MATHS AS LEVEL CORE 1
ALGEBRA AND FUNCTIONS
Indices Laws
am 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 FUNCTIONS
Drawing Graphs of Quadratic Equations
1. 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 Equations
1. Factorising
2. Quadratic Formula
3. Complete the Square
Quadratic Factorising for Coefficient Greater than One
1. 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 solve
EXAMPLE:
6x2 – 11x – 10
Multiply to make -60
Add to make -11
So -15 and 4
6x2 – 15x + 4x – 10
3x(2x-5) + 2(2x-5)
(3x + 2) (2x – 5)
x = -2/3 x = 5/2
Quadratic Formula
Completing the Square
x2 – 10x = 5
(x – 5)2 – 25 = 5
(x – 5)2 = 30
x – 5 =
x = + 5
The Discriminant
Typical Quadratic: ax2 + bx + c = 0
Discriminant: b2 – 4ac
If b2 – 4ac is a square number then the quadratic will factorise.
The Discriminant and Roots
Situation
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 INEQUALITIES
Solving Inequalities
1. Elimination
2. Substitution
3. Using methods used to solve linear equations
WHEN MULTIPLYING AN INEQUALITY BY A NEGATIVE NUMBER, TURN AROUND THE INEQUALITY SIGN.
Values Which Satisfy Two Inequalities
1. Draw a number line
2. The area where the two values overlap satisfies both solutions
Solving Quadratic Inequalities
1. Solve corresponding quadratic...