Following an example and starting a question are two different skills. You can have the first without the second, and the second can be trained on its own.
This page is part of the SPM Additional Mathematics guide. Once you can start, choosing the right method is the next step.
What does the student usually say?
“When the teacher does it, I get it. Then I open the exercise and my mind goes blank.” Some students add: “I feel I should know what to do, so I wait for the idea to come.”
The waiting is the problem. Ideas come after you write something down, not before.
An example that looks new
The class example: solve x² − 5x + 6 = 0. Factorise, and get x = 2 or x = 3.
The new question, invented for this page: the roots of x² − 5x + k = 0 differ by 3. Find k.
It looks unfamiliar because k is in the place of a number. Start by writing what you know, not what you will do.
- Givens. The roots differ by 3, and the quadratic is x² − 5x + k.
- Want. The value of k.
- Name the roots. Call them α and α + 3.
- Use a relationship you know. The sum of the roots is 5 (the coefficient of x with its sign changed). So α + α + 3 = 5, giving 2α = 2 and α = 1.
- Finish. The roots are 1 and 4, and k is their product, so k = 4.
Check: x² − 5x + 4 = (x − 1)(x − 4), and the roots 1 and 4 differ by 3. The class example and this question share the same facts about roots.
What can I change in how I practise?
| Instead of | Try |
|---|---|
| Reading the solution, then the question | Writing givens and want for two minutes first |
| Waiting for the idea | Writing one relationship you know, even if it does not solve it |
| Copying the method from the answer | Covering the answer and comparing only the first line |
What can I do this week?
- Pick three questions you have not seen. Write the givens and the want, and stop.
- Compare those two lines with a worked solution. Did you pick up the same facts?
- If not, read the topic lesson again, for example relating roots to coefficients.
- Note the result in your mistake log, including the questions where you started correctly.
The word-problem structure worksheet prints the givens, want and idea layout.
When might one-to-one tuition help?
If you are unsure what to write even for the givens, you may be missing a topic fact, not the starting habit. A teacher can ask the question that unlocks the first line, then slowly take that question away until you ask it yourself.
The one-hour trial class (from RM50) works well with a question you left blank. See online one-to-one Additional Mathematics tuition for how lessons are run.