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Mathematics 2026 Paper 2

Mathematics Paper 2

Paper 2 - Essay — instructions

Answer four questions only. All questions carry equal marks. All working must be clearly shown. Marks will not be awarded for correct answers without corresponding working.

1. [10]

BECE 2026 · Paper 2

Given that \( K = \{1, 2, 3, \ldots 11\} \): (i) list the prime numbers in \( K \); (ii) find the probability that a number selected at random from the set \( K \) is not a prime number.

2. [10]

BECE 2026 · Paper 2

Factorize completely: \( (x + y)(2m - n) - m(x + y) \).

3. [10]

BECE 2026 · Paper 2

A typist charges GH¢ 68.00 for the first 8 sheets typed, and GH¢ 11.00 for each additional sheet. Calculate the amount earned if the typist typed a total of 35 sheets.

4. [10]

BECE 2026 · Paper 2

The image of \( P(2,\ 5) \) when translated by the vector \( r \) is \( (-3,\ 8) \). Find: (i) \( r \); (ii) the image \( Q' \) of \( Q(-4,\ -6) \) when translated by \( r \).

5. [10]

BECE 2026 · Paper 2

Joyce and Richard contributed GH¢ 10,000.00 and GH¢ 5,000.00 respectively to start a business. They agreed that Richard will be paid one-third of the profit as a manager and the rest of the profit will be shared in the ratio of their contributions. If the profit of GH¢ 9,000.00 was made, how much did: (i) Joyce receive; (ii) Richard receive in total?

6. [10]

BECE 2026 · Paper 2

Asana was engaged to collect cashew-fruits on a farm and was paid a wage of GH¢ 25.00 a day. If the daily wage increased by 10% and she worked for 30 days, how much will she be paid?

7. [10]

BECE 2026 · Paper 2

The diagram shows the floor of a room with its dimensions (an L-shaped floor with outer dimensions 8 m × 5 m and a rectangular notch of 5 m × 3 m cut from one corner). Find the: (i) perimeter; (ii) area; (iii) cost of carpeting the floor if a carpet cost GH¢ 20.00 per square metre.

8. [10]

BECE 2026 · Paper 2

In a school, the monthly income of three workers Aku, Brako and Dagadu are GH¢ 5,000.00, GH¢ 6,500.00 and GH¢ 4,200.00 respectively. (i) Calculate the yearly income of each worker. (ii) Find the yearly income difference between Aku and Dagadu. (iii) Find the total yearly income of all the three workers.

9. [10]

BECE 2026 · Paper 2

A painter places a ladder against a building at the window. The angle the foot of the ladder makes with the horizontal ground is 60°. If the distance from the foot of the ladder to the base of the building is 5 m: (i) illustrate the information in a diagram; (ii) find, correct to one decimal place, the: (α) length of the ladder; (β) distance between the window and the foot of the building. [Take tan 60° = 1.732, and cos 60° = 1/2]

10. [10]

BECE 2026 · Paper 2

Simplify \( \dfrac{\sqrt{72}}{\sqrt{18} - \sqrt{12}} \), leave the answer in the form \( a + b\sqrt{c} \), where \( a \), \( b \) and \( c \) are integers.

11. [10]

BECE 2026 · Paper 2

Solve: \( \dfrac{1}{2}(2x + 1) \geq \dfrac{1}{3}x + 1\dfrac{9}{10} \).

12. [10]

BECE 2026 · Paper 2

An athlete runs four times round a circular truck of radius 70 m. Find, in metres, the total distance covered by the athlete. [Take \( \pi = \dfrac{22}{7} \)]

13. [10]

BECE 2026 · Paper 2

The data shows the shoe sizes of learners in a school: (a) Construct a frequency distribution table for the data. (b) If the school supplies shoes to the learners: (i) which size should be purchased in large quantities? (ii) give reason for the answer in (b)(i); (iii) which size will be purchased in less quantities? (iv) give reason for the answer in (b)(iii). (c) Find, correct to the nearest whole number, the mean shoe size.

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