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Quadratic equations, inequalities, simultaneous equations, surds and the nature of roots.
Watch the full lesson before attempting practice questions.
Master these ideas before attempting exam questions.
Solved by factorisation, completing the square, or the quadratic formula. Always check for extraneous solutions.
Δ = b² − 4ac. If Δ > 0: two real roots. Δ = 0: one equal root. Δ < 0: no real roots.
Solve as an equation first, then test intervals using a sign diagram or parabola sketch.
One linear, one quadratic: substitute the linear into the quadratic and solve the resulting equation.
Use properties of exponents and roots. Isolate the surd before squaring both sides.
Commit these to memory — they appear in almost every exam.
These are your learning targets for Algebra & Equations.
Avoid these errors — they cost marks every year.
The ± gives two solutions. Write both roots explicitly in every step.
Δ = b² − 4ac not b² + 4ac. Sign errors are the most common mark-losers.
Substitute both values back into both original equations to verify.
Request CAPS-aligned study materials for Algebra & Equations.
Comprehensive CAPS-aligned notes covering all key concepts, theorems, and worked examples for Algebra & Equations.
NSC-style exam questions with full memorandum. Ideal for timed practice and self-assessment before exams.
Graded practice questions organised by difficulty. Perfect for building confidence before Paper 1.
Straight answers to common Grade 12 CAPS questions about Algebra and Equations.
Algebra and Equations in Grade 12 CAPS covers quadratic equations, inequalities, simultaneous equations, surds, and the nature of roots. It builds the algebra skills you need for both Paper 1 and later topics.
Work step by step, practise simplifying expressions accurately, and revise the standard methods for solving equations and inequalities. Daily practice with past-paper style questions helps you improve quickly.
Common mistakes include sign errors, incorrect factorisation, skipping working, and forgetting to check restrictions or solution values. Small algebra slips often cost easy marks.
CAPS exams usually test algebra through equations, inequalities, surds, and function-based questions. These questions often reward method marks, so clear working is important.
Book a focused session with Chris Khomo and work through this topic step by step — at your own pace, online, from anywhere in South Africa.