S-Cool Revision Summary

S-Cool Revision Summary

Basic Skills

Expanding 1 and 2 brackets (Practice)

Factorising a common factor into 1 bracket

Factorising a quadratic into 2 brackets

Solving Linear Equations

Solving Simultaneous Equations

Quadratics

Solve a quadratic equation by:

  1. Rewriting the equation in the form ax2 + bx +c = 0.

  2. Factorise.

  3. Make each bracket = 0 to solve the equation

Alternatively: you can use the quadratic formula after step 1.

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Completing the square

  1. Rewrite in the form x2 + bx +c = 0, (if necessary divide by the multiple of x2)

  2. Rewrite the x2 + bx as (x - b/2)2 -(b/2)2 so that x2 + bx +c = (x - b/2)2 -(b/2)2 + c

This gives you the minimum value of a quadratic: minimum value is the constant

(-(b/2)2 + c), when x = b/2.

If you know the roots of an equation then the original quadratic was:

x2 - (sum of roots) x + product of roots

Inequalities

Solve linear inequalities like normal equations. Remember (multiplying by -1) or (taking reciprocals) reverses the inequality sign.

For quadratic inequalities: Solve the equation = 0, and then use the shape of the graph to finalise the answer.

Remainder Theorem:

When dividing f(x) by (x - a), the remainder is f(a).

Factor Theorem:

If f(a) = 0, then (x - a) is a factor of f(x)

(When factorising polynomials, choose numbers that multiply together to make the constant.)