Year 10 Maths Skills () « All Years

Australian Curriculum v9 aligned. Master each skill by earning 10 stars across 3 difficulty levels. Get instant feedback and step-by-step explanations when you need help.

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Linear Relationships
Algebra & Quadratics
Statistics
Measurement
Trigonometry
Geometry & Proofs
Probability
Financial Maths
10A Extension
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Linear Relationships

  1. Linear equations

    1. Solving one-step and two-step linear equations
    2. Solving multi-step linear equations (variables on both sides)
    3. Solving linear equations with fractions and brackets
    4. Writing equations from word problems

  2. Gradient and linear graphs

    1. Understanding gradient as rise over run
    2. Calculating gradient from two points
    3. Identifying positive, negative, zero and undefined gradients
    4. Sketching linear graphs from a table of values
    5. Sketching linear graphs using gradient-intercept method
    6. Sketching linear graphs using x- and y-intercepts

  3. Equations of lines

    1. Converting between y = mx + c and ax + by = c forms
    2. Finding the equation of a line given gradient and a point
    3. Finding the equation of a line given two points
    4. Identifying parallel lines (same gradient)
    5. Identifying perpendicular lines (m₁ × m₂ = −1)
    6. Finding equations of parallel and perpendicular lines

  4. Linear inequalities

    1. Graphing linear inequalities on a number line
    2. Solving linear inequalities (including reversing the sign)
    3. Writing inequalities from word problems

  5. Simultaneous equations

    1. Solving simultaneous equations by graphing
    2. Solving simultaneous equations by substitution
    3. Solving simultaneous equations by elimination
    4. Choosing the best method for simultaneous equations
    5. Simultaneous equations: word problems

  6. Distance and midpoint

    1. Distance between two points
    2. Midpoint of a line segment

Algebra & Quadratics 1

  1. Expanding

    1. Expanding single brackets (distributive law)
    2. Expanding double brackets (FOIL method)
    3. Expanding perfect squares
    4. Expanding difference of two squares

  2. Factorising

    1. Factorising by taking out HCF
    2. Factorising by grouping in pairs
    3. Factorising monic quadratic trinomials
    4. Factorising using difference of two squares
    5. Factorising using perfect square patterns

  3. Quadratic graphs

    1. Identifying quadratic graphs
    2. Matching quadratic equation to its graph
    3. Quadratic transformations: vertical shift
    4. Quadratic transformations: horizontal shift
    5. Quadratic transformations: stretch and compress
    6. Quadratic transformations: reflection
    7. Combining quadratic transformations
    8. Finding the turning point

  4. Algebraic fractions

    1. Simplifying algebraic fractions
    2. Adding and subtracting algebraic fractions
    3. Multiplying and dividing algebraic fractions

Algebra & Quadratics 2

  1. Solving quadratics

    1. Solving quadratics using the null factor law
    2. Solving quadratics by factorising
    3. Solving quadratics using the quadratic formula
    4. Discriminant and nature of roots

  2. Completing the square

    1. Completing the square (monic)
    2. Completing the square (non-monic, 10A)
    3. Solving by completing the square

  3. Sketching parabolas

    1. Sketching parabolas: intercepts, turning point and axis of symmetry
    2. Sketching parabolas from factorised form
    3. Sketching parabolas from turning point form

  4. 10A Extension

    1. Factorising non-monic quadratic trinomials
    2. Solving non-monic quadratic equations
    3. Quadratic equations: word problems
    4. Solving quadratic inequalities

Statistics

  1. Cumulative frequency

    1. Reading cumulative frequency tables
    2. Cumulative frequency curves (Ogives)
    3. Median and quartiles from an Ogive

  2. Box plots

    1. Drawing box plots from five-number summary
    2. Reading and interpreting box plots
    3. Identifying outliers using the IQR rule

  3. Comparing data

    1. Back-to-back stem-and-leaf plots
    2. Parallel box plots
    3. Describing distributions: centre, spread, shape
    4. Choosing appropriate data displays

  4. Bivariate data

    1. Drawing scatter plots
    2. Describing correlation
    3. Strength of correlation
    4. Line of best fit
    5. Equation of a line of best fit
    6. Interpolation and extrapolation

  5. Time series

    1. Reading time-series graphs
    2. Trends and seasonal patterns

  6. Evaluating data

    1. Evaluating statistical claims
    2. Bias, misleading graphs and sampling errors

  7. Standard deviation (10A)

    1. Calculating standard deviation
    2. Interpreting standard deviation

Measurement

  1. Area

    1. Area of composite shapes

  2. Surface area

    1. Surface area of prisms
    2. Surface area of cylinders
    3. Surface area of cones
    4. Surface area of pyramids
    5. Surface area of spheres
    6. Surface area of composite solids (10A)

  3. Volume

    1. Volume of prisms
    2. Volume of cylinders
    3. Volume of cones
    4. Volume of pyramids
    5. Volume of spheres
    6. Volume of composite solids

  4. Formulas and applications

    1. Rearranging formulas
    2. Rearranging formulas with squares and roots
    3. Applications of volume: capacity and displacement
    4. Measurement error
    5. Proportion and scale factors

