A variable W varies partly as M and Partly inversely as P. Which of the following correctly represents the relation with k$_1$ and k$_2$ constants?

C. W = k$_1$M + $\frac{k_2}{P}$

B. W = ($k_1 + k_2$)$\frac{\text{M}}{\text{P}}$

C. W = k$_1$M + $\frac{k_2}{P}$

For what values of y is $\frac{y + 2}{8y^2 - 10y + 3}$ not defined?

C. $\frac{3}{4}$, $\frac{1}{2}$

A. $\frac{-3}{4}$, $\frac{1}{2}$

B. $\frac{-3}{4}$, $\frac{-1}{2}$

C. $\frac{3}{4}$, $\frac{1}{2}$

D. $\frac{3}{4}$, $\frac{-1}{2}$

Make R the subject of the relation V = πl(R$^2$ - r$^2$)

A. R = $\sqrt{\frac{V}{πl} + r^2}$

B. R = $\sqrt{\frac{V}{πl} - r^2}$

How do I prepare for WAEC (WASSCE) Mathematics?

Practise past questions under timed conditions, focus on your weakest topics, and go back over every wrong answer until you understand why the right option is right. DeeepSolve gives you timed CBT-style practice, and you can ask the AI tutor to explain any question step by step.

Where can I find WAEC (WASSCE) Mathematics past questions?

DeeepSolve has WAEC (WASSCE) Mathematics past questions organised by exam year; this page links to every year we have. Sign up free to practise them — no card required.

How close is the DeeepSolve CBT simulator to the real WAEC (WASSCE)?

It is designed to feel familiar: a countdown timer, one question at a time, and keyboard shortcuts for answering and moving between questions. DeeepSolve is an independent practice app and is not affiliated with JAMB, WAEC or NECO.

Are the AI explanations accurate?

AI explanations can make mistakes. Tap Report on any AI answer to flag it.

WAEC (WASSCE) 2024

2024 WAEC (WASSCE) Mathematics Past Questions and Answers

The 2024 WAEC (WASSCE) Mathematics past questions with answers: 50 objective questions from the 2024 paper in the DeeepSolve question bank, each with its answer behind "Show answer". Try each question before you check, then practise the paper as a timed WAEC-style CBT.

Practise this paper as a timed WAEC-style CBT All WAEC (WASSCE) Mathematics years

