Year 10 skills
Numbers
Skills
- Order and compare numbers by magnitude
- Identify prime numbers
- Identify factors
- Prime factorisation
- Calculating with time
- Average speed, distance and time
- Average rate problems
- Converting units of speed
- Addition and subtraction of square roots
- Approximation of the square root
- Approximation of the cube root
- Evaluate expressions involving exponents
- Simplification of square and cubic roots
- Standard form - scientific notation
- Identify rational and irrational numbers
- Evaluate percentages
- Order of operations
- Finding values based on ratios
- Upper and lower bounds of a rounded measurement
Challenge Count occurrence of digits- Challenge How many numbers have a given set of digits
- Challenge Prime factor decomposition
- Challenge Special numbersPremium
- Challenge Level 1: Find integer solutions to linear equationsPremium
- Challenge Level 2: Find integer solutions to linear equationsPremium
- Challenge Numeric sequences from geometric shapes
Financial mathematics
Skills
Algebra
Premium exam preparation Parent Plus
Tests
Algebra: Quadratic equations: factorisation, discriminants, turning points, modellingPremium- Algebra: Solve linear equations and simultaneous linear systemsPremium
- Algebra: Simplify, add and subtract rational algebraic expressionsPremium
- Algebra: Polynomial factorisation, division and remainder theoremsPremium
- Algebra: Simplify expressions using integer and rational indicesPremium
- Algebra: Solve quadratic equations by factorisationPremium
Skills
- Coefficients and constants
Premium - Degree and leading coefficient of a polynomial
- Level 1: Simplification and expansion of algebraic expressions
Cheat sheet on the topic - Level 2: Simplification and expansion of algebraic expressions PremiumCheat sheet on the topic
- Level 3: Simplification and expansion of algebraic expressionsPremiumCheat sheet on the topic
- Level 1: Integer indicesCheat sheet on the topic
- Level 2: Integer indicesPremiumCheat sheet on the topic
- Rational indicesCheat sheet on the topic
- Symbolic substitution in algebraic expressionsCheat sheet on the topic
- Arithmetic sequences
- Geometric sequences
- Solve linear equationsCheat sheet on the topic
- Linear equations involving fractionsCheat sheet on the topic
- Solving simultaneous linear equationsCheat sheet on the topic
- Simultaneous linear equations word problemsPremiumCheat sheet on the topic
- Transposing formulasCheat sheet on the topic
- Solve inequalities in a single variableCheat sheet on the topic
- Word problems involving inequalities in a single variable
- Completing the squareCheat sheet on the topic
- Factorisation
- Level 1: Factorising polynomials
- Level 2: Factorising polynomials
- Level 3: Factorising polynomials
- Long division of polynomialsCheat sheet on the topic
- Remainder and factor from long division of polynomialsPremium
- Adding and subtracting polynomials
- Multiplying a polynomial by a binomial
- The remainder theorem
- The factor theorem
- Solving a cubic equation from its factorsPremium
- Level 1: The quadratic equation discriminantCheat sheet on the topic
Historical note - Level 2: The quadratic equation discriminantCheat sheet on the topicHistorical note
- Level 1: Solve the quadratic equation by factorisationCheat sheet on the topicHistorical note
- Level 2: Solve the quadratic equation by factorisationCheat sheet on the topicHistorical note
- Level 3: Solve the quadratic equation by factorisationCheat sheet on the topicHistorical note
- Quadratic models
- Level 1: Quadratic turning pointCheat sheet on the topic
- Level 2: Quadratic turning pointCheat sheet on the topic
- Level 1: Simplification of rational algebraic expressionsCheat sheet on the topic
- Level 2: Simplification of rational algebraic expressionsPremiumCheat sheet on the topic
- Level 1: Addition and subtraction of rational expressionsCheat sheet on the topic
- Level 2: Addition and subtraction of rational expressionsCheat sheet on the topic
- Level 3: Addition and subtraction of rational expressionsCheat sheet on the topic
Exponentials and logarithms
Skills
Coordinate geometry
Tests
Skills
- Coordinates of points on a line
- Level 1: Distance between points on a line and the midpoint
- Level 2: Distance between points on a line and the midpointPremium
- Linear intercepts
- The gradient of a line
- Transformation of a line
