WASSCE Core Maths Algebra and Functions: 15 Solved Problems with Common Mistakes to Avoid

Introduction

WASSCE Core Mathematics is a critical exam for students aiming to pursue higher education, particularly in fields like engineering, science, and economics. Among its most challenging sections, algebra and functions often trip up even the most prepared students. Common errors—such as misapplying formulas, sign mistakes, or overlooking domain restrictions—can cost valuable marks.

This guide presents 15 solved problems in algebra and functions, each accompanied by a breakdown of frequent mistakes students make and how to avoid them. We’ll also walk through a real case study of a student who transformed their performance by addressing these errors systematically.

Case Study: From Struggling to Scoring High in WASSCE Core Maths

Starting Situation

Amina, a high school student in Ghana, consistently scored below 50% in WASSCE Core Maths mock exams. Her primary struggle was with algebra and functions, where she often lost points due to careless errors. Despite studying hard, she felt her efforts weren’t translating into better results. Her teacher noticed a pattern: Amina frequently misapplied the quadratic formula, forgot to check for extraneous solutions in rational equations, and struggled with domain restrictions in functions.

Actions Taken

Amina decided to tackle her weaknesses head-on. She began by:

• Reviewing past exam papers: She identified that 70% of her mistakes in algebra and functions were due to sign errors and incorrect simplification.
• Focusing on error analysis: Instead of just redoing problems, she analyzed why she got them wrong. For example, she realized she often forgot to square the entire binomial when expanding expressions like (x + 3)².
• Using targeted resources: She turned to Lebocheur’s Bibliothèque, where she found solved problems with step-by-step corrections that highlighted common pitfalls. The platform’s exam-specific guides helped her understand the reasoning behind each solution.
• Practicing with time constraints: She simulated exam conditions by timing herself, which helped her manage stress and improve accuracy under pressure.

Measurable Outcome

After three months of focused practice, Amina’s mock exam scores improved by 25%. In her final WASSCE Core Maths exam, she scored 78%, a significant leap from her previous performance. Her teacher attributed this improvement to her systematic approach to error correction and her use of targeted resources like Lebocheur’s solved problems and guides.

Lessons Learned

Amina’s journey offers several key takeaways for students preparing for WASSCE Core Maths:

• Identify your weak spots: Don’t just practice—analyze where you’re going wrong and why.
• Use resources that explain mistakes: Generic solutions aren’t enough. Look for materials that highlight common errors and how to avoid them.
• Simulate exam conditions: Time management and stress can lead to careless mistakes. Practice under real exam conditions to build confidence.
• Leverage platforms like Lebocheur: The Bibliothèque provides solved problems, exam guides, and targeted corrections that address the exact challenges students face.

15 Solved WASSCE Core Maths Problems: Algebra and Functions

Below are 15 solved problems covering key topics in algebra and functions, each with a focus on common mistakes and how to correct them.

Problem 1: Solving Quadratic Equations

Question: Solve the equation 2x² – 5x + 3 = 0.

Common Mistake: Students often forget to divide all terms by the leading coefficient when using the quadratic formula, leading to incorrect roots.

Solution:
1. Identify coefficients: a = 2, b = -5, c = 3.
2. Apply the quadratic formula: x = [-b ± √(b² – 4ac)] / (2a).
3. Calculate discriminant: b² – 4ac = (-5)² – 4(2)(3) = 25 – 24 = 1.
4. Find roots: x = [5 ± √1] / 4 → x = (5 + 1)/4 = 6/4 = 3/2 or x = (5 – 1)/4 = 4/4 = 1.

Correction: Always ensure the entire denominator (2a) is used, and simplify fractions correctly.

Problem 2: Simplifying Rational Expressions

Question: Simplify (x² – 9) / (x – 3).

Common Mistake: Students often cancel terms incorrectly, forgetting that x² – 9 is a difference of squares.

Solution:
1. Factor numerator: x² – 9 = (x + 3)(x – 3).
2. Simplify: (x + 3)(x – 3) / (x – 3) = x + 3, where x ≠ 3.

Correction: Always factor first before canceling terms. Note the domain restriction (x ≠ 3).

Problem 3: Solving Simultaneous Equations

Question: Solve the system:
1. 3x + 2y = 12
2. 2x – y = 1

Common Mistake: Students often make sign errors when substituting or eliminating variables.

Solution:
1. Solve the second equation for y: y = 2x – 1.
2. Substitute into the first equation: 3x + 2(2x – 1) = 12 → 3x + 4x – 2 = 12 → 7x = 14 → x = 2.
3. Substitute x back: y = 2(2) – 1 = 3.

Correction: Double-check signs during substitution and elimination.

Problem 4: Function Composition

Question: If f(x) = 2x + 1 and g(x) = x² – 3, find f(g(2)).

Common Mistake: Students often misapply the order of composition, calculating g(f(x)) instead of f(g(x)).

Solution:
1. Find g(2): g(2) = (2)² – 3 = 4 – 3 = 1.
2. Find f(g(2)): f(1) = 2(1) + 1 = 3.

Correction: Remember that f(g(x)) means apply g first, then f.

Problem 5: Domain and Range of Functions

Question: Find the domain of the function f(x) = √(4 – x²).

Common Mistake: Students often forget to consider the radicand (expression under the square root) must be non-negative.

Solution:
1. Set radicand ≥ 0: 4 – x² ≥ 0 → x² ≤ 4 → -2 ≤ x ≤ 2.
2. Domain: [-2, 2].

Correction: Always solve inequalities for the domain when dealing with square roots or denominators.

Problem 6: Solving Inequalities

Question: Solve the inequality 2x – 5 > 3x + 1.

Common Mistake: Students often reverse the inequality sign incorrectly when multiplying or dividing by a negative number.

