A-Level Maths
Revision notes 2014
,Contents
Coordinate Geometry ........................................................................................................................... 2
Trigonometry ......................................................................................................................................... 4
Basic Algebra ......................................................................................................................................... 7
Advanced Algebra ................................................................................................................................. 9
Sequences and Series ........................................................................................................................ 11
Functions .............................................................................................................................................. 12
Differentiation ..................................................................................................................................... 14
Integration ........................................................................................................................................... 17
Numerical Methods ............................................................................................................................. 20
Vectors, Lines and Planes .................................................................................................................. 22
The Basics ............................................................................................................................................ 24
Representation of Data ...................................................................................................................... 26
Probability ............................................................................................................................................ 29
Probability Distributions ..................................................................................................................... 32
The Normal Distribution..................................................................................................................... 36
Bivariate Data ...................................................................................................................................... 38
These notes cover the main areas of this subject. Please check the specific areas you need with your exam
board. They are provided “as is” and S-cool do not guaranteed the suitability, accuracy or completeness of this
content and S-cool will not be liable for any losses you may incur as a result of your use or non-use of this
content. By using these notes, you are accepting the standard terms and conditions of S-cool, as stated in the s-
cool website (www.s-cool.co.uk).
1
, Coordinate Geometry
The Basics:
Find the distance between two points using Pythagoras' theorem.
The midpoint is the average (mean) of the coordinates.
The gradient =
Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1.
Straight Lines:
Equation of a straight line is y = mx + c, where m = gradient, c = y-intercept.
The equation of a line, if we know one point and the gradient is found using:
(y - y1) = m(x - x1)
(If given two points, find the gradient first, then use the formula.)
Two lines meet at the solution to their simultaneous equations.
Note: When a line meets a curve there will be 0,1, or two solutions.
1. Use substitution to solve the simultaneous equations
2. Rearrange them to form a quadratic equation
3. Solve the quadratic by factorising, or by using the quadratic formula.
4. Find the y-coordinates by substituting these values into the original equations.
Other Graphs (also in Functions):
Sketch the curve by finding:
1. Where the graph crosses the y-axis.
2. Where the graph crosses the x-axis.
3. Where the stationary points are.
4. Whether there are any discontinuities.
5. What happens as
Circles:
2
, Cartesian equation for a circle is (x - a)2 + (y - b)2 = r2 , where (a, b) is the centre of the circle and r is the radius.
Parametric Equations:
Sketch the graph by substituting in values and plotting points.
Find the cartesian form by either using substitution (use t = ...), or by using the identity, .
Find the gradient using the chain rule:
3
Revision notes 2014
,Contents
Coordinate Geometry ........................................................................................................................... 2
Trigonometry ......................................................................................................................................... 4
Basic Algebra ......................................................................................................................................... 7
Advanced Algebra ................................................................................................................................. 9
Sequences and Series ........................................................................................................................ 11
Functions .............................................................................................................................................. 12
Differentiation ..................................................................................................................................... 14
Integration ........................................................................................................................................... 17
Numerical Methods ............................................................................................................................. 20
Vectors, Lines and Planes .................................................................................................................. 22
The Basics ............................................................................................................................................ 24
Representation of Data ...................................................................................................................... 26
Probability ............................................................................................................................................ 29
Probability Distributions ..................................................................................................................... 32
The Normal Distribution..................................................................................................................... 36
Bivariate Data ...................................................................................................................................... 38
These notes cover the main areas of this subject. Please check the specific areas you need with your exam
board. They are provided “as is” and S-cool do not guaranteed the suitability, accuracy or completeness of this
content and S-cool will not be liable for any losses you may incur as a result of your use or non-use of this
content. By using these notes, you are accepting the standard terms and conditions of S-cool, as stated in the s-
cool website (www.s-cool.co.uk).
1
, Coordinate Geometry
The Basics:
Find the distance between two points using Pythagoras' theorem.
The midpoint is the average (mean) of the coordinates.
The gradient =
Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1.
Straight Lines:
Equation of a straight line is y = mx + c, where m = gradient, c = y-intercept.
The equation of a line, if we know one point and the gradient is found using:
(y - y1) = m(x - x1)
(If given two points, find the gradient first, then use the formula.)
Two lines meet at the solution to their simultaneous equations.
Note: When a line meets a curve there will be 0,1, or two solutions.
1. Use substitution to solve the simultaneous equations
2. Rearrange them to form a quadratic equation
3. Solve the quadratic by factorising, or by using the quadratic formula.
4. Find the y-coordinates by substituting these values into the original equations.
Other Graphs (also in Functions):
Sketch the curve by finding:
1. Where the graph crosses the y-axis.
2. Where the graph crosses the x-axis.
3. Where the stationary points are.
4. Whether there are any discontinuities.
5. What happens as
Circles:
2
, Cartesian equation for a circle is (x - a)2 + (y - b)2 = r2 , where (a, b) is the centre of the circle and r is the radius.
Parametric Equations:
Sketch the graph by substituting in values and plotting points.
Find the cartesian form by either using substitution (use t = ...), or by using the identity, .
Find the gradient using the chain rule:
3
