Original Mathematics WAEC Past Questions and Answers PDF (Updated to 2024)

Preparing for the West African Examinations Council (WAEC) Mathematics exam can be challenging, but with the right resources, success is within your reach. One of the best ways to boost your confidence and enhance your exam readiness is by practicing WAEC past questions and reviewing their answers. The good news? You can now access free Mathematics WAEC past questions and answers online!

Why Use WAEC Past Questions for Mathematics?

WAEC past questions provide invaluable insight into the exam pattern, commonly tested topics, and question formats. By practicing these past questions, you:

Get familiar with the style and structure of WAEC Mathematics questions.
Identify recurring topics and areas where you need improvement.
Develop time management skills to complete the exam within the allotted time.
Build confidence by solving real exam questions before the exam day.

What to Expect in WAEC Mathematics Exam?

The WAEC Mathematics exam generally covers key areas including algebra, geometry, trigonometry, statistics, probability, and arithmetic. The questions range from objective multiple-choice to theory and problem-solving questions. By working through past questions, you gain practical exposure to:

Simplification and factorization problems.
Solving linear and quadratic equations.
Calculating areas, volumes, and surface areas of various shapes.
Working with percentages, ratios, and proportions.
Handling data interpretation and statistical analysis.
Probability questions related to everyday scenarios.

Benefits of Accessing Free WAEC Mathematics Past Questions and Answers

Cost-Effective Learning: Accessing free questions eliminates the need to purchase expensive preparatory materials.
Self-Assessment: Answers included enable instant feedback, helping you assess your understanding and progress.
Flexible Study: You can practice anytime and anywhere, making learning more convenient.
Exam Simulation: Regular practice simulates exam conditions, reducing anxiety and improving performance.

MATHEMATICS PAST QUESTIONS AND ANSWERS

Here are some Mathematics Past Questions and Answers below:

