Consider the statements: p: Stephen is intelligent q: Stephen is good at Mathematics If p⇒q, which of the following is a valid conclusion?

B. If Stephen is not good at Mathematics, then he is not intelligent

A. If Stephen is good at Mathematics, then he is intelligent

B. If Stephen is not good at Mathematics, then he is not intelligent

C. If Stephen is not intelligent, then he is not good at Mathematics

D. If Stephen is not good at Mathematics, then he is intelligent

Solve 6x$^2$ = 5x - 1

C. x = $\frac{1}{2}$, $\frac{1}{3}$

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

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WAEC (WASSCE) 2022

2022 WAEC (WASSCE) Mathematics Past Questions and Answers

The 2022 WAEC (WASSCE) Mathematics past questions with answers: 46 objective questions from the 2022 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.
A trader made a loss of 15% when an article was sold. Find the ratio of the selling price : cost price
1. A.3:20
2. B.3:17
3. C.17:20
4. D.20:23
Show answer
Answer: C. 17:20
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2.
Three boys shared D 10,500.00 in the ratio 6:7:8. Find the largest share.
1. A.4000
2. B.5000
3. C.4500
4. D.3500
Show answer
Answer: A. 4000
AI explanation
Analyze the question: An amount of D 10,500 is shared among three boys in the ratio 6:7:8. We need the largest share, which belongs to the boy with ratio 8.
Concept: To share an amount in a ratio, add the ratio parts to get the total number of parts. Then each share = (part ÷ total parts) × total amount.
Solution:
Total parts = 6 + 7 + 8 = 21
Value of one part = 10,500 ÷ 21 = 500
Shares:
6 parts = 6 × 500 = 3,000
7 parts = 7 × 500 = 3,500
8 parts = 8 × 500 = 4,000
Check: 3,000 + 3,500 + 4,000 = 10,500 ✓
The largest share is 8 × 500 = D 4,000.
Tip: In ratio-sharing questions, first find the value of one part (total ÷ sum of ratio). Then multiply by each ratio number. Always add the shares at the end to confirm they equal the original amount. Here, 10,500 ÷ 21 divides neatly, which is a good sign you are on track.
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3.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
4.
In the diagram, triangle MNR is inscribed in circle MNR, and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR
1. A.39º
2. B.80º
3. C.110º
4. D.141º
Show answer
Answer: A. 39º
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5.
If a = 3 and b = -7, find the value of $\frac{5b+(a+b)^2}{(a-b)^2}$
1. A.0.51
2. B.0.91
3. C.-0.19
4. D.-0.51
Show answer
Answer: C. -0.19
AI explanation
Step 1: Analyze the question We substitute a = 3 and b = -7 into the expression and simplify, being careful with signs.
Step 2: Work out each part
Numerator: 5b + (a + b)² • 5b = 5(-7) = -35 • a + b = 3 + (-7) = -4, so (a + b)² = 16 • Numerator = -35 + 16 = -19
Denominator: (a - b)² • a - b = 3 - (-7) = 10 • (a - b)² = 100
Step 3: Divide
$\frac{-19}{100} = -0.19$
Step 4: Answer The value is -0.19, which is option C.
Tip: When a variable is negative, put it in brackets before squaring or subtracting. This avoids the common mistakes of writing a - b = 3 - 7 = -4, or of treating (-4)² as -16. A negative number squared is always positive, but 5b stays negative here.
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6.
A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?
1. A.3.611m
2. B.4.521m
3. C.4.792m
4. D.3.962m
Show answer
Answer: C. 4.792m
AI explanation
Analyze the question
The ladder, wall and ground form a right-angled triangle:
Hypotenuse = ladder = 6 m
Angle between ladder and ground = 53°
Height reached on the wall = the side opposite the 53° angle
Concept
Since we have the hypotenuse and want the opposite side, use sine:
sin θ = opposite / hypotenuse
Solution
Height = 6 × sin 53°
sin 53° ≈ 0.7986
Height = 6 × 0.7986 ≈ 4.792 m
Check against the options
This matches option C (4.
