Grade 10 · CAPS-aligned
Grade 10 Algebra Basics (CAPS)
Variables, expressions, and the algebra moves you'll use for the next three years.
Algebra in Grade 10 is the foundation for everything you'll do in Grade 11 and 12. CAPS expects you to fluently manipulate expressions, factorise, and solve linear equations. Simple quadratic equations appear in the wider algebra programme; this page focuses on the basics learners need first.
Why most learners find this hard
Most learners struggle here because Grade 9 was about doing one step at a time, while Grade 10 expects you to chain three or four moves without making sign errors. Mistakes with negatives and brackets are the #1 mark-killers.
What you'll learn
- Like terms, distributing brackets, and the FOIL method
- Factorising trinomials, common factor, and difference of squares
- Solving linear equations and inequalities
- Recognising simple quadratic forms when they appear in factorising work
- Setting up word problems as equations
Worked example
Solve for x: 3(x − 4) + 2x = 7 − (x + 1)
- 1Expand both sides: 3x − 12 + 2x = 7 − x − 1
- 2Collect like terms: 5x − 12 = 6 − x
- 3Get x on one side: 5x + x = 6 + 12 → 6x = 18
- 4Divide: x = 3
Answer: x = 3
Exam tips
- Always check your answer by substituting back into the original equation.
- When in doubt, expand brackets first before collecting like terms.
- Write each step on a new line — markers cannot give method marks they can't see.
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