A correct method can still give a wrong answer if the numbers are handled loosely. The slips are small and repeatable, so a few habits can fix them.
This page belongs to the SPM Additional Mathematics guide. If a slip happens early in a long solution, read recovering after an early mistake.
What does the student usually say?
“I did everything right, but my answer is 2.83 and the book says 2.81.” Or: “I checked my method three times and could not see the error.”
When the method is checked and the answer is still off, look at the numbers.
A rounding example
The question, invented for this page: solve 2ˣ = 7, giving x to three significant figures.
The method is to take logarithms: x = log 7 ÷ log 2.
Rounding early. The student writes log 7 = 0.85 and log 2 = 0.30, so x = 0.85 ÷ 0.30 = 2.83.
Rounding at the end. With full values, log 7 = 0.845098 and log 2 = 0.301030, so x = 0.845098 ÷ 0.301030 = 2.80735, which is 2.81 to three significant figures.
The early rounding changed the third significant figure, so the final answer is wrong. The method was identical.
Check by substituting: 2^2.81 ≈ 7.0, while 2^2.83 ≈ 7.1.
What are the four accuracy habits?
| Habit | Reason |
|---|---|
| Keep full values until the last line | Early rounding can change the final figure |
| Round once, to the accuracy stated | The question sets the standard |
| Read each signed term back after expanding | Sign slips lose marks easily |
| Substitute the answer into the original | It catches copying and entry errors |
What can I do myself?
- Use the calculator memory to store a value, rather than typing a rounded copy.
- Underline the accuracy instruction in the question before you start.
- After each question, do a two-second check that the final line matches the last working line.
- Log each slip by type in the mistake log and paper-error review, so you can see which type repeats most.
The units and significant figure checker lets you practise rounding to a stated accuracy.
When might one-to-one tuition help?
If one slip type keeps returning after you have tried these habits, a teacher can watch how you write and see where your attention drops. A short correction to your layout, such as where you put the equals signs, can be enough.
Bring two marked solutions with the slip circled to the one-hour trial class (from RM50). See online one-to-one Additional Mathematics tuition for how lessons work.