Tip
Use SOH-CAH-TOA to choose the ratio:
Sin = Opposite/Hypotenuse (used here)
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
For ladder problems, the height on the wall is usually L sin θ, and the distance of the foot from the wall is L cos θ, when θ is measured from the ground. Make sure your calculator is in degree mode.
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7.
A rectangle with width $\frac{3}{4}$ cm and area 3 $\frac{3}{8}$ cm $^2$ . Find the length
1. A.6cm
2. B.4 $\frac{1}{2}$ cm
3. C.2 $\frac{5}{8}$ cm
4. D.12cm
Show answer
Answer: B. 4 $\frac{1}{2}$ cm
AI explanation
Analyze the question: We know the width and the area of a rectangle, and we need the length.
Concept: Area = length × width, so Length = Area ÷ Width.
Solution:
Convert the mixed number to an improper fraction: 3 3/8 = (3×8 + 3)/8 = 27/8
Divide the area by the width: Length = 27/8 ÷ 3/4
Dividing by a fraction means multiplying by its reciprocal: Length = 27/8 × 4/3 = 108/24
Simplify: 108/24 = 9/2 = 4 1/2 cm
Check: 4 1/2 × 3/4 = 9/2 × 3/4 = 27/8 = 3 3/8 cm². ✓
Answer: B (4½ cm)
Tip: For any "find the missing side" question, rearrange the formula first (Length = Area ÷ Width). Then use "keep, change, flip" for fraction division: keep the first fraction, change ÷ to ×, and flip the second fraction. Always check by multiplying back.
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8.
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
1. A.15
2. B.17
3. C.20
4. D.23
Show answer
Answer: B. 17
AI explanation
Analyze the question: You are given the sizes of two sets and the size of their intersection (the elements they share). You need the size of their union (all elements in A or B or both). Concept: When you add n(A) and n(B), the elements in both sets get counted twice. So you subtract the overlap once: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) Solution: n(A ∪ B) = 8 + 12 − 3 n(A ∪ B) = 20 − 3 n(A ∪ B) = 17 Check: Only A has 8 − 3 = 5 elements, only B has 12 − 3 = 9 elements, and both have 3 elements. Total = 5 + 9 + 3 = 17. ✔ Tip: Always remember "add, then subtract the overlap." A common mistake is picking 20 (option C) by forgetting to subtract the intersection. In a Venn diagram, fill in the middle (the intersection) first, then work outward.
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9.
The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area
1. A.30cm $^2$
2. B.40cm $^2$
3. C.60cm $^2$
4. D.80cm $^2$
Show answer
Answer: B. 40cm $^2$
AI explanation
Analyze the question: We are given the length of a rectangle (10 cm) and its perimeter (28 cm). We need to find the width first, then the area.
Concept:
Perimeter of a rectangle: P = 2(l + w)
Area of a rectangle: A = l × w
Solution:
Step 1: Substitute into the perimeter formula. 28 = 2(10 + w)
Step 2: Divide both sides by 2. 14 = 10 + w
Step 3: Solve for w. w = 14 − 10 = 4 cm
Step 4: Find the area. A = l × w = 10 × 4 = 40 cm²
Check: Perimeter = 2(10 + 4) = 2(14) = 28 cm ✓
Answer: The area is 40 cm², which is option B.
Tip: For perimeter problems, always halve the perimeter first. Here, l + w = 28 ÷ 2 = 14, so w = 14 − 10 = 4. This saves time in the exam. Don't mix up perimeter (the distance around the shape) with area (the space inside it).
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10.
A boy 1.4 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.
1. A.70º
2. B.47º
3. C.19º
4. D.8º
Show answer
Answer: B. 47º
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11.
A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?
1. A.0.45
2. B.0.65
3. C.0.85
4. D.0.95
Show answer
Answer: C. 0.85
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12.
The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm $^2$ , find the perpendicular distance between the parallel sides.
1. A.5cm
2. B.7cm
3. C.10cm
4. D.15cm
Show answer
Answer: C. 10cm
AI explanation
Analyze the question: We are given a trapezium with parallel sides 9 cm and 12 cm and an area of 105 cm². We need the perpendicular height (the distance between the parallel sides).