Questions

1.
Given that P is 25 m on a bearing of 330º from Q, how far south of P is Q?
1. A.25.2 m
2. B.21.7 m
3. C.19.8 m
4. D.18.5 m
Show answer
Answer: B. 21.7 m
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
2.
Find the quadratic equation whose roots are $\frac{2}{3}$ and - 1
1. A.3x $^2$ - x - 2 = 0
2. B.3x $^2$ + x + 2 = 0
3. C.3x $^2$ + x - 2 = 0
4. D.3x $^2$ + x - 1 = 0
Show answer
Answer: C. 3x $^2$ + x - 2 = 0
AI explanation
Analyze the question: We need a quadratic equation whose roots (solutions) are 2/3 and -1.
Concept: If the roots are α and β, the equation is
x² - (α + β)x + αβ = 0
Solution:
Sum of roots: 2/3 + (-1) = 2/3 - 1 = -1/3
Product of roots: (2/3)(-1) = -2/3
Substitute into the formula:
x² - (-1/3)x + (-2/3) = 0 x² + (1/3)x - 2/3 = 0
Multiply through by 3 to clear the fractions:
3x² + x - 2 = 0
Check by factorising: 3x² + x - 2 = (3x - 2)(x + 1)
3x - 2 = 0 gives x = 2/3 ✓
x + 1 = 0 gives x = -1 ✓
Tip: Always use "x² - (sum)x + product = 0". Be careful with the sign in front of the sum. A fast check is to substitute one root, such as x = -1, into the options: for C, 3(1) + (-1) - 2 = 0 ✓.
AI can make mistakes. Report anything that looks wrong.
3.
The population of a town increases by 3% every year. In the year 2000, the population was 3000. Find the population in the year 2003.
1. A.3,182
2. B.3,278
3. C.6,591
4. D.7,515
Show answer
Answer: B. 3,278
AI explanation
Analyze the question: The population grows by 3% each year, which is compound growth. We start in 2000 with 3000 people and need the population 3 years later, in 2003.
Concept: For compound growth,
A = P(1 + r/100)ⁿ
where P is the starting amount, r is the percentage rate, and n is the number of years.
Solution:
P = 3000
r = 3%
n = 2003 − 2000 = 3 years
A = 3000 × (1.03)³
Calculate (1.03)³ step by step:
1.03² = 1.0609
1.0609 × 1.03 = 1.092727
A = 3000 × 1.092727 = 3278.18
So the population is about 3,278.
Check the year-by-year growth:
2001: 3000 × 1.03 = 3090
2002: 3090 × 1.03 = 3182.7
2003: 3182.7 × 1.03 = 3278.18 ✔
Option A (3,182) is the trap answer: it is the population after only 2 years.
Tip: Count the number of years by subtracting the dates (2003 − 2000 = 3). For "increase by r%" use the multiplier (1 + r/100), and for "decrease" use (1 − r/100). Always check whether an option matches an intermediate year, because examiners use those as distractors.
AI can make mistakes. Report anything that looks wrong.
4.
Multiply 3.4 x 10 $^{-5}$ by 7.1 x 10 $^8$ and leave the answer in standard form.
1. A.2.414 x 10 $^2$
2. B.2.414 x 10 $^3$
3. C.2.414 x 10 $^4$
4. D.2.414 x 10 $^5$
Show answer
Answer: C. 2.414 x 10 $^4$
AI explanation
Step 1: Analyze the question We need to multiply two numbers written in standard form and give the answer in standard form (a × 10ⁿ, where 1 ≤ a < 10). Step 2: Concept Multiply the decimal parts, then add the powers of 10: (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10^(m+n) Step 3: Solution Multiply the decimal parts: 3.4 × 7.1 = 24.14 Add the powers of 10: 10⁻⁵ × 10⁸ = 10^(−5+8) = 10³ Combine: 24.14 × 10³ 24.14 is not between 1 and 10, so convert it: 24.14 = 2.414 × 10¹ So: 2.414 × 10¹ × 10³ = 2.414 × 10⁴ Step 4: Answer The result is 2.414 × 10⁴, which is option C. Tip: After multiplying the decimal parts, always check whether the result is still between 1 and 10. If it is 10 or more, shift the decimal point left and increase the power of 10 by one for each place you move. Many students stop at 24.14 × 10³ and lose the mark.
AI can make mistakes. Report anything that looks wrong.
5.
The length and breadth of a cuboid are 15 cm and 8 cm respectively. If the volume of the cuboid is 1560 cm $^3$ , calculate the total surface area.
1. A.976cm $^2$
2. B.838cm $^2$
3. C.792cm $^2$
4. D.746cm $^2$
Show answer
Answer: B. 838cm $^2$
AI explanation
Step 1: Analyze the question We have a cuboid with length l = 15 cm, breadth b = 8 cm and volume V = 1560 cm³. We must find the height first, then the total surface area.
Step 2: Concept
Volume = l × b × h
Total surface area = 2(lb + lh + bh)
Step 3: Solution
Find the height: 15 × 8 × h = 1560 120h = 1560 h = 13 cm
Now the surface area:
lb = 15 × 8 = 120
lh = 15 × 13 = 195
bh = 8 × 13 = 104
Sum = 120 + 195 + 104 = 419
Total surface area = 2 × 419 = 838 cm²
Step 4: Answer
Tip: In cuboid problems, always find the missing dimension from the volume first. Then use 2(lb + lh + bh) and add the three pair-areas before doubling, which helps avoid arithmetic slips. Also, 120 × 13 = 1560 is a quick check on h.
AI can make mistakes. Report anything that looks wrong.
6.
The interior angle of a regular polygon is 168º. Find the number of sides of the polygon.
1. A.24
2. B.30
3. C.15
4. D.12
Show answer
Answer: B. 30
AI explanation
Analyze the question: We're told each interior angle of a regular polygon is 168° and must find the number of sides, n. Concept: The interior and exterior angles at a vertex lie on a straight line, so they add up to 180°. The exterior angles of any polygon add up to 360°, so for a regular polygon: Exterior angle = 360° / n Solution: Step 1: Find the exterior angle. Exterior angle = 180° − 168° = 12° Step 2: Use the exterior angle formula. 360° / n = 12° n = 360° / 12° = 30 Check using the interior angle formula: Interior angle = (n − 2) × 180° / n = (30 − 2) × 180° / 30 = 28 × 6° = 168° ✓ Answer: The polygon has 30 sides, which is option B. Tip: When you're given an interior angle of a regular polygon, go straight to the exterior angle (180° − interior) and divide 360° by it. It's much faster than solving (n − 2) × 180 / n = angle. Also, note that 15 (option C) would give an interior angle of 156°, so it's a trap for students who slip in the calculation.
