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Lessons in Mathematics K–10, Year 10

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Mathematics K–10 · Year 10

142 lessons in this selection

Learning Map for Mathematics K–10 · Year 10 142 concepts · 23 topics · builds on 45 concepts from earlier years

  1. Stage 5 · Years 9–10

    1. Indices, quadratics and simultaneous equations:
      6 of 6 concepts with lesson material
    2. Financial mathematics (Stage 5):
      6 of 6 concepts with lesson material
    3. Algebraic techniques (Stage 5):
      7 of 7 concepts with lesson material
    4. Indices and surds (Stage 5):
      8 of 8 concepts with lesson material
    5. Equations and inequalities (Stage 5):
      12 of 12 concepts with lesson material
    6. Linear relationships (Stage 5):
      15 of 15 concepts with lesson material
    7. Non-linear relationships (Stage 5):
      11 of 11 concepts with lesson material
    8. Variation and rates of change (Path):
      5 of 5 concepts with lesson material
    9. Polynomials (Path):
      6 of 6 concepts with lesson material
    10. Logarithms (Path):
      5 of 5 concepts with lesson material
    11. Functions and other graphs (Path):
      5 of 5 concepts with lesson material
    12. Pythagoras, trigonometry and similarity:
      6 of 6 concepts with lesson material
    13. Measurement, area and volume (Stage 5):
      9 of 9 concepts with lesson material
    14. Further trigonometry (Path):
      8 of 8 concepts with lesson material
    15. Further area and volume (Path):
      4 of 4 concepts with lesson material
    16. Congruence, similarity and geometrical proof (Path):
      8 of 8 concepts with lesson material
    17. Circle geometry (Path):
      2 of 2 concepts with lesson material
    18. Introduction to networks (Path):
      3 of 3 concepts with lesson material
    19. Comparing data sets:
      4 of 4 concepts with lesson material
    20. Bivariate data and lines of best fit:
      3 of 3 concepts with lesson material
    21. Multistage probability and simulation:
      3 of 3 concepts with lesson material
    22. Statistical inquiry (Path):
      2 of 2 concepts with lesson material
    23. Venn diagrams, sets and conditional probability (Path):
      4 of 4 concepts with lesson material

Each concept of Mathematics K–10 · Year 10, and what it builds on, is drawn in the map above.

Sequence: NSW syllabus, as used on the learning platform for Mathematics K–10. For NSW, read each concept beside your state or territory’s official curriculum.

Indices, quadratics and simultaneous equationsNumber and algebra

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Applies the index laws to simplify algebraic expressions with positive-integer and zero indicesStructure
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Expands binomial productsStructure
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Factorises quadratic expressionsStructure
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Solves quadratic equations by factorisingStructure
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Solves simultaneous linear equations graphically and algebraicallyStructure
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Graphs parabolas of the form y = kx² and y = kx² + c and describes their key featuresStructure
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Financial mathematics (Stage 5)Number and algebra

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Calculates earnings from wages, salaries, overtime, penalty rates, commission, piecework and leave loadingStructure
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Calculates taxable income, PAYG tax and net payStructure
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Applies the simple interest formula I = Prn to investment problemsStructure
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Compares the true cost of buying on terms, buy now pay later and short-term loansStructure
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Calculates compound interest using repeated multiplication and the formula FV = PV(1 + r)^nStructure
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Calculates the depreciation of an asset using S = V₀(1 − r)^nStructure
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Algebraic techniques (Stage 5)Number and algebra

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Simplifies algebraic fractions with numerical denominators using the four operationsStructure
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Expands and simplifies algebraic expressions using the distributive lawStructure
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Simplifies and operates with algebraic fractions involving indices and pronumerals in the denominatorStructure
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Factorises algebraic expressions by taking out a common algebraic factorStructure
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Proves and applies the special products (a − b)(a + b), (a + b)² and (a − b)²Structure
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Selects factorisation strategies, including grouping in pairs and non-monic quadratic trinomialsStructure
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Operates with algebraic fractions with binomial numerators and simplifies fractions by factorisingStructure
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Indices and surds (Stage 5)Number and algebra

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Establishes and evaluates negative-integer indices for numerical basesStructure
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Applies the index laws to algebraic expressions involving negative-integer indicesStructure
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Uses x⁻¹ as a reciprocal and simplifies expressions of the form (a/b)⁻ⁿStructure
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Distinguishes rational from irrational numbers within the real numbersStructure
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Describes surds as exact values and the conditions under which they are definedStructure
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Applies the surd results and the four operations to simplify surdsStructure
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Expands expressions involving surds and rationalises denominatorsStructure
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Converts between surd and index form and evaluates fractional indicesStructure
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Equations and inequalities (Stage 5)Number and algebra