Concept: The area of a trapezium is
Area = ½ × (sum of parallel sides) × height A = ½(a + b)h
Solution:
Substitute the values: 105 = ½ × (9 + 12) × h
Add the parallel sides: 105 = ½ × 21 × h
Multiply both sides by 2: 210 = 21h
Divide by 21: h = 210 ÷ 21 = 10
So the perpendicular distance is 10 cm.
Check: ½ × (9 + 12) × 10 = ½ × 21 × 10 = 105 cm² ✓
Tip: In trapezium questions, first find the sum of the parallel sides, then use "Area × 2 ÷ (sum of parallel sides)" to get the height directly: 105 × 2 ÷ 21 = 10. Always check by substituting your answer back into the formula.
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13.
What value of p will make (x $^2$ - 4x + p) a perfect square?
1. A.-2
2. B.16
3. C.4
4. D.-8
Show answer
Answer: C. 4
AI explanation
Analyze the question: We want x² - 4x + p to be a perfect square, meaning it can be written as (x - a)² for some number a.
Concept: Completing the square. (x - a)² = x² - 2ax + a²
Solution: Compare x² - 4x + p with x² - 2ax + a²:
Coefficient of x: -2a = -4, so a = 2
Constant term: p = a² = 2² = 4
Shortcut: p = (half of the coefficient of x)² = (-4/2)² = (-2)² = 4
Check: x² - 4x + 4 = (x - 2)² ✓
The other options fail:
p = -2: x² - 4x - 2 has discriminant 16 + 8 = 24, which is not 0
p = 16: discriminant 16 - 64 = -48, not 0
p = -8: discriminant 16 + 32 = 48, not 0
A quadratic is a perfect square only when its discriminant b² - 4ac = 0. Here 16 - 4p = 0, so p = 4.
Tip: For x² + bx + p to be a perfect square, always use p = (b/2)². Halve the middle coefficient, then square it. The sign of b does not matter, because squaring makes the result positive.
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14.
If 4 $^{3x}$ = 16 $^{x+1}$ , find the value of x
1. A.2
2. B.3
3. C.4
4. D.5
Show answer
Answer: A. 2
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15.
Given that sin (5x-28)° = cos (3x-50)", 0°≤ x ≤ 90°, find the value of x.
1. A.39
2. B.32
3. C.21
4. D.14
Show answer
Answer: C. 21
AI explanation
Analyze the question: We have sin(5x − 28)° = cos(3x − 50)°, and we need x between 0° and 90°.
Concept: sin θ = cos(90° − θ), so if sin A = cos B, then A + B = 90° (for angles in the acute range).
Solution:
(5x − 28) + (3x − 50) = 90 8x − 78 = 90 8x = 168 x = 21
Check:
5(21) − 28 = 105 − 28 = 77°, so sin 77°
3(21) − 50 = 63 − 50 = 13°, so cos 13°
sin 77° = cos(90° − 77°) = cos 13° ✓
Other possibilities: Cosine can also be equal for angles related by A = 90° − B + 360°n or sin A = sin(180° − A), which gives other equations:
sin A = cos B means A = 90° − B or A = 90° + B (since cos B = cos(−B), sin(90°+B) = cos B).
Using A = 90° + B: 5x − 28 = 90 + 3x − 50 gives 2x = 68, x = 34. Check: sin(142°) = sin 38° ≈ 0.616, and cos(52°) ≈ 0.616. This also works mathematically, but 34 is not among the options.
Answer: C (21)
Tip: When you see sin = cos, immediately think "complementary angles": add the two angles and set the sum equal to 90°. It saves a lot of time in the exam. Then check your answer against the options.
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16.
Consider the statements: p: Stephen is intelligent q: Stephen is good at Mathematics If p⇒q, which of the following is a valid conclusion?
1. A.If Stephen is good at Mathematics, then he is intelligent
2. B.If Stephen is not good at Mathematics, then he is not intelligent
3. C.If Stephen is not intelligent, then he is not good at Mathematics
4. D.If Stephen is not good at Mathematics, then he is intelligent
Show answer
Answer: B. If Stephen is not good at Mathematics, then he is not intelligent
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17.
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the lower quartile
1. A.12
2. B.13
3. C.15
4. D.20
Show answer
Answer: C. 15
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18.
