Form 4 Mathematics national exam 2024/2025 with answers
The 2024/2025 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.
- 62 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.
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Instructions to candidates
Answer all questions. Read each question carefully before answering. Write your answers on the exam paper. Time: 2 hours.
Circle the letter of the correct answer (40 marks)
- 11 mark
The imaginary part of the complex number Z = -5 + 6i is:
- A.-5
- B.-6
- C.1
- D.6
- 21 mark
The sum rule for Cos(A+B) =:
- A.CosAsinB+sinAcosB
- B.CosAcosB+SinAsinB
- C.CosAcosB-SinAsinB
- D.CosAsinB+CosBsinA
- 31 mark
The number of population in a village was 2400. If it decreased by 15% then the new number of the population will be:
- A.4020
- B.2760
- C.2040
- D.4200
- 41 mark
If set A = {a, b, d, f} and set B = {b, c, e, f} then A ∩ B is:
- A.{b, f}
- B.{b, d, f}
- C.{d, f}
- D.{a, d, f}
- 51 mark
If two dice are thrown once, the probability of getting two 6s is:
- A.2/6
- B.1/36
- C.2/36
- D.1/6
- 61 mark
The value of the limit: lim (x→3) 5 =:
- A.3
- B.5
- C.8
- D.15
- 71 mark
The sum of the two complex numbers of (-3 + i) and (2 + 5i) is:
- A.-1 + 6i
- B.-1 - 6i
- C.-1 + 4i
- D.5 + 6i
- 81 mark
Evaluate ∫(4x^3 - 3)dx is:
- A.x^4/4 - 3x + c
- B.x^4 + 3x + c
- C.4x^4/4 + c
- D.x^4 - 3x + c
- 91 mark
The first term of arithmetic progression is denoted by:
- A.D
- B.r
- C.n
- D.a
- 101 mark
Quadratic equations can be solved by:
- A.factorization
- B.Elimination
- C.comparison
- D.addition
- 111 mark
The derivative of a the function x = y^2 with respect to y is:
- A.2x
- B.2y
- C.0
- D.2x + 2y
- 121 mark
The lines are without:
- A.Length
- B.plane
- C.width
- D.point
- 131 mark
The number 3 is a factor for:
- A.20
- B.48
- C.16
- D.all
- 141 mark
The mean of 5 numbers is 14, four of the numbers are 4, 8, 12 and 22. The 5th number is
- A.11.5
- B.24
- C.42
- D.9.2
- 151 mark
The mode of the data: w, e, m, l, e, w, r, n, l, m, n, l is:
- A.W
- B.n
- C.l
- D.m
- 161 mark
The simplification of sqrt(48) is:
- A.2sqrt(12)
- B.8sqrt(6)
- C.3sqrt(16)
- D.4sqrt(3)
- 171 mark
The length of the perpendicular line OM in the circle below is (OB = 5 and MB = 3):
- A.5
- B.8
- C.3
- D.4
- 181 mark
The gradient of the line segment joining the two points: A(6,-5) and B(3,1) is:
- A.-2
- B.1.3
- C.0.75
- D.2
- 191 mark
The number of ways 3 committee students be selected from a class of 20 students is
- A.1140
- B.6480
- C.6840
- D.1410
- 201 mark
3π/2 in degrees is:
- A.45°
- B.270°
- C.0°
- D.90°
- 211 mark
The type of the triangle at the right is:
- A.Right angled triangle
- B.Isosceles triangle
- C.Obtuse triangle
- D.Equilateral triangle
- 221 mark
The common ratio of the geometric progression of 3, -6, 12, ... is:
- A.3
- B.-2
- C.-9
- D.2
- 231 mark
If a die is rolled once, the probability of getting a even number is:
- A.1/4
- B.1/2
- C.1/3
- D.1/6
- 241 mark
The expansion of (a - b)^2 =:
- A.a^2 + 2ab + b^2
- B.a^2 - b^2
- C.a^2 - 2ab + b^2
- D.a^2 + b^2
- 251 mark
The equation y = 4ax^2 is an equation of:
- A.Circle
- B.ellipse
- C.hyperbola
- D.parabola
- 261 mark
The term which divides the data into ten equal parts is called:
- A.Median
- B.percentile
- C.quartile
- D.decile
- 271 mark
The straight line joining any two points on the circumference of a circle is called:
- A.diameter
- B.radius
- C.chord
- D.center
- 281 mark
If sinx = 3/5 and cosx = 4/5, then cos2x =:
