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:
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Rewriting the equation in the form ax2 + bx +c = 0.
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Factorise.
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Make each bracket = 0 to solve the equation
Alternatively: you can use the quadratic formula after step 1.
Completing the square
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Rewrite in the form x2 + bx +c = 0, (if necessary divide by the multiple of x2)
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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.)