Form 4 Mathematics national exam 2021 with answers
The 2021 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.
- 33 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. Time: 2 hours.
Part one: Circle the correct letter for the following choices (2 marks each question, 40 marks Total)
- 12 marks
The exact value of sin 15° is:
- A.(sqrt(6) - sqrt(2))/4
- B.(sqrt(6) + sqrt(2))/4
- C.(-sqrt(6) - sqrt(2))/4
- D.(sqrt(6) - sqrt(2))/4
- 22 marks
If cos 2θ = 4/5 the value of sin θ in quadrant II equals
- A.sqrt(10)/5
- B.sqrt(10)/10
- C.5/10
- D.9/5
- 32 marks
The imaginary and real parts of the complex number 3 + 9i are respectively:
- A.3, 9
- B.9, 3
- C.3, 9i
- D.3, -9i
- 42 marks
(3 + 2i)(4 - 2i) =
- A.2 + 16i
- B.-16 - 2i
- C.6 - 2i
- D.16 + 2i
- 52 marks
In the national form IV mathematics examination, candidates are asked to solve six out of ten probability questions. How many possible combinations of six questions could you choose?
- A.115200
- B.151200
- C.210
- D.151210
- 62 marks
Grade 12 mathematics contains seven chapters with their lessons 6, 7, 8, 4, 5, 7 and 3; hence the average of the lessons is
- A.5.71
- B.280
- C.7
- D.40
- 72 marks
If the marks of 4 students are 25, 54, 54, 67, the range is:
- A.45
- B.48
- C.30
- D.42
- 82 marks
If a coin is tossed, then the sample space is
- A.Two heads
- B.two tails
- C.head and tail
- D.one tail
- 92 marks
The limit of f(x) = x^2 + 4x - 1 at x = 1 is:
- A.-4
- B.4
- C.2
- D.-2
- 102 marks
lim (x -> 2) 7 is:
- A.-6
- B.-7
- C.7
- D.4
- 112 marks
The derivative of f(x) = 20, is :
- A.20
- B.20x
- C.0
- D.40x
- 122 marks
The differentiation of g(x) = (x + 1)/(x - 4) is:
- A.x/(x-4)^2
- B.-5/(x-4)^2
- C.-4/(x-4)^2
- D.-1/(x-4)^2
- 132 marks
To derive y = 2sinx - 3secx equals:
- A.4cosx - 6cscx
- B.cosx - secxtanx
- C.2 - 3cscx
- D.2cosx - 3secxtanx
- 142 marks
The equation of the tangent line to the graph of f(x) = x^2 - 4x + 6 at x = 1 is
- A.y = -2x + 5
- B.y = -5x - 2
- C.y = -x + 5
- D.y = -4x + 5
- 152 marks
The integrand of ∫ dx is:
- A.3x + c
- B.x + c
- C.3x^2/2
- D.3 + c
- 162 marks
The ∫ (1/x) dx is:
- A.lnx
- B.lnx + c
- C.ln(1/x)
- D.lnx^-1
- 172 marks
The second derivative of f(x) = (3x + 2)^10:
- A.30(3x + 2)^9
- B.810(3x + 2)^8
- C.270(3x + 2)^8
- D.10(3x + 2)^8
- 182 marks
Probability of getting a 5 from throwing a dice is:
- A.1/4
- B.2/6
- C.1/6
- D.3/4
- 192 marks
The set of all possible outcomes of an experiment is called:
- A.Sample space
- B.event
- C.subsets
- D.element
- 202 marks
In how many ways can we arrange the three books (mathematics, physics, and chemistry) on a shelf?
- A.12 ways
- B.14 ways
- C.6 ways
- D.3 ways
Part two: Structured Questions (60 Marks)
- 2.15 marks
Find cos(A + B) having sin A = 4/5 and sin B = 12/13 in the quadrant I
- 2.26 marks
Using identities to find exact value of cos 40° cos 50° - sin 40° sin 50°
- 2.33 marks
Verify that tan x sin 2x = 2 sin^2 x.
- 2.43 marks
Solve the equation x^2 - 4x + 24 = 0.
- 2.54 marks
Find the modulus and argument of 1 - sqrt(3) i
- 2.65 marks
Find the Conjugate of -10 - 10i
- 2.74 marks
Simplify i^17
- 2.84 marks
work out : (1 + 3i) + (6 - 5i)
- 2.95 marks
A group of 4 adults and 3 children are to be formed from 8 adults and 5 children. How many possible groups are there.
- 2.105 marks
A bag contains 8 black balls and 4 white balls. If two balls are drawn from the bag, one at a time, find the probability of drawing a black ball followed by a white ball without replacement
- 2.116 marks
Given the following set of values relating to grade 12 mathematics chapters, and lessons 6, 7, 8, 4, 5, 7 and 3. Find the mean, variance and standard deviation
- 2.125 marks
Find the derivative of g(x) = (3x - 1)(2x + 4).
- 2.135 marks
Find the area under the curve y = x^2 + 2 between x = 1 and x = 3.
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.
