C1 Essentials: Summary of AQA Core 1 content not provided in the formula book Inequalities:

< > Quadratic inequalities:

Find critical values by solving = 0. Sketch the curve to identify the required region.

Rationalising the denominator:

1

+ =

( + )( )=

2

Straight lines:

1 = ( 1) Gradient=

Perpendicular lines have 12 = 1 Quadratic formula: 2 + + = 0

= 2 4

2

Completing the square:

2 + + = ( +

2)

2

2

4+

Roots of quadratics: No roots: 2 4 < 0 One root: 2 4 = 0

Two roots: 2 4 > 0

Circle equation: Centre (, ), radius :

( )2 + ( )2 = 2

Factor theorem: ( ) is a factor is a root

Remainder theorem: () ( ) has remainder () =

Differentiation:

=

= 1

is the rate of change of with respect to .

gives the gradient of the curve .

> 0 Function is increasing.

< 0 Function is decreasing.

Stationary points (eg max/min) occur when

= 0.

= 0 and

2

2> 0 min

= 0 and

2

2< 0 max

Integration:

=+1

+ 1+

is the area under the curve .

gives the area bounded by the curve, the -axis and the

lines = and = . If below the axis, integral will be < 0.