Introduction
This S3 Maths MGS question tests your ability to:
- square algebraic expressions correctly
- cross-multiply fractions
- collect like terms carefully
- factorise expressions to isolate a variable
We follow the teacher’s exact working shown on the board.
The Question
Given that:
\(a = \dfrac{4 + bcd}{2c – 3}\)
Express \(c\) in terms of \(a, b,\) and \(d\).
Step-by-Step Working (Teacher Working)
Start by squaring both sides:
\(a^2 = \dfrac{4 + bcd}{2c – 3}\)
Cross-multiply:
\(a^2(2c – 3) = 4 + bcd\)
Expand the left-hand side:
\(2a^2c – 3a^2 = 4 + bcd\)
Bring terms involving \(c\) to one side:
\(2a^2c – bcd = 4 + 3a^2\)
Factorise \(c\):
\(c(2a^2 – bd) = 4 + 3a^2\)
Divide both sides by \((2a^2 – bd)\):
\(c = \dfrac{4 + 3a^2}{2a^2 – bd}\)
✅ Final Answer
\(c = \dfrac{4 + 3a^2}{2a^2 – bd}\)
Key Concepts
| Concept | Why It Matters |
|---|---|
| Squaring expressions | Removes square roots |
| Cross-multiplication | Clears fractions |
| Collecting like terms | Simplifies equations |
| Factorisation | Allows isolation of variables |
| Algebraic division | Final step to solve for a variable |
Tips for Students
- Always square both sides carefully
- Expand brackets fully before rearranging
- Group terms with the same variable together
- Factorise before dividing
For Parents
Algebraic manipulation questions strengthen:
- logical thinking
- accuracy in multi-step working
- readiness for upper secondary algebra
These skills are essential for success in both E-Maths and A-Maths.