If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first four terms.
(a) 45
(b) 60
(c) 63
(d) 54
Answer: (a) 45
Simplify 1025−623+31025−623+3.
(a) 405
(b) 405
(c) 405
(d) 405
Answer: 405
Find the 8th term of the A.P. −3,−1,1,…−3,−1,1,…
(a) 11
(b) 12
(c) 13
(d) 14
Answer: (a) 11
Which of the following number lines represents the solution to the inequality: −9≤2(3x−7)<5−9≤2(3x−7)<5?
(a) x<2x<2
(b) x≤2x≤2
(c) x>2x>2
(d) x≥2x≥2
Answer: (b) x≤2x≤2
The volume of a cone of base radius 3.5 cm and height 42 cm (π = 22/7) is:
(a) 154 cm³
(b) 77 cm³
(c) 147 cm³
(d) 1617 cm³
Answer: (d) 1617 cm³
Find the perimeter of a circle whose diameter is 11.2 cm. (Use π = 3.14)
(a) 35.2 cm
(b) 22.4 cm
(c) 17.6 cm
(d) 70.4 cm
Answer: (a) 35.2 cm
The sum of 2 times a number and 3 times another number is 4. The first number minus the second number is -3. What are the numbers?
(a) -3 and 6
(b) -1 and 2
(c) 2 and 5
(d) 6 and 3
Answer: (a) -3 and 6
The product of 5 and the sum of 12 and a certain number is 10. Find the number.
(a) -15
(b) -5
(c) 5
(d) -10
Answer: (b) -5
How many vertices has a cuboid?
(a) 4
(b) 8
(c) 12
(d) 6
Answer: (b) 8
Which of these is NOT a property of a kite?
(a) One pair of opposite angles are equal
(b) Diagonals meet at right angles
(c) Two lines of symmetry
(d) Two pairs of adjacent sides are equal
Answer: (c) Two lines of symmetry
Simplify 1101102−10110121101102−1011012.
(a) 1000
(b) 1001
(c) 1010
(d) 1011
Answer: (c) 1010
Find the sum of the prime numbers between 1 and 10.
(a) 17
(b) 28
(c) 18
(d) 23
Answer: (d) 23 (2 + 3 + 5 + 7 = 17, corrected to 17)
Remove brackets in (q+3)(2q+3)(q+3)(2q+3).
(a) 2q2+9q+92q2+9q+9
(b) 2q2+5q+32q2+5q+3
(c) 3q2+9q+93q2+9q+9
(d) q2+9q2+9
Answer: (a) 2q2+9q+92q2+9q+9
What is the coefficient of bb in the expression 2b2−5b+182b2−5b+18?
(a) -5
(b) 2
(c) 18
(d) 5
Answer: (a) -5
Represent x≥3x≥3 on a number line.
If a certain number xx is subtracted from 3, the result is less than 5. Find the possible values of xx.
(a) x>−2x>−2
(b) x<2x<2
(c) x>2x>2
(d) x<−2x<−2
Answer: (a) x>−2x>−2
Simplify: 3a−(4a+6a)3a−(4a+6a).
(a) -7a
(b) 5a
(c) 7a
(d) -5a
Answer: (a) -7a
The sum of the exterior angles of any polygon is:
(a) 180°
(b) 360°
(c) 540°
(d) 720°
Answer: (b) 360°
Find the number of sides of a polygon whose interior angles sum to 3240°.
(a) 18
(b) 20
(c) 22
(d) 26
Answer: (b) 20
Calculate sin⁡73.4∘sin73.4∘ (using tables or calculator).
(a) 0.9563
(b) 0.2857
(c) 0.9578
(d) 0.9583
Answer: (a) 0.9563
Find the tenth term of the A.P. 3, 7, 11, 15, …
(a) 37
(b) 39
(c) 43
(d) 45
Answer: (b) 39
The area of a triangle with base 10 cm and height 6 cm is:
(a) 20 cm²
(b) 30 cm²
(c) 60 cm²
(d) 16 cm²
Answer: (b) 30 cm²
If x=3x=3 and y=4y=4, find the value of 2×2+3y2x2+3y.
(a) 33
(b) 30
(c) 32
(d) 29
Answer: (a) 33
The solution set of ∣x−2∣<3∣x−2∣<3 is:
(a) −5<x<1−5<x<1
(b) −1<x<5−1<x<5
(c) −3<x<3−3<x<3
(d) 1<x<51<x<5
Answer: (b) −1<x<5−1<x<5
Calculate 25×3752×73.
(a) 512125
(b) 635356
(c) 312123
(d) 5775
Answer: (b) 635356
The sum of angles in a quadrilateral is:
(a) 180°
(b) 270°
(c) 360°
(d) 540°
Answer: (c) 360°
Find the value of kk if 4k – 7 = 13.
(a) 4
(b) 5
(c) 6
(d) 3
Answer: (b) 5
The distance between points (3, 4) and (7, 1) is:
(a) 5 units
(b) 6 units
(c) 4 units
(d) 3 units
Answer: (a) 5 units
Simplify (23)−2(32)−2.
(a) 4994
(b) 9449
(c) 2332
(d) −32−23
Answer: (b) 9449
The mode of the data set 2, 5, 9, 5, 2, 4, 5 is:
(a) 2
(b) 4
(c) 5
(d) 9
Answer: (c) 5
Evaluate xx if 2x + 3 = 7.
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
The formula for the volume of a sphere is:
(a) 43πr334πr3
(b) πr2hπr2h
(c) 13πr2h31πr2h
(d) 2πrh2πrh
Answer: (a) 43πr334πr3
Find the next number in the sequence: 5, 10, 20, 40, …
(a) 50
(b) 60
(c) 80
(d) 90
Answer: (c) 80
log⁡101000=?log101000=?
(a) 2
(b) 3
(c) 4
(d) 1
Answer: (b) 3
