A-level · Algebra & functions

Simultaneous equations and inequalitiesExam-style questions

Two conditions at once, and conditions that pick out a range. What solving simultaneously means on a graph; a line meeting a curve, with the answers given as pairs; counting the meeting points with the discriminant; linear inequalities, and why dividing by a negative turns the sign round; quadratic inequalities from the critical values and a sketch; and the outside region, set notation and combining two conditions.

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15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    (a) Solve the inequality

    x+4x−2⩽3\dfrac{x + 4}{x - 2} \leqslant 3

    (5 marks)
    (b) Hence, or otherwise, solve the inequality

    ∣x∣+4∣x∣−2⩽3\dfrac{|x| + 4}{|x| - 2} \leqslant 3

    (3 marks)
    Level 5 · 8 marksTry it