Mary has $3.00 more than Ben but$ 5.00 less than Jane. If Mary has $ x, how much does Jane and Ben have altogether?
1. A.$(2x-8)
2. B.$(2x+8)
3. C.$(2x-2)
4. D.$(2x+2)
Show answer
Answer: D. $(2x+2)
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19.
Simplify $\frac{2-18m^2}{1+3m}$
1. A.2[1+3m]
2. B.2[1-3m]
3. C.2[1-3m $^2$ ]
4. D.2[1+3m $^2$ ]
Show answer
Answer: B. 2[1-3m]
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20.
If the equations x $^2$ - 5x + 6 = 0 and x $^2$ + px + 6 = 0 have the same roots, find the value of p.
1. A.5
2. B.6
3. C.-5
4. D.-6
Show answer
Answer: C. -5
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21.
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the mean
1. A.33.35
2. B.35.54
3. C.34.45
4. D.36.44
Show answer
Answer: C. 34.45
AI explanation
Analyze the question: We need the mean (average) age of the 11 members.
Concept: Mean = (Sum of all values) ÷ (Number of values)
Solution:
Add the ages step by step:
12 + 47 = 59
59 + 49 = 108
108 + 15 = 123
123 + 43 = 166
166 + 41 = 207
207 + 13 = 220
220 + 39 = 259
259 + 43 = 302
302 + 41 = 343
343 + 36 = 379
Sum = 379, and there are 11 values.
Mean = 379 ÷ 11 = 34.4545... ≈ 34.45
Tip: When adding many numbers, count your data points first (here 11) so you divide by the right number. You can also group numbers that add to round figures, such as 12 + 47 + 41 = 100 to speed up your addition and reduce mistakes.
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22.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
23.
If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x $^2$ -9y $^2$ )?
1. A.20
2. B.16
3. C.2
4. D.8
Show answer
Answer: D. 8
AI explanation
Analyze the question: We are given two equations and asked for 25x² − 9y². Notice that this expression is a difference of two squares.
Concept: a² − b² = (a + b)(a − b)
Here, 25x² = (5x)² and 9y² = (3y)², so:
25x² − 9y² = (5x + 3y)(5x − 3y)
Solution:
Substitute the given values directly:
(5x + 3y)(5x − 3y) = 4 × 2 = 8
Check (optional): Adding the equations gives 10x = 6, so x = 0.6. Then 3y = 4 − 3 = 1, so y = 1/3.
25x² = 25(0.36) = 9
9y² = 9(1/9) = 1
9 − 1 = 8 ✓
Answer: D (8)
Tip: Whenever you see a difference of two squares in the target expression and the given equations look like (a + b) and (a − b), don't solve for x and y. Just multiply the two equations. This saves time in the exam.
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24.
The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error
1. A.4 $\frac{4}{7}$
2. B.2 $\frac{6}{7}$
3. C.2 $\frac{7}{9}$
4. D.4 $\frac{7}{9}$
Show answer
Answer: B. 2 $\frac{6}{7}$
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25.
Evaluate 23 x 54 (mod 7)
1. A.2
2. B.3
3. C.5
4. D.6
Show answer
Answer: B. 3
AI explanation
Analyze the question: We need the remainder when 23 × 54 is divided by 7. The question could be read in two ways: as 23 × 54 in the usual base ten, or as numbers in another base. The "(mod 7)" means we want a remainder after dividing by 7.
Concept: In modular arithmetic, you can reduce each number mod 7 first, then multiply: (a × b) mod n = [(a mod n) × (b mod n)] mod n
Solution:
23 ÷ 7 = 3 remainder 2, so 23 ≡ 2 (mod 7)
54 ÷ 7 = 7 remainder 5, so 54 ≡ 5 (mod 7)
Multiply the remainders: 2 × 5 = 10, and 10 ÷ 7 = 1 remainder 3
So 23 × 54 ≡ 3 (mod 7).
Check directly: 23 × 54 = 1242. Since 7 × 177 = 1239, the remainder is 1242 − 1239 = 3. ✓
Tip: In mod questions, reduce each number first so you work with small values. Then check by doing the full multiplication if time allows.
