Basic Mathematics Form Three Terminal Examination

Basic Mathematics Form Three Terminal Examination

Instructions:

1. This paper consists of ten (10) questions in section A and section B
2. Answer all questions
3. All work done must be shown clearly
4. Four figure mathematical tables may be used
5. Calculators and any unauthorized materials are not allowed in the examination room
6. Cellphones are not allowed in the examination room
7. Write your examination number on every page of your answer booklet

Section A (40 Marks)

Answer all questions in this section

1. (a) Given the relation R = {(1, a), (2, b), (3, c), (4, a)}, state the domain and range of R. (2 marks)

(b)  If f(x) = 3x - 5, find the value of f(4). (2 marks)

2. (a) Convert 45° to radians. (2 marks)

(b)  Find the mean of the following data set: 10, 14, 18, 20, 28. (2 marks)

3. (a) A bag contains 5 red balls and 3 blue balls. A ball is picked at random. What is the probability of picking a blue ball? (2 marks)

(b)  Given vectors **a** = 2**i** + 3**j** and **b** = **i** - **j**, find **a** + **b**. (2 marks)

4. (a) Determine whether the relation R = {(1, 2), (2, 3), (3, 1)} is a function. Give reason. (2 marks)

(b)  Find the value of sin 30°. (2 marks)

5. (a) Find the mode of the following data set: 5, 8, 5, 12, 10, 5, 8. (2 marks)

(b)  A fair coin is tossed twice. Find the probability of getting two heads. (2 marks)

Section B (60 Marks)

Answer all questions in this section

6. (a) Given the function g(x) = x² + 2x - 1, find:

(i)  g(-2) (3 marks)

(ii) g(x + h) (3 marks)

(b)  Find the inverse of the relation y = 4x + 7. (4 marks)

7. (a) Solve the following triangle ABC, given that angle A = 60°, angle B = 45°, and side a = 12 cm. (6 marks)

(b)  The heights of students in a class are as follows:

| Height (cm) | 150-154 | 155-159 | 160-164 | 165-169 | 170-174 |
| :----------: | :-----: | :-----: | :-----: | :-----: | :-----: |
|  Frequency   |    5    |     8    |    12    |     9    |     6    |

Calculate the median height. (6 marks)

8. (a) Two dice are thrown. Find the probability of getting a sum of 7. (6 marks)

(b)  In a class of 30 students, 18 like mathematics and 15 like physics. 5 students like both subjects. Find the probability that a student chosen at random likes either mathematics or physics or both. (6 marks)

9. (a) Given vectors p = 4i - 2j and q = -i + 5j, find:

(i)  2**p** - **q** (3 marks)

(ii) |**p** + **q**| (magnitude of **p** + **q**) (3 marks)

(b)  Find the equation of the line passing through the points (2, 4) and (5, 10). (4 marks)

10. (a) The data below shows marks obtained by 40 students in a mathematics test

30 70 65 52 75 42 45 56 62 55

48 68 78 59 63 49 50 61 67 35

57 72 60 44 64 71 58 47 74 66

53 41 69 73 54 76 39 51 65 77

Prepare a frequency distribution table using a class interval of 5. (6 marks)

(b)  Use the table in 10(a) to calculate the mean. (6 marks)