WAEC 2012 Mathematics · Question 11
Simplify:
Options
- A.6(1 - 3k2)
- B.6(3k2 - 1)
- C.6(3k - 1)
- D.6(1 - 3k)
Answer: C. 6(3k - 1)
Explanation written with AI and checked against the answer key
Analyze the question: We need to simplify a fraction whose numerator can be factorised. The best approach is to factor out the common factor, then use the difference of two squares. Concept: Difference of two squares: a² − b² = (a − b)(a + b) Solution: Step 1: Factor out the common factor 6 from the numerator. 54k² − 6 = 6(9k² − 1) Step 2: Recognise 9k² − 1 as a difference of two squares, since 9k² = (3k)² and 1 = 1². 9k² − 1 = (3k − 1)(3k + 1) Step 3: Substitute back into the fraction. (54k² − 6)/(3k + 1) = 6(3k − 1)(3k + 1) / (3k + 1) Step 4: Cancel the common factor (3k + 1). = 6(3k − 1) Answer: Option C, 6(3k − 1). Check: Let k = 1. The original expression is (54 − 6)/(3 + 1) = 48/4 = 12. Option C gives 6(3 − 1) = 12. ✓ Exam tip: When you see a numerator like 54k² − 6, first pull out the common number (here 6). This often reveals a difference of two squares, which is a favourite WASSCE and JAMB pattern. You can also quickly test options by substituting a simple value like k = 1.AI can make mistakes. Report anything that looks wrong.
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