A mixed-topic question is two ordinary questions joined end to end. The skill is splitting the joined question and passing one answer to the next step.
This page sits in the SPM Additional Mathematics guide. For picking a method at the start, read choosing the right method in an unfamiliar question.
What does the student usually say?
“The question is about a curve, then a line, then a point, and I do not know what to start with.” Or: “I write down every formula I remember and hope one of them fits.”
A worked split: tangent, then intercept
The question, invented for this page: find the equation of the tangent to y = x² − 4x + 5 at x = 3, then find where this tangent meets the x-axis.
Lay out the plan in three columns before calculating.
| Given | Need | Idea |
|---|---|---|
| Curve, and x = 3 | The point on the curve | Substitute x = 3 |
| Curve | The gradient at x = 3 | Differentiation |
| Point and gradient | The tangent line | Equation of a line |
| Tangent line | Where y = 0 | Substitute y = 0 |
Now follow the plan.
Point (substitution). y = 9 − 12 + 5 = 2, so the point is (3, 2).
Gradient (differentiation). dy/dx = 2x − 4, and at x = 3 the gradient is 2.
Tangent (coordinate geometry). y − 2 = 2(x − 3), so y = 2x − 4.
Meets the x-axis. Set y = 0, so 2x − 4 = 0 and x = 2. The point is (2, 0).
Every line has a label, and every label is a topic you already know.
What can I do myself?
- Use the three-column layout before any calculation on a mixed question.
- After each step, write the quantity it found, for example “gradient = 2”.
- Check that each step’s output is what the next step needs.
- Redo a solved mixed question a week later using only the plan.
The word-problem structure worksheet has a layout for this. Keep your slips in the mistake log and paper-error review.
When might one-to-one tuition help?
If the plan itself is where you get lost, a teacher can ask “what do you need next?” at each step and listen to how you answer. A worked solution cannot ask you that question.
The one-hour trial class (from RM50) works well with one mixed question you could not finish. Find out how lessons work at online one-to-one Additional Mathematics tuition.