All 2 questions from the Basic Education Certificate Examination (Junior WAEC) (BECE) Mathematics 2023 Theory paper, with the correct answer and a full explanation for each. Free, no signup needed.
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(a) Simplify 1 1/2 × (2/3 − 1/4) ÷ 2 1/2. (b) A piece of wood is 220cm long. If 66 cm is cut away from the wood, what percentage of it remains?
Model answer
(a) 2/3 − 1/4 = 8/12 − 3/12 = 5/12. 1 1/2 × 5/12 = 3/2 × 5/12 = 5/8. 5/8 ÷ 2 1/2 = 5/8 ÷ 5/2 = 5/8 × 2/5 = 1/4. (b) Remaining length = 220 − 66 = 154cm. Percentage remaining = 154/220 × 100 = 70%.
The table below shows the ages of children in a particular orphanage home. Age: 1, 2, 3, 4, 5, 6 No. of children: 10, 15, 21, 20, 16, 18 Use the information to find the: (i) Mean (ii) Median (iii) Mode (iv) Range
Model answer
Total number of children = 10 + 15 + 21 + 20 + 16 + 18 = 100. (i) Mean: Σfx = (1×10) + (2×15) + (3×21) + (4×20) + (5×16) + (6×18) = 10 + 30 + 63 + 80 + 80 + 108 = 371. Mean = 371 ÷ 100 = 3.71. (ii) Median: cumulative frequencies are 10, 25, 46, 66, 82, 100. The 50th and 51st children both fall in age 4, so the median = 4. (iii) Mode: the highest frequency is 21, which belongs to age 3. Mode = 3. (iv) Range = 6 − 1 = 5.
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