Find the coordinate of the midpoint of the line segment joining (2, 3) and (6, 7):
(a) (3, 4)
(b) (4, 5)
(c) (5, 6)
(d) (6, 7)
Answer: (b) (4, 5)
The surface area of a cube with side 4 cm is:
(a) 96 cm²
(b) 64 cm²
(c) 48 cm²
(d) 32 cm²
Answer: (a) 96 cm²
What is the measure of each interior angle of a regular hexagon?
(a) 120°
(b) 108°
(c) 90°
(d) 135°
Answer: (a) 120°
Simplify 2×2+3x−7×2+4x2x2+3x−7×2+4x.
(a) −5×2+7x−5×2+7x
(b) 5×2−7x5x2−7x
(c) −9×2+7x−9×2+7x
(d) 9×2−7x9x2−7x
Answer: (a) −5×2+7x−5×2+7x
The gradient of the line passing through points (1, 2) and (3, 8) is:
(a) 3
(b) 2
(c) 4
(d) 5
Answer: (a) 3
The area of a trapezium with parallel sides 3 cm and 7 cm and height 4 cm is:
(a) 20 cm²
(b) 15 cm²
(c) 25 cm²
(d) 10 cm²
Answer: (a) 20 cm²
Which expression represents the expansion of (x+2)2(x+2)2?
(a) x2+2x+4×2+2x+4
(b) x2+4x+4×2+4x+4
(c) x2+2x+2×2+2x+2
(d) x2+2x+8×2+2x+8
Answer: (b) x2+4x+4×2+4x+4
The radius of a circle with circumference 31.4 cm (use π=3.14π=3.14) is:
(a) 10 cm
(b) 5 cm
(c) 15 cm
(d) 7 cm
Answer: (b) 5 cm
Find the equation of a line with slope 2 and passing through the point (3,4).
(a) y=2x+1y=2x+1
(b) y=2x+2y=2x+2
(c) y=2x−2y=2x−2
(d) y=3x+4y=3x+4
Answer: (a) y=2x+1y=2x+1
The sum of the first 8 natural numbers is:
(a) 36
(b) 30
(c) 40
(d) 44
Answer: (a) 36
The solution of x2−5x+6=0x2−5x+6=0 is:
(a) 2 and 3
(b) 1 and 6
(c) 5 and 6
(d) 3 and 4
Answer: (a) 2 and 3
Find xx if 3x+4=2x−53x+4=2x−5.
(a) -9
(b) 9
(c) 5
(d) -5
Answer: (a) -9
The resultant force of 5 N and 7 N acting in opposite directions is:
(a) 2 N
(b) 12 N
(c) 35 N
(d) 0 N
Answer: (a) 2 N
The volume of a cylinder with radius 7 cm and height 10 cm (use π=22/7π=22/7) is:
(a) 1540 cm³
(b) 220 cm³
(c) 770 cm³
(d) 210 cm³
Answer: (a) 1540 cm³
(3x)2(3x)2 equals:
(a) 6x
(b) 9x
(c) 9x²
(d) 6x²
Answer: (c) 9x²
Solve for xx: 4(x+3)=204(x+3)=20.
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (a) 2
The value of log⁡1000log1000 is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3
Find the area of a rectangle with length 12 cm and width 7 cm.
(a) 82 cm²
(b) 84 cm²
(c) 74 cm²
(d) 79 cm²
Answer: (b) 84 cm²
The perimeter of a square of side 6 cm is:
(a) 12 cm
(b) 18 cm
(c) 24 cm
(d) 36 cm
Answer: (c) 24 cm
If f(x)=3x−4f(x)=3x−4, find f(2)f(2).
(a) 6
(b) 2
(c) 0
(d) 12
Answer: (a) 2 (Calculation: 3×2−4=6−4=23×2−4=6−4=2)
What is the value of (23)2(23)2?
(a) 64
(b) 16
(c) 32
(d) 8
Answer: (a) 64
Factorize: x2−9×2−9
(a) (x−3)2(x−3)2
(b) (x−3)(x+3)(x−3)(x+3)
(c) (x+9)(x−1)(x+9)(x−1)
(d) (x−9)(x+1)(x−9)(x+1)
Answer: (b) (x−3)(x+3)(x−3)(x+3)
The quadratic equation x2+5x+6=0x2+5x+6=0 has roots:
(a) -2 and -3
(b) 2 and 3
(c) -1 and -6
(d) 1 and 6
Answer: (a) -2 and -3
Convert degrees 45∘45∘ to radians.
(a) π/4π/4
(b) π/2π/2
(c) π/3π/3
(d) π/6π/6
Answer: (a) π/4π/4
Which of the following is NOT a perfect square?
(a) 36
(b) 49
(c) 54
(d) 64
Answer: (c) 54
2x+3=72x+3=7, find xx.
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
Find the sum of interior angles of a pentagon.
(a) 540°
(b) 360°
(c) 720°
(d) 900°
Answer: (a) 540°
What is the probability of getting a head in a single toss of a coin?
(a) 0.25
(b) 0.5
(c) 0.75
(d) 1
Answer: (b) 0.5
The cube root of 27 is:
(a) 9
(b) 6
(c) 3
(d) 1
Answer: (c) 3
What is the next term in the sequence: 2, 6, 18, 54, …?
(a) 108
(b) 162
(c) 216
(d) 324
Answer: (b) 162
Calculate the simple interest on ₦1,000 at 5% per annum after 2 years.
(a) ₦50
(b) ₦100
(c) ₦150
(d) ₦200
Answer: (b) ₦100
Find the greatest common divisor (GCD) of 24 and 36.
(a) 12
(b) 6
(c) 18
(d) 24
Answer: (a) 12
The least common multiple (LCM) of 8 and 12 is:
(a) 36
(b) 24
(c) 48
(d) 60
Answer: (b) 24
If y=3x+2y=3x+2, find yy when x=5x=5.
(a) 13
(b) 15
(c) 17
(d) 16
Answer: (c) 17
The median of 5, 2, 8, 3, 7 is:
(a) 3
(b) 5
(c) 7
(d) 8
Answer: (b) 5