AI can make mistakes. Report anything that looks wrong.
7.
A variable W varies partly as M and Partly inversely as P. Which of the following correctly represents the relation with k $_1$ and k $_2$ constants?
1. A.W = $\frac{k_1M}{k_2P}$
2. B.W = ( $k_1 + k_2$ ) $\frac{\text{M}}{\text{P}}$
3. C.W = k $_1$ M + $\frac{k_2}{P}$
4. D.W = (k $_1 + k_2$ )M + P
Show answer
Answer: C. W = k $_1$ M + $\frac{k_2}{P}$
AI explanation
Analyze the question
"Partly varies as M and partly inversely as P" is a partial variation (joint of two parts added together). We need the form that adds a direct-variation term and an inverse-variation term.
Concept
W varies directly as M: W ∝ M, so W = k₁M
W varies inversely as P: W ∝ 1/P, so W = k₂/P
"Partly... and partly..." means the two parts are added:
W = k₁M + k₂/P
Checking the options
A. W = k₁M/(k₂P): this is a single product/quotient (joint variation), not a sum. ✗
B. W = (k₁ + k₂)M/P: this makes W vary directly as M and inversely as P together, with one combined constant. ✗
C. W = k₁M + k₂/P: a direct part plus an inverse part, each with its own constant. ✓
D. W = (k₁ + k₂)M + P: P appears directly with no constant, and there is no inverse variation. ✗
Exam tip: The word "partly" signals addition of terms, each with its own constant. Words like "jointly" signal multiplication instead. For example, "partly constant and partly varies as x" gives y = k₁ + k₂x.
AI can make mistakes. Report anything that looks wrong.
8.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
9.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
10.
A piece of rod of length 44 m is cut to form a rectangular shape such that the ratio of the length to the breadth is 7: 4. Find the breath.
1. A.8m
2. B.14m
3. C.16m
4. D.24m
Show answer
Answer: A. 8m
AI explanation
Analyze the question A rod 44 m long is bent to form a rectangle. This means the perimeter of the rectangle is 44 m. The length : breadth = 7 : 4, and we need the breadth. Concept Perimeter of a rectangle = 2(l + b) Solution Let length = 7x and breadth = 4x. 2(7x + 4x) = 44 2(11x) = 44 22x = 44 x = 2 Breadth = 4x = 4 × 2 = 8 m (Length = 7 × 2 = 14 m. Check: 2(14 + 8) = 44 ✓) Answer The breadth is 8 m, which is option A. Tip When a wire or rod is "bent" or "cut to form" a shape, its length equals the perimeter of that shape. Also, always use a ratio multiplier (like x) and check your answer by plugging it back into the perimeter. Note that 14 m (option B) is the length, not the breadth, so read the question carefully for what is being asked.
AI can make mistakes. Report anything that looks wrong.
11.
A number is added to both the numerator and the denominator of the fraction $\frac{1}{8}$ if the result is $\frac{1}{2}$ , find the number.
1. A.3
2. B.4
3. C.5
4. D.6
Show answer
Answer: D. 6
AI explanation
Analyze the question: We add the same number, call it x, to both the top and bottom of 1/8. The new fraction equals 1/2. We need x. Concept: Set up an equation from the words, then cross-multiply to solve. Solution: (1 + x)/(8 + x) = 1/2 Cross-multiply: 2(1 + x) = 1(8 + x) 2 + 2x = 8 + x 2x − x = 8 − 2 x = 6 Check: (1 + 6)/(8 + 6) = 7/14 = 1/2 ✓ Answer: D (6) Tip: In "add the same number to numerator and denominator" questions, always form (a + x)/(b + x) and cross-multiply. You can also test the options quickly by substitution. Here, only 6 gives 7/14 = 1/2.
AI can make mistakes. Report anything that looks wrong.
12.
Gifty, Justina, and Frank shared 60 oranges in the ratio 5: 3: 7 respectively. How many oranges did Justina receive?
1. A.16
2. B.12
3. C.20
4. D.28
Show answer
Answer: B. 12
AI explanation
Analyze the question: 60 oranges are shared among Gifty, Justina and Frank in the ratio 5 : 3 : 7. We need Justina's share, which corresponds to the "3" part.
Concept: To share a quantity in a ratio, add the ratio parts to get the total number of parts. Then each person's share is (their part ÷ total parts) × the total quantity.
Solution:
Total parts = 5 + 3 + 7 = 15
Justina's part = 3
Justina's share = (3/15) × 60 = (1/5) × 60 = 12
Check:
Gifty: (5/15) × 60 = 20
Justina: (3/15) × 60 = 12
Frank: (7/15) × 60 = 28
Total: 20 + 12 + 28 = 60 ✓
Justina received 12 oranges, which is option B.
Tip: Always add up the ratio parts first. Then find the value of one part (60 ÷ 15 = 4) and multiply by each person's ratio number. Justina: 3 × 4 = 12. The check that all shares add up to the total quickly catches mistakes. Options A, C and D are distractors (C and D are Gifty's and Frank's shares).
AI can make mistakes. Report anything that looks wrong.
13.
If (3 - 4 $\sqrt{2}$ )(1 + 3 $\sqrt{2}$ ) = a + b $\sqrt{2}$ , find the value of b
1. A.-5
2. B.5
3. C.-21
4. D.21
Show answer
Answer: B. 5
AI explanation
Analyze the question: We need to expand the product of two surds and write it in the form a + b√2, then read off b (the coefficient of √2).
Concept: Expand using FOIL (First, Outer, Inner, Last), remembering that √2 × √2 = 2.
Solution:
(3 - 4√2)(1 + 3√2)
