Form 4 Mathematics national exam 2020 with answers
The 2020 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.
- 50 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
Write all answers on the answer booklet. Write legibly in dark blue pen only. Answer all questions as provided in the question paper.
PART A: Multiple Choice Questions (40 marks)
Choose the correct answer and write it in the answer booklet.
- 12 marks
Choose the number when increased by 12, becomes 20.
- A.7
- B.8
- C.12
- D.10
- 22 marks
If a card is picked at random from a pack of playing cards, the probability of getting a king of spades is:
- A.1/13
- B.1/52
- C.1/26
- D.4/13
- 32 marks
The mode of the following set of data: 4, 9, 3, 7, 5, 6, 7, 8, 7 is:
- A.8
- B.5
- C.4
- D.7
- 42 marks
Cos(A+B) is equal to:
- A.cosAcosB + sinAsinB
- B.sinAcosB + cosAsinB
- C.cosAcosB - sinAsinB
- D.sinAcosB - cosAsinB
- 52 marks
The sum of (3 - i) + (2 + 3i) is:
- A.5 + 2i
- B.5 - 2i
- C.6 + 3i
- D.2 + 5i
- 62 marks
The radius of a circle with an equation of: x^2 + y^2 = 25 is:
- A.25
- B.10
- C.5
- D.15
- 72 marks
What is the determinant of a given matrix = [8 3; 4 2]?
- A.20
- B.4
- C.10
- D.-4
- 82 marks
The value of lim x->2 (5x + 4) is equal to _____
- A.14
- B.10
- C.5
- D.11
- 92 marks
The simplest form of (1/25)^(-3/2) is _____
- A.8
- B.27
- C.15
- D.125
- 102 marks
Calculate dy/dx when y = 3x^2 + 5x + 10
- A.6x + 5
- B.6x + 10
- C.3x + 5
- D.6x^2 + 5
- 112 marks
State the simplest form of Cos2x / (Cosx - sinx).
- A.cosx + sinx
- B.cosxsinx
- C.cosx - sinx
- D.sinx
- 122 marks
What is the value of i^25?
- A.i
- B.-i
- C.5
- D.i+1
- 132 marks
State the number of ways in which two books can be selected from a group of 5.
- A.20
- B.-25
- C.15
- D.15
- 142 marks
State the focus of the parabola where the equation in y = -16x^2.
- A.4
- B.-8
- C.16
- D.-4
- 152 marks
How many sides does a polygon have if the sum of its interior angles is 720°?
- A.7 sides
- B.8 sides
- C.6 sides
- D.5 sides
- 162 marks
A box contains 3 red, 4 blue and 3 green beads. The probability of selecting a blue or red bead at random will be:
- A.10/7
- B.5/4
- C.3/11
- D.7/10
- 172 marks
If Sin A = 5/13 and cos B = 4/5, where A and B are in the 2nd quadrant. The value of Sin(A+B) is:
- A.7/60
- B.-16/65
- C.65/33
- D.7/12
- 182 marks
The integration of ∫ dx is
- A.dx
- B.x
- C.Zero
- D.x + c
- 192 marks
If the number of boys is 320 out of 500 students, what will be the percentage of girls in the school.
- A.40%
- B.36%
- C.27%
- D.39%
- 202 marks
The derivative of a constant number f(x) = C, will be
- A.Cx
- B.-2c
- C.Zero
- D.C + 1
PART B: Structured Questions (60 marks)
Answer all of the following questions and write your answer in the answer booklet.
- 21ai1 mark
21. Trigonometry. If sinB = 3/5 and cosB = 4/5 then find: sin2B
- 21aii1 mark
21. Trigonometry. If sinB = 3/5 and cosB = 4/5 then find: cos2B
- 21b3 marks
Write the difference of sin7A - sin3A as a product.
- 21c2 marks
Use half angle identity to find the exact value of tan 15°
- 21d3 marks
Calculate the area of a triangle, two sides of which are 8cm and 11cm and its perimeter is 32cm.
- 22ai2 marks
22. Complex numbers. Perform the following operation: (8 - i) - (4 - i)
- 22aii2 marks
22. Complex numbers. Perform the following operation: (3 + 2i)^2
- 22b3 marks
Use the quadratic Formula to solve x^2 - 2x + 2 = 0
- 22c3 marks
Write the conjugate of 3 + 2i
- 23ai1 mark
23. Probability. Calculate: P(8,3)
- 23aii1 mark
23. Probability. Calculate: C(7,4)
- 23b2 marks
A box contains 3 blue, 7 green and 11 red balls. What is the probability that a ball selected at random will be red?
- 23c2 marks
Find the probability of getting a sum of 7 and 4 of the first and the second throw of two dices.
- 23di1 mark
If a dice is flipped, what is the probability of getting: An even number
- 23dii1 mark
If a dice is flipped, what is the probability of getting: A number less than 5
- 23e2 marks
If the probability of success is 1/4. Find the probability of failure?
- 24a2 marks
24. Statistics. Find the mean of 8, 5, 14, 6, 4, 12.
- 24bi2 marks
If you are given a set of data 12, 17, 6, 9, 8, 9, 16, 15, 10. Calculate the: Lower quartile (Q1)
- 24bii2 marks
If you are given a set of data 12, 17, 6, 9, 8, 9, 16, 15, 10. Calculate the: Upper Quartile
- 24biii1 mark
If you are given a set of data 12, 17, 6, 9, 8, 9, 16, 15, 10. Calculate the: Range
- 24c2 marks
Table: Class 30-39 frequency 3; 40-49: 13; 50-59: 14; 60-69: 6; 70-79: 4. Complete the table below (cumulative frequency column).
- 24ci2 marks
Table: Class 30-39 frequency 3; 40-49: 13; 50-59: 14; 60-69: 6; 70-79: 4. Work out the cumulative frequency and the median.
- 24d2 marks
Calculate the variance of the following data: 7, 15, 12, 17, 20, 14, 9
- 24e2 marks
Find the mean of the following data: 45, 21, 53, 49, 50, 37, 48, 30
- 25a3 marks
25. Calculus. Evaluate the limit of: lim x->3 cuberoot(x^2 - 1)
- 25b2 marks
Find the derivative of the function: y = (2x - 3)/(x + 4)
- 25c3 marks
Calculate the equation of the tangent line to a curve y = x^2 at point P(2, 4)
- 25d3 marks
Evaluate integral from 0 to 2 of (3x^2 + 2x + 1) dx
- 25e2 marks
A mother is three times heavier than her daughter and together they weigh 72kg. Find the weight of each.
- 25f2 marks
Find the gradient of the equation 2x + 3y - 6 = 0.
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.
