GCSE Maths: Inequalities

Inequalities appear on both GCSE Mathematics tiers: Foundation papers ask you to solve a linear inequality and show it on a number line, while Higher papers add set notation, quadratic inequalities and regions defined by several inequalities on a graph. This material follows the inequalities content of the GCSE subject content for England.

The quiz has eleven questions. You solve a one-step and a two-step linear inequality, including one where you divide by a negative number and must reverse the sign, find which integers satisfy a double inequality, translate a number line described in words (open and filled circles) into inequality notation, find the largest integer that satisfies an inequality, and use an inequality to answer a question about a monthly phone bill in pounds. The Higher-tier questions write a solution in set notation, solve $x^2<16$ and a factorised quadratic inequality, test points against a region defined by three inequalities, and check the convention of dashed and solid boundary lines. The wrong options are the mistakes examiners see every year: forgetting to reverse the sign, including or excluding an end point wrongly, writing $x<4$ for $x^2<16$, and choosing the inside of the roots when the answer lies outside.

The flashcards cover the four inequality symbols, open and closed circles, when to reverse the sign, set notation, the method for quadratic inequalities, and dashed and solid lines for regions.

The printable written work has eight problems with full working: solving inequalities with brackets and with a negative coefficient, a double inequality with its integer values, integers that satisfy two inequalities at once, two quadratic inequalities, counting the integer points inside a region, and a rectangle problem where a perimeter limit and an area condition combine into one range of values. Each item asks for method as well as the answer, including a short explanation of why the sign reverses.

Linear inequalities and number lines are content for both tiers; set notation, quadratic inequalities and regions are Higher tier. The material suits Year 10 and Year 11 students and builds directly on linear and quadratic equations elsewhere in the category.

• Solve linear inequalities, reversing the sign when multiplying or dividing by a negative number
• Solve double inequalities and list integer solutions
• Represent solutions on a number line with open and closed circles
• Form and solve inequalities from a context
• Write solutions in set notation and solve quadratic inequalities (Higher)
• Identify regions defined by inequalities on a graph (Higher)

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Number N1 and Algebra A22 (solving inequalities).