First: 3 × 1 = 3
Outer: 3 × 3√2 = 9√2
Inner: -4√2 × 1 = -4√2
Last: -4√2 × 3√2 = -12(√2 × √2) = -12 × 2 = -24
Now combine:
Rational part: 3 - 24 = -21, so a = -21
Surd part: 9√2 - 4√2 = 5√2, so b = 5
So the expression equals -21 + 5√2, which means b = 5.
Check against the options: The value -21 (option C) is a, not b, and that is a common trap.
Tip: In questions like this, always find both a and b and then check which one the question asks for. Examiners often put the value of a among the options as a distractor. Also remember that √2 × √2 = 2, so the "Last" term becomes rational.
AI can make mistakes. Report anything that looks wrong.
14.
A die is tossed once. Find the probability of getting a prime number.
1. A. $\frac{1}{2}$
2. B. $\frac{1}{6}$
3. C. $\frac{1}{3}$
4. D. $\frac{2}{3}$
Show answer
Answer: A. $\frac{1}{2}$
AI explanation
Analyze the question: A fair six-sided die has outcomes {1, 2, 3, 4, 5, 6}. We need the probability that the number showing is prime.
Concept: Probability = (number of favourable outcomes) ÷ (total number of possible outcomes).
A prime number is a number greater than 1 that has exactly two factors: 1 and itself. Note that 1 is not prime, and 2 is the only even prime.
Solution:
Sample space: {1, 2, 3, 4, 5, 6}, so n(S) = 6
Prime numbers in the sample space: • 1: not prime • 2: prime • 3: prime • 4: not prime (2 × 2) • 5: prime • 6: not prime (2 × 3)
Favourable outcomes: {2, 3, 5}, so n(E) = 3
P(prime) = 3/6 = 1/2
Tip: For die questions, quickly list the primes: 2, 3, 5. Remember that 1 is never prime, since this is the most common trap in WASSCE and JAMB probability questions. Always simplify your fraction at the end (3/6 → 1/2).
AI can make mistakes. Report anything that looks wrong.
15.
Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.
1. A.60 $^O$
2. B.100 $^O$
3. C.120 $^O$
4. D.150 $^O$
Show answer
Answer: D. 150 $^O$
AI explanation
Analyze the question: A hexagon has 6 angles. Four of them add up to 420°, and the other two are equal. We need to find each of those two equal angles.
Concept: The sum of the interior angles of an n-sided polygon is (n − 2) × 180°.
Solution:
Sum of interior angles of a hexagon = (6 − 2) × 180° = 4 × 180° = 720°
Four angles sum to 420°, so the remaining two angles sum to 720° − 420° = 300°
The two remaining angles are equal, so each is 300° ÷ 2 = 150°
Check: 420° + 150° + 150° = 720° ✓
Answer: Each of the remaining angles is 150°, which is option D.
Tip: For any polygon question, start by writing down the angle sum formula (n − 2) × 180°. Then subtract the known angles and divide the remainder by the number of equal angles left. Memorize the hexagon total of 720° because it appears often in exams.
AI can make mistakes. Report anything that looks wrong.
16.
If 3x - 2y = - 5 and x + 2y = 9, find the value of $\frac{x - y}{x + y}$
1. A. $\frac{5}{3}$
2. B. $\frac{3}{5}$
3. C. $\frac{-3}{5}$
4. D. $\frac{-5}{3}$
Show answer
Answer: C. $\frac{-3}{5}$
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
17.
If log $_3^{2x - 1}$ = 5, find the value of x
1. A.8
2. B.16
3. C.64
4. D.122
Show answer
Answer: D. 122
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
18.
For what values of x is $\frac{x - 3}{4}$ + $\frac{x + 1}{8}$ $\geq$ 2 ?
1. A.x $\geq$ 5
2. B.x $\geq$ 6
3. C.x $\geq$ 7
4. D.x $\geq$ 8
Show answer
Answer: C. x $\geq$ 7
AI explanation
Step 1: Analyze the question We need all values of x that satisfy the inequality (x − 3)/4 + (x + 1)/8 ≥ 2. Step 2: Concept To solve an inequality with fractions, multiply every term by the LCM of the denominators. Because the LCM is positive, the inequality sign does not change. Step 3: Solution The LCM of 4 and 8 is 8. Multiply every term by 8: 8·(x − 3)/4 + 8·(x + 1)/8 ≥ 8·2 2(x − 3) + (x + 1) ≥ 16 2x − 6 + x + 1 ≥ 16 3x − 5 ≥ 16 3x ≥ 21 x ≥ 7 Check: Let x = 7: (7 − 3)/4 + (7 + 1)/8 = 1 + 1 = 2, which equals 2, so the boundary is correct. Try x = 8: 5/4 + 9/8 = 19/8 = 2.375 ≥ 2 ✓. Step 4: Answer x ≥ 7, which is option C. Tip: In inequality questions, always clear the fractions first using the LCM. Then plug the boundary value back in to confirm that it gives equality. Only flip the inequality sign if you multiply or divide by a negative number.
AI can make mistakes. Report anything that looks wrong.
19.
Find the range of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, and 25.
1. A.22
2. B.24
3. C.25
4. D.27
Show answer
Answer: B. 24
AI explanation
Analyze the question: The range of a data set is the difference between the largest value and the smallest value.
Concept: Range = Highest value − Lowest value
Solution:
Step 1: List the numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25
Step 2: Arrange in order (optional, but it helps avoid mistakes): 15, 20, 25, 26, 28, 29, 33, 37, 38, 39
Step 3: Identify the extremes:
Highest = 39
Lowest = 15
Step 4: Calculate: Range = 39 − 15 = 24
Answer: Option B (24).
Tip: Scan the list once for the biggest and smallest numbers, then subtract. Be careful not to pick a number like 20 as the smallest just because it appears near the end. Always check the whole list. Also, don't confuse range with the median or the mean, which need more steps.
AI can make mistakes. Report anything that looks wrong.
20.
Express in index form: log $_a^x$ + log $_a^y$ = 3
1. A.x + y = 3
2. B.xy = 3
3. C.xy = a $^3$
4. D.x + y = a $^3$
Show answer
