Flip the sign when × or ÷ by a negative
Treat the inequality as an equation, except reverse the inequality sign whenever you multiply or divide both sides by a negative number.
Quadratic inequality: factorise & sketch
Find the critical values (roots), sketch the parabola, and read off where it is above () or below () the -axis.
Regions: draw, label and shade
Draw each boundary line, decide which side satisfies each inequality, and shade the overlap. Solid line for or , dashed for or .
Drawn from real examiner reports.
Not reversing for a negative
With a negative - or -coefficient, keeping the original sign, or replacing the inequality with an equals sign or a bare number. Dividing by a negative flips to .
Reported on the November 2024 Higher Paper 1H (Q8b).
Wrong region for a quadratic
Quoting when the answer is or (or vice versa); not sketching, or writing factors that do not expand to the given quadratic.
Reported on the November 2024 Higher Paper 2H (Q20).
Unlabelled boundary lines
Drawing the line for through the wrong intercepts, or not labelling the lines and not indicating the shaded region.
Reported on the November 2024 Higher Paper 2H (Q7).
Solid vs dashed line mix-up
Using a dashed line for or , or a solid line for strict or . Solid includes the boundary; dashed excludes it — the wrong style loses the accuracy mark.
(general exam technique)
Wrong end included in a list
For the integers are : include (the end) but exclude (the strict end). Slips add or drop .
(general exam technique)
Final answer must be an inequality
After the algebra, write the answer with the correct inequality sign — not an equals sign or a single number.
Test a point to pick the side
For a region, substitute an easy point such as the origin into the inequality; keep the side that makes it true. It settles which side to shade in one step.
Sketch, do not guess, the region
For a quadratic inequality, always sketch the parabola through its roots. Above the axis () is outside the roots; below () is between them — read the region off the picture.
Solve exactly like an equation — but reverse the sign when you multiply or divide both sides by a negative: Your final answer must be an inequality, not "" or a lone number.
Solid vs dashed boundary line?
Solve .