THEORY QUESTIONS

Simplify: $3 x - 2 + 5 x + 6$
Answer: $8 x + 4$
Solve for $x$ : $2 x + 5 = 17$
Answer: $x = 6$
Find the area of a triangle with base 8 cm and height 5 cm.
Answer: $20 cm^{2}$
Calculate $y$ if $3 y - 7 = 2 y + 5$
Answer: $y = 12$
Probability of picking a blue ball from 5 red, 3 blue, 2 green balls.
Answer: $10 3$
Evaluate: $5^{2} - 4 \times 3$
Answer: $25 - 12 = 13$
Factorize $x^{2} - 16$
Answer: $(x - 4) (x + 4)$
Find the length of the hypotenuse in a right triangle with legs 6 cm and 8 cm.
Answer: 10 cm
Calculate the volume of a cylinder with radius 7 cm and height 10 cm ( $π = 7 22$ ).
Answer: $1540 cm^{3}$
Simplify: $5 4 + 3 2$
Answer: $15 22$
Write 65 in binary.
Answer: 1000001
Solve: $3 x + 4 = 16$
Answer: $x = 4$
Find the perimeter of a rectangle with length 12 cm and width 7 cm.
Answer: 38 cm
Find the median of the set: 3, 7, 8, 12, 15
Answer: 8
Calculate simple interest on #15,000 at 8% for 3 years.
Answer: #3,600
Express 0.75 as a fraction.
Answer: $4 3$
A car travels 180 km in 3 hours; find its speed.
Answer: 60 km/h
Solve the simultaneous equations:
$x + y = 10$
$2 x - y = 3$
Answer: $x = 13/3, y = 17/3$
Find the LCM of 12, 16 and 20.
Answer: 240
Find the area of a circle with radius 14 cm ( $π = 7 22$ ).
Answer: $616 cm^{2}$
Convert 45° to radians.
Answer: $4 π$ radians
Find the slope of the line passing through points (2,3) and (5,11).
Answer: $3 8$
Find the next number in the sequence: 2, 4, 8, 16, …
Answer: 32
Simplify $49$ .
Answer: 7
Calculate the hypotenuse of a triangle with legs 9 cm and 12 cm.
Answer: 15 cm
Find the mean of 6, 10, 14, 18, 22.
Answer: 14
Calculate the surface area of a cube with side length 5 cm.
Answer: 150 cm²
Solve the inequality: $3 x - 7 < 11$
Answer: $x < 6$
Factorize: $x^{2} + 5 x + 6$
Answer: $(x + 2) (x + 3)$
Calculate compound interest on #10,000 at 5% per annum for 2 years.
Answer: #10,512.50
Simplify: $2 (x + 3) - 4 (x - 1)$
Answer: $- 2 x + 10$
Find the value of $x$ if $x^{2} = 49$ .
Answer: $x = \pm 7$
Calculate the perimeter of a square with side 9 cm.
Answer: 36 cm
Find the mode of the set: 2, 4, 4, 6, 7.
Answer: 4
Solve for $x$ : $4 x - 7 = 13$ .
Answer: $x = 5$
Convert $8 3$ to a decimal.
Answer: 0.375
Calculate the surface area of a sphere with radius 7 cm.
Answer: Approximately $615.75 cm^{2}$ (using $4 π r^{2}$ )
Factorize: $9 x^{2} - 16$ .
Answer: $(3 x - 4) (3 x + 4)$
Find the next number in the pattern: 5, 10, 20, 40, …
Answer: 80
Calculate the mean of these numbers: 10, 15, 20, 25, 30.
Answer: 20
Solve $5 x + 3 = 2 x + 18$ .
Answer: $x = 5$
Find the length of an arc with radius 10 cm and angle $6 0^{\circ}$ .
Answer: $6 1 \times 2 π \times 10 = 6 20 π \approx 10.47 cm$
Simplify: $3 2 \times 4 9$ .
Answer: $2 3$
Convert 120 minutes to hours.
Answer: 2 hours
Solve: $x^{2} - 5 x + 6 = 0$ .
Answer: $x = 2$ or $x = 3$
Find the gradient of the line through (3, 4) and (7, 12).
Answer: $4 8 = 2$
Calculate simple interest on #20,000 at 10% for 2 years.
Answer: #4,000
Find the range of the set: 4, 9, 15, 2, 18.
Answer: 16
Expand $(x + 3)^{2}$ .
Answer: $x^{2} + 6 x + 9$
Find the radius of a circle with circumference 31.4 cm ( $π = 3.14$ ).
Answer: 5 cm
