Algebra: equations and inequalities

This topic is about solving: quadratic equations, exponential equations, equations with surds, simultaneous equations and inequalities. The 6 questions here are worth 24 marks in the November 2024 Paper 1 set. Of the 24 marks, 14 are for the correct final answer and 10 for method and working. Method earns marks separately from the answer, so show every line.

The 2024 Diagnostic Report says candidates treat a quadratic inequality as an equation and then join the answers with "and" or a chain of signs that does not match the solution. They do not put an equation in standard form, so b and c take the wrong signs in the quadratic formula. And they do not check solutions: a value that fails the original equation has to be rejected, and an expression such as 2 to the power x equal to minus 4 has no solution. Always test your answers in the question.

Where marks are lost: in our words, from Department of Basic Education, NSC 2024 Diagnostic Report, Part 1 (Book 1).