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Solves linear equations of up to 3 steps, including pronumerals on both sides and grouping symbolsStructure
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Solves linear equations involving one algebraic fractionStructure
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Solves linear equations arising from formulas and word problemsStructure
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Solves cubic equations of the form ax³ = kStructure
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Solves linear inequalities and graphs their solutions on a number lineStructure
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Solves linear equations of more than 3 steps and equations with two or more fractionsStructure
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Rearranges literal equations by changing the subject of a formulaStructure
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Solves quadratic equations by completing the squareStructure
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Applies the quadratic formula and uses the discriminant to describe the solutionsStructure
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Selects and verifies the most appropriate method for solving a quadratic equationStructure
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Models and solves problems using quadratic equations, including substitution into formulasStructure
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Relates identities and contradictions to coincident and parallel linesStructure
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Linear relationships (Stage 5)Number and algebra

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Finds the gradient of an interval on the Cartesian plane using rise over runStructure
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Finds the midpoint of an interval on the Cartesian planeStructure
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Finds the distance between two points on the Cartesian plane using Pythagoras’ theoremStructure
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Graphs linear relationships from tables of values and identifies their interceptsStructure
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Graphs and explains horizontal, vertical and parallel linesStructure
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Interprets and applies the gradient/slope–intercept form y = mx + cStructure
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Finds the equations of parallel and perpendicular linesStructure
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Applies the midpoint and gradient formulas to an interval on the Cartesian planeStructure
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Establishes and applies the distance formulaStructure
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Converts between gradient–intercept and general form and graphs a line given in any formStructure
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Uses the point–gradient form to find the equation of a line through a point or through two pointsStructure
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Finds and justifies the equations of parallel and perpendicular lines given in any formStructure
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Solves problems involving geometrical figures by applying coordinate geometry formulasStructure
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Identifies line and rotational symmetry in plane shapes and in graphsStructure
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Describes translations, reflections and rotations on the Cartesian plane using coordinatesStructure
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Non-linear relationships (Stage 5)Number and algebra

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Connects algebraic and graphical representations of quadratic and exponential relationshipsStructure
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Graphs exponential curves of the form y = a^x and describes their featuresStructure
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Distinguishes between linear, quadratic and exponential relationships from their graphs and equationsStructure
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Graphs parabolas in turning-point form and describes their transformationsStructure
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Finds the intercepts, axis of symmetry and vertex of y = ax² + bx + c and sketches it by handStructure
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Graphs exponential relationships of the form y = ka^x + c and describes their transformationsStructure
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Graphs hyperbolas and describes their features and transformationsStructure
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Derives and graphs the equation of a circle centred at the originStructure
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Graphs circles with centre (a, b) and finds the centre and radius by completing the squareStructure
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Identifies and compares graph types from their equations and finds intersections with a lineStructure
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Graphs and compares curves of the form y = kxⁿ and describes their transformationsStructure
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Variation and rates of change (Path)Number and algebra

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Identifies, describes and represents direct variationStructure
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Identifies, describes and represents inverse variationStructure
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Recognises graphs of direct and inverse variation and solves variation problemsStructure
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Interprets graphs that increase or decrease at a constant rateStructure
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Interprets and constructs graphs with a variable rate of changeStructure
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Polynomials (Path)Number and algebra

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Defines polynomials and their terminology and uses P(x) notationStructure
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Adds, subtracts and multiplies polynomialsStructure
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Divides a polynomial by a linear polynomial and expresses the result as P(x) = D(x)Q(x) + R(x)Structure
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Applies the remainder and factor theorems to factorise polynomials and find their zeroesStructure
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Graphs polynomials from their zeroes using multiplicity and the leading termStructure
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Compares transformations of polynomial graphsStructure
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Logarithms (Path)Number and algebra

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Defines logarithms and converts between index and logarithmic formStructure
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Compares the graphs of exponential and logarithmic functionsStructure
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Deduces and applies the laws of logarithmsStructure
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Solves simple equations involving exponents or logarithmsStructure
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Examines logarithmic scales and explains their use in contextStructure
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Functions and other graphs (Path)Number and algebra

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Defines relations and functions and applies the vertical line testStructure
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Uses function notation f(x) and evaluates f(c)Structure
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Determines the domain and range of a functionStructure
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Graphs and describes transformations of y = f(x)Structure
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Graphs regions corresponding to linear inequalities in one and two variablesStructure
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Pythagoras, trigonometry and similarityMeasurement and space

