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Solving & Graphing Inequalities (Cambridge (CIE) IGCSE Maths)

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  • True or False?

    A solid line is used when drawing the line for the inequality y less or equal than x plus 1.

    True.

    A solid line is used when drawing the line for the inequality y less or equal than x plus 1.

    Solid lines are used when the inequality includes an equals, ≤ or ≥.

  • Which side of the line x equals 1 satisfies the inequality x less or equal than 1?

    The side to the left of the line x equals 1 (including the line itself) satisfies the inequality x less or equal than 1.

  • True or False?

    The region below the line y equals x minus 2 satisfies the inequality y greater than x minus 2.

    False.

    The region below the line y equals x minus 2 does not satisfy the inequality y greater than x minus 2.

    The region above the line satisfies the inequality.

  • How could you use the point open parentheses 0 comma space 0 close parentheses to determine which side of the line 2 x plus 3 y equals 12 satisfies the inequality 2 x plus 3 y greater than 12?

    To use the point open parentheses 0 comma space 0 close parentheses to determine which side of the line 2 x plus 3 y equals 12 satisfies the inequality 2 x plus 3 y greater than 12:

    • Substitute x equals 0 and y equals 0 into 2 x plus 3 y.

    • If the answer is greater than 12 then the side of the line containing open parentheses 0 comma space 0 close parentheses satisfies the inequality.

    • If the answer is less than 12 then the side of the line which does not contain open parentheses 0 comma space 0 close parentheses satisfies the inequality.

  • How can you identify the inequalities needed to define a region from a graph?

    A graph with three intersecting lines and a shaded region bound by all three lines.

    To identify the inequalities needed to define a region from a graph:

    • Identify the equation of each line.

    • Substitute the coordinates of a point within the region into each equation.

      • If the answer is less than the given value in the equation, then it satisfies the inequalityless than (if the line is dotted) or less or equal than (if the line is solid)

      • If the answer is greater than the given value in the equation, then it satisfies the inequalitygreater than (if the line is dotted) or greater or equal than (if the line is solid)

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    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

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      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

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      Percentages Toolkit

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      Linear Graphs

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      Quadratic Graphs

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      Further Graphs & Tangents

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      Solving & Graphing Inequalities

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      Real-Life Graphs

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