Solution:
1. Subtract 2x from both sides: -5 > x + 1.
2. Subtract 1 from both sides: -6 > x → x < -6.

Correction: Reverse the inequality sign only when multiplying or dividing by a negative number.

Problem 7: Exponential Functions

Question: If f(x) = 3^x, find f(2) + f(-1).

Common Mistake: Students often misapply exponents, especially with negative values.

Solution:
1. Find f(2): 3² = 9.
2. Find f(-1): 3^(-1) = 1/3.
3. Sum: 9 + 1/3 = 28/3.

Correction: Remember that a^(-n) = 1/a^n.

Problem 8: Logarithmic Equations

Question: Solve log₂(x) + log₂(4) = 5.

Common Mistake: Students often forget to combine logarithms before solving.

Solution:
1. Combine logs: log₂(4x) = 5.
2. Rewrite in exponential form: 4x = 2^5 → 4x = 32 → x = 8.

Correction: Use the product rule (logₐ(b) + logₐ(c) = logₐ(bc)) to simplify.

Problem 9: Absolute Value Equations

Question: Solve |2x – 3| = 7.

Common Mistake: Students often forget to consider both positive and negative cases for the absolute value.

Solution:
1. Case 1: 2x – 3 = 7 → 2x = 10 → x = 5.
2. Case 2: 2x – 3 = -7 → 2x = -4 → x = -2.

Correction: Always split into two cases for absolute value equations.

Problem 10: Polynomial Division

Question: Divide 2x³ + 5x² – 3x – 6 by (x + 2).

Common Mistake: Students often make arithmetic errors during long division.

Solution:
1. Divide 2x³ by x: 2x².
2. Multiply (x + 2) by 2x²: 2x³ + 4x².
3. Subtract from original: (2x³ + 5x²) – (2x³ + 4x²) = x².
4. Bring down -3x: x² – 3x.
5. Divide x² by x: x.
6. Multiply (x + 2) by x: x² + 2x.
7. Subtract: (x² – 3x) – (x² + 2x) = -5x.
8. Bring down -6: -5x – 6.
9. Divide -5x by x: -5.
10. Multiply (x + 2) by -5: -5x – 10.
11. Subtract: (-5x – 6) – (-5x – 10) = 4.
12. Quotient: 2x² + x – 5, Remainder: 4.

Correction: Double-check each step to avoid arithmetic errors.

Problem 11: Inverse Functions

Question: Find the inverse of f(x) = 4x – 7.

Common Mistake: Students often forget to switch x and y or solve incorrectly for y.

Solution:
1. Replace f(x) with y: y = 4x – 7.
2. Switch x and y: x = 4y – 7.
3. Solve for y: x + 7 = 4y → y = (x + 7)/4.
4. Inverse function: f^(-1)(x) = (x + 7)/4.

Correction: Always switch x and y first, then solve for y.

Problem 12: Factoring Quadratics

Question: Factor x² – 6x + 8.

Common Mistake: Students often choose incorrect pairs of numbers that multiply to c but don’t add to b.

Solution:
1. Find two numbers that multiply to 8 and add to -6: -2 and -4.
2. Factor: (x – 2)(x – 4).

Correction: List all factor pairs of c and check their sums.

Problem 13: Rationalizing Denominators

Question: Rationalize the denominator of 5 / √3.

Common Mistake: Students often forget to multiply the numerator and denominator by the same radical.

Solution:
1. Multiply numerator and denominator by √3: (5√3) / (√3 * √3) = (5√3) / 3.

Correction: Multiply both numerator and denominator by the radical to eliminate it from the denominator.

Problem 14: Solving for Variables in Formulas

Question: Solve for r in the formula A = πr².

Common Mistake: Students often forget to take the square root or misapply the order of operations.

Solution:
1. Divide both sides by π: r² = A / π.
2. Take the square root: r = √(A / π).

Correction: Isolate the variable first, then apply inverse operations.

Problem 15: Direct and Inverse Variation

Question: If y varies directly as x and y = 10 when x = 2, find y when x = 5.

Common Mistake: Students often confuse direct and inverse variation or misapply the constant of proportionality.

Solution:
1. Direct variation: y = kx.
2. Find k: 10 = k(2) → k = 5.
3. Find y when x = 5: y = 5(5) = 25.

Correction: Identify the type of variation and use the correct formula.

Why These Mistakes Matter

The WASSCE Core Maths exam tests not just your knowledge but your ability to apply it accurately under pressure. Common mistakes in algebra and functions often stem from:

• Carelessness: Sign errors, incorrect simplification, or misapplying formulas.
• Lack of practice: Without consistent practice, even familiar concepts can become rusty.
• Poor time management: Rushing through problems can lead to avoidable errors.

Addressing these mistakes requires targeted practice and error analysis. Resources like Lebocheur’s Bibliothèque provide solved problems, step-by-step corrections, and exam-specific guides to help students identify and fix their weaknesses.

How to Avoid Common Mistakes in WASSCE Core Maths

To minimize errors in algebra and functions, follow these strategies:

• Understand the concepts: Don’t just memorize formulas—know why they work.
• Practice with past papers: Familiarize yourself with the types of questions and common pitfalls.
• Check your work: Always review your answers for careless mistakes before submitting.
• Use targeted resources: Platforms like Lebocheur offer solved problems, corrections, and guides tailored to WASSCE Core Maths.

Conclusion

WASSCE Core Maths, particularly algebra and functions, can be mastered with the right approach. By identifying common mistakes, practicing with solved problems, and using targeted resources, students can significantly improve their performance. Amina’s case study shows that systematic error analysis and focused practice lead to measurable results.

To go further, Lebocheur offers concrete resources to help you move forward with your application process. Explore the Bibliothèque for solved problems, exam guides, and corrections tailored to your needs.