BOTSWANA EXAMINATIONS COUNCIL
Botswana General Certificate of Secondary Education
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
MATHEMATICS II
1237
Paper 1
For Examination from 2025
SPECIMEN PAPER
2 hours
Candidates answer on the Question Paper
Additional Materials:
Answer Booklet
INSTRUCTIONS
• Answer all questions.
• Write your name, Centre number and candidate number in the spaces provided at the top of this
page and on all work you hand in.
• Write in dark blue or black pen.
• Write your answer to each question in the spaces provided.
• You may use HB pencil for any diagrams, graphs or rough working.
• Do not use staples, paper clips, highlighters, glue or correction fluid.
• Do not write in any barcodes.
• Electronic calculators may be used.
INFORMATION
• The total marks for this paper is 80.
• You may lose marks if you do not show your working or if
you do not use appropriate units.
• The number of marks is given in brackets [ ] at the end of each
question or part question.
This document consists of 10 printed pages and 2 blank pages.
© BEC 2022
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1
What is the measure in radians of the angle 320 degrees?
Answer ………………………………………[1]
2
What is the 35th term of 5, 9, 13, …?
Answer ………………………………………[2]
3
Solve the inequality 2x + 3  x + 1.
Answer ………………………………………[2]
4
Given that A = {4,5,6,7, 8} and B = {5,7,9,11}
Find
(a)
AỤB
Answer:(a)…………………………………[1]
(b)
AꓵB
Answer:(b)…………………………………[1]
© BEC 2022
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5
A radio station transmits signals up to a radius of 200km.
Use a scale of 1 cm to represent 40km to show the maximum signal coverage from point R. [2]
•R
6
A bag contains 5 yellow balls and 3 red balls. Two balls are picked at random and not replaced.
What is the probability of picking at least one red ball
Answer ………………………………………[2]
7
The first four terms of a sequence are 3, 10, 19 and 30.
What is the expression for the nth term?
Answer ………………………………………[3]
© BEC 2022
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On the axes provided, draw the graph of 𝑦 = 𝑥 + 2 and its inverse.
8
[2]
```
7
6
5
4
3
2
1
0
0
9
1
2
3
Expand the brackets
4
5
6
(x – 2)3
Answer ………………………………………[2]
10
Solve the equation 2x2 – 3x -1 = 0 correct to 2 decimal places
Answer ………………………………………[5]
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11
The equation of a circle is given as (𝑥 − 2)2 + (𝑦 + 3)2 = 16
Find
(a) the radius,
Answer ………………………………………[2]
(b) the centre of the circle.
Answer ………………………………………[2]
12
A sum of P4000 is borrowed and the rate of interest is 6% per annum.
What is the daily compound interest rate for 2 years?
Answer ………………………………………[2]
13
simplify
1+ 2
.
2 2 −3
Answer ………………………………………[3]
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14
The mass of a wooden pot is measured in as 350 g correct to the nearest 10g and the volume
of wood used to make the pot is given as 500 cm3 to the nearest unit.
Calculate the lower bound of the density of the wood.
Answer ………………………………………[3]
15
Find log3
1
.
243
Answer ………………………………………[2]
16
The diagram below shows triangle ABC, with AB = 10 cm, BC = 6.5 cm and the size of angle
ABC = 70 degrees.
A
10
70
B
6.5
C
Calculate the length of the side AC,
Answer ………………………………………[3]
© BEC 2022
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17
The weights of 25 patients at a hospital were recorded as follows
Weight (kg)
Frequency
(a)
40 – 50
3
0.3
50 – 65
4
0.27
65 – 85
5
0.25
85 – 110
7
0.28
110 - 120
6
0.6
Draw the histogram to represent this information.
[3]
```
1
0.8
0.6
0.4
0.2
0
40
50
(b)
60
70
80
90
100
110
120
State the modal class.
Answer ………………………………………[1]
18
Find the first derivative of s =
3t 2 +4t 5
.
t3
Answer ………………………………………[3]
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19
Show that SinθCotθ = Cosθ
Answer ………………………………………[2]
20
Find the area bounded by y = x + 2 and y =x2 + 2x – 2
Answer …….………………………………………[5]
21
3
4
Given the matrix 
5

7 
Calculate
(a)
the determinant,
Answer ………………………………………[2]
(b)
the inverse of the matrix
Answer ………………………………………[2]
© BEC 2022
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−2
22
Evaluate
27 3 .
Answer ………………………………………[2]
____________________________________________________________________________
23
Convert 1.565656…………….. into a fraction.
Answer ………………………………………[2]
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24
A survey was conducted in a school of 200 students, 100 students are members of Mathematics
club, 55 students are members of English debate club and 30 are members of both clubs.
How many students are not members of either of the clubs?
Answer ………………………………………[2]
___________________________________________________________________________
25
The diagram below shows triangle ABC, with AB = 8 cm, BC = 15 cm and size of angle
ABC = 75°.
15
75°
8
Calculate the area of the triangle.
Answer ………………………………………[2]
_________________________________________________________________________________
© BEC 2022
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26
⃗⃗⃗⃗⃗⃗ = (5) , 𝑂𝑃
⃗⃗⃗⃗⃗ = (−3) and 𝑃𝑄
⃗⃗⃗⃗⃗ = ( 8 )
Vector 𝑂𝑀
7
−5
2
(a)
Show that M and Q are coincident points.
Answer ………………………………………[3]
(b)
Calculate the magnitude of ⃗⃗⃗⃗⃗⃗
𝑂𝑀.
Answer ………………………………………[2]
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27
Simplify the algebraic fractions
𝑥 2 +2𝑥
.
𝑥 2 +5𝑥+6
Answer ………………………………………[2]
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28 Factorise the expression 3𝑥 2 + 7𝑥 + 2.
Answer ………………………………………[3]
© BEC 2022
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29
The ages, in years, of a group of 30 teachers are shown in the grouped frequency table.
Age (t years)
26 - 30
31 - 35
36 - 40
41 - 45
46 - 50
Frequency
7
9
5
6
3
(a) Write down the mid- value of the class 26 < 𝑡 ≤ 30.
Answer ………………………………………[1]
(b) Calculate an estimate of the mean ages of the teachers.
Answer ………………………………………[3]
_________________________________________________________________________________
© BEC 2022
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