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WAEC Mathematics: practice questions.
12 free questions with answers and explanations, plus the topics to revise.
Below are free WAEC Mathematics practice questions with answers and explanations. They are original eZine questions, written and reviewed by teachers in the style of the WAEC WASSCE; we do not publish past questions. eZine's published WAEC Mathematics bank holds 457 questions across 31 topics (counted 29 October 2026); the largest topics are Trigonometry, Mensuration, Chord Properties.
eZine's WAEC subject mock uses 50 questions in 60 minutes estimated. WAEC sets the objective paper's length per subject and publishes it in each subject's syllabus; eZine holds no WAEC paper figures yet, so this is a practice default.
WAEC Mathematics practice questions
Choose an option to check it, or open the answer. Each is an eZine practice question (original, teacher-reviewed).
Question 1 · Surds
Simplify √75 − √27.
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Answer: D. 2√3
√75 = √(25 × 3) = 5√3 and √27 = √(9 × 3) = 3√3, so √75 − √27 = 2√3. √48 subtracts under the root (√a − √b ≠ √(a − b)); 4√3 = √48 is the same error simplified; 8√3 adds instead of subtracting.
eZine practice question (original, teacher-reviewed)
Question 2 · Gradient of a Curve
Find the gradient of the line 3y − 6x + 2 = 0.
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Answer: B. 2
Make y the subject: 3y = 6x − 2 ⇒ y = 2x − 2/3, so the gradient (coefficient of x) is 2. −2 has a sign error; 6 forgets to divide by 3; −2/3 is the y-intercept.
eZine practice question (original, teacher-reviewed)
Question 3 · Surds
Simplify √50 + √18 − √8.
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Answer: A. 6√2
√50 = 5√2, √18 = 3√2, √8 = 2√2; 5√2 + 3√2 − 2√2 = 6√2. √60 combines under one root (illegal); 10√2 adds all three; 4√2 subtracts 3√2 as well.
eZine practice question (original, teacher-reviewed)
Question 4 · Trigonometry
From the top of a 60 m high water tower in Jos, the angle of depression of a car parked on level ground is 35°. How far is the car from the foot of the tower, correct to one decimal place? (tan 35° = 0.7002)
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Answer: C. 85.7 m
The angle of depression from the top equals the angle of elevation from the car (alternate angles), so tan 35° = 60/d ⇒ d = 60/0.7002 = 85.7 m. 42.0 m multiplies instead of dividing; 104.6 m is the line-of-sight (slant) distance; 34.4 m uses sine instead of tangent (sin relates opposite to hypotenuse, and the hypotenuse is not given).
eZine practice question (original, teacher-reviewed)
Question 5 · Trigonometry
If sin theta = 3/5 and theta is an acute angle, find tan theta.
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Answer: A. 3/4
sin theta = opposite/hypotenuse = 3/5, so the adjacent side = sqrt(25 - 9) = 4. tan theta = opposite/adjacent = 3/4. 4/3 inverts the ratio (that is 1/tan); 4/5 is cos theta; 5/4 is 1/cos theta.
eZine practice question (original, teacher-reviewed)
Question 6 · Proof of Some Basic Theorems
Each exterior angle of a regular polygon is 24°. How many sides does the polygon have?
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Answer: A. 15
The exterior angles of any convex polygon add up to 360°, so n = 360/24 = 15. 13 subtracts 2 as if using the interior-angle sum (n - 2) x 180; 24 repeats the angle; 30 is 720/24.
eZine practice question (original, teacher-reviewed)
Question 7 · Chord Properties
AB is a diameter of a circle and C is a point on the circumference. If ∠CAB = 35°, find ∠CBA.
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Answer: D. 55°
The angle in a semicircle is a right angle: ∠ACB = 90°. Then ∠CBA = 180° − 90° − 35° = 55°. 35° assumes the triangle is isosceles; 145° = 180° − 35° ignores the right angle; 70° doubles 35°.
eZine practice question (original, teacher-reviewed)
Question 8 · Mensuration
A sector of a circle of radius 10 cm with angle 216° is folded to form a cone, with no overlap. Find the height of the cone.
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Answer: D. 8 cm
The arc becomes the base circumference: (216/360) × 2π × 10 = 2πr ⇒ r = 6 cm. The radius of the sector becomes the slant height l = 10 cm. h = √(l² − r²) = √(100 − 36) = 8 cm. 6 cm is the base radius; 10 cm is the slant height; 11.66 cm adds the squares instead of subtracting.
eZine practice question (original, teacher-reviewed)
Question 9 · Gradient of a Curve
A student draws the tangent to the curve y = x² at the point (3, 9). The tangent also passes through the point (2, 3). What is the gradient of the curve at x = 3?
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Answer: C. 6
Gradient of tangent = (9 − 3)/(3 − 2) = 6, so the gradient of y = x² at x = 3 is 6. 3 is just the x-coordinate; 9 is the y-coordinate; 18 doubles the y-coordinate (2y instead of 2x). Read the gradient from two points on the drawn tangent, using a large triangle for accuracy.
eZine practice question (original, teacher-reviewed)
Question 10 · Mensuration
Find the area of a sector of a circle of radius 7 cm which subtends an angle of 72° at the centre. (Take pi = 22/7.)
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Answer: A. 30.8 cm^2
Area of sector = (theta/360) x pi r^2 = (72/360) x (22/7) x 49 = (1/5) x 154 = 30.8 cm^2. 8.8 is the arc length formula (2 pi r theta/360); 154 is the area of the whole circle; 61.6 doubles the sector.
eZine practice question (original, teacher-reviewed)
Question 11 · Simple Equations and Variations
y varies directly as the square root of x, and y = 12 when x = 16. Find x when y = 21.
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Answer: B. 49
y = k√x ⇒ 12 = 4k ⇒ k = 3. Then 21 = 3√x ⇒ √x = 7 ⇒ x = 49. 28 treats y ∝ x (16 × 21/12); 7 stops at √x; 441 squares 21 instead of 7.
eZine practice question (original, teacher-reviewed)
Question 12 · Trigonometry
From a point on level ground 30 m from the foot of a vertical mast in Enugu, the angle of elevation of the top of the mast is 30°. Find the height of the mast, correct to one decimal place.
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Answer: B. 17.3 m
tan 30° = height/30, so height = 30 tan 30° = 30 x 0.5774 = 17.3 m. 15.0 uses sin 30°; 26.0 uses cos 30°; 52.0 divides by tan 30° instead of multiplying.
eZine practice question (original, teacher-reviewed)
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Practise free on eZine →Topics in eZine's WAEC Mathematics practice bank
- Trigonometry (52)
- Mensuration (40)
- Chord Properties (29)
- Quadratic Equations (28)
- Sequence and Series (21)
- Sets (20)
- Simple Equations and Variations (20)
- Probability (18)
- Simultaneous Linear and Quadratic Equations (17)
- Measures of Central Tendency (15)
- Proof of Some Basic Theorems (15)
- Measures of Dispersion (14)
- Logarithms (13)
- Gradient of a Curve (12)
- Linear Inequalities (12)
- Number Base System (1) (12)
- Cumulative Frequency Graph (Ogive) (11)
- Data Presentation (11)
- Number and Numeration (11)
- Construction (10)
- Laws of Indices (10)
- Surds (10)
- Bearings (9)
- Algebraic Fractions (8)
Published questions per topic, counted 29 October 2026. eZine does not reproduce WAEC's own Mathematics syllabus here; check the official syllabus with your school or at the WAEC website.