C1 – Basic Algebra Summary
 Properties of surds:
a  b = ab
a
b

 Properties of surds:
a b



a  b = ab
a c  b c  ( a  b) c
a
b
a
b
 To rationalise the denominator, in general
1
C1 – Basic Algebra Summary
1
, multiply its numerator and its denominator by a  b
a b

Expressing a quadratic in the form y  ( x  p)  q is called completing
the square.
In summary,
Halve the coefficient of x to obtain p.
Subtract the square of the constant to obtain q.

2
2

2

Nb/ take care when the coefficient of x is not 1.

 b  b  4ac
2a
D  b 2  4ac is called the discriminant of the quadratic equation.


a
b
 To rationalise the denominator, in general
General form of a quadratic y  ax  bx  c , with a  0 .
When a > 0 the graph of y is  shaped and y has a minimum value.
When a < 0 the graph of y is  shaped and y has a maximum value.
Quadratic factors used to give information about the graph and to solve the
equation.
x

a c  b c  ( a  b) c
General form of a quadratic y  ax  bx  c , with a  0 .
When a > 0 the graph of y is  shaped and y has a minimum value.
When a < 0 the graph of y is  shaped and y has a maximum value.
Quadratic factors used to give information about the graph and to solve the
equation.
2
Expressing a quadratic in the form y  ( x  p)  q is called completing
the square.
In summary,
Halve the coefficient of x to obtain p.
Subtract the square of the constant to obtain q.
2
2

Nb/ take care when the coefficient of x is not 1.

 b  b 2  4ac
2a
D  b 2  4ac is called the discriminant of the quadratic equation.
2
When D > 0, the equation has two distinct real roots.
When D < 0, the equation has no real roots.
When D = 0, the equation has one repeated root.
To solve a quadratic inequality you should sketch a graph of the quadratic
function involved.
Simultaneous Equations, one linear and one quadratic. Substitute the
linear equation into the quadratic equation.
, multiply its numerator and its denominator by a  b
x


When D > 0, the equation has two distinct real roots.
When D < 0, the equation has no real roots.
When D = 0, the equation has one repeated root.
To solve a quadratic inequality you should sketch a graph of the quadratic
function involved.
Simultaneous Equations, one linear and one quadratic. Substitute the
linear equation into the quadratic equation.