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

- Be able to use set notation to represent equalities.
- Represent linear equalities and their solutions graphically.
- Solve a quadratic equation in the form x
^{2}+ bx + c = 0 - Solve a pair of simultaneous equations by elimination.

- Solve linear inequalities, e.g. ax + b > cx + d
- Solve quadratic inequalities, e.g. ax
^{2}+ 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.

- 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.

- 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, x
^{2}– 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.

November 5, 2023

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

September 24, 2023

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