Answer: C. xy = a $^3$
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
21.
A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?
1. A.5: 4
2. B.4: 3
3. C.3: 2
4. D.3: 4
Show answer
Answer: B. 4: 3
AI explanation
Analyze the question: A cone and a cylinder have equal volumes. The cone's radius is twice the cylinder's radius. We need the ratio of the cylinder's height to the cone's height.
Concept:
Volume of cylinder = πr²h
Volume of cone = (1/3)πR²H
Solution:
Let the cylinder have radius r and height h. The cone then has radius R = 2r and height H.
Equal volumes:
πr²h = (1/3)π(2r)²H
πr²h = (1/3)π(4r²)H
Cancel πr² from both sides:
h = (4/3)H
So h : H = 4 : 3
Check: If H = 3, then h = 4. Cone volume = (1/3)π(4r²)(3) = 4πr². Cylinder volume = πr²(4) = 4πr². They match.
Exam tip: In "equal volume" problems, write both formulas, set them equal, and cancel the common factors (π and r²). Remember that the cone's 1/3 combined with the squared radius ratio (2² = 4) gives 4/3.
AI can make mistakes. Report anything that looks wrong.
22.
A cliff on the bank of a river 87 m high. A boat on the river is 22 m away from the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
1. A.76 $^o$
2. B.64 $^o$
3. C.36 $^o$
4. D.24 $^o$
Show answer
Answer: A. 76 $^o$
AI explanation
Analyze the question: The cliff is 87 m high and the boat is 22 m horizontally from the base of the cliff. We need the angle of depression from the top of the cliff to the boat.
Concept: The angle of depression is measured downward from the horizontal at the observer's eye level. Because that horizontal line is parallel to the river surface, the angle of depression equals the angle of elevation of the cliff top as seen from the boat (alternate angles).
Solution:
Let θ be the angle of depression. In the right-angled triangle:
Opposite side (height of the cliff) = 87 m
Adjacent side (distance of the boat from the cliff) = 22 m
tan θ = opposite / adjacent = 87 / 22 = 3.9545
θ = tan⁻¹(3.9545) ≈ 75.8°, which is 76° to the nearest degree.
Check: tan 76° ≈ 4.01 and tan 75° ≈ 3.73, so 3.95 lies between them, closer to 76°. ✔
Answer: The angle of depression is 76°, which is option A.
Tip: In depression and elevation questions, draw the right-angled triangle first. If the height is much bigger than the horizontal distance, the angle must be steep (above 45°). That alone removes options C and D here. Also remember that the angle of depression is measured from the horizontal, not from the cliff face. Measuring it from the cliff face would give the wrong answer, 14°.
AI can make mistakes. Report anything that looks wrong.
23.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
24.
A ladder 15 m long leans against a vertical pole, making an angle of 72º with the horizontal. Calculate, correct to one decimal place, the distance between the foot of the ladder and the pole.
1. A.15.8 m
2. B.14.3 m
3. C.4.9 m
4. D.4.6 m
Show answer
Answer: D. 4.6 m
AI explanation
Analyze the question: The ladder (15 m) is the hypotenuse of a right-angled triangle. The pole is vertical and the ground is horizontal. The ladder makes 72° with the horizontal. We need the distance from the foot of the ladder to the pole, which is the horizontal side, adjacent to the 72° angle. Concept: Cosine relates the adjacent side to the hypotenuse: cos θ = adjacent / hypotenuse Solution: cos 72° = d / 15 d = 15 × cos 72° cos 72° ≈ 0.3090 d = 15 × 0.3090 = 4.635 ≈ 4.6 m Check: The height up the pole would be 15 sin 72° ≈ 14.3 m (this is option B, the distractor for the wrong side). The distance along the ground must be shorter than the ladder, and with such a steep angle it should be small, so 4.6 m makes sense. Also, 4.6² + 14.3² ≈ 21.2 + 204.5 ≈ 225.7, close to 15² = 225, so it is consistent. Tip: Draw the triangle and label the sides relative to the given angle. "Distance from the pole along the ground" is the side next to the angle, so use cosine (CAH in SOH-CAH-TOA). If the question asked for the height reached on the pole, you would use sine instead. Option B is the trap for that mix-up.
AI can make mistakes. Report anything that looks wrong.
25.
The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y
1. A.2
2. B.4
3. C.-4
4. D.-3
Show answer
Answer: C. -4
AI explanation
Analyze the question: We are given two points, P(2, -8) and Q(1, y), and the gradient (slope) of the line through them is -4. We need to find y. Concept: The gradient of a line through (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁) / (x₂ - x₁) Solution: Let P = (2, -8) and Q = (1, y). m = (y - (-8)) / (1 - 2) -4 = (y + 8) / (-1) Multiply both sides by -1: 4 = y + 8 y = 4 - 8 = -4 Check: Gradient = (-4 + 8)/(1 - 2) = 4/(-1) = -4 ✓ Answer: y = -4, which is option C. Tip: Always subtract the coordinates in the same order on the top and bottom (y₂ - y₁ over x₂ - x₁). Mixing the order is the most common cause of sign errors. Always substitute your answer back to confirm it gives the stated gradient.
AI can make mistakes. Report anything that looks wrong.
26.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
27.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
28.
A trader gave a change of # 540.00 instead of # 570.00 to a customer. Caculate the percentage error.
1. A.5 $\frac{5}{19}$ %
2. B.5 $\frac{5}{9}$ %
3. C.5 $\frac{7}{19}$ %
4. D.5 $\frac{7}{9}$ %
Show answer
