MATHS AS LEVEL CORE 1ALGEBRA AND FUNCTIONSIndices Lawsam x an = am+n

am ? an = am-n

(am)n = amn

a1/n = (for the nth root of x)

am/n = (a1/n)m or ()m

a-m = 1/am

a0 = 1

Surds

Rationalising Fraction Denominators ? multiply top and bottom by ? multiply top and bottom by a – ? multiply top and bottom by a + QUADRATIC FUNCTIONSDrawing Graphs of Quadratic Equations1. Draw table of values for values asked for

2. Plot points and join them in a parabola

(a > 0 there will be minimum)

(a < 0 there will be maximum)

Solving Quadratic Equations1. Factorising

2. Quadratic Formula

3. Complete the Square

Quadratic Factorising for Coefficient Greater than One1. Multiply a and c

2. Look for two numbers that multiply to make ac and add to make b

3. Split the equation in half and use the common bracket to solveEXAMPLE:

6×2 – 11x – 10

Multiply to make -60

Add to make -11

So -15 and 46×2 – 15x + 4x – 10

3x(2x-5) + 2(2x-5)

(3x + 2) (2x – 5)

x = -2/3 x = 5/2

Quadratic Formula

Completing the Squarex2 – 10x = 5

(x – 5)2 – 25 = 5

(x – 5)2 = 30

x – 5 =

x = + 5

The DiscriminantTypical Quadratic: ax2 + bx + c = 0

Discriminant: b2 – 4acIf b2 – 4ac is a square number then the quadratic will factorise.

The Discriminant and RootsSituation

Meaning

Graph

b2 > 4ac

Two distinct roots

Crosses x-axis twice

b2 = 4ac

Two equal roots

Touches x-axis once

b2 < 4ac

No real roots

Does not touch x-axis

EQUATIONS AND INEQUALITIESSolving Inequalities1. Elimination

2. Substitution

3. Using methods used to solve linear equationsWHEN MULTIPLYING AN INEQUALITY BY A NEGATIVE NUMBER, TURN AROUND THE INEQUALITY SIGN.

Values Which Satisfy Two Inequalities1. Draw a number line

2. The area where the two values overlap satisfies both solutions

Solving Quadratic Inequalities1. Solve corresponding quadratic…

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