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Algebraic Fractions

• Adding and subtracting algebraic fractions
• Multiplying and dividing algebraic fractions
• Simplifying algebraic fractions

Expanding and factorising

• Collecting like terms
• Expanding a single bracket
• Expanding double brackets
• Expanding Triple Brackets
• Factorising single brackets
• Factorising quadratics
• Algebraic Index Laws

Functions and function notation

• Function Machines
• Composite functions
• Evaluating a function
• Inverse functions

Graphs

• Coordinates in four quadrants
• Graph Transformations
• Travel Graphs
• Recognising graph shapes
• Key points on exponential and trigonometric graphs
• Sensitivity reasoning without calculation
• Quadratic graphs
• Real Life Graphs

Inequalities

• Solving quadratic inequalities
• Inequalities on a Number line
• Solving linear inequalities
• Graphical Inequalities

Solving linear equations

• One-step and two-step equations
• Unknowns on both sides
• Equations with brackets
• Equations with fractions

Notation and vocabulary

• Notation conventions
• Vocabulary: expression, equation, formula, identity

Plotting cubic, reciprocal and exponential graphs

• Plotting cubic, reciprocal and exponential graphs

Proof

• Algebraic proof

Solving quadratic equations

• Completing the square
• Factorising to solve ax² + bx + c = 0 (a ≠ 1)
• Factorising to solve x² + bx + c = 0
• The Quadratic Formula

Rearranging formulae

• Rearranging formulae

Sequences

• Arithmetic Sequences
• Quadratic Sequences
• Iteration
• Geometric sequences
• Other Sequences

Simultaneous equations

• Linear simultaneous equations
• Linear and Non-linear simultaneous equations

Straight-line graphs

• Circle Equations
• Equation of Parallel and Perpendicular Lines
• Equations of Straight lines
• Plotting a straight-line graph

Substitution into formulae

• Kinematics formula substitution
• Substitution

Differentiation and stationary points

• Differentiation and stationary points

3D shapes, plans and elevations

• Nets
• Interpreting plans and elevations
• Properties of 3D shapes

Angles and Bearings

• Angles in polygons
• Vertically opposite angles
• Angles in triangles and quadrilaterals
• Angles on a straight line and at a point
• Parallel lines angle rules
• Bearings

Arcs and Sectors

• Arc length
• Sector area
• Sector angles at the centre

Area and Perimeter

• Area of a circle
• Area of parallelograms
• Area of trapezia
• Area of triangles
• Circumference of a circle
• Perimeter of composite shapes
• Area of composite shapes

Circle chord and tangent properties

• Circle chord and tangent properties

Circle theorems

• The angle at the centre
• Angles in the same segment
• Circle theorem proofs: tangents from an external point
• Cyclic quadrilaterals
• Radii and isosceles triangles
• Circle theorems: tangent and radius
• The alternate segment theorem
• The angle in a semicircle

Congruence and similarity

• Similar figures: area scale factor
• Similar figures: length scale factor
• Similar figures: volume scale factor
• Geometric Proofs
• Congruent Triangles

Constructions and loci

• Construction
• Loci
• Measuring

Coordinate geometry problems

• Distance between two points
• Dividing a line segment

Frustum: surface area and volume

• Frustum: surface area and volume

Pythagoras' theorem and trigonometry

• 2D Pythagoras
• 3D Pythagoras
• 3D trigonometry
• Exact trigonometric values
• Right Angled Trigonometry

Quadrilaterals and triangles properties

• Special quadrilateral properties
• Triangle properties

Non-Right Angled Trigonometry

• Cosine rule
• Sine rule
• Area of a triangle using ½ab sin C
• Sine rule: finding an angle (ambiguous case)

Surface area

• Surface area of composite solids
• Surface area of cones
• Surface area of pyramids
• Surface area of spheres

Transformations

• Combined Transformations
• Reflections
• Rotations
• Enlargements Negative Scale Factor
• Enlargements Positive Scale Factor
• Translations

Vectors

• Describing translations as vectors
• Vector arithmetic
• Vector geometric proofs

Vocabulary and notation

• Circle parts vocabulary
• Conventions, points, lines, and angles
• Polygon properties and symmetry

Volume

• Volume of prisms and cylinders
• Volume of composite solids
• Volume of Cones, Spheres and Pyramids