Answer: A. 5 $\frac{5}{19}$ %
AI explanation
Analyze the question: The trader gave ₦540 when the correct change was ₦570. We need the percentage error.
Concept: Percentage error = (error ÷ true value) × 100%
The true (correct) value is ₦570, and the error is the difference between the correct and the given amount.
Solution:
Error = 570 − 540 = ₦30
Percentage error = (30 ÷ 570) × 100% = (1/19) × 100% = 100/19 %
Dividing: 100 ÷ 19 = 5 remainder 5, so
= 5 5/19 %
Check against the options:
A. 5 5/19 % ✔
B. 5 5/9 % (this would come from 30/540, which wrongly uses the given amount as the base)
C and D do not match.
Tip: Percentage error is always measured against the true/correct value, not the wrong one. Here the correct change was ₦570, so divide by 570. Many students fall into the trap of dividing by 540, which gives option B.
AI can make mistakes. Report anything that looks wrong.
29.
The fourth and eighth terms of an Arithmetic Progression are 16 and 40 respectively. Find the common difference.
1. A.- 6
2. B.6
3. C.-2
4. D.2
Show answer
Answer: B. 6
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
30.
Which of the following points lies on the line 3x - 8y = 11?
1. A.(1, 1)
2. B.(1, -1)
3. C.(-1, 1)
4. D.(-1, -1)
Show answer
Answer: B. (1, -1)
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
31.
A cylindrical metallic barrel of height 2.5m and radius 0.245 is closed at one end. Find, correct to one decimal place, the total surface area of the barrel (Take π = $\frac{22}{7}$ )
1. A.2.1 m $^2$
2. B.3.5 m $^2$
3. C.4.0 m $^2$
4. D.9.4 m $^2$
Show answer
Answer: C. 4.0 m $^2$
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
32.
A car valued at $ 600,000.00 depreciates by 10% each year. What will be the value of the car at the end of two years?
1. A.$ 120,000.00
2. B.$ 480,000.00
3. C.$ 486,000.00
4. D.$ 540,000.00
Show answer
Answer: C. $ 486,000.00
AI explanation
Analyze the question: The car loses 10% of its value each year. Because the depreciation is applied to the current value each year (not the original value), this is compound depreciation.
Concept: Value after n years = P × (1 − r)ⁿ, where P is the original value and r is the depreciation rate.
Solution:
Here P = 600,000, r = 10% = 0.10, n = 2.
Value = 600,000 × (1 − 0.10)² = 600,000 × (0.9)² = 600,000 × 0.81 = 486,000
Check year by year:
End of Year 1: 600,000 − 10% of 600,000 = 600,000 − 60,000 = 540,000
End of Year 2: 540,000 − 10% of 540,000 = 540,000 − 54,000 = 486,000
The value at the end of two years is **$486,000.
Why the others are wrong:
A (120,000) is wrong. It comes from subtracting 10% of 600,000 for 8 years, which makes no sense here.
B (480,000) comes from subtracting 10% of the original value twice (600,000 − 120,000). That is simple depreciation, not compound.
D (540,000) is the value after only one year.
Exam tip: When a question says "each year" and the value is changing, think "multiply by 0.9" for a 10% drop. For two years, multiply by 0.9 twice (0.81). Always check whether you are working from the new value each time.
AI can make mistakes. Report anything that looks wrong.
33.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
34.
For what values of y is $\frac{y + 2}{8y^2 - 10y + 3}$ not defined?
1. A. $\frac{-3}{4}$ , $\frac{1}{2}$
2. B. $\frac{-3}{4}$ , $\frac{-1}{2}$
3. C. $\frac{3}{4}$ , $\frac{1}{2}$
4. D. $\frac{3}{4}$ , $\frac{-1}{2}$
Show answer
Answer: C. $\frac{3}{4}$ , $\frac{1}{2}$
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
35.
Two opposite sides of a rectangle are (5x + 3) m and (2x + 9) m. If an adjacent side is (6x - 7) m, find in m $^2$ , the area of the rectangle.
1. A.45
2. B.65
3. C.125
4. D.165
Show answer
Answer: B. 65
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
36.
The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.
1. A.Seven
2. B.Eight
3. C.Nine
4. D.Ten
Show answer
Answer: A. Seven
AI explanation
Let me work through it carefully.
Analyze the question: 6244 − 1621 = 4323, all in base x. Equivalently, 1621 + 4323 = 6244 in base x.
Column-by-column check (units first):
Units: 1 + 3 = 4. No carry, which works in any base above 4.
Tens: 2 + 2 = 4. No carry.
Hundreds: 6 + 3 = 9. The digit in the answer is 2, so 9 = x + 2, which gives x = 7, with a carry of 1.
Thousands: 1 + 4 + carry 1 = 6. This matches the 6 in 6244.
So x = 7.
Verification with base-10 conversion (base 7):
6244₇ = 6(343) + 2(49) + 4(7) + 4 = 2058 + 98 + 28 + 4 = 2188
1621₇ = 343 + 6(49) + 2(7) + 1 = 343 + 294 + 14 + 1 = 652
4323₇ = 4(343) + 3(49) + 2(7) + 3 = 1372 + 147 + 14 + 3 = 1536
2188 − 652 = 1536 ✓
Also, the digit 6 appears, so the base must be greater than 6, and 7 fits.
Answer: A. Seven
Tip: In base questions like this, convert subtraction to addition (check the result + subtrahend = minuend). Then look for the column where a carry happens: the sum minus the digit written equals the base.
AI can make mistakes. Report anything that looks wrong.
37.
The area of a sector of a circle with radius 7cm is 51.3 cm $^2$ . Calculate, correct to the nearest whole number, the angle of the sector. (Take $\pi$ = $\frac{22}{7}$ )
1. A.60 $^0$
2. B.120 $^0$
3. C.150 $^0$
4. D.150 $^0$
Show answer
Answer: B. 120 $^0$
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
38.
The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the variance of the distribution.
1. A.35
2. B.36
3. C.40
