Question 1

PAPER III - THEORY

1(a) Solve the equation (3x - 5)/10 = (8 + 5x)/5.

Accepted Answer

Multiply both sides by 10:
3x - 5 = 2(8 + 5x)
3x - 5 = 16 + 10x
3x - 10x = 16 + 5
-7x = 21
x = -3

Question 2

1(b) Express 342_five in binary.

Accepted Answer

Step 1: change 342_five to base ten.
342_five = 3 × 5² + 4 × 5 + 2 = 75 + 20 + 2 = 97
Step 2: change 97 to base two by dividing by 2:
97 ÷ 2 = 48 r 1
48 ÷ 2 = 24 r 0
24 ÷ 2 = 12 r 0
12 ÷ 2 = 6 r 0
6 ÷ 2 = 3 r 0
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1
Read the remainders from the bottom up: 1100001.
Answer: 342_five = 1100001_two

Question 3

2(a) Calculate the 4th angle of a quadrilateral whose other three angles are 52°, 120° and 125°.

Accepted Answer

The angles of a quadrilateral add up to 360°.
Sum of the three given angles = 52° + 120° + 125° = 297°
4th angle = 360° - 297° = 63°

Question 4

2(b) The table below shows the scores of students in a test.
Scores: 21, 22, 23, 24, 25
No. of students: 3, 2, 1, 4, 5
(i) What is the modal score?
(ii) How many students took part in the test?
(iii) Find the median score.

Accepted Answer

(i) The modal score is the score with the highest frequency. 25 has the highest frequency (5), so the mode is 25.
(ii) Number of students = 3 + 2 + 1 + 4 + 5 = 15
(iii) With 15 students the median is the 8th score when arranged in order.
Cumulative frequency: 21 → 3, 22 → 5, 23 → 6, 24 → 10, 25 → 15.
The 8th score falls in the 24 group, so the median score is 24.

BECE Mathematics 2022 Theory Past Questions

Mathematics 2022 Theory — Question 1

Mathematics 2022 Theory — Question 2

Mathematics 2022 Theory — Question 3

Mathematics 2022 Theory — Question 4

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