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3 difficulty levels · worked examples
Mathematics practice for secondary school students in Years 7 to 11. Work through KS3 and GCSE mathematics topics at Foundation, Core and Higher level, with worked examples, hints and a clear explanation of every mistake. It is tuition-style help and homework support your teenager can use in five minutes a day, earning rewards along the way.
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Topic · 01Not started
Fractions
- Equivalent fractions
- Adding & subtracting
- Multiplying & dividing
- Mixed numbers
- Fractions of an amount
Levels
BMH
Topic · 02Not started
Percentages
- Percentage of a number
- Increase & decrease
- Reverse percentages
- Percentage change
- Simple interest
Levels
BMH
Topic · 03Not started
Algebra
- Simplifying expressions
- Solving equations
- Expanding brackets
- Factorising
- Substitution
Levels
BMH
Topic · 04Not started
Ratio & Proportion
- Simplifying ratios
- Sharing in a ratio
- Direct proportion
- Inverse proportion
- Scale drawings
Levels
BMH
Topic · 05Not started
Geometry & Angles
- Angles on a line
- Triangles & polygons
- Parallel lines
- Area & perimeter
- Pythagoras' theorem
Levels
BMH
Topic · 06Not started
Probability & Statistics
- Likelihood scale
- Single-event probability
- Two-way tables
- Averages (mean, median, mode)
- Range & spread
Levels
BMH
Topic · 07Not started
Number Sense & Calculations
- Place value & rounding
- Negative numbers
- Order of operations
- Factors, multiples & primes
- Indices & standard form
Levels
BMH
Topic · 08Not started
Measures
- Metric units & conversions
- Perimeter & area
- Volume of solids
- Speed, density & pressure
- Scale & maps
Levels
BMH
Topic · 09Not started
Money & Finance
- Coins, prices & change
- Best buys
- Discounts & VAT
- Wages & budgeting
- Interest & currency
Levels
BMH
Topic · 10Not started
Statistics & Data Handling
- Mean, median & mode
- Range & spread
- Charts & graphs
- Grouped data
- Sampling & correlation
Levels
BMH
Topic · 11Not started
Rounding & Estimation
- Decimal places
- Significant figures
- Estimating calculations
- Error intervals
- Bounds in calculations
Levels
BMH
Topic · 12Not started
Factors, Multiples & Primes
- Factors
- Multiples
- Prime numbers
- Prime factor form
- HCF and LCM
Levels
BMH
Topic · 13Not started
Indices & Powers
- Index laws
- Powers of 10
- Zero and negative indices
- Fractional indices
- Combining index laws
Levels
BMH
Topic · 14Not started
Standard Form
- Writing in standard form
- Converting to ordinary numbers
- Multiplying in standard form
- Dividing in standard form
- Adding and subtracting in standard form
Levels
BMH
Topic · 15Not started
Surds
- Simplifying surds
- Adding like surds
- Multiplying surds
- Expanding brackets
- Rationalising denominators
Levels
BMH
Topic · 16Not started
Recurring Decimals & Exact Fractions
- Terminating vs recurring
- Fraction to decimal
- Decimal to fraction
- Algebraic method
- Recurring decimal arithmetic
Levels
BMH
Topic · 17Not started
Expressions & Simplifying
- Collecting like terms
- Multiplying terms
- Substitution
- Writing expressions
- Simplifying
Levels
BMH
Topic · 18Not started
Solving Equations
- One-step equations
- Two-step equations
- Unknowns on both sides
- Brackets in equations
- Fractional equations
Levels
BMH
Topic · 19Not started
Brackets & Expanding
- Single brackets
- Double brackets
- Expanding and simplifying
- Negative brackets
- Three brackets
Levels
BMH
Topic · 20Not started
Factorising
- Common factors
- Factorising quadratics
- Difference of two squares
- Harder quadratics
- Checking by expanding
Levels
BMH
Topic · 21Not started
Formulae & Substitution
- Substituting into formulae
- Writing formulae
- Rearranging formulae
- Formulae with powers
- Real-life formulae
Levels
BMH
Topic · 22Not started
Sequences
- Term-to-term rules
- nth term of linear sequences
- Special sequences
- Using the nth term
- Quadratic sequences
Levels
BMH
Topic · 23Not started
Inequalities
- Inequality symbols
- Solving linear inequalities
- Number lines
- Integer solutions
- Regions
Levels
BMH
Topic · 24Not started
Simultaneous Equations
- Elimination
- Substitution
- Forming from word problems
- Graphical solutions
- Linear and quadratic
Levels
BMH
Topic · 25Not started
Quadratic Equations
- Factorising
- Quadratic formula
- Completing the square
- Discriminant
- Word problems
Levels
BMH
Topic · 26Not started
Algebraic Fractions
- Simplifying
- Adding and subtracting
- Multiplying and dividing
- Solving equations
- Complex expressions
Levels
BMH
Topic · 27Not started
