JAMB Mathematics: practice questions.

Answer: D. 50√3 m

The angle of depression equals the angle of elevation from the canoe: tan 30° = 50/d ⇒ d = 50/tan 30° = 50√3 m. The answer is 50√3 m. Why the other options are wrong: 50√3/3 m — it uses tan 30° = d/50, putting the angle at the wrong vertex. 100 m — this is the slant distance (50/sin 30°). 25 m — it uses 50 sin 30°.

Answer: D. 8 cm

Intersecting chords: AE × EB = CE × ED ⇒ 24 = 3 × ED ⇒ ED = 8 cm. The answer is 8 cm. Why the other options are wrong: 4.5 cm — it uses AE/EB = CE/ED instead of AE × EB = CE × ED. 7 cm — it uses AE + EB = CE + ED. 2 cm — it divides AE by CE (6 ÷ 3) instead of using AE × EB = CE × ED.

Answer: D. 21/50

Tails = 200 − 116 = 84. Experimental probability = 84/200 = 21/50. The answer is 21/50. Why the other options are wrong: 29/50 — this is the experimental probability of a head. 1/2 — this is the theoretical probability, not the experimental one. 84/116 — it divides tails by heads instead of by the total tosses.

Answer: A. 21.2

N/2 = 15. Cumulative frequency reaches 13 by 19.5, so the median class is 20–29 (f = 12). Median = 19.5 + (15 − 13)/12 × 10 = 21.2 (1 d.p.). The answer is 21.2. Why the other options are wrong: 21.7 — it uses the class limit 20 instead of the boundary 19.5. 24.5 — this is the mid-point of the median class. 21.5 — it uses f = 10 instead of the median-class frequency 12.

Answer: A. 14/3

∫x^(1/2) dx = ⅔x^(3/2). [⅔x^(3/2)]₁⁴ = ⅔(8) − ⅔(1) = 14/3. The answer is 14/3. Why the other options are wrong: 7/3 — it uses ⅓x^(3/2) instead of ⅔x^(3/2). 1/4 — it differentiates √x and evaluates. 16/3 — it does not subtract the value at the lower limit.

Answer: B. ₦10 800

I = PRT/100 = 45 000 × 8 × 3 / 100 = ₦10 800. The answer is ₦10 800. Why the other options are wrong: ₦55 800 — this is the amount (principal + interest), not the interest. ₦3 600 — this is the interest for one year only. ₦1 080 — it divides by 1000 instead of 100.

Answer: A. x = 1

dy/dx = 6x² − 18x + 12 = 6(x − 1)(x − 2). d²y/dx² = 12x − 18 is −6 at x = 1 (maximum). The answer is x = 1. Why the other options are wrong: x = 2 — d²y/dx² = 12(2) − 18 = 6 > 0 there: a minimum. x = 0 — dy/dx = 12 at x = 0, not 0. x = 3/2 — this is where d²y/dx² = 0, not a turning point.

Answer: B. 7

3 * (−2) = 3 + (−2) − (3)(−2) = 1 + 6 = 7. The answer is 7. Why the other options are wrong: −5 — it subtracts 6 instead of adding: −ab = −(3)(−2) = +6. 1 — it ignores the ab term. −7 — every sign has been reversed.

Answer: B. 60π cm²

Curved surface area = πrl = π × 6 × 10 = 60π cm². The answer is 60π cm². Why the other options are wrong: 96π cm² — this is the total surface area (adding the base 36π). 120π cm² — it uses 2πrl. 96 cm² — it multiplies r by (r + l) and leaves out π.

Answer: D. 120

LAGOS has 5 different letters, so there are 5! = 120 arrangements. The answer is 120. Why the other options are wrong: 25 — it computes 5². 24 — this is 4!, as for a circular arrangement. 60 — it divides by 2! although no letter is repeated.

Answer: A. ₦36 000

Selling at a 5% loss means SP = 95% of CP. CP = 34 200 ÷ 0.95 = ₦36 000. The answer is ₦36 000. Why the other options are wrong: ₦35 910 — it adds 5% of the selling price; the 5% is a percentage of the cost price. ₦32 490 — it takes 5% off the selling price, which would make the cost lower than the selling price. ₦36 200 — it adds a guessed ₦2 000 rather than solving 0.95 × CP = 34 200.

Answer: D. (a − b)(x + 2)

Group: x(a − b) + 2(a − b) = (a − b)(x + 2). The answer is (a − b)(x + 2). Why the other options are wrong: (a + b)(x − 2) — expands to ax − 2a + bx − 2b; signs wrong. (a − b)(x − 2) — expands to ax − 2a − bx + 2b. (x − b)(a + 2) — expands to ax + 2x − ab − 2b.