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26.
Find the area of the sector OPSQ
1. A.15.40cm $^2$
2. B.17.64cm $^2$
3. C.23.10cm $^2$
4. D.32.34cm $^2$
Show answer
The answer for this question isn't available yet.
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27.
The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line
1. A.-5
2. B.-3
3. C.3
4. D.5
Show answer
Answer: A. -5
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28.
Solve $\frac{y+2}{4}$ - $\frac{y-1}{3}$ > 1
1. A.y < -10
2. B.y < -2
3. C.y < 2
4. D.y < 10
Show answer
Answer: B. y < -2
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29.
The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y
1. A.2
2. B.4
3. C.6
4. D.8
Show answer
Answer: C. 6
AI explanation
Analyze the question: We're told the mean of x and y is 4, and we need the mean of the four numbers x, 2x, y and 2y. Concept: Mean = (sum of the numbers) ÷ (how many numbers there are). Solution: Step 1: Use the first piece of information. (x + y) / 2 = 4 So x + y = 8 Step 2: Add up the four numbers. x + 2x + y + 2y = 3x + 3y = 3(x + y) Step 3: Substitute x + y = 8. 3(8) = 24 Step 4: Divide by 4 (there are four numbers). Mean = 24 ÷ 4 = 6 Check with an example: Let x = 3 and y = 5 (their mean is 4). The four numbers are 3, 6, 5, 10. Sum = 24, and 24 ÷ 4 = 6. ✔ The correct option is C. **Tip: When a question gives you a mean, immediately convert it to a sum (mean × count). Here, the four numbers are just 1.5 times the original two numbers' contribution, so the new mean is 4 × 1.5 = 6. Looking for factoring shortcuts like 3(x + y) saves time in the exam.
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30.
Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1/2 and with blue eyes is 1/4. What is the probability that she will give birth to a girl with blue eyes?
1. A.1
2. B. $\frac{3}{4}$
3. C. $\frac{1}{8}$
4. D. $\frac{1}{4}$
Show answer
Answer: C. $\frac{1}{8}$
AI explanation
Analyze the question: We want the probability of two things happening together: the baby is a girl AND has blue eyes. Gender and eye colour are treated as independent events.
Concept: For independent events A and B:
P(A and B) = P(A) × P(B)
Solution:
P(girl) = 1/2
P(blue eyes) = 1/4
P(girl with blue eyes) = 1/2 × 1/4 = 1/8
Check against the options:
A (1) would mean it is certain, which is not the case.
B (3/4) is what you would get by adding 1/2 + 1/4. Adding is for "or" events, not "and" events.
C (1/8) matches our working.
D (1/4) is just the blue-eyes probability and ignores the girl condition.
Answer: C. 1/8
Exam tip: Think of the words as signals. "AND" means multiply (independent events). "OR" means add (for mutually exclusive events). Also, the probability of two events happening together can never be larger than either single probability, so 1/8 being smaller than both 1/2 and 1/4 is a good sanity check.
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31.
If √24 + √96 - √600 = y√6, find the value of y
1. A.4
2. B.2
3. C.-2
4. D.-4
Show answer
Answer: D. -4
AI explanation
Analyze the question: We need to simplify each surd into a multiple of √6, then add and subtract the coefficients.
Concept: Simplify a surd by pulling out perfect-square factors: √(a²b) = a√b.
Solution:
√24 = √(4 × 6) = 2√6
√96 = √(16 × 6) = 4√6
√600 = √(100 × 6) = 10√6
Substitute:
2√6 + 4√6 − 10√6 = (2 + 4 − 10)√6 = −4√6
Comparing with y√6:
y = −4
Tip: In surd questions like this, break every number into (perfect square) × (the common surd). Look for 4, 9, 16, 25, 36, 100 as factors. Once all the surds are the same, you can treat √6 like a variable, just as you would combine "2x + 4x − 10x".
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32.
Solve 6x $^2$ = 5x - 1
1. A.x = 2,3
2. B.x = 0,3
3. C.x = $\frac{1}{2}$ , $\frac{1}{3}$
4. D.x = $\frac{1}{2}$ , $\frac{-1}{3}$
Show answer
Answer: C. x = $\frac{1}{2}$ , $\frac{1}{3}$
AI explanation
Analyze the question: We need to find the values of x that satisfy the quadratic equation 6x² = 5x − 1.
