WAEC (WASSCE) Mathematics Past Questions and Answers (2026)

Answer: E

In a geometric progression (G.P.), the nth term can be expressed as a * r^(n-1), where 'a' is the first term and 'r' is the common ratio. Given that the 2nd term is 6, we have a * r = 6. For the 5th term, a * r^4 = 48. Dividing these two equations gives r^3 = 8, so r = 2. Substituting r back into the first equation gives a = 3. The first four terms are 3, 6, 12, and 24. Their sum is 3 + 6 + 12 + 24 = 45. Therefore, the correct answer is E. The other options are incorrect because they do not match the calculated sum of the first four terms.

Answer: C

To find tan(θ) given sin(θ) = K, we use the identity tan(θ) = sin(θ) / cos(θ). Since sin(θ) = K, we need to find cos(θ). Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we have cos²(θ) = 1 - K², which gives cos(θ) = √(1 - K²). Therefore, tan(θ) = K / √(1 - K²). Option C is correct. Option A (1-K) does not relate to the trigonometric identities. Option B (k/(k-1)) is incorrect as it does not follow from the definitions. Option D (k/(1-k)) is also incorrect for the same reason. Option E (k/√(k²-1)) is invalid since k²-1 is negative for 0 ≤ k < 1, which is outside the defined range for θ.

Answer: E

To find the roots of the equation 2x^2 - 3x - 2 = 0, we can use the quadratic formula: x = [-b ± sqrt(b² - 4ac)] / 2a, where a = 2, b = -3, and c = -2. Plugging in these values gives us x = [3 ± sqrt((-3)² - 4*2*(-2))] / (2*2) = [3 ± sqrt(9 + 16)] / 4 = [3 ± 5] / 4. This results in x = 2 or x = -1/2. Thus, the correct answer is E: x = -1/2 or 2. The other options are incorrect because they do not match the calculated roots.

Answer: D

To determine the value of k that makes the expression m^2 - 8m + k a perfect square, we can use the formula for completing the square. The expression can be rewritten as (m - 4)^2 when k = 16, since (m - 4)(m - 4) expands to m^2 - 8m + 16. Therefore, k must be 16 for the expression to be a perfect square. For the other options: A (2) gives m^2 - 8m + 2, which cannot be factored into a perfect square; B (4) gives m^2 - 8m + 4, which is (m - 4)^2 - 12; C (8) gives m^2 - 8m + 8, which cannot be factored into a perfect square; E (64) gives m^2 - 8m + 64, which is (m - 4)^2 + 48. None of these options yield a perfect square.

Answer: C

To find q from log_{10} q = 2.7078, we use the definition of logarithms: q = 10^{2.7078}. Calculating this gives q ≈ 510.2, which corresponds to option C. The other options are incorrect because they do not equal 10^{2.7078}. Option A (5102) is too high, option B (849.9) is also incorrect, option D (84.99) is too low, and option E (51.02) is significantly lower than the correct value.

Answer: C

In the unit circle, cosine (cos x) is negative in the second and third quadrants, while sine (sin x) is negative in the third and fourth quadrants. Therefore, both cos x and sin x are negative only in the third quadrant, which corresponds to the range 180o < x < 270o. The other options are incorrect because: A (0o < x < 90o) is in the first quadrant where both functions are positive; B (90o < x < 180o) is in the second quadrant where cos x is negative but sin x is positive; D (270o < x < 360o) is in the fourth quadrant where sin x is positive; E (-90o < x < 90o) includes angles where both functions can be positive or only one can be negative.

Answer: D

To simplify 0.63954 ÷ 0.003, we first perform the division: 0.63954 ÷ 0.003 = 213.18. Rounding this to two significant figures gives us 210. The other options are incorrect because: A (213.18) is not rounded to two significant figures, B (213.00) is also not rounded correctly, C (213) is not in two significant figures, and E (21) is too low.

Answer: E

The equation log_{10} a = 4 means that a is equal to 10 raised to the power of 4. Therefore, a = 10^4 = 10000. The other options are incorrect because: A (0.4) is 10^-1, B (40) is 10^1.6, C (400) is 10^2.6, and D (1000) is 10^3, none of which equal 10^4.

Answer: D

To find the actual length of the room, we first calculate the absolute error based on the percentage error. The percentage error is 5% of the measured value (3.99m). Thus, the absolute error is 0.05 * 3.99m = 0.1995m. Since the student's measurement is smaller than the actual length, we add the absolute error to the measured value: 3.99m + 0.1995m = 4.1895m, which rounds to approximately 4.19m. Among the options provided, the closest and correct answer is D. 4.20m. The other options are incorrect because they do not account for the 5% error correctly or are not close enough to the calculated actual length.

Answer: D

To find the distance from point P to the plane by line of sight, we can use trigonometry. The angle of elevation is 30 degrees, and the height of the plane is 800m. We can use the tangent function: tan(30°) = opposite/adjacent = 800/d. Therefore, d = 800/tan(30°). Since tan(30°) = 1/√3, we have d = 800√3. Calculating this gives approximately 1385.6m. However, to find the line of sight distance, we use the cosine function: cos(30°) = adjacent/hypotenuse. The hypotenuse (line of sight distance) is thus 800/cos(30°) = 800/(√3/2) = 1600m. Therefore, the correct answer is D (1600m). The other options are incorrect because they do not satisfy the trigonometric relationships given the height and angle of elevation.

Answer: C

To solve the equation 3loga + 5loga - 6loga = log64, we first combine the logarithmic terms: (3 + 5 - 6)loga = log64, which simplifies to 2loga = log64. Dividing both sides by 2 gives loga = log64^(1/2) = log8. Therefore, a = 8. The other options are incorrect because they do not satisfy the equation when substituted back into the logarithmic expression.

Answer: D

In a geometric progression (G.P.), the second term can be expressed as ar (where a is the first term and r is the common ratio), and the fourth term can be expressed as ar^3. Given that the second term is 8, we have ar = 8, and for the fourth term which is 32, we have ar^3 = 32. Dividing the second equation by the first gives r^2 = 4, so r = 2. Substituting r back into the first equation gives a = 4. The first four terms are: a, ar, ar^2, ar^3 which are 4, 8, 16, and 32 respectively. The sum of these terms is 4 + 8 + 16 + 32 = 60. Therefore, the correct answer is D. The other options are incorrect because they do not match the calculated sum of the first four terms.