Most calculus mistakes in Add Maths start as algebra mistakes. This page lists five algebra skills worth checking before differentiation and integration, with a one-line test for each.
Return to the SPM Additional Mathematics guide for the whole course. The algebra step repair trainer gives you extra practice on any skill you miss.
What does the student usually say?
“I know the rule for dy/dx, but my answer is still wrong.” Or: “I follow the steps in class, then at home the expression turns into something I cannot simplify.”
The rule was applied correctly. The expression it was applied to was the problem.
Which five skills should I test?
| Skill | One-line test | Where it reappears |
|---|---|---|
| Expanding brackets | Expand (x + 3)(2x − 1) | Differentiating products |
| Factorising | Factorise x² − 5x + 6 | Finding stationary points |
| Fractions with letters | Simplify (6x² − 4x) ÷ 2x | Quotients and integration |
| Indices and roots | Write 1 ÷ x² and √x as powers of x | Every power-rule question |
| Rearranging | Make x the subject of y = 3x − 7 | Inverse and rate questions |
Answers: 2x² + 5x − 3; (x − 2)(x − 3); 3x − 2; x⁻² and x^(1/2); x = (y + 7) ÷ 3.
A worked repair
Take y = (x³ + 2x²) ÷ x. A student who skips simplifying tries the quotient rule and produces a long expression with easy places to slip.
Simplify first: each term divides by x, so y = x² + 2x. Then dy/dx = 2x + 2.
The two routes give the same answer when done correctly, but the simplified route has far fewer places to go wrong. The repair is the habit: look for a simplification before reaching for a rule.
What can I do myself?
- Take the five tests above on paper, without notes, and mark yourself.
- For each test you miss, write two similar questions and solve them.
- Put the five tests in the mistake log and paper-error review as a weekly check.
- Come back to a differentiation question only after you can rewrite its expression in simple terms.
When might one-to-one tuition help?
Self-repair works well when one or two tests fail. If three or more fail, or you keep repeating the same slip, a teacher can see the pattern faster than a checklist can. Lessons then start on the skill that blocks the most chapters and work forward.
You can begin with the one-hour trial class (from RM50) and bring the test answers you marked wrong. For the decision itself, read should I repair algebra before revising differentiation. Learn how lessons work at online one-to-one Additional Mathematics tuition.