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Cambridge IGCSE Mathematics practice

exam practice - Represent and interpret inequalities, including on a number line, using open circles for strict inequalities (<, >) and closed circles for inclusive inequalities (≤, ≥). Construct, solve, and interpret linear inequalities such as 3x < 2x + 4 and 3x - 2 < 7. Graphically represent and interpret linear inequalities in two variables, using broken lines for strict inequalities and solid lines for inclusive inequalities, with shading to indicate unwanted regions. List inequalities that define a specified region, excluding linear programming problems. - Inequalities

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Topic

Inequalities

Exam-style question

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Paper 2Core or Extended Mathematics4 marks

Graphical representation of linear inequalities in two variables.

Diagram Description

Graphing Inequalities

Consider the inequalities y ≥ 2x - 1 and y < -x + 4. Represent these inequalities on a graph and identify the region that satisfies both.

  1. a

    Sketch Draw the boundary lines for both inequalities on the same graph.

    Aim for approximately 2 distinct marking points.

    [2]
  2. b

    Describe Shade the region that satisfies both inequalities and explain your shading.

    Aim for approximately 2 distinct marking points.

    [2]

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Maths method check

  • Topic focus: Inequalities.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Inequalities

Paper 2Core or Extended Mathematics4 marks

Description

Linear Inequality

Solve the inequality 3x - 2 < 7 and represent the solution on a number line.

  1. a

    Calculate Find the solution set for the inequality 3x - 2 < 7.

    Aim for approximately 2 distinct marking points.

    [2]
  2. b

    Construct Draw a number line showing the solution to the inequality.

    Aim for approximately 2 distinct marking points.

    [2]