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Identifies similar figures and uses scale factorsStructure
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Uses sine, cosine and tangent ratios to find unknown sidesStructure
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Uses trigonometry to find unknown anglesStructure
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Enlarges, reduces and interprets scale drawingsStructure
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Solves problems involving angles of elevation and depressionStructure
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Solves practical problems involving true and compass bearingsStructure
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Measurement, area and volume (Stage 5)Measurement and space

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Interprets unit prefixes for very small and very large measurementsStructure
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Finds the precision, absolute error and percentage error of a measurementStructure
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Rounds numbers to a given number of significant figures and judges accuracyStructure
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Represents and calculates with numbers in scientific notationStructure
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Solves practical problems involving the area of composite shapesStructure
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Solves problems involving the surface area of composite solidsStructure
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Finds the volume of right prisms with composite and circular cross-sectionsStructure
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Calculates the volume and capacity of composite solids made from prisms and cylindersStructure
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Calculates the surface area of prisms and cylindersStructure
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Further trigonometry (Path)Measurement and space

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Applies Pythagoras' theorem and trigonometry to solve 3-dimensional problemsStructure
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Applies the sine rule to non-right-angled trianglesStructure
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Applies the cosine rule to non-right-angled trianglesStructure
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Uses the area rule and selects the appropriate rule for non-right-angled trianglesStructure
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Uses the unit circle to define and graph the trigonometric functionsStructure
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Relates the gradient of a line to its angle of inclinationStructure
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Derives and applies the exact trigonometric ratios for 30, 45 and 60 degreesStructure
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Solves trigonometric equations, including the ambiguous caseStructure
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Further area and volume (Path)Measurement and space

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Finds the surface area of right pyramids and right conesStructure
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Finds the surface area of spheres and composite solidsStructure
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Finds the volume of right pyramids and right conesStructure
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Finds the volume of spheres and related composite solidsStructure
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Congruence, similarity and geometrical proof (Path)Measurement and space

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Identifies congruent figures and matches their sides and anglesStructure
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Establishes and uses the congruence tests for trianglesStructure
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Establishes and uses the similarity tests for trianglesStructure
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Relates area and volume ratios to the similarity ratio of similar figures and solidsStructure
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Applies interior and exterior angle results for polygonsStructure
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Finds unknown sides and angles in plane shapes, giving geometrical reasonsStructure
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Constructs formal proofs of congruent and similar trianglesStructure
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Proves properties and tests for triangles and quadrilateralsStructure
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Circle geometry (Path)Measurement and space

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Proves and applies chord and angle properties of circlesStructure
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Proves and applies tangent and secant properties of circlesStructure
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Introduction to networks (Path)Measurement and space

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Describes networks using vertices, edges and degreeStructure
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Identifies planar graphs and applies Euler's formulaStructure
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Explains and finds Eulerian trails and circuitsStructure
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Comparing data setsStatistics and probability

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Constructs and compares box plots using five-number summariesStructure
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Determines the five-number summary and interquartile range of a datasetStructure
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Compares two or more datasets using parallel box plots, shape and summary statisticsStructure
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Uses standard deviation to measure and compare the spread of datasetsStructure
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Bivariate data and lines of best fitStatistics and probability

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Identifies bivariate data and distinguishes association from causationStructure
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Fits a line of best fit by eye and uses it to interpolate and extrapolateStructure
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Draws scatter plots and describes the relationship between two variablesStructure
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Multistage probability and simulationStatistics and probability

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Distinguishes independent and dependent events and lists outcomes for multistage experimentsStructure
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Calculates probabilities for multistage chance experiments, with and without replacementStructure
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Designs, runs and evaluates probability simulations using digital toolsStructure
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Statistical inquiry (Path)Statistics and probability

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Plans and conducts a statistical inquiry and reports its findingsStructure
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Critically evaluates sampling, surveys and statistical claims in media reportsStructure
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Venn diagrams, sets and conditional probability (Path)Statistics and probability

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Represents data in Venn diagrams and two-way tables and converts between themStructure
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Uses set language and notation to describe eventsStructure
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Describes and calculates probabilities of compound events, mutually exclusive or notStructure
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Calculates conditional probabilities and interprets conditional languageStructure
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Curriculum details for Mathematics K–10

NSW school sequence.

Stage 5 in the NSW source sequence · Years 9–10.

The Mathematics K–10 collection follows its named source sequence. For New South Wales, read each concept beside your state or territory’s official curriculum.

In Mathematics K–10, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

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