Functions
- Function notation
- Evaluating functions
- Composite functions
- Inverse functions
- Domain and range
Levels
BMH
Topic · 28Not started
Iteration & Trial and Improvement
- Iterative formulae
- Filling a table
- Converging to a root
- Trial and improvement
- Accuracy
Levels
BMH
Topic · 29Not started
Algebraic Proof
- Expressing even/odd numbers
- Consecutive numbers
- Proving identities
- Counter-examples
- Multi-step proofs
Levels
BMH
Topic · 30Not started
Coordinates & Midpoints
- Quadrants
- Plotting points
- Midpoint of a line
- Length of a line segment
- 3D coordinates
Levels
BMH
Topic · 31Not started
Linear Graphs
- y=mx+c form
- Gradient
- Intercepts
- Drawing lines
- Parallel & perpendicular lines
Levels
BMH
Topic · 32Not started
Quadratic & Non-Linear Graphs
- Parabola shape
- Tables of values
- Roots and turning points
- Cubic graphs
- Reciprocal graphs
Levels
BMH
Topic · 33Not started
Real-Life Graphs
- Conversion graphs
- Distance-time context
- Cost graphs
- Reading gradient in context
- Reading intercept in context
Levels
BMH
Topic · 34Not started
Motion-Time Graphs
- Distance-time gradient = speed
- Speed-time gradient = acceleration
- Area under speed-time graph
- Interpreting motion graphs
- Estimating with tangents
Levels
BMH
Topic · 35Not started
2D Shapes & Properties
- Naming polygons
- Symmetry
- Quadrilateral properties
- Interior angles
- Exterior angles
Levels
BMH
Topic · 36Not started
3D Shapes & Nets
- Naming solids
- Faces, edges, vertices
- Nets
- Plans and elevations
- Euler's formula
Levels
BMH
Topic · 37Not started
Angles & Angle Rules
- Angles on a line/point
- Triangles & quadrilaterals
- Parallel line rules
- Angle reasoning
- Vertically opposite angles
Levels
BMH
Topic · 38Not started
Bearings
- Three-figure bearings
- Measuring from north
- Back bearings
- Bearings with distance
- Scale drawings
Levels
BMH
Topic · 39Not started
Perimeter & Area
- Perimeter
- Area of rectangles & triangles
- Parallelograms & trapeziums
- Compound shapes
- Area problem solving
Levels
BMH
Topic · 40Not started
Circles
- Parts of a circle
- Circumference
- Area of a circle
- Arcs
- Sectors
Levels
BMH
Topic · 41Not started
Surface Area & Volume
- Volume of cuboids
- Volume of prisms & cylinders
- Surface area
- Cones & spheres
- Frustums
Levels
BMH
Topic · 42Not started
Constructions & Loci
- Using compasses
- Perpendicular bisector
- Angle bisector
- Constructing triangles
- Loci
Levels
BMH
Topic · 43Not started
Transformations
- Translation
- Reflection
- Rotation
- Enlargement
- Combined transformations
Levels
BMH
Topic · 44Not started
Similarity & Congruence
- Congruence conditions
- Similar shapes
- Scale factors
- Missing sides/angles
- Area & volume scale factors
Levels
BMH
Topic · 45Not started
Pythagoras' Theorem
- Finding the hypotenuse
- Finding a shorter side
- Checking right angles
- Pythagoras with coordinates
- 3D Pythagoras
Levels
BMH
Topic · 46Not started
Trigonometry
- SOHCAHTOA sides
- SOHCAHTOA angles
- Exact trig values
- Sine rule
- Cosine rule & area
Levels
BMH
Topic · 47Not started
Circle Theorems
- Angle in a semicircle
- Angles in the same segment
- Cyclic quadrilaterals
- Tangent rules
- Alternate segment theorem
Levels
BMH
Topic · 48Not started
Vectors
- Column vectors
- Adding & subtracting vectors
- Scalar multiples
- Magnitude of a vector
- Vector geometry proofs
Levels
BMH
Topic · 49Not started
Geometric Proof
- Angle fact reasons
- Proving congruence
- Proving similarity
- Structured proof writing
- Circle theorem proofs
Levels
BMH
Topic · 50Not started
Proportion
- Unitary method
- Direct proportion
- Inverse proportion
- Best value
- Proportion formulae (k)
Levels
BMH
Topic · 51Not started
Compound Measures
- Speed distance time
- Density mass volume
- Pressure force area
- Unit conversion of rates
- Mixed compound measures
Levels
BMH
Topic · 52Not started
Tree Diagrams & Combined Events
- Listing outcomes
- Independent events
- With replacement
- Without replacement
- Conditional probability
Levels
BMH
Topic · 53Not started
Venn Diagrams & Set Notation
- Two-set Venn diagrams
- Union and intersection
- Complement
- Set notation
- Probability from a Venn diagram
Levels
BMH
Topic · 54Not started
Handling Data
- Averages and range
- Mode median mean from lists
- Frequency tables
- Grouped data estimated mean
- Comparing distributions
Levels
BMH
Topic · 55Not started
Statistical Diagrams
- Bar charts and pictograms
- Pie charts
- Scatter graphs and correlation
- Stem and leaf diagrams
- Cumulative frequency and box plots
Levels
BMH
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