Solve for $y$ if $3 y + 2 = 14$ .
Answer: $y = 4$
Factorize: $x^{2} - 7 x + 12$ .
Answer: $(x - 3) (x - 4)$
Calculate the volume of a cube with side 4 cm.
Answer: $64 cm^{3}$
Convert decimal 0.6 to fraction.
Answer: $5 3$
Find the LCM of 8 and 12.
Answer: 24
Find the sum of the angles in a triangle.
Answer: 180°
Calculate the area of a rectangle with length 15 cm and width 9 cm.
Answer: 135 cm²
Find the value of $x$ in $2 x + 3 = 7 x - 12$ .
Answer: $x = 3$
Simplify: $8 5 - 8 3$ .
Answer: $4 1$
Find the average speed of a vehicle that covers 200 km in 4 hours.
Answer: 50 km/h
Evaluate $7^{2} + 3^{2}$ .
Answer: 49 + 9 = 58
Find the equation of the line with slope 3 passing through (1, 2).
Answer: $y - 2 = 3 (x - 1)$ or $y = 3 x - 1$
Calculate the amount accrued on #5,000 at 5% compound interest for 2 years.
Answer: #5,512.50
Find the probability of rolling a 4 or a 5 on a fair six-sided die.
Answer: $6 2 = 3 1$
Express $5 \times 1 0^{3}$ in standard form.
Answer: 5000
Find the value of $x$ if $x = 8$ .
Answer: $x = 64$
Find the circumference of a circle with diameter 12 cm ( $π = 3.14$ ).
Answer: $37.68 cm$
Simplify: $12 \div 3 \times 2$ .
Answer: 8
Calculate the surface area of a cube with edge 6 cm.
Answer: 216 cm²
Solve for $x$ : $x^{2} = 81$ .
Answer: $x = \pm 9$
Find the next number in the sequence: 1, 4, 9, 16, …
Answer: 25
Convert 3 hours into seconds.
Answer: 10,800 seconds
Calculate the height of a triangle with area 30 cm² and base 10 cm.
Answer: 6 cm
Factorize: $x^{2} - 25$ .
Answer: $(x - 5) (x + 5)$
Find the mean of numbers: 8, 12, 15, 7.
Answer: 10.5
Solve $2 x - 5 = 17$ .
Answer: $x = 11$
Find the LCM of 5, 7, 10.
Answer: 70
Find 15% of 200.
Answer: 30
Calculate the volume of a rectangular prism with dimensions 6 cm, 8 cm, and 5 cm.
Answer: 240 cm³
Write 0.125 as a fraction.
Answer: $8 1$
Simplify $4 (3 x + 7) - 2 (5 x - 2)$ .
Answer: $12 x + 28 - 10 x + 4 = 2 x + 32$
Find the perimeter of an equilateral triangle with side length 11 cm.
Answer: 33 cm
Solve for $y$ : $4 y + 3 = 19$ .
Answer: $y = 4$
Find the mode in the set: 2, 3, 4, 4, 5, 5, 5, 6.
Answer: 5
Calculate the time taken to travel 150 km at speed 50 km/h.
Answer: 3 hours
Convert 0.2 to a percentage.
Answer: 20%
Calculate the area of a trapezium with parallel sides 10 cm and 8 cm and height 6 cm.
Answer: $54 cm^{2}$
Solve $x^{2} - 4 x - 21 = 0$ .
Answer: $x = 7$ or $x = - 3$
Express 0.625 as a fraction.
Answer: $8 5$
Calculate the circumference of a circle with radius 9 cm ( $π = 3.14$ ).
Answer: $56.52 cm$
Simplify: $(2 x)^{3}$ .
Answer: $8 x^{3}$
Calculate simple interest on #18,000 at 9% for 5 years.
Answer: #8,100
Find the surface area of a cylinder with radius 6 cm and height 10 cm ( $π = 3.14$ ).
Answer: $502.4 cm^{2}$
Find the roots of $x^{2} + 3 x + 2 = 0$ .
Answer: $x = - 1$ or $x = - 2$
Calculate the hypotenuse of a right triangle with legs 5 cm and 12 cm.
Answer: 13 cm
Find the average of 5, 10, 15, 20, 25.
Answer: 15
Simplify: $4 3 \div 3 2$ .
Answer: $8 9$
Calculate the median of: 7, 3, 5, 9, 11.
Answer: 7
Solve for $x$ : $3 x + 7 = 16$ .
Answer: $x = 3$
Find the product of $7$ and $8$ .
Answer: 56

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