Difficult BECE Mathematics Questions with Answers for Serious Students Only
Difficult BECE Mathematics Questions with Answers for Serious Students Only
If you are not a serious student, don’t attempt these questions. It is made up of 22 difficult BECE mathematics questions.
These questions cover a range of topics including algebra, geometry, probability, and statistics. They should provide a good challenge for students preparing to sit for the Basic Education Certificate Examination.
Naturally, these questions demands students have full grasp of the topics mentioned in the first paragraph.
Write out all the questions and in your exercise books so the internet doesn’t distract you. In case you have a challenge with any one of the questions, you can contact your friends or teachers for assistance.
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Mathematics BECE Questions
Answer to Difficult Mathematics Questions
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BECE Mathematics Questions
1. Simplify the expression: (3a + 4b)(2a – 5b).
2. Solve the equation: 5(x + 3) = 7x – 4.
3. Calculate the mean, median, and mode of the following set of numbers: 5, 8, 6, 9, 5, 7, 6, 8.
4. Find the volume of a cone with a radius of 5 cm and a height of 12 cm.
5. A box contains 24 red balls and 36 blue balls. What is the probability of drawing a red ball?
6. Solve the equation: 2(x – 4) + 3(2x + 1) = 5(3x – 2).
7. A triangle has side lengths of 8 cm, 12 cm, and 15 cm. Is it a right triangle?
8. Find the slope-intercept form of the equation for a line passing through the points (2, 5) and (4, 9).
9. Evaluate the expression: (32 + 23) ÷ (4 + 50).
10. A cylindrical tank has a radius of 5 meters and a height of 12 meters. What is the total surface area of the tank?
11. Solve the quadratic equation: 2x2 – 5x + 3 = 0.
Simplify the expression: √(27x3 y5) ÷ √(3xy).
12. Calculate the standard deviation for the following set of numbers: 12, 15, 18, 21, 24.
13. A store offers a 20% discount on all items. If the original price of a shirt is $40, what is the sale price?
14. Solve the equation: 3/4x – 1/2 = 1/3 – 2/5x.
15. Calculate the area of a trapezoid with bases measuring 6 cm and 9 cm, and a height of 4 cm.
16. Determine the LCM (Least Common Multiple) of 12 and 18.
17. Find the value of x in the equation 2(3x + 4) = 32.
18. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble?
19. Solve the system of equations: 3x – 2y = 5 and 2x + 3y = 4.
20. Calculate the area of a triangle with side lengths of 9 cm, 12 cm, and 15 cm using Heron’s formula.
21. Find the equation of a line perpendicular to y = 2x + 1 and passing through the point (4, -3).
22. A rectangular prism has dimensions of 6 cm, 8 cm, and 10 cm. What is its volume?
Answers to Difficult BECE Mathematics Questions
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1. Simplify the expression: (3a + 4b)(2a – 5b).
Answer: 6a^2 – 7ab – 20b^2
2. Solve the equation: 5(x + 3) = 7x – 4.
Answer: x = 17
3. Calculate the mean, median, and mode of the following set of numbers: 5, 8, 6, 9, 5, 7, 6, 8.
Answer: Mean = 6.75, Median = 6.5, Mode = 5 and 6
4. Find the volume of a cone with a radius of 5 cm and a height of 12 cm.
Answer: Volume = 1/3 x 22/7 x 52 x 12 = 314.16 cm3 (rounded to two decimal places)
5. A box contains 24 red balls and 36 blue balls. What is the probability of drawing a red ball?
Answer: Probability of drawing a red ball = 24/(24 + 36) = 0.4 or 40%
6. Solve the equation: 2(x – 4) + 3(2x + 1) = 5(3x – 2).
Answer: x = 3
7. A triangle has side lengths of 8 cm, 12 cm, and 15 cm. Is it a right triangle?
Answer: Yes, it is a right triangle because 8^2 + 12^2 = 15^2.
8. Find the slope-intercept form of the equation for a line passing through the points (2, 5) and (4, 9).
Answer: The equation of the line is y = 2x + 1.
9. Evaluate the expression: (32 + 23) ÷ (4 + 50).
Answer: (32 + 23) ÷ (4 + 50) = (9 + 8) ÷ (4 + 1) = 17 ÷ 5 = 3.4
10. A cylindrical tank has a radius of 5 meters and a height of 12 meters. What is the total surface area of the tank?
Answer: Total surface area = 2πrh + 2πr2
= 2π(5)(12) + 2π(5)^2
= 420π m^2 (rounded to two decimal places)
11. Solve the quadratic equation: 2x2 – 5x + 3 = 0.
Answer: x = 1/2 or x = 3/2
12. Simplify the expression: √(27x3 y5) ÷ √(3xy).
Answer: √(27x3 y5) ÷ √(3xy) = 3xy2
13. Calculate the standard deviation for the following set of numbers: 12, 15, 18, 21, 24.
Answer: Standard deviation = 4.32 (rounded to two decimal places)
14. A store offers a 20% discount on all items. If the original price of a shirt is $40, what is the sale price?
Answer: The discount amount is 20% of $40, which is (20/100) x $40 = $8. Therefore, the sale price of the shirt is $40 – $8 = $32.
15. Solve the equation: 3/4x – 1/2 = 1/3 – 2/5x.
Answer: x = 5/4
16. Calculate the area of a trapezoid with bases measuring 6 cm and 9 cm, and a height of 4 cm.
Answer: Area = (1/2) x (6 + 9) x 4 = 30 cm²
17. Determine the LCM (Least Common Multiple) of 12 and 18.
Answer: LCM of 12 and 18 = 36
18. Find the value of x in the equation 2 (3x + 4) = 32.
Answer: x = 0
19. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble?
Answer: Probability of drawing a blue marble = 3/(5 + 3 + 2) = 3/10
20. Solve the system of equations: 3x – 2y = 5 and 2x + 3y = 4.
Answer: x = 23/17 and y = -11/17
21. Calculate the area of a triangle with side lengths of 9 cm, 12 cm, and 15 cm using Heron’s formula.
Answer: Area = √(s(s-a)(s-b)(s-c)), where s = (a + b + c)/2
s = (9 + 12 + 15)/2 = 18
Area = √(18(18-9)(18-12)(18-15)) = 54 cm²
22. Find the equation of a line perpendicular to y = 2x + 1 and passing through the point (4, -3).
Answer: The slope of the line perpendicular to y = 2x + 1 is -1/2. Using the point-slope form, the equation is y – (-3) = (-1/2)(x – 4), which simplifies to y = (-1/2)x + 1.
23. A rectangular prism has dimensions of 6 cm, 8 cm, and 10 cm. What is its volume?
Answer: Volume = length x width x height
= 6 x 8 x 10 = 480 cm³
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