ZIMSEC O Level · Mathematics · Form 2, Form 3, Form 4
An equation is true for particular values of the unknown. Solving means finding those values.
Linear equations
Worked example: Solve 5(x − 2) = 3x + 4.
5x − 10 = 3x + 4 → 2x = 14 → x = 7
Simultaneous equations
Use elimination (make one unknown's coefficients equal, then add or subtract) or substitution.
Worked example: Solve 2x + y = 11 and x − y = 1.
Add the equations: 3x = 12 → x = 4. Substitute: 4 − y = 1 → y = 3.
Quadratic equations (Form 3–4)
Rearrange to ax² + bx + c = 0, then factorise, or use the formula x = [−b ± √(b² − 4ac)] ÷ 2a.
Worked example: Solve x² − x − 6 = 0.
(x − 3)(x + 2) = 0 → x = 3 or x = −2
Inequalities
Solve like equations, but reverse the sign when multiplying or dividing by a negative number. Show solutions on a number line: a closed dot for ≤ or ≥, an open dot for < or >.
Worked example: Solve 3 − 2x < 9.
−2x < 6 → x > −3 (sign reversed)
Linear programming (Form 4)
Write the inequalities from the question, draw their boundary lines, shade the unwanted regions, and test the corners of the wanted region to find a maximum or minimum.
Check yourself
- Solve 4x − 7 = 2x + 9.
- Solve the simultaneous equations 3x + 2y = 12 and x + 2y = 8.
- Solve 2x² + 5x − 3 = 0.
Show answers
- x = 8
- x = 2, y = 3
- (2x − 1)(x + 3) = 0 → x = ½ or x = −3
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