 1458. Find the common ratio.
- A.1
- B.2
- C.3
- D.4
- 162 marks
The value of sin(π - x) is:
- A.cos x
- B.sin x
- C.sec x
- D.tan x
- 172 marks
lim as h→0 of (f(x+h) - f(x))/h =
- A.f(x)
- B.f'(x)
- C.f(a)
- D.f'(a)
- 182 marks
From a class of 25 students 4 are selected to work on a special assignment. In how many different ways can the 4 students be selected?
- A.6375600
- B.12650
- C.13800
- D.303600
- 192 marks
If P(A) = 0.53, P(B) = 0.36, and P(A ∪ B) = 0.74, then P(A ∩ B) =
- A.0.47
- B.0.64
- C.0.15
- D.0.26
- 202 marks
The value of 1/i^7 is equal to
- A.i
- B.-i
- C.1
- D.-1
PART TWO: MATCH COLUMN A WITH COLUMN B (10 MARKS)
- M11 mark
Match Column A with Column B. If f(s) = s^2 + 3s - 2, then f(-2) = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M21 mark
Match Column A with Column B. The integral of constant k with respect to x is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M31 mark
Match Column A with Column B. 2(i)^58 = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M41 mark
Match Column A with Column B. P(A') can not be higher than Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M51 mark
Match Column A with Column B. 6 cos(π/2 - x) sec(π/2 - x) = Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M61 mark
Match Column A with Column B. The number of rows of the matrix (1 2 0 0; 1 1 3 0; 0 2 1 4) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M71 mark
Match Column A with Column B. There are 16 students in a class. If the ratio of boys to Girls is 3:5. Then the number of girls in the class is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M81 mark
Match Column A with Column B. lim as x→0 of (1 - cos x)/x Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M91 mark
Match Column A with Column B. The magnitude of the vector (9, 12) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
- M101 mark
Match Column A with Column B. The distance between (-1,3) and (3,3) is Column B: 3, -2, 4, -4, 1, 15, 0, kx + c, 6, 10.
PART THREE: STRUCTURED QUESTIONS (50 MARKS)
- T14 marks
Trigonometry: Find the value of x that satisfies cot x = tan 65° [4 Marks]
- T25 marks
Trigonometry: Show that cos 3x = 4cos^3 x - 3 cos x [5 Marks]
- C14 marks
Complex Number: Use De Moivre's theorem to calculate the value of 1/(1 - i)^6 [4 Marks]
- C25 marks
Complex Number: Show that [(1 + i)/(1 - i)]^4 + [(1 - i)/(1 + i)]^4 = 2. Hint: Multiply each part by its conjugate and then simplify by applying the power. [5 Marks]
Paper set by the Federal Ministry of Education, Culture and Higher Education (MoECHE), Somalia. Shared free of charge to help students prepare. The answers and explanations are written by Sheerxirfad teachers.