4. D.50
Show answer
Answer: A. 35
AI explanation
Step 1: Find the mean Sum = 59 + 44 + 53 + 49 + 57 + 40 + 48 + 50 = 59+44 = 103; +53 = 156; +49 = 205; +57 = 262; +40 = 302; +48 = 350; +50 = 400 Mean = 400 / 8 = 50 Step 2: Find the deviations from the mean and square them | x | x − 50 | (x − 50)² | |---|---|---| | 59 | 9 | 81 | | 44 | −6 | 36 | | 53 | 3 | 9 | | 49 | −1 | 1 | | 57 | 7 | 49 | | 40 | −10 | 100 | | 48 | −2 | 4 | | 50 | 0 | 0 | Sum of squares = 81 + 36 + 9 + 1 + 49 + 100 + 4 + 0 = 280 Step 3: Calculate the variance Variance = Σ(x − mean)² / n = 280 / 8 = 35 (Using n − 1 would give 280/7 = 40, which is option C. But WASSCE questions on "variance of a distribution" use the population formula, dividing by n.) Answer: A (35) Tip: Always compute the mean first, then the deviations. Check that the deviations sum to zero (9 − 6 + 3 − 1 + 7 − 10 − 2 + 0 = 0), which confirms your mean is right. In WASSCE, variance = Σ(x − x̄)²/n unless the question says "sample variance."
AI can make mistakes. Report anything that looks wrong.
39.
The probability that Amaka will pass an examination is $\frac{3}{7}$ and that Bala will pass is $\frac{4}{9}$ . Find the probability that both will pass the examination.
1. A. $\frac{2}{21}$
2. B. $\frac{4}{21}$ .
3. C. $\frac{5}{21}$
4. D. $\frac{9}{21}$
Show answer
Answer: B. $\frac{4}{21}$ .
AI explanation
Analyze the question: We want the probability that both Amaka and Bala pass. Their results are independent events, since one person's performance doesn't affect the other's. Concept: For independent events A and B: P(A and B) = P(A) × P(B) Solution: P(both pass) = 3/7 × 4/9 = (3 × 4) / (7 × 9) = 12/63 Divide the top and bottom by 3: = 4/21 Check: 12 ÷ 3 = 4 and 63 ÷ 3 = 21, so the fraction simplifies correctly to 4/21. Tip: In probability, "and" means multiply, and "or" means add (for mutually exclusive events). Before multiplying fractions, cross-cancel common factors. Here the 3 in the numerator and the 9 in the denominator cancel to leave 1/7 × 4/3, which is also 4/21.
AI can make mistakes. Report anything that looks wrong.
40.
The first term of an Arithmetic Progression (A.P) is 2 and the last term is 29. If the common difference is 3, how many terms are in the A.P.?
1. A.8
2. B.9
3. C.10
4. D.11
Show answer
Answer: C. 10
AI explanation
Analyze the question We are given an A.P. with first term a = 2, last term l = 29, and common difference d = 3. We need the number of terms, n. Concept The nth term of an A.P. is: Tₙ = a + (n − 1)d Solution Set the last term equal to 29: 29 = 2 + (n − 1)(3) 29 − 2 = 3(n − 1) 27 = 3(n − 1) n − 1 = 9 n = 10 Check: The terms are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29. Counting them gives 10 terms, and the last one is 29. ✓ Answer: C. 10 Tip: For an A.P., the number of terms is n = (l − a)/d + 1. Here that is (29 − 2)/3 + 1 = 9 + 1 = 10. Do not forget the "+1", because the difference only counts the gaps between terms, and there is one more term than there are gaps. Choosing 9 is the usual mistake.
AI can make mistakes. Report anything that looks wrong.
41.
Factorize completely: 27x $^2$ - 48y $^2$
1. A.3(3x + 4y)(3x - 4y)
2. B.3(3x + 4y)(3x + 4y)
3. C.3(9x - 16y)(9x + 16y)
4. D.3(9x - 16y)(9x - 16y)
Show answer
Answer: A. 3(3x + 4y)(3x - 4y)
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
42.
The perimeter of a rectangular garden is 90 m. If the width is 7 m less than the length, find the length of the garden.
1. A.19 m
2. B.23 m
3. C.24 m
4. D.26 m
Show answer
Answer: D. 26 m
AI explanation
Analyze the question: We are given the perimeter of a rectangle (90 m) and a relationship between width and length (width = length − 7). We need the length. Concept: Perimeter of a rectangle = 2(length + width) = 2(l + w) Solution: Let the length = l, so the width = l − 7. 2(l + l − 7) = 90 2(2l − 7) = 90 2l − 7 = 45 2l = 52 l = 26 m Check: Width = 26 − 7 = 19 m. Perimeter = 2(26 + 19) = 2(45) = 90 m ✓ Answer: The length is 26 m, which is option D. Note that 19 m (option A) is the width, not the length, which is a common trap. Tip: Always re-read what the question asks for (length or width) before choosing. A quick way to start is to divide the perimeter by 2 to get l + w = 45, then find two numbers that add to 45 and differ by 7: 26 and 19.
AI can make mistakes. Report anything that looks wrong.
43.
The following are the masses (in kg) of members in a club: 59, 44, 53, 49, 57, 40, 48, and 50. Calculate the mean mass.
1. A.44 kg
2. B.50 kg
3. C.40 kg
4. D.53 kg
Show answer
Answer: B. 50 kg
AI explanation
Analyze the question: We need the mean (average) of 8 masses.
Concept: Mean = (sum of all values) ÷ (number of values)
Solution:
Add the masses step by step:
59 + 44 = 103
103 + 53 = 156
156 + 49 = 205
205 + 57 = 262
262 + 40 = 302
302 + 48 = 350
350 + 50 = 400
Sum = 400 kg, and there are 8 members.
Mean = 400 ÷ 8 = 50 kg
Answer: Option B (50 kg).
Tip: For mean questions, always count your values first (here, 8) and add carefully in pairs to avoid slips. You can also check by picking a guess (like 50) and adding the deviations: +9, -6, +3, -1, +7, -10, -2, 0 = 0, which confirms 50 is the mean.
AI can make mistakes. Report anything that looks wrong.
44.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
45.
Simplify: (2p - q) $^2$ - (p + q) $^2$
1. A.3p(p - 2q)
2. B.2p(p - 3q)
3. C.3p(2p - q)
