You can decide in ten minutes, without a teacher. Four questions tell you whether algebra or differentiation is the thing to fix first.
This page belongs to the SPM Additional Mathematics guide. For the skills to repair, read algebra foundations to repair before calculus.
What does the student usually say?
“I do not know whether I should go back to algebra or just keep doing differentiation questions.” Some add: “If I go back, I will run out of time before the exam.”
The four-question test
Do these on paper, without notes, in ten minutes. The first two need only the power rule. The last two need algebra before the rule applies.
- Differentiate y = 4x³ − 5x. The answer is 12x² − 5.
- Differentiate y = x⁵ + 2x². The answer is 5x⁴ + 4x.
- Differentiate y = (x + 2)(x − 3). Expand first: y = x² − x − 6, so dy/dx = 2x − 1.
- Differentiate y = (6x² − 4x) ÷ 2x. Simplify first: y = 3x − 2, so dy/dx = 3.
What does my score say?
| Result | What it suggests | What to do |
|---|---|---|
| 1 and 2 right, 3 and 4 wrong | The gap is algebra | Repair expanding and fractions first, in short daily blocks |
| 1 and 2 wrong | The power rule is not secure | Revise the rule with simple questions before anything else |
| All four right | Algebra is not the main gap | Revise differentiation and review your errors for the pattern |
| 3 right, 4 wrong | Fractions with letters are weak | Repair that one skill, then retry |
What can I do myself?
- If the gap is algebra, use the algebra step repair trainer for ten minutes a day.
- Keep doing two differentiation questions a day that need no simplifying, so the rule stays fresh.
- Try the polynomial differentiation tutor to check each answer.
- Retake the test after a week with new numbers and see whether questions 3 and 4 move.
Record the result in the mistake log and paper-error review.
When might one-to-one tuition help?
If you retake the test and questions 3 and 4 still fail, a teacher can repair algebra inside differentiation questions. That way the two topics move together and you do not wait to finish one before starting the other.
Bring your marked test to the one-hour trial class (from RM50). See online one-to-one Additional Mathematics tuition for how lessons are run.