Rules of Indices
Surd Rules
Rationalising Surds 1
Rationalising Surds 2
Difference of two squares
General form of a quadratic equation
y = ax2 + bx + c
a, b and c are constants
a cannot equal zero
Completing the Square Example
Remember to factor out any coefficient on the a
Remember to half the coefficient of b
Remember to minus any other bits
Quadratic Formula
ax2 + bx + c = 0 can be solved with the quadratic formula
Sketching Quadratic Graphs
If a>0 = smiley shaped curve
if a<0 = unhappy shaped curve
put y=0 to find the x-axis crossing points
put x=0 to find the y-axis crossing points
The discriminant:
equal roots: b2 =4ac (equals x axis points)
real roots: b2>4ac (crosses x axis points)
no real roots: b2<4ac (doesn't cross x axis)
Simultaneous Equations
Both elimination and substitution for linear equations
Use substitution for one linear and one quadratic
How to solve a quadratic inequality
Solve the corresponding quadratic equation
Sketch the graph of the quadratic function
Use the sketch to find the required set of values
ie, if equation > 0 look above x axis (separate inequalities)
if equation < 0 look below x axis (joined inequalities)
If question has another equation, sketch both on a graph and then calculate the set of values for x which satisfy the inequalities
What should be done when multiplying or dividing an inequality by a negative number?
The inequality sign should be flipped
