Equations and Inequalities

Scheme of work: Year 12 A-Level: Pure 1: Equations and Inequalities

Prerequisite Knowledge

  • Be able to use set notation to represent equalities.
  • Represent linear equalities and their solutions graphically.
  • Solve a quadratic equation in the form x2 + bx + c = 0
  • Solve a pair of simultaneous equations by elimination.

Success Criteria

  • Solve linear inequalities, e.g. ax + b > cx + d
  • Solve quadratic inequalities, e.g. ax2 + bx + c > 0
  • Solve simultaneous linear equations by substitution.
  • Use the substitution method to solve simultaneous equations where one equation is linear and the other is quadratic.
  • Give solutions of inequalities using set notation.
  • Represent quadratic inequalities and their solutions graphically.

Key Concepts

  • Linear simultaneous equations can be solved by elimination or substitution.
  • When using graphs with solving simultaneous quadratic and linear equations the number of intersections is equal to the number of solutions.
  • When you multiply or divide an inequality by a negative number, you need to change the inequality sign to its opposite. 
  • To solve a quadratic inequality
    • find the roots and intercept of the quadratic equation
    • sketch the graph of the quadratic function, then
    • use the sketch to find the required set of values.

Common Misconceptions

  • Students often forget to change the inequality sign when multiplying or dividing by a negative.
  • Students can get confused with the set notation for solving quadratic inequalities.  Encourage them to sketch a graph and marked on the desired range of values.  For instance, x2 – 7x + 12 < 0 can have the incorrect solution of x < 3 and x > 4 rather than 3 < x < 4.
  • When solving simultaneous equations students often forget to find both the x and y solutions after finding one.

Equations and Inequalities Resources

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