How to Solve Maths Problems Step by Step (Matric Method)

Steps

1. Diagnose the topic. Ask: which CAPS topic is this? Quadratic? Trig identity? Annuity? The first word of your method should match a topic in the syllabus.
2. Plan the technique. Write one line: 'I will use the quadratic formula' or 'I will use the cosine rule.' This commits you and stops mid-question switching.
3. Execute one line at a time. Show every line. Markers award method marks even when the final answer is wrong.
4. Verify the answer. Substitute back, check units, sketch the graph, or estimate. 30 seconds of checking saves 5 marks.

Worked example

Solve for x: 3x² − 7x + 2 = 0.

1. Diagnose: quadratic equation, a = 3, b = −7, c = 2.
2. Plan: try factorising; if it doesn't split in 20 seconds, switch to the formula.
3. Execute: (3x − 1)(x − 2) = 0 ⇒ x = 1/3 or x = 2.
4. Verify: 3(1/3)² − 7(1/3) + 2 = 1/3 − 7/3 + 2 = 0 ✓ and 3(2)² − 7(2) + 2 = 12 − 14 + 2 = 0 ✓.

Common mistakes

• Skipping the 'plan' line and switching techniques halfway.
• Writing only the final answer with no working — marker can't award method marks.
• Never verifying, so sign errors slip through.

Exam tips

• Use the framework for every question, even the easy ones — it builds the habit.
• If you're stuck after 90 seconds, write what you know and move on. Come back.
• Snap&Learn shows the diagnose-plan-execute-verify breakdown for any question you upload.
• Number your steps and write one operation per line, so a marker can follow your method.

Frequently asked questions

Is there one method that works for every maths problem?

Yes — the 4-stage framework (diagnose, plan, execute, verify) works for every CAPS topic from algebra to 3D trig.

How do I get method marks if my final answer is wrong?

Show every line of working. NSC markers award marks for correct method even when the final answer has a slip.

What if I can't start a problem?

Write down what is given and what is asked, draw a sketch if you can, and try a simpler version of the same problem first.

How do I check my answer?

Substitute it back into the original problem, check the units, and ask whether the size of the answer makes sense.

What should I do if I get stuck halfway?

Re-read the question for information you have not used yet, check the last line of working for a sign error, then try a simpler version of the problem. If you are still stuck, move on and come back later.