Form 4 Mathematics national exam 2018 with answers
The 2018 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.
- 45 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
This paper consists of 12 printed pages. There are 2 sections: PART 1: 20 Multiple Choice Questions (40 marks), PART 2: 12 Structured Questions (60 marks). Answer all questions in the spaces provided. No extra paper is allowed.
PART 1: 20 MULTIPLE CHOICE QUESTIONS
Answer all questions. Circle the correct answer only (40marks)
- 12 marks
Cos (A+B) is equal to
- A.CosACosB - SinASinB
- B.CosACosB+SinASinB
- C.SinACosB+CosASinB
- D.SinACosB- CosASinB
- 22 marks
If Cos θ = 5/13, then Sin θ =
- A.5/12
- B.12/5
- C.13/12
- D.5/13
- 32 marks
Sin 135° is equal to
- A.1/2
- B.sqrt(2)/2
- C.-sqrt(2)/2
- D.-sqrt(3)/2
- 42 marks
Sec β is equal to
- A.1/Cos β
- B.1/Sin β
- C.1/Cosec β
- D.1/Tan β
- 52 marks
(2+ i) + (3- i) is equal to
- A.6
- B.5+2 i
- C.5
- D.6 - i^2
- 62 marks
3/(2+3i) is equal to
- A.3/(2+3i)
- B.6/13 + 9i/13
- C.6+9i
- D.6/13 - (9/13)i
- 72 marks
(1/2 + i)(-1/2 - i) is equal to
- A.1/4 - i^2
- B.1/4 + i^2
- C.(1/4)i^2
- D.i^2 + 1/4
- 82 marks
Using the diagram shown above, find the equation of the line.
- A.y = 3x + 2
- B.y = x - 2
- C.y = (1/3)x + 2
- D.y = (1/4)x + 5
- 92 marks
C_2^3 is equal to
- A.3
- B.3i
- C.8
- D.10
- 102 marks
The median of the following set of data is: 33, 30, 31, 32, 38, 37, 35, 39, 36.
- A.34
- B.31
- C.33
- D.35
- 112 marks
Simplify sqrt(1 - cos^2 θ)/cos θ
- A.cos θ/sin θ
- B.sin θ/cos θ
- C.csc θ/sin θ
- D.sec θ/csc θ
- 122 marks
The mean of four numbers is 12 and the mean of three number is 13 what is the fourth number?
- A.9
- B.18
- C.16
- D.24
- 132 marks
The derivative of y = 3x^2 is
- A.6x^2
- B.5x
- C.6x
- D.3x
- 142 marks
If f(x) = (2x+3)/6, then f(2) is
- A.1
- B.2/5
- C.6/7
- D.7/6
- 152 marks
If y = 3x^2 + 3x - 6, then dy/dx =
- A.6x - 6
- B.6x + 3
- C.x^3 + 3x
- D.6x + 3x - 6
- 162 marks
integral of (2x^2 + 4x + 5) dx is
- A.2x^3 + 4x^2 + 5x
- B.4x+4
- C.(2/3)x^3 + 2x^2 + 5x + c
- D.2x^2 + 4x + 5
- 172 marks
The derivative of 1/x^2 is
- A.-2/x^3
- B.2/x^3
- C.2x^3
- D.6x^2
- 182 marks
The truth of the statement is if 3+5=8 then 8+14=16
- A.F
- B.T
- C.TT
- D.TF
- 192 marks
Evaluate lim (x - 1) as x -> -1
- A.1
- B.-1
- C.0
- D.-2
- 202 marks
In a single throw of two dice, the probability of getting a total of 9 is :
- A.1/6
- B.1/9
- C.1/36
- D.1/12
Part 2: Answer ALL Questions (60 marks)
- B13 marks
Find the area of a triangle whose sides are: a= 5cm, b=3cm, c= 4cm.
- B23 marks
Show that: 1 + Sin2θ = (Sinθ + Cosθ)^2.
- B34 marks
Find the exact value of Sin 75°
- B43 marks
Solve for complex number solutions: 3x^2 + 2x + 5 = 0
- B54 marks
Find the quotient Z1/Z2 of the complex numbers Z1 = 24(Cos300° + iSin300°) and Z2 = 8(Cos75° + iSin75°)
- B63 marks
A student sat for Physics and Mathematics papers. Let PM denote "Passing Mathematics" and PP denote "Passing Physics", FM denote "Failing Mathematics" and FP denote "Failing Physics". Let the Mathematics test be the first activity and Physics be the second activity. Draw a tree diagram showing the possible outcomes of the two sets.
- B73 marks
Evaluate integral from 0 to 1 of (3x^2 + 5) dx
- B85 marks
Construct the table below: a truth table with columns p, q, p ∧ q, p ∨ q, p ⇒ q
- B93 marks
Find the area of this triangle (Sin 60° = 0.866). [Two sides 3 cm and 6 cm with the angle 60° between them.]
- B103 marks
If f(x) = 3x + 1 and g(x) = x^2 - 1, find f(g)(2)
- B113 marks
A wooden pole was broken by wind. Before it broke, the total height of the pole above the ground was 25 m. After it broke, the top of the pole touched the ground 15 m from the base as shown in the diagram. How tall was the part of the pole that was left standing shown by x?
- B124 marks
Evaluate integral of ((2x + 1)/x^4) dx
- B13a1 mark
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) a) State the upper class limit of the first class interval
- B13b1 mark
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) b) The lower class boundary of the last class interval
- B13c1 mark
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) c) The class size
- B13d4 marks
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) d) Complete the table to show the mid-points, fx, Σf = and Σfx =
- B13e1 mark
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) e) Which is the modal class
- B13f2 marks
For the grouped data: Number of plants 10-14, frequency 8; 14-18, frequency 10; 18-22, frequency 20; 22-26, frequency 7; 26-30, frequency 5. (Table columns: Number of plants, Frequency, Mid point x, fx, with totals Σf = and Σfx =.) f) Calculate the mean
- B143 marks
Find the limit. lim (x^2 + x - 6)/(x + 3) as x -> -3
- B15i1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: i) The 1st Quartile (lower quartile) - Q1
- B15ii1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: ii) The 2nd quartile (median) - Q2
- B15iii1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: iii) The 3rd Quartile (Upper quartile) - Q3
- B15iv1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: iv) Range
- B15v1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: v) Interquartile range
- B15vi1 mark
For the data: 12, 17, 6, 9, 8, 9, 16, 15, 10. Find: vi) Quartile deviation.
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.