Symmetry of solids

• Symmetry of solids

Calculating with integers, decimals and fractions

• Inverse operations and reciprocals
• Order of operations
• Addition and Subtraction of Negative numbers
• Addition and Subtraction of Positive numbers
• Multiplication and Division of Negative numbers
• Multiplication and Division of Positive numbers

Estimation, rounding and accuracy

• Error Intervals
• Estimation
• Limits of accuracy and bounds
• Rounding to decimal places and significant figures
• Rounding to 1, 10, 100, 1000

Surds

• Rationalising denominators
• Simplifying surds

Factors, multiples and primes

• Factors, Multiples and Primes
• HCF and LCM
• Prime factorisation
• Smallest total satisfying fraction and percentage constraints

Fractions and percentages as operators

• Finding a percentage of an amount
• Fraction of the remainder problems
• Finding a fraction of a quantity
• Percentage increase and decrease (percentage method)
• Reverse percentage problems
• Writing one quantity as a fraction of another

Fractions, decimals and percentages: conversion

• Recurring decimals to fractions
• Terminating decimals to fractions

Operations with Fractions

• Adding and Subtracting Fractions
• Dividing fractions
• Multiplying fractions

Ordering and comparing numbers

• Using inequality symbols to compare numbers
• Ordering fractions
• Ordering integers and decimals
• Ordering fractions, decimals and percentages

Powers, roots and indices

• Index Laws
• Squares, cubes and roots
• Estimating powers and roots

Set language and notation

• Set language and notation

Standard form

• Addition and subtraction with standard form
• Converting between standard and Normal form
• Multiplication and Division with standard form

Systematic listing and counting

• The product rule for counting
• Systematic listing strategies

Time zones and time differences

• Time zones and time differences

Expected and relative frequency

• Calculating expected frequency
• Relative Frequency

Probability scale and basic principles

• Mutually exclusive
• Probability scale
• Missing probabilities from a spinner

Tree diagrams and combined events

• Independent events with replacement
• Conditional probability: tree diagrams and the formula
• Tree Diagrams
• Dependent events without replacement
• Sample space diagrams
• Frequency Trees

Two-way tables and Venn diagrams

• Two-way tables
• Venn Diagrams

Direct and inverse proportion

• Direct and Inverse Proportion Problems
• Reading values from a proportionality graph
• Percentage change with a power relationship
• Direct Proportions
• Inverse proportion

Fractions of quantities and relationships

• Express a multiplicative relationship as a ratio or fraction
• Express one quantity as a fraction of another

Financial Maths

• Compound interest
• Depreciation
• Simple interest
• Recurrence relation population model

Percentages

• Percentage change as a fraction or decimal
• Percentage increase and decrease (multiplier method)
• Percentages greater than 100%
• Reverse Percentages

Proportion as equality of ratios

• Equivalent ratios and proportion
• Ratio as a fraction and a linear function

Rates of change from graphs

• Gradient and Rate of Change from Graphs

Ratio notation and sharing

• Best buys
• Linked ratios with a shared term
• Ratio: mixing and concentrations
• Ratio in real contexts: conversion and comparison
• Sharing in a given ratio
• Simplifying ratios
• Three-way ratio redistribution

Scale diagrams and maps

• Map Scales and Scale Diagrams

Similarity and comparing measures

• Comparing areas and volumes using ratio
• Comparing lengths using ratio
• Similar right-angled triangles with trigonometric ratios

Units and compound measures

• Converting standard units
• Density
• Pressure
• Rates of pay
• Speed

Averages, spread and comparing distributions

• Average and Range from a list
• Averages problems
• Box plots
• Comparing distributions
• Quartiles and interquartile range

Bar and pie charts

• Composite bar charts
• Drawing bar charts
• Drawing pie charts
• Dual bar charts
• Pie charts

Frequency tables

• Averages and Range from Frequency Tables
• Averages from Grouped Frequency Tables

Grouped and continuous data diagrams

• Cumulative Frequency
• Frequency polygons
• Histograms

Sampling and populations

• Capture-recapture
• Sampling
• Types of Data

Scatter graphs and correlation

• Lines of best fit
• Plotting scatter graphs
• Describing correlation

Stem-and-leaf diagrams

• Dual Stem and Leaf Diagrams
• Stem and Leaf Diagrams

Tables, pictograms and other diagrams

• Misrepresentation of statistical diagrams
• Frequency Tables
• Line graphs
• Pictograms
• Vertical line charts