2025 WAEC Nov/Dec Further Mathematics (Obj/Essay) Answers

Get free 2025 WAEC Nov/Dec Further Mathematics (Obj/Essay) Questions and Answers for Private Candidates | WAEC Further Maths Questions and Answers(11th Nov, 2025).

The 2025 WAEC GCE (Nov/Dec) Further Mathematics Examination is one of the most challenging papers for candidates in the second series of the General Certificate Examination. This subject is designed for students with strong mathematical backgrounds and prepares them for advanced courses in engineering, physical sciences, statistics, and related fields.

According to the official WAEC timetable, the exam will hold on Tuesday, 11th November, 2025 and consists of two papers: Paper 2 (Essay): 08:30 a.m. – 11:00 a.m. (2 hours 30 minutes) and Paper 1 (Objective): 01:00 p.m. – 02:00 p.m. (1 hour). get free waec gce futher mathematics syllabus questions and answers.

This article will walk you through the structure of the exam, provide sample questions and solutions, and share expert tips to help you succeed.

Exam Overview

• Exam: WAEC GCE (Nov/Dec) Further Mathematics

• Date: Tuesday, 11th November, 2025

• Paper 2: Further Mathematics/Mathematics 2 (Essay) – 08:30 a.m. – 11:00 a.m.

• Paper 1: Further Mathematics/Mathematics 1 (Objective) – 01:00 p.m. – 02:00 p.m.

• Total Duration: 3 hours 30 minutes

Paper 2 tests your ability to solve structured problems, while Paper 1 focuses on multiple-choice questions that assess speed and accuracy.

Structure of the Papers

1. Further Mathematics Paper 2 (Essay):

• Duration: 2 hours 30 minutes

• Consists of 10–12 questions divided into sections (Pure Mathematics, Mechanics, Statistics).

• Candidates are usually required to answer any 8 questions, selecting a mix from different sections.

• Solutions must show full workings, as marks are awarded for correct steps, not just final answers.

2. Further Mathematics Paper 1 (Objective):

• Duration: 1 hour

• Consists of 50 multiple-choice questions covering the full syllabus.

• Tests speed, accuracy, and ability to apply formulas quickly.

Sample Questions and Answers (Practice)

Here are sample-style practice questions to prepare for the 2025 WAEC GCE (Nov/Dec) Further Mathematics exam:

Sample Paper 2 (Essay) Questions

Question 1:
Solve the quadratic equation 3×2−5x−2=03x^2 – 5x – 2 = 03x2−5x−2=0.

Answer:
Using the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​

Here $a=3,b=-5,c=-2$.

x=5±(−5)2−4(3)(−2)6=5±25+246=5±76x = \frac{5 \pm \sqrt{(-5)^2 – 4(3)(-2)}}{6} = \frac{5 \pm \sqrt{25+24}}{6} = \frac{5 \pm 7}{6}x=65±(−5)2−4(3)(−2)​​=65±25+24​​=65±7​ x=2orx=−13x = 2 \quad \text{or} \quad x = -\frac{1}{3}x=2orx=−31​

Question 2:
Differentiate y=4×3−3×2+2x−5y = 4x^3 – 3x^2 + 2x – 5y=4x3−3x2+2x−5 with respect to $x$.

Answer:

dydx=12×2−6x+2\frac{dy}{dx} = 12x^2 – 6x + 2dxdy​=12x2−6x+2

Question 3:
Find the mean and variance of the numbers 3, 5, 7, 9.

Answer:
Mean:

xˉ=3+5+7+94=6\bar{x} = \frac{3+5+7+9}{4} = 6xˉ=43+5+7+9​=6

Variance:

σ2=(3−6)2+(5−6)2+(7−6)2+(9−6)24=9+1+1+94=5\sigma^2 = \frac{(3-6)^2+(5-6)^2+(7-6)^2+(9-6)^2}{4} = \frac{9+1+1+9}{4} = 5σ2=4(3−6)2+(5−6)2+(7−6)2+(9−6)2​=49+1+1+9​=5

Sample Paper 1 (Objective) Questions

Question 1:
If sin⁡θ=35\sin \theta = \frac{3}{5}sinθ=53​, find $\cos \theta$.

Answer:

cos⁡θ=1−sin⁡2θ=1−925=45\cos \theta = \sqrt{1 – \sin^2 \theta} = \sqrt{1 – \frac{9}{25}} = \frac{4}{5}cosθ=1−sin2θ​=1−259​​=54​

Question 2:
Simplify: 2x2y4xy2\frac{2x^2y}{4xy^2}4xy22x2y​.

Answer:

=x2y= \frac{x}{2y}=2yx

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Tips for Passing 2025 WAEC GCE (Nov/Dec) Further Mathematics

1. Master the Syllabus: Revise topics in Pure Mathematics, Mechanics, and Statistics.

2. Practice Past Questions: Get familiar with common question types and patterns.

3. Work on Speed: Time yourself while solving objective questions.

4. Show All Workings: In Paper 2, marks are given for steps, not just final answers.

5. Memorize Key Formulas: Quadratic equations, differentiation, integration, and probability formulas should be at your fingertips.

6. Stay Calm: Manage your time well — spend more time on questions you can solve correctly.

Common Areas to Focus On

• Algebra & Functions: Quadratics, inequalities, logarithms

• Calculus: Differentiation, integration, maxima & minima problems

• Vectors & Matrices: Addition, multiplication, determinants

• Mechanics: Motion, velocity, acceleration, Newton’s laws

• Probability & Statistics: Mean, median, variance, probability distributions

Conclusion

The 2025 WAEC GCE (Nov/Dec) Further Mathematics Papers 1 and 2 scheduled for Tuesday, 11th November, 2025 are crucial for candidates pursuing careers in science, engineering, and technology. By practicing past questions, revising key formulas, and managing time effectively, you can excel in both the essay and objective papers.

Use the sample questions above for practice, focus on understanding each topic, and approach the exam with confidence. With proper preparation, you can score very high and secure your path to advanced studies.