Concept: Move every term to one side so the equation equals zero (ax² + bx + c = 0), then factorise.
Solution:
Rearrange: 6x² − 5x + 1 = 0
Factorise by finding two numbers that multiply to 6 × 1 = 6 and add to −5. These are −2 and −3.
Split the middle term: 6x² − 2x − 3x + 1 = 0
Group: 2x(3x − 1) − 1(3x − 1) = 0
Factor out the common bracket: (3x − 1)(2x − 1) = 0
Set each factor to zero: • 3x − 1 = 0 → x = 1/3 • 2x − 1 = 0 → x = 1/2
Check:
x = 1/2: 6(1/4) = 1.5 and 5(1/2) − 1 = 1.5 ✓
x = 1/3: 6(1/9) = 2/3 and 5(1/3) − 1 = 2/3 ✓
Answer: C
Tip: After rearranging, you can quickly test the options by substituting them back. Also, if the middle term is negative and the last term is positive (like −5x and +1), both roots will be positive. That immediately rules out option D, which has a negative root. For options A and B, the values 2, 3, and 0 are too large or don't work, so you can eliminate them fast.
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33.
M varies directly as n and inversely as the square of p. If M= 3 when n = 2 and p = 1, find M in terms of n and p.
1. A. $\frac{3n}{2p^2}$
2. B. $\frac{2n}{3p^2}$
3. C. $\frac{2n}{3p}$
4. D. $\frac{3n^2}{2p^2}$
Show answer
Answer: A. $\frac{3n}{2p^2}$
AI explanation
Analyze the question: M varies directly as n and inversely as p², so we write a variation equation with a constant k and then find k from the given values.
Concept:
Direct variation: M ∝ n
Inverse variation: M ∝ 1/p²
Combined: M = kn/p²
Solution:
Write the equation: M = kn/p²
Substitute M = 3, n = 2, p = 1: 3 = k(2)/(1)² 3 = 2k k = 3/2
Put k back into the equation: M = (3/2)(n/p²) = 3n/(2p²)
Check: n = 2, p = 1 gives M = 3(2)/(2·1) = 3 ✓
Answer: A. M = 3n/(2p²)
Tip: In variation questions, always follow the same three steps: write the equation with k, find k from the given values, then rewrite the equation with k substituted. "Directly" puts the variable on top, and "inversely" puts it at the bottom. Squares and other powers go with the variable they describe.
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34.
Evaluate, correct to four significant figures, (573.06 x 184.25).
1. A.105600.00
2. B.105622.00
3. C.105500.00
4. D.105632.00
Show answer
Answer: A. 105600.00
AI explanation
Compute 573.06 × 184.25 exactly.
573.06 × 184.25 = 573.06 × 184 + 573.06 × 0.25
573.06 × 184:
573.06 × 100 = 57306
573.06 × 80 = 45844.8
573.06 × 4 = 2292.24
Sum = 57306 + 45844.8 + 2292.24 = 105443.04
573.06 × 0.25 = 143.265
Total = 105443.04 + 143.265 = 105586.305
Rounding to 4 significant figures: 105586.305 → the first four digits are 1, 0, 5, 5, and the next digit is 8, so we round up: 1056 followed by zeros, giving 105600.
Check against the options:
A. 105600.00 is 105586.305 rounded to 4 s.f. ✔
B. 105622.00 has 8 s.f. and isn't the product.
C. 105500.00 would result from rounding down, which is wrong because the next digit is 8.
D. 105632.00 isn't the product.
Answer: A
Tip: For significant figures, count digits from the first non-zero digit. Look at the digit right after your cut-off: 5 or more rounds up, and the remaining places are filled with zeros. Estimating first (≈ 573 × 184 ≈ 105,400) helps you spot wrong options quickly.
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35.
