WAEC Further Mathematics
Past Questions

AI Explanation

**The reasoning** When you toss a coin twice, you're looking at **independent events** — each toss doesn't affect the other. List all possible outcomes: - HH (heads, then heads) - HT (heads, then tails) - TH (tails, then heads) - TT (tails, then tails) That's **4 equally likely outcomes**. Only **1 of them is HH**. So: P(HH) = Number of favorable outcomes ÷ Total outcomes = 1/4 Or use the **multiplication rule**: P(H on first toss) × P(H on second toss) = 1/2 × 1/2 = **1/4** **Why the wrong options tempt you** **B) 1/2** — You might think "either I get HH or I don't," but that ignores that HT, TH, and TT are three *different* ways to "not get HH." **C) 3/4** — Confusing this with "probability of at least one H" (which is indeed 3/4). **D) 1** — Thinking it's certain, but nothing's guaranteed in probability! **Quick takeaway** With two coin tosses, there are always **four** equally likely outcomes — write them out, count your target, and divide.

AI Explanation

**The reasoning** Variance measures how spread out numbers are from their mean (average). **Step 1:** Find the mean Mean = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) ÷ 8 = 40 ÷ 8 = **5** **Step 2:** Find how far each value is from the mean, then square those distances (2−5)² = 9 (4−5)² = 1 (appears 3 times = 3) (5−5)² = 0 (appears 2 times = 0) (7−5)² = 4 (9−5)² = 16 **Step 3:** Add all squared distances 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = **32** **Step 4:** Divide by the number of values Variance = 32 ÷ 8 = **4** **Why the wrong options tempt you** **Option A (2):** You might pick this if you forgot to square the differences or divided incorrectly. **Option C (5):** That's the mean, not the variance! Don't confuse them. **Option D (7):** That's just one of the data points—completely different concept. **Quick takeaway** Variance = average of squared distances from the mean. Always square first, then average!

AI Explanation

## The reasoning This is **Newton's Second Law of Motion** — the foundation of dynamics. The formula F = ma tells us that force equals mass times acceleration. Given: - m = 2 kg - a = 3 m/s² Simply substitute: F = ma = 2 kg × 3 m/s² = **6 N** The unit "Newton (N)" comes from kg·m/s², so when you multiply mass in kg by acceleration in m/s², you automatically get force in Newtons. Straightforward multiplication — no tricks here! ## Why the wrong options tempt you **Option A (5 N):** You might add instead of multiply (2 + 3 = 5). Remember, F = ma means *multiply*, not add. **Option C (9 N):** This comes from squaring the acceleration (3² = 9) and forgetting about the mass. Don't overthink it! **Option D (12 N):** You might multiply then double something (2 × 3 × 2), confusing yourself with extra steps. ## Quick takeaway **F = ma is pure multiplication: plug in the numbers, multiply straight, and watch your units — kg × m/s² always gives Newtons.** This formula appears in every mechanics exam, so master it now!