Pre IB Mathematics

Solving Linear Inequalities

When you multiply or divide both sides of an inequality by a negative number, the sense of thee inequality is reversed.

Factorising Quadratic Expressions

GCF & Factorising
ac = factors that add up to b 

Solving Quadratic Inequalities

Values of x 0
Substituting x value from each subinterval tells the value of expression
0 < +ve portions 0 > -ve portions

The Discriminant

Discriminant of Quadration Equation = b^2  - 4ac
> 0 = 2 real roots rational if perfect square
= 0 = 1 real root rational
< 0 = 0 real roots 

Functions

f ° g (x) = f x g
f[g(x)] = g x f

Inverse Functions

BIDMAS to inverse functions

loga(MN) = loga(M) + loga(N)
loga(M/N) = loga(M) - loga(N)
loga(M^y) = yloga(M) 

loga(MN) = loga(M) + loga(N)
loga(M/N) = loga(M) - loga(N)
loga(M^y) = yloga(M) 

The Slope-Intercept Equation of a Line

If a line has slope (gradient) m and y-intercept c, its equation is y = mx + c.

The Point-Slope Equation of a Line

If a line has a slope of m and passes through (xv1,yv1), its equation is y-yv1 = m(x-xv1).

Parallel & Perpendicular Lines

Parallel equal slopes. Perpendicular opposite reciprocal slopes (product -1)

Arithmetic Sequence - constant difference d 

U1+(n-1)d

Arithmetic Series

1/2n[2uv1+(n-1)d]

Geometric Sequence - constant ratio r

Uv1 x r^n-1

Geometric Series

uv1[r^n-1]/[r-1]

Uv1 = 1st term