Find the correct to two decimal places, the volume of a sphere whose radius is 3cm. [Take π = $\frac{22}{7}$ ]
1. A.72.57cm $^3$
2. B.88.12cm $^3$
3. C.10529cm $^3$
4. D.113.14cm $^3$
Show answer
Answer: D. 113.14cm $^3$
AI explanation
Analyze the question: We need the volume of a sphere with radius 3 cm, using π = 22/7, correct to 2 decimal places. Concept: Volume of a sphere = (4/3)πr³ Solution: V = (4/3) × (22/7) × 3³ V = (4/3) × (22/7) × 27 The 3 and 27 simplify: 27 ÷ 3 = 9 V = 4 × (22/7) × 9 V = (4 × 22 × 9) / 7 V = 792 / 7 V = 113.142857... V ≈ 113.14 cm³ Checking the options: 113. Tip: Always cancel before multiplying. Since r³ = 27 and the formula has a 3 in the denominator, the cancellation gives a clean 9 and makes the arithmetic faster. Also remember that the sphere formula is (4/3)πr³, while the surface area is 4πr². Examiners often include wrong options that come from mixing up formulas or miscalculating the cube.
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36.
Change 432 $_{five}$ to a number in base three.
1. A.10100 $_{three}$
2. B.11100 $_{three}$
3. C.11101 $_{three}$
4. D.10110 $_{three}$
Show answer
Answer: B. 11100 $_{three}$
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37.
.Find the value of x such that $\frac{1}{x}$ + $\frac{4}{3x}$ - $\frac{5}{6x}$ + 1 = 0
1. A. $\frac{1}{6}$
2. B. $\frac{1}{4}$
3. C. $\frac{-3}{2}$
4. D. $\frac{-7}{6}$
Show answer
Answer: C. $\frac{-3}{2}$
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38.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
39.
A weaver bought a bundle of grass for $50.00 from which he made 8 mats. If each mat was sold for$ 15.00, find the percentage profit.
1. A.240%
2. B.140%
3. C.120%
4. D.40%
Show answer
Answer: B. 140%
AI explanation
Analyze the question: We need the percentage profit. Cost price is $50.00, and he sells 8 mats at$ 15.00 each.
Concept:
Profit = Selling Price − Cost Price
Percentage Profit = (Profit ÷ Cost Price) × 100%
Solution:
Total selling price = 8 × $15.00 =$ 120.00
Profit = $120.00 −$ 50.00 = $70.00
Percentage profit = (70 ÷ 50) × 100% = 140%
Answer: B. 140%
Tip: Percentage profit is always calculated on the cost price, not the selling price. A common mistake is to pick 240% (which is 120/50 × 100, the selling price over cost price) because the student forgot to subtract the cost. Always find the profit first.
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40.
A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area
1. A.126.5cm $^2$
2. B.165.0cm $^2$
3. C.212.0cm $^2$
4. D.214.5cm $^2$
Show answer
Answer: D. 214.5cm $^2$
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41.
Given that log $_3$ 27 = 2x + 1, find the value of x.
1. A.0
2. B.1
3. C.2
4. D.3
Show answer
Answer: B. 1
AI explanation
Analyze the question: We are given log₃ 27 = 2x + 1 and need to find x. Concept: A logarithm answers the question "to what power must the base be raised to give this number?" log_b N = p means b^p = N. Solution: Step 1: Evaluate log₃ 27. 27 = 3³, so log₃ 27 = 3. Step 2: Substitute into the equation. 3 = 2x + 1 Step 3: Solve for x. 2x = 3 − 1 = 2 x = 1 Check: 2(1) + 1 = 3, and log₃ 27 = 3. ✓ Answer: x = 1, which is option B. Tip: Always rewrite the number as a power of the base (27 = 3³, 81 = 3⁴, 125 = 5³). Once you do this, the log is just the exponent. Memorize the powers of 2, 3, and 5 up to about 5 or 6, since they appear often in WASSCE, NECO and JAMB.
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42.
An exterior angle of a regular polygon is 22.5°. Find the number of sides.