Trigonometry

  1. Trigonometric ratios

    1. Identifying opposite, adjacent and hypotenuse
    2. Writing trigonometric ratios (SOH CAH TOA)

  2. Finding sides

    1. Using sine to find unknown sides
    2. Using cosine to find unknown sides
    3. Using tangent to find unknown sides
    4. Choosing the correct ratio

  3. Finding angles

    1. Finding angles using inverse trig
    2. Mixed finding sides and angles

  4. Elevation and depression

    1. Angles of elevation
    2. Angles of depression
    3. Mixed elevation and depression

  5. Bearings and applications

    1. Three-figure bearings
    2. Bearings: distances and angles
    3. Multi-step trigonometry problems
    4. Trigonometry in context

Geometry & Proofs

  1. Congruent triangles

    1. Identifying congruent triangles (SSS, SAS, ASA, RHS)
    2. Proving triangles are congruent
    3. Using congruence to find unknowns
    4. Proofs using congruent triangles

  2. Similar triangles

    1. Identifying similar triangles (AA, SSS, SAS)
    2. Proving triangles are similar
    3. Using similarity to find unknowns
    4. Proofs using similar triangles

  3. Quadrilaterals

    1. Properties of special quadrilaterals
    2. Proving quadrilateral properties

  4. Circle theorems

    1. Angles at centre and circumference
    2. Angles in the same segment
    3. Angle in a semicircle
    4. Cyclic quadrilateral properties
    5. Tangent properties
    6. Chord properties
    7. Circle theorem proofs

Probability

  1. Probability basics

    1. Experimental vs theoretical probability
    2. Calculating probabilities using sample spaces

  2. Venn diagrams and tables

    1. Venn diagrams: reading and interpreting
    2. Venn diagrams: calculating probabilities
    3. Two-way tables: reading and interpreting
    4. Two-way tables: calculating probabilities

  3. Compound events

    1. Mutually exclusive events
    2. Non-mutually exclusive events
    3. Tree diagrams: with replacement
    4. Tree diagrams: without replacement

  4. Conditional probability

    1. Conditional probability: using the formula
    2. Conditional probability: from Venn diagrams
    3. Conditional probability: from two-way tables
    4. Independent events
    5. Dependent events
    6. Probability word problems

Financial Maths

  1. Interest

    1. Calculating simple interest: I = PRT
    2. Calculating compound interest
    3. Comparing simple and compound interest
    4. Compound interest: finding P, r or n
    5. Comparing interest rates

  2. Growth and depreciation

    1. Depreciation: straight-line and reducing balance
    2. Growth and decay

  3. Applications

    1. Financial word problems
    2. Inflation and purchasing power
    3. Recursion for compound interest (10A)

Surds & Irrationals

  1. Number classification

    1. Classifying numbers: rational vs irrational

  2. Surd operations

    1. Simplifying surds
    2. Multiplying surds
    3. Dividing surds
    4. Adding and subtracting like surds

  3. Expanding with surds

    1. Expanding brackets with surds
    2. Expanding double brackets with surds
    3. Expanding conjugate pairs

  4. Rationalising

    1. Rationalising the denominator (simple)
    2. Rationalising the denominator (conjugate)

Non-Linear Graphs & Logarithms

  1. Non-linear graphs

    1. Identifying non-linear graphs
    2. Sketching y = 1/x (hyperbola)
    3. Sketching x² + y² = r² (circle)
    4. Sketching exponential graphs
    5. Transformations of non-linear graphs

  2. Index laws

    1. Summary of index laws
    2. Zero and negative indices
    3. Fractional indices and surds (10A)

  3. Logarithms (10A)

    1. Converting between index and log form
    2. Evaluating logarithms
    3. Applying logarithm laws
    4. Logarithmic scales
    5. Sketching logarithmic graphs

Advanced Trigonometry (10A)

  1. Unit circle and exact values

    1. 3D Trigonometry
    2. The unit circle
    3. Exact trig values
    4. Trig values in all four quadrants (ASTC)
    5. Solving trig equations

  2. Sine and cosine rules

    1. The sine rule
    2. The cosine rule
    3. Choosing sine or cosine rule
    4. Applications of sine and cosine rules

  3. Area and mixed problems

    1. Area of a triangle using trigonometry
    2. Mixed advanced trig problems

Polynomials (10A)

  1. Understanding polynomials

    1. Polynomial degree and leading coefficient
    2. Evaluating polynomials
    3. Sketching y = x^n
    4. Transformations of y = x^n

  2. Operations

    1. Adding, subtracting and multiplying polynomials
    2. Long division of polynomials

  3. Theorems and factorising

    1. The remainder theorem
    2. The factor theorem
    3. Factorising cubics

  4. Graphing

    1. Sketching polynomial functions
    2. Equation of a polynomial from a graph

Networks (10A)

  1. Graph theory

    1. Vertices, edges and degree
    2. Representing situations as networks
    3. Connected and disconnected graphs

  2. Paths and applications

    1. Euler paths and circuits
    2. Shortest path problems
    3. Minimum spanning trees

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