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Chapter Overview
Chapter Overview
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Forces and motion
Variable acceleration
Constant acceleration
Modelling in mechanics
Hypothesis testing I
Binomial distribution
Probability
Representation of data
Measures of location and spread
Data collection
Vectors I
Integration I
Differentiation I
Exponentials and logarithms
Trigonometric equations
Trigonometry
Binomial expansion I
Circles
Straight line graphs
Transformations
Sketching graphs
Polynomials
Equations and inequalities
Quadratics
Indices and surds
Proof I
138 Lessons
828 Exercises
Forces and motion
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Force diagrams
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Forces as vectors
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Forces and acceleration
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Motion in two dimensions
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Connected particles
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Pulleys
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Variable acceleration
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Functions of time: Displacement, velocity, acceleration
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Using differentiation to find velocity and acceleration
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Maxima and minima problems
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Using integration to find velocity and displacement
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Constant acceleration formulae
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Constant acceleration
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Displacement-time graphs
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Velocity-time graphs
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Constant acceleration: Deriving formulae
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Constant acceleration formulae: SUVAT
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Vertical motion under gravity
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Modelling in mechanics
Modelling assumptions
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Quantities and units in mechanics
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Working with vectors
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Hypothesis testing I
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Hypothesis testing
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Hypothesis testing: Finding critical values
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One-tailed tests
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Two-tailed tests
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Binomial distribution
Probability distributions
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The binomial distribution
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Cumulative probabilities
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Probability
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Calculating probabilities
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Venn diagrams
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Probability: Mutually exclusive and independent events
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Probability: Tree diagrams
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Representation of data
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Outliers
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Box plots
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Cumulative frequency
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Histograms
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Comparing data sets
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Correlation
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Linear regression
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Measures of location and spread
Measures of central tendency: Mean, median, mode
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Measures of spread: Range
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Variance and standard deviation
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Data collection
Population and samples
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Sampling techniques
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Types of data
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Vectors I
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Vectors
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Representing vectors
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Magnitude and direction of a vector
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Position vectors and displacement vectors
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Solving geometric problems
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Modelling with vectors
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Integration I
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Integrating x^n
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Indefinite integrals
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Finding functions by integrating
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Definite integrals
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Area under a curve
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Area under the x-axis
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Area between a curve and a line
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Differentiation I
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Finding the gradient of a curve
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Differentiation from first principles
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Differentiating x^n
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Differentiating functions with multiple terms
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Gradients, tangents and normals
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Increasing and decreasing functions
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Second order derivatives
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Stationary points
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Sketching gradient functions
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Modelling with differentiation
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Exponentials and logarithms
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Exponential functions
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y = e^x
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Exponential modelling
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Logarithms
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Laws of logarithms
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Solving equations using logarithms
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Natural logarithms
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Logarithms and non-linear data
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Harder exponential modelling
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Trigonometric equations
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Angles in all four quadrants
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Exact trigonometric values
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Trigonometric identities
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Simple trigonometric equations
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Harder trigonometric equations
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Equations and identities
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Trigonometry
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The cosine rule
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The sine rule
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Area of a triangle
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Solving triangle problems
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Trig graphs: sin x, cos x, tan x
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Transforming trigonometric graphs
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Binomial expansion I
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Pascal's triangle
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Factorial notation
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Binomial expansion
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Solving binomial problems
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Binomial estimation
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Circles
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Midpoints and perpendicular bisectors
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Equation of a circle
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Intersection of straight lines and circles
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Using tangent and chord properties
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Circles and triangles
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Intersection of two circles
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Straight line graphs
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y = mx + c
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Equations of straight lines
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Parallel and perpendicular lines
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Length and area
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Modelling with straight lines
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Transformations
Translating graphs
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Stretching and reflecting graphs
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Transforming graphs
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Sketching graphs
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Cubic graphs
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Quartic graphs
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Reciprocal graphs
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Points of intersection
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Using the discriminant
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Direct and inverse proportion
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Polynomials
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Functions
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Expanding brackets
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Factorising
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Simplifying algebraic fractions
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Polynomial division
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The factor theorem
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Equations and inequalities
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Linear simultaneous equations
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Quadratic simultaneous equations
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Set notation and interval notation
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Linear inequalities
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Quadratic inequalities
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Inequalities on graphs
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Inequality regions
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Quadratics
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Solving quadratic equations
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Completing the square
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Quadratic graphs
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Identifying the discriminant
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Solving disguised quadratics
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Indices and surds
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Laws of indices
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Negative and fractional indices
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Surds
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Rationalising the denominator
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Proof I
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Mathematical structure and arguments
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Disproof by counterexample
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Proof by deduction
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Proof by exhaustion
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Popular Chapters in All Year Groups
Fractions
Algebra
Statistics
Multiplication and division
Measurement
Trigonometry
Graphs
Geometry - properties of shapes
Probability
Shapes and area
Differentiation I
Exponentials and logarithms
Formulae and equations
Functions
Addition and subtraction
Integration I
Vectors I
Beta