1. A.13
2. B.14
3. C.15
4. D.16
Show answer
Answer: D. 16
AI explanation
Analyze the question We're given one exterior angle of a regular polygon (22.5°) and asked for the number of sides. Concept The exterior angles of any polygon add up to 360°. In a regular polygon all exterior angles are equal, so: Number of sides, n = 360° ÷ (one exterior angle) Solution n = 360 ÷ 22.5 To remove the decimal, multiply the top and bottom by 2: n = 720 ÷ 45 = 16 Check: 16 × 22.5 = 360° ✓ The polygon has 16 sides. Tip: For regular polygons, "exterior angle" questions are always solved with n = 360 ÷ exterior angle. If given an interior angle instead, first find the exterior angle with 180° − interior angle. Also, you can quickly check that interior + exterior = 180° (here the interior angle is 157.5°).
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43.
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
1. A.15.5cm $^3$
2. B.21.0cm $^3$
3. C.142cm $^3$
4. D.154cm $^3$
Show answer
Answer: D. 154cm $^3$
AI explanation
Analyze the question: We need the volume of a cone with radius r = 3.5 cm and vertical height h = 12 cm, using π = 22/7.
Concept: The volume of a cone is one-third the volume of a cylinder with the same base and height:
V = (1/3)πr²h
Solution:
Substitute the values: V = (1/3) × (22/7) × (3.5)² × 12
Calculate r²: (3.5)² = 12.25
The 12 and the 1/3 combine nicely: (1/3) × 12 = 4 V = (22/7) × 12.25 × 4
Simplify (22/7) × 12.25: 12.25 ÷ 7 = 1.75, and 1.75 × 22 = 38.5
Multiply by 4: V = 38.5 × 4 = 154 cm³
Tip: When the radius is 3.5 (which is 7/2), the 7 in π = 22/7 cancels nicely. Write r = 7/2, so r² = 49/4. Then V = (1/3)(22/7)(49/4)(12) = 154. Look for such cancellations to save time in the exam. Also, always remember the 1/3 for cones, since forgetting it would give 462 cm³, which is a common trap.
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44.
Find the 17term of the Arithmetic Progression (A.P):-6,-1,4
1. A.-91
2. B.-86
3. C.74
4. D.79
Show answer
Answer: C. 74
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45.
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.
1. A.75
2. B.65
3. C.55
4. D.45
Show answer
Answer: B. 65
AI explanation
Analyze the question: We are given the mean of all 10 numbers and the mean of the first 9 numbers, and we need to find the 10th number.
Concept: Mean = (Sum of numbers) ÷ (Number of numbers), so Sum = Mean × Number of numbers.
Solution:
Sum of all 10 numbers = 56 × 10 = 560
Sum of the first 9 numbers = 55 × 9 = 495
10th number = 560 − 495 = 65
Check: (495 + 65) ÷ 10 = 560 ÷ 10 = 56 ✓
Tip: In "missing number" mean problems, always convert each mean back into a total (mean × count). Then subtract the smaller total from the larger one to get the missing value.
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46.
Make t the subject of k = $m \sqrt \frac{t-p}{r}$
1. A. $\frac{k^2r + p}{m^2}$
2. B. $\frac{k^2r + pm^2}{m^2}$
3. C. $\frac{k^2r - p}{m^2}$
4. D. $\frac{k^2r + p^2}{m^2}$
Show answer
Answer: B. $\frac{k^2r + pm^2}{m^2}$
AI explanation
Analyze the question: We need to rearrange k = m√((t − p)/r) so that t stands alone on one side.
Concept: To remove a square root, square both sides. Then use inverse operations to isolate t.
Solution:
Start with: k = m√((t − p)/r)
Divide both sides by m: k/m = √((t − p)/r)
Square both sides: k²/m² = (t − p)/r
Multiply both sides by r: k²r/m² = t − p
Add p to both sides: t = k²r/m² + p
Combine over a common denominator: t = (k²r + pm²)/m²
Matching to the options: This is exactly option B, (k²r + pm²)/m².
Check the others:
A, (k²r + p)/m², would be wrong because p was not multiplied by m² when combining the fractions.
C has the wrong sign and the same missing m².
D uses p² instead of pm², which has no basis in the working.
Tip: When you have a "subject of the formula" question with a square root, always follow this order: isolate the root, square both sides, then clear the fractions. When you add a plain term like p to a fraction with denominator m², remember to multiply it by m² to get a common denominator. That is where many students lose marks.
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