2026 BECE 50 Mathematics Practice Questions With Answers And Solving Steps
Prepare for 2026 BECE Excellence: The Ultimate Mathematics Practice Hub
As the 2026 BECE approaches, mastering Mathematics requires more than just memorizing formulas—it demands the ability to solve real-world problems through logical reasoning. Under the Common Core Programme (CCP), examiners are looking for students who can demonstrate clear methods and critical thinking. To help you succeed, we have compiled 50 essential practice questions covering every strand of the syllabus, from Algebra and Geometry to Consumer Arithmetic and Statistics.
Question 1: In a class of 30 students, 18 like Mathematics and 15 like Science. If 5 students like both, how many students like neither Mathematics nor Science?
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Step 1: Math only = 18 – 5 = 13. Science only = 15 – 5 = 10.
Step 2: Total who like at least one = 13 + 10 + 5 = 28.
Calculation: 30 (Total) – 28 = 2 students.
Question 2: Find the sum of 1102 and 1112 in base two.
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Rule: 1 + 1 = 10 in binary; 1 + 1 + 1 = 11.
Calculation: 110 + 111 = 11012.
Question 3: Factorize completely: ax + ay – bx – by.
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Method: Factorizing by grouping.
Step 1: a(x + y) – b(x + y).
Calculation: (a – b)(x + y).
Question 4: The price of a textbook increased from GH₵ 80.00 to GH₵ 100.00. Find the percentage increase.
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Formula: (Increase / Original) × 100.
Step 1: Increase = 100 – 80 = 20.
Calculation: (20 / 80) × 100 = 25%.
Question 5: Point P(2, 3) is reflected in the x-axis. State the coordinates of the image P’.
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Rule: Reflection in x-axis: (x, y) → (x, -y).
Calculation: P'(2, -3).
Question 6: Simplify (2a3)2.
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Rule: (xy)n = xnyn and (xa)b = xa×b.
Calculation: 22 × a3×2 = 4a6.
Question 7: A bag contains 4 red balls and 6 blue balls. If a ball is picked at random, what is the probability it is not red?
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Step 1: Total balls = 4 + 6 = 10.
Step 2: Not red means blue = 6.
Calculation: 6/10 = 3/5 (or 0.6).
Question 8: Solve for k: 4k – 7 = 2k + 5.
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Step 1: 4k – 2k = 5 + 7.
Step 2: 2k = 12.
Calculation: k = 12/2 = 6.
Question 9: Calculate the volume of a cube with a side length of 4cm.
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Formula: Volume = s3.
Calculation: 4 × 4 × 4 = 64 cm3.
Question 10: Express 0.00045 in standard form.
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Rule: Move decimal 4 places to the right.
Calculation: 4.5 × 10-4.
Question 11: Find the value of tan 45°.
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Rule: In a right-angled isosceles triangle, Opposite = Adjacent.
Calculation: 1.
Question 12: A phone is sold for GH₵ 900.00 after a 10% discount. What was the original price?
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Method: Original Price × 0.9 = 900.
Calculation: 900 / 0.9 = GH₵ 1,000.00.
Question 13: If the radius of a circle is 7cm, find its circumference. (Take π = 22/7)
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Formula: C = 2πr.
Calculation: 2 × (22/7) × 7 = 44 cm.
Question 14: Solve the inequality: 2x + 3 < 11.
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Step 1: 2x < 11 – 3.
Step 2: 2x < 8.
Calculation: x < 4.
Question 15: Find the Mean of 10, 15, 20, 25, 30.
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Formula: Sum / Count.
Step 1: 10+15+20+25+30 = 100.
Calculation: 100 / 5 = 20.
Question 16: A car travels 150 km in 2.5 hours. Calculate its average speed.
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Formula: Speed = Distance / Time.
Calculation: 150 / 2.5 = 60 km/h.
Question 17: Given vectors u = (2, -1) and v = (3, 5), find u + v.
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Method: Add x-components and y-components separately.
Calculation: (2+3, -1+5) = (5, 4).
Question 18: Find the next term in the sequence: 2, 5, 10, 17, …
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Rule: The pattern is +3, +5, +7, +9.
Calculation: 17 + 9 = 26.
Question 19: If 3 books cost GH₵ 45.00, how much will 7 books cost?
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Step 1: Find the cost of 1 book = 45 / 3 = 15.
Calculation: 15 × 7 = GH₵ 105.00.
Question 20: A coin is tossed twice. What is the probability of getting two heads?
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Step 1: Sample space = {HH, HT, TH, TT} = 4 outcomes.
Calculation: 1 / 4 = 0.25.
Question 21: Factorize completely the expression: 12ab + 15ac.
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Method: Find the Highest Common Factor (HCF) of the terms.
Step 1: HCF of 12 and 15 is 3. The common variable is ‘a’.
Calculation: 3a(4b + 5c).
Question 22: A man is x years old. His son is 25 years younger than him. Write an expression for the son’s age.
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Rule: “Younger than” means subtraction.
Calculation: (x – 25) years.
Question 23: Convert 2510 to a base two (binary) number.
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Method: Repeated division by 2.
Calculation: 25/2=12 R1, 12/2=6 R0, 6/2=3 R0, 3/2=1 R1, 1/2=0 R1.
