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WAEC Further Mathematics: practice questions.
12 free questions with answers and explanations, plus the topics to revise.
Below are free WAEC Further 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 They are original eZine questions, written and reviewed by teachers in the style of the WAEC WASSCE; we do not publish past questions.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 Further Mathematics bank holds 208 questions across 20 topics (counted 29 October 2026); the largest topics are Equations, Functions, Kinematics.
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 Further Mathematics practice questions
Choose an option to check it, or open the answer. Each is an eZine practice question (original, teacher-reviewed).
Question 1 · Introduction to Operation Research
In the graphical method of linear programming, the feasible region is
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Answer: B. the set of points that satisfy all the constraints at the same time
Every point of the feasible region satisfies all the constraints simultaneously; the optimum is then found at one of its vertices. The best point is the optimal solution, not the region; satisfying only one constraint is not enough; the objective line is moved over the region but does not define it.
eZine practice question (original, teacher-reviewed)
Question 2 · Statistics I (Data Presentation and Summarisation)
Marks recorded as whole numbers are grouped in the class 20 – 29. What are the class boundaries?
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Answer: A. 19.5 and 29.5
For whole-number data the boundaries lie half a unit outside the limits: 20 − 0.5 = 19.5 and 29 + 0.5 = 29.5. 20 and 29 are the class limits; 20.5 adds instead of subtracting at the lower end; 19 and 30 subtract and add a whole unit.
eZine practice question (original, teacher-reviewed)
Question 3 · Introduction to Operation Research
Minimise C = 5x + 4y subject to x + y ≥ 6, x ≥ 2, y ≥ 1. The corner points of the (unbounded) feasible region are (2, 4) and (5, 1). Find the minimum value of C.
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Answer: A. 26
C(2, 4) = 10 + 16 = 26 and C(5, 1) = 25 + 4 = 29; because the region opens upwards and to the right, C only increases away from these corners, so the minimum is 26. 29 is the larger corner value; 24 comes from (0, 6), which violates x ≥ 2; 30 comes from (6, 0), which violates y ≥ 1.
eZine practice question (original, teacher-reviewed)
Question 4 · Equations
Find the quadratic equation whose roots are 2/3 and −1.
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Answer: D. 3x² + x − 2 = 0
Sum = 2/3 − 1 = −1/3, product = −2/3. x² + (1/3)x − 2/3 = 0, i.e. 3x² + x − 2 = 0. Check: (3x − 2)(x + 1) ✓. 3x² − x − 2 has roots −2/3 and 1 (sign of the sum wrong); 3x² − 5x + 2 has roots 2/3 and 1; 2x² + x − 3 has roots 1 and −3/2.
eZine practice question (original, teacher-reviewed)
Question 5 · Functions
Using the vertical line test, which of these graphs does NOT represent y as a function of x?
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Answer: A. The circle x² + y² = 9
A vertical line such as x = 0 meets the circle at (0, 3) and (0, −3): one input, two outputs, so it is not a function. Every vertical line meets the straight line, the parabola and y = 2ˣ at most once, so those are functions.
eZine practice question (original, teacher-reviewed)
Question 6 · Introduction to Problem Solving and Algorithms
Arrange these steps in the correct order for an algorithm to find the area of a rectangle: (I) OUTPUT area (II) INPUT length, breadth (III) area = length × breadth (IV) START (V) END
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Answer: D. IV, II, III, I, V
An algorithm starts, takes input, processes it, gives output and ends: START, INPUT, compute area, OUTPUT, END = IV, II, III, I, V. Computing before input uses values that do not yet exist; input before START is outside the algorithm; output before processing prints an undefined area.
eZine practice question (original, teacher-reviewed)
Question 7 · Kinematics
A velocity–time graph shows a car accelerating uniformly from rest to 12 m s⁻¹ in 4 s, moving at 12 m s⁻¹ for 6 s, then decelerating uniformly to rest in 2 s. Find the total distance travelled.
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Answer: A. 108 m
Distance = area under the graph = ½(4)(12) + 6(12) + ½(2)(12) = 24 + 72 + 12 = 108 m. 144 m treats the whole 12 s as constant speed; 96 m leaves out the last triangle; 72 m counts only the constant-speed part.
eZine practice question (original, teacher-reviewed)
Question 8 · Flowcharts
In a flowchart a counter c starts at 1. Each pass through the loop prints a name and then adds 1 to c, and the decision "Is c > 6?" sends control back to the print step when the answer is No. How many names are printed?
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Answer: A. 6
Names are printed for c = 1, 2, 3, 4, 5, 6; after the sixth print c becomes 7 > 6 and the loop ends. 5 forgets the first pass when c = 1; 7 counts the value that ends the loop; 1 assumes the flowchart has no loop.
eZine practice question (original, teacher-reviewed)
Question 9 · Sets
n(A) = 20, n(B) = 15 and n(A ∪ B) = 28. Find the number of elements in A only.
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Answer: C. 13
n(A ∩ B) = 20 + 15 − 28 = 7, so A only = 20 − 7 = 13. 7 is n(A ∩ B); 8 is B only (15 − 7); 5 is n(A) − n(B), which has no meaning here.
eZine practice question (original, teacher-reviewed)
Question 10 · Binary Operations
Today is a Wednesday in Abuja. Using modulo 7 arithmetic, what day of the week will it be 100 days from today?
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Answer: A. Friday
100 = 14 × 7 + 2, so 100 ≡ 2 (mod 7). Two days after Wednesday is Friday. Thursday counts only one day forward; Saturday uses 100 ≡ 3; Tuesday counts backwards.
eZine practice question (original, teacher-reviewed)
Question 11 · Equations
For what value of k is x = 4 the solution of kx + 6 = 3x − 2k?
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Answer: D. k = 1
Substitute x = 4: 4k + 6 = 12 − 2k, so 6k = 6 and k = 1. k = −1 is a sign slip; k = 3 comes from matching the x-coefficients; k = 6 forgets to divide by 6.
eZine practice question (original, teacher-reviewed)
Question 12 · Statistics II (Measures of Central Tendency)
Find the mean of the distribution: class 1–5 (f = 4), 6–10 (f = 6), 11–15 (f = 8), 16–20 (f = 2).
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Answer: D. 10
Midpoints 3, 8, 13, 18. Σfx = 12 + 48 + 104 + 36 = 200, Σf = 20, mean = 200/20 = 10. 10.5 is the average of the midpoints, ignoring the frequencies; 50 divides by the number of classes (4); 13 is the midpoint of the modal class 11–15, which is not the mean.
eZine practice question (original, teacher-reviewed)
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Practise free on eZine →Topics in eZine's WAEC Further Mathematics practice bank
- Equations (15)
- Functions (13)
- Kinematics (13)
- Vectors (13)
- Binomial Expansion (12)
- Trigonometry (11)
- Binary Operations (10)
- Inequalities (10)
- Logarithms (10)
- Logic (10)
- Sequence and Series (10)
- Sets (10)
- Statistics III (Measures of Dispersion) (10)
- Surds (10)
- Indices (9)
- Statistics I (Data Presentation and Summarisation) (9)
- Statistics II (Measures of Central Tendency) (9)
- Flowcharts (8)
- Introduction to Operation Research (8)
- Introduction to Problem Solving and Algorithms (8)
Published questions per topic, counted 29 October 2026. eZine does not reproduce WAEC's own Further Mathematics syllabus here; check the official syllabus with your school or at the WAEC website.