- Level 1: System of linear inequalities in two variables
- Level 2: System of linear inequalities in two variablesPremium
- Level 1: Coordinate of a point on a line given the length
- Level 2: Coordinate of a point on a line given the lengthPremium
- Coordinates of a planar shape from a line
- Number of intersections between a line and a parabolaPremium
- Tangent line to a parabolaPremium
- Point of intersection of a line and a parabolaPremium
- Intersection of two graphs
- The parabola
- Sketch the parabola
- Level 1: Point position relative to a circle
- Level 2: Point position relative to a circlePremium
- Level 1: Equation of a circle
- Level 2: Equation of a circlePremium
- Level 1: Radius of a circle from its equation
- Level 2: Radius of a circle from its equationPremium
- Level 1: Recognise the equation of a circle
- Level 2: Recognise the equation of a circlePremium
- Level 1: Point position relative to a parabola
- Level 2: Point position relative to a parabolaPremium
- Level 1: Parabolas with no x-intercepts
- Level 2: Parabolas with no x-interceptsPremium
- Level 1: Direction a parabola opens
- Level 2: Direction a parabola opensPremium
- Level 1: Point position relative to a hyperbolaPremium
- Level 2: Point position relative to a hyperbolaPremium
- Level 1: Equation of a hyperbolaPremium
- Level 2: Equation of a hyperbolaPremium
- Level 1: Asymptotes of a hyperbolaPremium
- Level 2: Asymptotes of a hyperbolaPremium
- Level 1: Recognise the equation of a hyperbolaPremium
- Level 2: Recognise the equation of a hyperbolaPremium
Geometry
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Skills
- Congruent triangles
- Line and rotational symmetry
- Convert metric units
- Pythagoras' theorem
- Similar triangles
- Circle theorems involving chords, secants and tangentsPremium
- Theorem on cyclic quadrilateralsPremium
- Calculate the area of a compound shape
- Angles in a circle
- Classify angle types
- Level 1: Circumference of a circle
- Level 2: Circumference of a circlePremium
- Level 1: Calculate the properties of compound planar shapes
- Level 2: Calculate the properties of compound planar shapes
- Covering shapes with tilesPremium
- Calculate the properties of basic three-dimensional shapes
- Level 1: Calculate the surface area of a pyramid
- Level 2: Calculate the surface area of a pyramidPremium
Trigonometry
Skills
- Conversions between radians and degrees
- Angle of elevation and angle of depression
- Evaluate trigonometric functions
- Sketch trigonometric functions
- Trigonometric functions and trianglesPremium
- Calculations involving bearingsPremium
- The sine and cosine lawsPremium
- Trigonometric relations involving circlesPremium
- Trigonometric relations involving complex geometric shapesPremium
Discrete mathematics
Skills
- Vector arithmetic
- Position vectors and ratios
- Level 1: Matrix addition and subtraction
- Level 2: Matrix addition and subtractionPremium
- Matrix multiplicationPremium
- Permutations
- Combinations
- Challenge How to get home in bekomazePremium
- Challenge Tic-tac-toePremium
- Challenge Permutations of digits in numbersPremium
Calculus
Set theory
Skills
Functions and relations
Tests
Skills
Probability
Skills
- Sample spaces and event language
- Probability of simple events
- Probability from two-way tables
- Conditional probability from a two-way tablePremium
- Probability of compound events
- Conditional probability and independencePremium
- Conditional probability from given probabilitiesPremium
- Conditional probability and independence: conceptsPremium
- Testing independence with the multiplication rule
- Probability of independent events combined
- Challenge Winning the tic-tac-toePremium
Statistics
Skills
- Understanding frequency tables
- Understanding bar charts
- Understanding stem-and-leaf plots
- Stem-and-leaf plots of decimal dataPremium
- Skewness of the stem-and-leaf plotPremium
- Understanding histograms
- Summary and spread of data
- Understanding pie charts
- Standard deviation of a small data set
- Comparing standard deviations
- Effect of a shift or scale on the mean and standard deviationPremium
- Level 1: Understanding box plots
- Level 2: Understanding box plotsPremium
- Understanding scatter plots
- CorrelationPremium
- Line of best fitPremium
- Interpolation and extrapolationPremium
- Components of a time seriesPremium
- Moving averages and trendPremium
Graph theory