Your Basket 0 items - £0.00

**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.

August 1, 2024

Explore key concepts, FAQs, and applications of estimating solutions for Key Stage 3, GCSE and IGCSE mathematics.

July 28, 2024

Explore key concepts, FAQs, and applications of equivalent fractions in Key Stage 3 mathematics.

July 24, 2024

Guide for teaching how to transform graphs using function notation for A-Level mathematics.