A-Level Maths (P): Chapter 3 - Equations and Inequalities

Simultaneous Equations on Graphs

- Solutions to the equations can be found using the point of intersection

How to solve Quadratic Inequalities

1) Rearrange so the right hand side = 0 2) Solve the quadratic to get critical values 3) Sketch the graph 4) Identify the region required

2 Ways of Solving Linear Simultaneous Equations

Elimination and Substitution

How to find a Graphical Inequality

Find the point of intersection between the lines by: - Making them equal each other - Putting everything on one side so it equals 0 - Factorising to find the roots

y > f(x)

Region of the curve above y = f(x)

y < f(x)

Region of the curve below y = f(x)

f(x) > g(x)

The values of x for which the curve y = f(x) is above the curve y = g(x) satisfy the inequality...

f(x) < g(x)

The values of x for which the curve y = f(x) is below the curve y = g(x) satisfy the inequality...

< and >

Use a dotted line (values not included)

≤ and ≥

Use a solid line (values included)

Solving Quadratic Simultaneous Equations

Usually needs substitution