# maths

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)
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
So -15 and 46×2 – 15x + 4x – 10
3x(2x-5) + 2(2x-5)
(3x + 2) (2x – 5)
x = -2/3 x = 5/2
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