Form 4 Mathematics national exam 2022 with answers
The 2022 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.
- 47 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 in the ANSWER BOOKLET.
Part one: Circle the letter of the correct answer (50 marks)
- 12 marks
cosAcosB - sinAsinB is
- A.sin(A + B)
- B.cos(A + B)
- C.cos(A - B)
- D.sinAcosB
- 22 marks
The exact value of cos30° By using half angle formula is
- A.2/sqrt(3)
- B.sqrt(2)/2
- C.1/2
- D.sqrt(3)/2
- 32 marks
The probability of failing exam is P(F) = 0.1, then the probability of passing exam is
- A.0.8
- B.0.9
- C.0.7
- D.0.6
- 42 marks
The number of ways that five textbooks can be arranged on a shelf is
- A.140
- B.120
- C.130
- D.150
- 52 marks
The imaginary part of the complex number z1 = 2 + 3i is
- A.Im(z) = 2
- B.Im(z) = 3i
- C.Im(z) = i
- D.Im(z) = 3
- 62 marks
If z1 = 2 - 5i and z2 = 1 + 4i then the addition of z1 and z2 is
- A.4 - i
- B.3 + i
- C.3 - i
- D.4 + i
- 72 marks
The marks of Maryam of six subjects in standard eight class was 24, 26, 35, 28, 50, 14. The range is
- A.16
- B.36
- C.18
- D.34
- 82 marks
If the variance of a data was 49, then the standard deviation is
- A.49
- B.48
- C.7
- D.6
- 92 marks
The exact value of lim (x -> 0) 18 equals
- A.0
- B.1
- C.180
- D.18
- 102 marks
The exact value of this lim (x -> -infinity) (2 - 1/x) will be:
- A.1
- B.1/2
- C.2
- D.-2
- 112 marks
If a given function of y = 6x^2 - 8x + 1 then dy/dx is
- A.dy/dx = 12x + 8
- B.dy/dx = 12x - 8
- C.dy/dx = 12x^2 + 8
- D.dy/dx = 12x
- 122 marks
The derivative of 40
- A.40x
- B.40x + c
- C.0
- D.-40
- 132 marks
The integration of integral of 2 dx is equal
- A.2x
- B.2
- C.2x + c
- D.2x^2 + c
- 142 marks
The conjugate of 3 + i is
- A.-3
- B.3 - 5i
- C.-3 + i
- D.3 - i
- 152 marks
The number of 2 letter permutation that can be formed from the letters in the word BURCO.
- A.20
- B.7
- C.8
- D.10
- 162 marks
The value of integral from 1 to 2 of 5x^3 dx equals
- A.4/65
- B.-73/4
- C.75/4
- D.4/75
- 172 marks
In how many ways can Amarn, Fardowsa and Zeynab arrange themselves in queue?
- A.4
- B.6
- C.5
- D.8
- 182 marks
The value of sinx + 2 = 3 will be:
- A.180°
- B.270°
- C.90°
- D.45°
- 192 marks
In the recent presidential election of Somalia, five candidates got the following votes in the first round of election: Hassan sheikh Mohamud 52, Farmajo 59, Khaire 47, Deni 65. The mean of their votes is
- A.70
- B.50
- C.55.75
- D.45
- 202 marks
The coordinate of stationary point of the given function y = x^2 - 4x is
- A.(2, -2)
- B.(2, 4)
- C.(-4, 2)
- D.(2, -4)
- 212 marks
Hafsa has five grades from assessments and quizzes. They are all weighted equally. If her grades are 50, 70, 88, 70, and 88, what is her current average grade?
- A.73.2
- B.61.3
- C.91.5
- D.88.4
- 222 marks
If an event is impossible, then its probability will be
- A.1
- B.0
- C.0.1
- D.0.5
- 232 marks
The integration of integral of sinx dx is
- A.cosx + c
- B.-cosx + c
- C.tanx + c
- D.cscx + c
- 242 marks
Mohamed has the following scores of the subject 60, 70, 80, 50, 80, his mode of score is
- A.70
- B.80
- C.60
- D.59
- 252 marks
The exact value of cos40°cos50° - sin40°sin50° is
- A.-1
- B.0
- C.-1
- D.infinity
Part two: Match Column A with Column B (10 marks)
- M11 mark
Match with Column B: The integral of integral of (3/x) dx is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M21 mark
Match with Column B: A box contains 3 math papers, 2 physics, and 4 chemistry papers. The probability of getting math paper is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M31 mark
Match with Column B: The modulus of 8 + 6i is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M41 mark
Match with Column B: The value of [cos(pi/4) + i sin(pi/4)]^2 is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M51 mark
Match with Column B: The exact value of lim (x -> 0) sinx/x equals Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M61 mark
Match with Column B: The order of this matrix A = [3 2 1; 0 4 5] (first row 3 2 1, second row 0 4 5) is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M71 mark
Match with Column B: If a given function of y = 6x^2 - 8x + 1 then dy/dx is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M81 mark
Match with Column B: The number of ways can 5 textbooks arranged on a shelf is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M91 mark
Match with Column B: (1/2)sin(2A) Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
- M101 mark
Match with Column B: The value of integral of dx is Column B choices: 10; i; 3ln x + c; 2 x 3; 120; 1/3; 1; sinAcosA; x + c; dy/dx = 12x - 8.
Part three: Structure Questions (40 Marks)
- Q1.13 marks
Question one: Analytic trigonometry. Use identities to identify the exact value of cos(-105°)
- Q1.23 marks
Question one: Analytic trigonometry. Express sin 3x in terms of sin x
- Q1.33 marks
Question one: Analytic trigonometry. Simplify the expression (1 - cos5x)/(sin 5x)
- Q1.43 marks
Question one: Analytic trigonometry. Find the values of tan2θ if the cosθ = 3/5 and sinθ < 0.
- Q2.14 marks
Question two: Statistics. The following are marks of mathematic students, describe the range. 29, 54, 54, 64, 74.
- Q2.24 marks
Question two: Statistics. Determine the mean, variance and standard deviation of the temperature reading below: 15°C, 16°C, 17°C, 18°C, 19°C, 20°C, 22°C, 24°C
- Q3.1a2 marks
Questions three: Complex Numbers. Simplify each of the following: a) i^3
- Q3.1b2 marks
Questions three: Complex Numbers. Simplify each of the following: b) i^7
- Q3.23 marks
Questions three: Complex Numbers. Add the following complex numbers z1 = 7 + 5i and z2 = -1 + 0i
- Q3.33 marks
Questions three: Complex Numbers. Write (1 + 3i)/(4 - i) in terms of a + bi
- Q4.15 marks
Question four: Probability. If you were to roll the die one time what is the probability of it landing on a 2? (A picture of an ordinary six sided die is shown.)
- Q4.25 marks
Question four: Probability. In a class, there are 12 boys and 16 girls. One of them is called out using student registration number, what is the probability that the one called is a girl?
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.