- A.7/25
- B.24/25
- C.25/24
- D.-7/25
- 291 mark
The derivative of a constant number is:
- A.Zero
- B.one
- C.variable
- D.undefined
- 301 mark
Express 81% as a decimal:
- A.81
- B.8100
- C.81/100
- D.0.81
- 311 mark
The exact value of cos15°
- A.(sqrt(2) - sqrt(6))/4
- B.(sqrt(6) - sqrt(2))/4
- C.(sqrt(6) + sqrt(2))/4
- D.(sqrt(6) + sqrt(2))/2
- 321 mark
The intersection of the two sets A and B in the figure at the right is:
- A.{1,3}
- B.{2,4}
- C.{1,3,5}
- D.{1,2,3,4,5}
- 331 mark
The base of the common logarithm is:
- A.10
- B.0
- C.π
- D.e
- 341 mark
The value of: ∫ from 0 to 2 of (3x^2 + 2x)dx is:
- A.16
- B.12
- C.5
- D.4
- 351 mark
The range of the marks 51, 43, 54, 73, 54 is:
- A.54
- B.11
- C.30
- D.55
- 361 mark
A class of 60 students was examined. If 75% of them passed the test, the number of students failed the exam is:
- A.20
- B.45
- C.15
- D.10
- 371 mark
The polar form of the complex number Z = -1 + sqrt(3)i is:
- A.2cis60°
- B.2cis120°
- C.4cis120°
- D.2cis240°
- 381 mark
At the point, for which the gradient is zero is called:
- A.Minimum point
- B.maximum point
- C.stationary point
- D.intersection point
- 391 mark
The simplification of 10!/(3! x 4!) =:
- A.52200
- B.22500
- C.2520
- D.25200
- 401 mark
The limit of a constant function is:
- A.Zero
- B.constant
- C.one
- D.unknown
Part two: structured questions (60 marks)
- 41a3 marks
Verify the following identity. a. (sinx + cosx)^2 = 1 + sin2x
- 41b1 mark
Verify the following identity. b. Cosx tanx = sinx
- 42a2 marks
a. Expand Sin (A+B).
- 42b2 marks
b. Expand Tan (A-B)
- 434 marks
State the real and imaginary parts of the complex number w = (x - 3) + (y - 9)i
- 445 marks
Write [2(cos20° + isin20°)]^3 in the standard form a+bi.
- 454 marks
If two coins are thrown once, list the outcomes of the sample space.
- 46a2 marks
A card is selected at random from an ordinary pack of 52 cards. Find the probability that the card is: a. A king
- 46b2 marks
A card is selected at random from an ordinary pack of 52 cards. Find the probability that the card is: b. A heart
- 474 marks
A bag contains 8 black balls and 5 white ones. If two balls are picked from the bag one at a time, find the probability of getting a white ball and a black ball without replacement.
- 48a3 marks
a. Complete the table below. Class 1-3: frequency 12; class 3-5: frequency 22; class 5-7: frequency 27; class 7-9: frequency 19. Columns: Class, Frequency, Midpoints (x), F.X, with a Total row.
- 48b2 marks
b. Find the mean of the data given in the above table. Class 1-3: frequency 12; class 3-5: frequency 22; class 5-7: frequency 27; class 7-9: frequency 19. Columns: Class, Frequency, Midpoints (x), F.X, with a Total row.
- 494 marks
If set A = {1, 3, 5} and set B = {2, 4, 6}. Determine A ∪ B.
- 502 marks
Find the common difference of the arithmetic progression of 4, 7, 10, ...
- 512 marks
What is the measure of a right angle?
- 52a2 marks
Evaluate: a. lim (x→2) (x^2 - 4x + 1)
- 52b3 marks
Evaluate: b. lim (x→0) ((x^2 - x)/x)
- 53a1 mark
Differentiate with respect to x. a. f(x) = x^5
- 53b3 marks
Differentiate with respect to x. b. f(x) = (x^2 + 1)(2 - x^2)
- 544 marks
Differentiate sinx - cosx with respect to x.
- 55a2 marks
Evaluate the following integrals a. ∫(x^2 + x + 3) dx
- 55b3 marks
Evaluate the following integrals b. Find the area of the region bounded by the curve y = 2x^2, the lines x = 1, x = 4 and the x-axis.
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.
