Super Simple Maths

Contents
Number and arithmetic
	Introducing numbers
	Decimals
	Written addition and subtraction
	Adding and subtracting decimals
	Negative numbers
	Multiplying and dividing by 10, 100, and 1000
	Methods of multiplication
	Methods of division
	Mental addition and subtraction
	Mental multiplication and division
	Powers of numbers
	Factors and multiples
	Prime numbers
	Prime factorization
	Common factors and multiples
	Order of operations
Angles and shapes
	Angles
	Angle facts
	Angles and parallel lines
	Measuring and drawing angles
	Symmetry
	Properties of triangles
	Properties of quadrilaterals
	Properties of polygons
	Angles in a triangle
	Angles in a quadrilateral
	Exterior angles of a polygon
	Interior angles of a polygon
	Properties of a circle
	Practice question: Working with angles
Fractions, decimals, and percentages
	Fractions
	Improper fractions and mixed numbers
	Comparing fractions
	Adding and subtracting fractions
	Fraction of an amount
	Multiplying fractions
	Dividing fractions
	Percentages
	Fractions, decimals, and percentages
	Percentage of an amount
	Mental percentage calculations
	Finding the percentage change
	Percentage increase and decrease
	Reverse percentages
	Growth and decay
	Compound interest
	Recurring decimals
	Recurring decimals and fractions
Measure
	Metric units of measure and time
	Imperial units of measure
	Converting units of measure
	Converting units of area and volume
	Compound units of measure
	Practice questions: Working with compound units
	Perimeter and area
	Area formulas
	How area formulas work
	Circumference and area of a circle
	Length of an arc and area of a sector
	Practice questions: Compound 2-D shapes
	3-D shapes
	3-D sections
	Plans and elevations
	Volume of a cuboid
	Surface area of a cuboid
	Volume and surface area of a prism
	Volume and surface area of a cylinder
	Volume and surface area of a pyramid
	Volume and surface area of a cone
	Volume and surface area of a sphere
	Practice questions: Compound 3-D shapes
	Rounding and estimating
	Bounds of accuracy
Introducing algebra
	Algebraic terms
	Expressions
	Substitution
	Indices in algebra
	Expanding brackets
	Expanding quadratics
	Factorizing
	Factorizing quadratics
	Factorizing harder quadratic expressions
	The difference of two squares
	Algebraic fractions
	Adding and subtracting algebraic fractions
	Multiplying and dividing algebraic fractions
	Formulas
	Rearranging formulas
	Functions
	Inverse functions
	Composite functions
Powers and calculations
	Higher powers and estimating powers
	Roots
	Negative powers
	Multiplying and dividing with powers
	Raising a power to a power
	Fractional powers and roots
	Practice questions: Calculating with powers
	Surds and irrational numbers
	Simplifying surd expressions
	Surds in fractions
	Exact calculations
	Standard form
	Multiplying and dividing with standard form
	Adding and subtracting with standard form
Equations and graphs
	Equations
	Solving simple equations
	Solving harder equations
	Equations with brackets
	Simultaneous equations
	Practice question: Real-world simultaneous equations
	Solving simple quadratic equations
	Solving harder quadratic equations
	Completing the square
	How to complete the square
	The quadratic formula
	Practice question: Choosing a method for quadratic problems
	Trial and improvement
	The coordinate grid
	Linear graphs
	Equation of a straight line
	Parallel and perpendicular lines
	Length and midpoint of a line segment
	Quadratic graphs
	Quadratics in the real world
	Solving simple equations using graphs
	Solving harder equations using graphs
	Inequalities
	Graphing linear inequalities
	Quadratic inequalities
Ratio and proportion
	Ratios
	Dividing in a given ratio
	Direct proportion
	Inverse proportion
	Unitary method
	Scaling method
	Proportion
	Comparing proportions
	Proportion equations
	Practice questions: Ratio and proportion
Geometry
	Vectors
	Working with vectors
	Adding and subtracting vectors
	Multiplying vectors
	Practice question: Vectors and geometry
	Translations
	Reflections
	Rotations
	Constructing rotations
	Enlargements
	Fractional and negative enlargements
	Scaling area and volume
	Practice questions: Combinations of transformations
	Scale drawings
	Bearings
	Constructing perpendicular lines
	Constructing angles
	Loci
	Practice questions: Using loci
	Congruent and similar shapes
	Congruent triangles
	Similar triangles
	Practice questions: Similarity and congruence
	Constructing triangles
	Circle theorems 1
	Circle theorems 2
Trigonometry
	Pythagoras’s theorem
	Trigonometry
	Sine, cosine, and tangent
	Finding lengths and angles
	Special angles
	The sine rule
	The cosine rule
	Area of a triangle
	Practice question: Using trigonometry
	Angles of elevation and depression
	Pythagoras in 3-D
	Practice question: 3-D trigonometry
Probability
	Probability scale
	Calculating probability
	Mutually exclusive events
	Counting outcomes
	Probability of two events
	Tree diagrams
	Conditional probability
	Conditional probability tables
	Venn diagrams
	Venn diagrams and probability
	Relative frequency
	Frequency trees
	Probability distributions
Statistics
	Statistical inquiry
	Types of data
	Populations and samples
	Frequency tables
	Bar charts
	Pictograms
	Line graphs
	Pie charts
	Mean, median, mode, and range
	Frequency tables and averages
	Standard deviation
	Practice question: Using standard deviation
	Cumulative frequency
	Quartiles
	Histograms
	Drawing histograms
	Time series
	Box plots
	Practice questions: Comparing distributions
	Scatter graphs
	Lines of best fit
Further graphs
	Distance-time graphs
	Speed-time graphs
	Area under a curve
	Gradient of a curve
	Linear real-life graphs
	Non-linear real-life graphs
	Domain and range of a function
	Cubic graphs
	Reciprocal graphs
	Exponential graphs
	Trigonometric graphs
	Transformations of graphs
	Equation of a circle
Sequences
	Number sequences
	Term-to-term rule
	Position-to-term rule
	Finding the nth term
	The nth term formula
	Arithmetic pattern sequences
	Arithmetic series
	Square and cube number sequences
	The triangular number sequence
	Quadratic sequences
	Geometric sequences
	The Fibonacci sequence
Glossary
Index
Acknowledgments