A level Mathematics Revision Guide
Introduction
1.
Surds & Indices
1.1.
Types of Numbers
1.1.1.
Integers
1.1.2.
Rational Numbers
1.1.3.
Irrational Numbers
1.1.4.
Real Numbers
1.2.
Raising Powers
1.3.
Index Notation
1.4.
Multiplication Rule
1.5.
Division Rule
1.6.
Power-On-Power Rule
1.7.
Factor Rule
1.8.
Negative Powers
1.9.
Zero Power
1.10.
Roots
1.10.1.
Square Roots
1.10.2.
Cube Roots
1.10.3.
nth Roots
1.11.
Surds
1.12.
Multiplying Surds
1.13.
Dividing Surds
1.14.
Simplifying Surds
1.15.
Rationalise Denominators
1.16.
Difference of Two Squares
1.17.
Fractional Indices
2.
Coordinate Geometry
2.1.
Cartesian Coordinates
2.2.
Distances
2.3.
Straight Lines
2.4.
Line Segments
2.5.
Midpoint
2.6.
Gradient
2.7.
x-Intercept
2.8.
y-Intercept
2.9.
Lines Have Equations
2.9.1.
Vertical Lines
2.9.2.
Horizontal Lines
2.9.3.
Slope Intercept Form
2.9.4.
Point & Gradient
2.9.5.
Two Points
2.9.6.
General Equation
2.10.
Finding Gradient & y-Intercept
2.11.
Intersection of Two Lines
2.12.
Perpendicular Lines
3.
Velocity & Acceleration
3.1.
Scalars & Vectors
3.2.
Describing Motion
3.3.
Displacement & Distance
3.4.
Velocity & Speed
3.5.
Area Under a Graph
3.6.
Constant Velocity
3.7.
Acceleration & Deceleration
3.8.
Constant Acceleration
3.8.1.
Velocity After Time
3.8.2.
Displacement After Time
3.8.3.
Velocity After Displacement
3.8.4.
Average Velocity
3.9.
Splitting Scenario into Stages
4.
Representation of Data
5.
Location & Spread
6.
Quadratics
7.
Inequalities
8.
Functions
9.
Factorials
10.
Probability
11.
Perms & Combs
11.1.
Counting
11.2.
Adding Rule
11.2.1.
Adding Examples
11.2.2.
Adding Quiz
11.3.
Multiplying Rule
11.4.
Repeated Addition
11.5.
Multi-step Processes
11.6.
Avoid Duplicate Outcomes
11.7.
Arrangements
11.7.1.
Placing Object by Object
11.7.2.
Putting Objects into Boxes
11.7.3.
Assigning Objects to each Box
11.8.
Factorial Notation
11.9.
Permutations
11.10.
Permutations Examples
11.11.
Combinations
11.12.
Grouping
12.
Newton's Laws of Motion
13.
Differentiation
14.
Trigonometry
14.1.
Trig are Ratios
14.2.
Unit Circle
14.3.
Period & Amplitude
14.4.
Sine Curve
14.5.
Cosine Curve
14.6.
Tangent Curve
14.7.
Common Values
14.8.
Periodic Properties
14.9.
Translation Properties
14.10.
Solving Trig
14.11.
Identities
15.
Radians
15.1.
Using Radians
15.2.
Common Angles
15.3.
Arc Length
15.4.
Sector Area
15.5.
Segment Area
15.6.
Trig Graphs
15.7.
Trig Symmetry
15.8.
Inverse Trig
16.
Friction
16.1.
What's Happening?
16.2.
Coefficient of Friction
17.
Arithmetic Series
17.1.
Sequences
17.2.
Describing Sequences
17.3.
Inductive Definition
17.4.
Triangle Numbers
17.5.
Arithmetic Progressions
17.6.
Summing APs
18.
Binomial Theorem
18.1.
The Long Way
18.2.
Binomial Expansion
18.3.
Finding the Coefficients
19.
Geometric Series
19.1.
Geometric Sequece
19.2.
Summing GPs
19.3.
Converging
19.4.
Diverging
19.5.
Oscillating
19.6.
Exponential Growth & decay
20.
Vectors
20.1.
Vectors as Arrows
20.2.
Vectors aren't Arrows
20.3.
Column Vectors
20.4.
Scalars
20.5.
Multiplying by Scalars
20.6.
Adding Vectors
20.7.
Subtracting Vectors
20.8.
Unit Vectors
20.9.
Position Vectors
20.10.
Writing Vectors
21.
Vectors in 3D
21.1.
Three Components
21.2.
Base Vectors
21.3.
Adding, Subtracting, Multiplying
21.4.
No More Gradients
21.5.
Skew Lines
21.6.
Planes
21.7.
Collinear Points
21.8.
Magnitude
21.9.
Multiplying Magnitude
21.10.
Scalar Products
21.10.1.
Sum of Components
21.10.2.
From Angle
21.10.3.
What Does It Mean?
21.11.
Unit Vectors
21.12.
Finding Angles
21.13.
Projections
22.
Appendix – Useful Stuff
22.1.
Sets
22.2.
Triangle Terms
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A level Mathematics Revision Guide
Chapter 7
Inequalities