4. D.2p(3p - q)
Show answer
Answer: A. 3p(p - 2q)
Get a step-by-step AI explanation in the app Get a step-by-step AI explanation in the app
46.
Find the sum for which $1,250.00 will amount to$ 2,031.25 at 12.5% per annum simple interest.
1. A.2 years
2. B.3 years
3. C.4 years
4. D.5 years
Show answer
Answer: D. 5 years
AI explanation
Analyze the question: The wording says "find the sum," but the options are all lengths of time. So the question is really asking for the time it takes $1,250.00 to grow to$ 2,031.25 at 12.5% simple interest per annum.
Concept: For simple interest,
I = PRT/100
Amount A = P + I
Solution:
Interest earned = 2,031.25 − 1,250.00 = $781.25
Substitute into I = PRT/100:
781.25 = (1,250 × 12.5 × T) / 100
Simplify the right side:
(1,250 × 12.5) / 100 = 15,625 / 100 = 156.25
So 781.25 = 156.25 × T
Solve for T:
T = 781.25 / 156.25 = 5 years
Check: Yearly interest = 156.25. Over 5 years, 156.25 × 5 = 781.25. Then 1,250 + 781.25 = 2,031.25 ✓
Answer: D (5 years)
Tip: When the options don't match the wording of the question, look at what the options are (years, naira, percent) to see which quantity is really being asked for. Also, always find the interest first by subtracting the principal from the amount: I = A − P.
AI can make mistakes. Report anything that looks wrong.
47.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
48.
Given that P = {p: 1< p < 20}, where p is an integer and R = {r : 0 $\leq$ r $\leq$ 25, where r is a multiple of 4}. Find P ∩ R
1. A.{4, 8, 10, 16}
2. B.{4, 8, 12, 16}
3. C.{4, 8, 12, 16, 20}
4. D.{4, 8, 12, 16, 20, 24}
Show answer
Answer: B. {4, 8, 12, 16}
AI explanation
Analyze the question: We need the elements common to both sets P and R.
Concept: The intersection (P ∩ R) contains only the elements that belong to both sets.
Step 1: List P P = {p: 1 < p < 20}, with p an integer. The strict inequalities exclude both 1 and 20, so P = {2, 3, 4, ..., 19}
Step 2: List R R = {r: 0 ≤ r ≤ 25, r a multiple of 4}. The inequalities here include 0 and 25, so R = {0, 4, 8, 12, 16, 20, 24}
Step 3: Find the common elements
0 is not in P (since 0 is not greater than 1)
4, 8, 12 and 16 are all between 1 and 20, so they are in P
20 is not in P (since p < 20 is strict)
24 is not in P
So P ∩ R = {4, 8, 12, 16}
Answer: B
Tip: Always check the inequality signs at the boundaries. "<" excludes the end value, while "≤" includes it. Here, the strict "p < 20" is what removes 20 from the answer, and this is exactly where option C tempts students.
AI can make mistakes. Report anything that looks wrong.
49.
Make R the subject of the relation V = πl(R $^2$ - r $^2$ )
1. A.R = $\sqrt{\frac{V}{πl} + r^2}$
2. B.R = $\sqrt{\frac{V}{πl} - r^2}$
3. C.R = $\sqrt{V - πlr^2}$
4. D.R = $\sqrt{V + πlr^2}$
Show answer
Answer: A. R = $\sqrt{\frac{V}{πl} + r^2}$
AI explanation
Analyze the question: We need to rearrange V = πl(R² − r²) so that R stands alone on one side.
Concept: Use inverse operations to undo what has been done to R, working from the outside in: undo the multiplication, then the subtraction, then the square.
Solution:
Start with the formula: V = πl(R² − r²)
Divide both sides by πl: V/(πl) = R² − r²
Add r² to both sides: R² = V/(πl) + r²
Take the square root of both sides (R is a positive length): R = √(V/(πl) + r²)
Checking the options:
A: √(V/(πl) + r²) matches our result.
B has a minus sign, which is wrong because r² is added, not subtracted.
C and D fail to divide V by πl properly. They multiply πlr² instead.
Answer: A
Tip: When making a variable the subject, "undo" operations in reverse order of BODMAS. Here the bracket was multiplied by πl, so divide first. Then move −r² across, which becomes +r². Finally, take the square root. Always remember that moving a term across the equals sign changes its sign.
AI can make mistakes. Report anything that looks wrong.
50.
Consider the following statements: m = Edna is respectful n = Edna is brilliant, If m ⇒ n, which of the following is valid?
1. A.¬n ⇒ ¬m.
2. B.¬m ⇒ ¬n.
3. C.n ⇒ ¬m.
4. D.m ⇒ n.
Show answer
Answer: A. ¬n ⇒ ¬m.
AI explanation
Analyze the question: We are given the conditional statement m ⇒ n ("If Edna is respectful, then Edna is brilliant"). We must pick the option that is a valid statement that follows from it.
Concept: For a conditional p ⇒ q, there are three related statements:
Converse: q ⇒ p (not logically equivalent)
Inverse: ¬p ⇒ ¬q (not logically equivalent)
Contrapositive: ¬q ⇒ ¬p (logically equivalent to the original)
Solution:
Original: m ⇒ n
Contrapositive: ¬n ⇒ ¬m, which means "If Edna is not brilliant, then Edna is not respectful."
Checking each option:
A. ¬n ⇒ ¬m: this is the contrapositive, so it is always valid.
B. ¬m ⇒ ¬n: this is the inverse, which is not necessarily valid. Edna could be brilliant without being respectful.
C. n ⇒ ¬m: this does not follow from m ⇒ n.
D. m ⇒ n: this is the given statement itself. It is true by assumption, but it is not a new deduction. The question asks which is valid, and the intended answer is the equivalent form, the contrapositive.
A note on D: D is technically true because it was given.
Answer: A
Tip: Remember "flip and negate." To get the contrapositive, swap the two statements and negate both. The contrapositive always has the same truth value as the original. The converse and inverse do not.
AI can make mistakes. Report anything that looks wrong.