2026 BECE 50 Mathematics Practice Questions With Answers And Solving Steps

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.

Rule: 1 + 1 = 10 in binary; 1 + 1 + 1 = 11.
Calculation: 110 + 111 = 1101₂.

Method: Factorizing by grouping.
Step 1: a(x + y) – b(x + y).
Calculation: (a – b)(x + y).

Formula: (Increase / Original) × 100.
Step 1: Increase = 100 – 80 = 20.
Calculation: (20 / 80) × 100 = 25%.

Rule: Reflection in x-axis: (x, y) → (x, -y).
Calculation: P'(2, -3).

Rule: (xy)ⁿ = xⁿyⁿ and (x^a)^b = x^a×b.
Calculation: 2² × a^3×2 = 4a⁶.

Step 1: Total balls = 4 + 6 = 10.
Step 2: Not red means blue = 6.
Calculation: 6/10 = 3/5 (or 0.6).

Step 1: 4k – 2k = 5 + 7.
Step 2: 2k = 12.
Calculation: k = 12/2 = 6.

Formula: Volume = s³.
Calculation: 4 × 4 × 4 = 64 cm³.

Rule: Move decimal 4 places to the right.
Calculation: 4.5 × 10^-4.

Rule: In a right-angled isosceles triangle, Opposite = Adjacent.
Calculation: 1.

Method: Original Price × 0.9 = 900.
Calculation: 900 / 0.9 = GH₵ 1,000.00.

Formula: C = 2πr.
Calculation: 2 × (22/7) × 7 = 44 cm.

Step 1: 2x < 11 – 3.
Step 2: 2x < 8.
Calculation: x < 4.

Formula: Sum / Count.
Step 1: 10+15+20+25+30 = 100.
Calculation: 100 / 5 = 20.

Formula: Speed = Distance / Time.
Calculation: 150 / 2.5 = 60 km/h.

Method: Add x-components and y-components separately.
Calculation: (2+3, -1+5) = (5, 4).

Rule: The pattern is +3, +5, +7, +9.
Calculation: 17 + 9 = 26.

Step 1: Find the cost of 1 book = 45 / 3 = 15.
Calculation: 15 × 7 = GH₵ 105.00.

Step 1: Sample space = {HH, HT, TH, TT} = 4 outcomes.
Calculation: 1 / 4 = 0.25.

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).

Rule: “Younger than” means subtraction.
Calculation: (x – 25) years.

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.

Formula: Area = ½ × base × height.
Calculation: ½ × 10 × 8 = 5 × 8 = 40 cm².

Step 1: 3x = 19 – 4.
Step 2: 3x = 15.
Calculation: x = 15/3 = 5.

Step 1: Total letters = 9.
Step 2: Number of ‘E’s = 1.
Calculation: 1/9.

Formula: (Profit / Cost Price) × 100.
Step 1: Profit = 75 – 60 = 15.
Calculation: (15/60) × 100 = ¼ × 100 = 25%.

Rule: Multiply by 100.
Calculation: (5/8) × 100 = 500/8 = 62.5%.

Step 1: 3x > 7 + 5.
Step 2: 3x > 12.
Calculation: x > 4.

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.

Rule: If bearing is < 180, add 180. If > 180, subtract 180.
Calculation: 60 + 180 = 240°.

Formula: [(n – 2) × 180] / n.
Calculation: [(5 – 2) × 180] / 5 = (3 × 180) / 5 = 540/5 = 108°.

Rule: Add powers for ×, subtract for ÷.
Calculation: 2^(3+4-5) = 2² = 4.

Formula: I = PRT / 100.
Calculation: (500 × 10 × 2) / 100 = 5 × 10 × 2 = GH₵ 100.00.

Step 1: Substitute: 3(2) – 2(-3).
Step 2: 6 – (-6) = 6 + 6.
Calculation: 12.

Formula: m = (y₂ – y₁) / (x₂ – x₁).
Calculation: (9 – 3) / (5 – 2) = 6 / 3 = 2.

Step 1: Find 15% of 400 = 0.15 × 400 = 60.
Step 2: Subtract: 400 – 60.
Calculation: 340 litres.

Calculation: 12 + 5 = 17.

Step 1: 75/100.
Step 2: Divide both by 25.
Calculation: 3/4.

Equation: x + (x+1) + (x+2) = 33.
Step 1: 3x + 3 = 33.
Step 2: 3x = 30.
Calculation: x = 10.

Rule: Sum of angles in a triangle = 180°.
Step 1: 180 – (45 + 85).
Calculation: 180 – 130 = 50°.

Formula: V = ⁴⁄₃ πr³.
Calculation: ⁴⁄₃ × 3.14 × 27 = 4 × 3.14 × 9 = 113.04 cm³.

Step 1: 2m = 8 × 3.
Step 2: 2m = 24.
Calculation: m = 12.

Rule: The most frequent number.
Result: 7.

Step 1: -5 – 8 + 3.
Step 2: -13 + 3.
Calculation: -10.

Calculation: 4 × 50,000 = 200,000 cm = 2 km.

Step 1: y = kx → 10 = k(2) → k=5.
Step 2: y = 5(5).
Calculation: 25.

Method: FOIL.
Calculation: x² – 2x + 3x – 6 = x² + x – 6.

Formula: Area = d² / 2.
Calculation: 32 / 2 = 16 cm².

Formula: 2ⁿ.
Calculation: 2³ = 8.