Result: 110012.
Question 24: Calculate the area of a triangle with a base of 10cm and a height of 8cm.
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Formula: Area = ½ × base × height.
Calculation: ½ × 10 × 8 = 5 × 8 = 40 cm2.
Question 25: Find the value of x if 3x + 4 = 19.
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Step 1: 3x = 19 – 4.
Step 2: 3x = 15.
Calculation: x = 15/3 = 5.
Question 26: What is the probability of picking an ‘E’ from the word ‘EDUCATION’?
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Step 1: Total letters = 9.
Step 2: Number of ‘E’s = 1.
Calculation: 1/9.
Question 27: A watch was bought for GH₵ 60.00 and sold for GH₵ 75.00. Find the Percentage Profit.
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Formula: (Profit / Cost Price) × 100.
Step 1: Profit = 75 – 60 = 15.
Calculation: (15/60) × 100 = ¼ × 100 = 25%.
Question 28: Express 5/8 as a percentage.
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Rule: Multiply by 100.
Calculation: (5/8) × 100 = 500/8 = 62.5%.
Question 29: Solve the inequality: 3x – 5 > 7.
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Step 1: 3x > 7 + 5.
Step 2: 3x > 12.
Calculation: x > 4.
Question 30: Find the HCF of 18, 24, and 36.
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Method: Listing factors or prime factorization.
Calculation: Factors of 18{1,2,3,6,9,18}, 24{1,2,3,4,6,8,12,24}, 36{1,2,3,4,6…}.
Result: 6.
Question 31: The bearing of B from A is 060°. What is the bearing of A from B?
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Rule: If bearing is < 180, add 180. If > 180, subtract 180.
Calculation: 60 + 180 = 240°.
Question 32: Find the interior angle of a regular pentagon.
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Formula: [(n – 2) × 180] / n.
Calculation: [(5 – 2) × 180] / 5 = (3 × 180) / 5 = 540/5 = 108°.
Question 33: Simplify: 23 × 24 ÷ 25.
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Rule: Add powers for ×, subtract for ÷.
Calculation: 2(3+4-5) = 22 = 4.
Question 34: Calculate the Simple Interest on GH₵ 500 for 2 years at 10% per annum.
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Formula: I = PRT / 100.
Calculation: (500 × 10 × 2) / 100 = 5 × 10 × 2 = GH₵ 100.00.
Question 35: If a = 2 and b = -3, evaluate 3a – 2b.
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Step 1: Substitute: 3(2) – 2(-3).
Step 2: 6 – (-6) = 6 + 6.
Calculation: 12.
Question 36: Find the gradient of the line passing through (2, 3) and (5, 9).
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Formula: m = (y2 – y1) / (x2 – x1).
Calculation: (9 – 3) / (5 – 2) = 6 / 3 = 2.
Question 37: A tank contains 400 litres of water. If 15% is used, how many litres remain?
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Step 1: Find 15% of 400 = 0.15 × 400 = 60.
Step 2: Subtract: 400 – 60.
Calculation: 340 litres.
Question 38: Evaluate: √(144) + √(25).
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Calculation: 12 + 5 = 17.
Question 39: Convert 0.75 to a fraction in its simplest form.
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Step 1: 75/100.
Step 2: Divide both by 25.
Calculation: 3/4.
Question 40: The sum of three consecutive numbers is 33. Find the smallest number.
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Equation: x + (x+1) + (x+2) = 33.
Step 1: 3x + 3 = 33.
Step 2: 3x = 30.
Calculation: x = 10.
Question 41: Find the value of x in the triangle where the other two angles are 45° and 85°.
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Rule: Sum of angles in a triangle = 180°.
Step 1: 180 – (45 + 85).
Calculation: 180 – 130 = 50°.
Question 42: Calculate the volume of a sphere with radius 3cm. (Take π = 3.14)
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Formula: V = 4⁄3 πr3.
Calculation: 4⁄3 × 3.14 × 27 = 4 × 3.14 × 9 = 113.04 cm3.
Question 43: Solve for m: 2m/3 = 8.
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Step 1: 2m = 8 × 3.
Step 2: 2m = 24.
Calculation: m = 12.
Question 44: What is the Mode of 2, 4, 4, 5, 6, 7, 7, 7, 8?
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Rule: The most frequent number.
Result: 7.
Question 45: Evaluate: (-5) + (-8) – (-3).
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Step 1: -5 – 8 + 3.
Step 2: -13 + 3.
Calculation: -10.
Question 46: A map is drawn to a scale of 1:50,000. Find the actual distance if the map distance is 4cm.
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Calculation: 4 × 50,000 = 200,000 cm = 2 km.
Question 47: If y ∝ x and y=10 when x=2, find y when x=5.
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Step 1: y = kx → 10 = k(2) → k=5.
Step 2: y = 5(5).
Calculation: 25.
Question 48: Expand: (x + 3)(x – 2).
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Method: FOIL.
Calculation: x2 – 2x + 3x – 6 = x2 + x – 6.
Question 49: Find the area of a square whose diagonal is √32 cm.
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Formula: Area = d2 / 2.
Calculation: 32 / 2 = 16 cm2.
Question 50: If a set has 3 elements, how many subsets does it have?
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Formula: 2n.
Calculation: 23 = 8.
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