# 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

### Mr Mathematics Blog

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing