Course Content
A. Numbers and Counting
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A.01. Represent numbers on a number line
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A.02. Convert between fractions, decimals, and percentages
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A.03. Compare and order rational numbers using number lines and inequalities
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A.04. Identify and classify rational and irrational numbers
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A.05. Determine the prime factorisation of a given number
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A.06. Calculate square roots of perfect squares
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A.07. Estimate and approximate square roots of non-perfect squares
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A.08. Calculate cube roots of perfect cubes
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A.09. Explore the properties of the real number system
B. Operations with Integers and Rational Numbers
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B.01. Add and subtract integers using number lines and rules
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B.02. Multiply and divide integers, understanding the rules for signs
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B.03. Evaluate numerical expressions involving integers using the order of operations (PEMDAS/BODMAS)
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B.04. Evaluate variable expressions involving integer values for variables
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B.05. Add and subtract rational numbers, including fractions and decimals
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B.06. Multiply and divide rational numbers, including fractions and decimals
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B.07. Evaluate numerical expressions involving rational numbers using order of operations
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B.08. Evaluate variable expressions involving rational number values for variables
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B.09. Solve real-world problems involving operations with rational numbers
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B.10. Apply the distributive property to simplify expressions
C. Consumer Maths
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C.01. Calculate simple interest earned on a principal amount
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C.02. Calculate compound interest earned on a principal amount
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C.03. Calculate the percentage of a number (e.g., VAT, discount)
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C.04. Determine the percentage represented by a discount or mark-up
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C.05. Solve multi-step problems involving percentages
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C.06. Apply consumer maths concepts to solve real-world financial problems
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C.07. Compare different financial options using consumer maths calculations
D. Linear Equations
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D.01. Identify linear equations in one and two variables
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D.02. Calculate the slope of a line from its graph
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D.03. Determine the slope of a line given two points on the line
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D.04. Find a missing coordinate of a point on a line, given the slope and another point
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D.05. Identify the slope and y-intercept of a linear equation in slope-intercept form
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D.06. Graph a linear equation in slope-intercept form
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D.07. Write a linear equation in slope-intercept form from a graph
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D.08. Write a linear equation in slope-intercept form given the slope and y-intercept
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D.09. Write a linear equation in slope-intercept form from a table of values
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D.10. Write a linear equation in slope-intercept form from a word problem
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D.11. Write linear equations to solve word problems
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D.12. Compare linear equations, graphs, and tables
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D.13. Write equations in standard form (Ax + By = C)
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D.14. Find the x- and y-intercepts of a linear equation in standard form
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D.15. Graph a linear equation in standard form using intercepts
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D.16. Determine the equations of horizontal and vertical lines
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D.17. Graph horizontal and vertical lines
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D.18. Identify and compare the slopes of parallel and perpendicular lines
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D.19. Write an equation for a line parallel or perpendicular to a given line, passing through a specific point
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D.20. Find the distance between a point and a line
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D.21. Find the distance between two parallel lines
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D.22. Model real-world scenarios with linear equations
E. Pairs of Linear Equations (Systems of Equations)
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E.01. Determine if an ordered pair (x, y) is a solution to a pair of linear equations
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E.02. Solve a pair of linear equations by graphing
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E.03. Solve a pair of linear equations by graphing: word problems
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E.04. Determine the number of solutions (none, one, or infinite) to a pair of linear equations by graphing
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E.05. Determine the number of solutions to a pair of linear equations without graphing, using algebraic methods
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E.06. Solve a pair of linear equations using the substitution method
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E.07. Solve a pair of linear equations using the substitution method: word problems
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E.08. Solve a pair of linear equations using the elimination method
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E.09. Solve a pair of linear equations using the elimination method: word problems
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E.10. Choose the most efficient method (graphing, substitution, or elimination) to solve a system of equations
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E.11. Analyse and interpret the solutions of systems of equations in real-world contexts
F. Polynomials
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F.01. Define and identify polynomial vocabulary (terms, coefficients, degree, etc.)
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F.02. Model polynomials using algebra tiles
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F.03. Add and subtract polynomials using algebra tiles
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F.04. Add and subtract polynomials algebraically
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F.05. Add polynomials to find the perimeter of geometric figures
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F.06. Multiply and divide monomials
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F.07. Simplify expressions involving powers of monomials
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F.08. Multiply a polynomial by a monomial
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F.09. Multiply two polynomials using algebra tiles
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F.10. Multiply two binomials, including using the FOIL method
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F.11. Multiply two binomials involving special cases (e.g., difference of squares, perfect square trinomials)
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F.12. Multiply polynomials of various degrees
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F.13. Apply polynomial operations to solve geometric problems
G. Factorising
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G.01. Find the highest common factor (HCF) of monomials
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G.02. Factorise out a monomial from a polynomial expression
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G.03. Factorise quadratic expressions with a leading coefficient of 1
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G.04. Factorise quadratic expressions with leading coefficients other than 1
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G.05. Factorise quadratic expressions involving special cases (e.g., difference of squares, perfect square trinomials)
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G.06. Factorise quadratic expressions using algebra tiles
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G.07. Factorise polynomials by grouping
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G.08. Factorise polynomials of various degrees using different techniques
H. Quadratic Equations
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H.12. Model real-world scenarios using quadratic equations
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H.01. Identify the key characteristics of quadratic equations (coefficients, roots, vertex, axis of symmetry)
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H.02. Complete a table of values for a quadratic equation
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H.03. Solve a quadratic equation using square roots
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H.04. Solve a quadratic equation using the zero product property
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H.05. Solve a quadratic equation by factorising
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H.06. Complete the square for a quadratic expression
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H.07. Solve a quadratic equation by completing the square
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H.08. Solve a quadratic equation using the quadratic formula
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H.09. Use the discriminant to determine the number and type of solutions to a quadratic equation
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H.10. Graph a quadratic equation, identifying key features such as vertex and intercepts
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H.11. Match quadratic functions with their corresponding graphs
I. Rational Expressions
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I.01. Simplify complex fractions
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I.02. Simplify rational expressions by cancelling common factors
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I.03. Multiply and divide rational expressions
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I.04. Divide polynomials using long division or synthetic division
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I.05. Add and subtract rational expressions with like and unlike denominators
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I.06. Solve rational equations
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I.07. Identify restrictions on the variable in a rational expression or equation
J. Matrices
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J.01. Understand and use matrix vocabulary (rows, columns, elements, dimensions)
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J.02. Apply matrix operation rules and properties
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J.03. Add and subtract matrices of compatible dimensions
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J.04. Multiply a matrix by a scalar
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J.05. Multiply two matrices of compatible dimensions
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J.06. Use matrices to represent and solve real-world problems
K. Arithmetic Sequences
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K.01. Identify and define arithmetic sequences
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K.02. Evaluate variable expressions for arithmetic sequences, finding specific terms
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K.03. Write variable expressions (explicit and recursive formulas) for arithmetic sequences
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K.04. Calculate partial sums of arithmetic series
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K.05. Apply arithmetic sequences to solve real-world problems
L. Points, Lines and Segments
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L.01. Define and differentiate between lines, line segments, and rays
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L.02. Calculate the lengths of segments on number lines
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L.03. Apply the additive property of length (segment addition postulate)
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L.04. Determine the midpoint of a line segment
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L.05. Identify and prove congruent line segments
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L.06. Apply the Perpendicular Bisector Theorem
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L.07. Use the midpoint formula to find the midpoint of a line segment in the coordinate plane
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L.08. Use the distance formula to find the distance between two points in the coordinate plane
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L.09. Derive the distance and midpoint formulas
M. Two-Dimensional Figures
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M.01. Understand and use polygon vocabulary (sides, vertices, angles, diagonals)
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M.02. Calculate the perimeter of various polygons
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M.03. Calculate the area of triangles and quadrilaterals (squares, rectangles, parallelograms, trapezoids, kites, rhombuses)
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M.04. Calculate area and perimeter of figures in the coordinate plane
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M.05. Calculate area and circumference of circles
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M.06. Calculate the area of compound figures by decomposing them into simpler shapes
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M.07. Calculate the area between two shapes
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M.08. Determine the relationship between area and perimeter of similar figures
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M.09. Calculate perimeters and areas of similar figures using scale factors
N. Transformations
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N.01. Perform translations and determine the coordinates of the image
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N.02. Perform reflections over various lines and determine the coordinates of the image
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N.03. Perform rotations about a point and determine the coordinates of the image
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N.04. Identify congruence transformations (translations, reflections, rotations)
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N.05. Perform compositions of congruence transformations and graph the resulting image
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N.06. Identify transformations that carry a polygon onto itself
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N.07. Perform dilations and graph the image
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N.08. Perform dilations and determine the coordinates of the image
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N.09. Determine the scale factor of a dilation and classify it as an enlargement or reduction
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N.10. Investigate the relationship between dilations and parallel lines
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N.11. Explore the properties preserved and not preserved under different transformations
O. Triangles
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O.01. Classify triangles by their sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse)
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O.02. Apply the Triangle Angle-Sum Theorem to find missing angles in a triangle
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O.03. Apply properties of midsegments of triangles
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O.04. Apply properties of triangles and angle bisectors
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O.05. Identify medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle
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O.06. Analyse the relationships between angles and sides in triangles
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O.07. Apply the Triangle Inequality Theorem to determine if three side lengths can form a triangle
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O.08. Prove congruence theorems (SSS, SAS, ASA, AAS)
P. Similarity
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P.01. Identify similar figures based on corresponding angles and proportional sides
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P.02. Determine ratios in similar figures
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P.03. Write similarity statements for similar figures
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P.04. Determine side lengths and angle measures in similar figures
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P.05. Apply similar triangles to solve indirect measurement problems
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P.06. Determine the relationship between the perimeters of similar figures
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P.07. Apply similarity rules (AA, SSS, SAS) to prove triangle similarity
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P.08. Relate similar triangles to similarity transformations (dilations)
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P.09. Determine the relationship between the areas of similar figures
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P.10. Use similarity to solve real world problems involving scale models and maps.
Q. Right Triangles
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Q.01. Apply Pythagoras’ Theorem to find missing side lengths in right triangles
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Q.02. Apply the Converse of Pythagoras’ Theorem to determine if a triangle is a right triangle
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Q.03. Apply Pythagoras’ Inequality Theorems to classify triangles as acute or obtuse
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Q.04. Apply properties of special right triangles (30-60-90 and 45-45-90) to find side lengths
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Q.05. Solve real-world problems involving right triangles
R. Circles
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R.01. Identify and define parts of a circle (centre, radius, diameter, chord, secant, tangent)
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R.02. Define and measure central angles in a circle
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R.03. Calculate arc measure and arc length
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R.04. Calculate the area of sectors of a circle
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R.05. Solve mixed review problems involving circle measurements
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R.06. Apply properties of arcs and chords
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R.07. Apply properties of tangent lines to a circle
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R.08. Calculate the perimeter of polygons with an inscribed circle
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R.09. Apply properties of inscribed angles
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R.10. Apply properties of angles in inscribed right triangles
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R.11. Apply properties of angles in inscribed quadrilaterals
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R.12. Construct circles using a compass and straightedge
S. Trigonometry
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S.01. Define and calculate trigonometric ratios (sin, cos, tan) in right triangles
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S.02. Define and calculate reciprocal trigonometric ratios (csc, sec, cot)
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S.03. Apply trigonometric functions of complementary angles
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S.04. Find trigonometric functions of special angles (30°, 45°, 60°)
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S.05. Find trigonometric functions using a calculator
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S.06. Understand and apply inverses of trigonometric functions
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S.07. Use trigonometric ratios to find a side length in a right triangle
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S.08. Use trigonometric ratios to find an angle measure in a right triangle
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S.09. Solve a right triangle by finding all missing side lengths and angle measures
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S.10. Apply trigonometry to solve real-world problems
T. Surface Area and Volume
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T.01. Understand the concepts of surface area and volume
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T.02. Calculate the surface area of prisms and cylinders
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T.03. Calculate the surface area of cones
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T.04. Calculate the volume of prisms and cylinders
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T.05. Calculate the volume of cones
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T.06. Calculate the surface area and volume of spheres
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T.07. Understand the concept of similar solids
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T.08. Calculate the surface area and volume of similar solids
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T.09. Review surface area and volume concepts
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T.10. Use surface area and volume to solve design and optimization problems
U. Measurement
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U.01. Convert rates and measurements within and between different units
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U.02. Understand the concept of precision in measurement
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U.03. Determine the greatest possible error in a measurement
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U.04. Determine the minimum and maximum possible area and volume based on measurement precision
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U.05. Calculate percent error in a measurement
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U.06. Calculate percent error in area and volume measurements
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U.07. Apply measurement concepts to real-world problems involving scaling and estimation
V. Problem Solving
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V.01. Solve problems involving consecutive integers
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V.02. Solve rate of travel word problems
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V.03. Solve weighted averages word problems
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V.04. Solve exponential growth and decay word problems
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V.05. Develop problem-solving strategies for various mathematical contexts
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V.06. Analyse and solve multi-step word problems involving a variety of mathematical concepts
W. Logic
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W.05. Understand and use conditional statements (if-then)
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W.06. Formulate negations of statements
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W.07. Formulate converses, inverses, and contrapositives of conditional statements
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W.08. Understand and use biconditional statements (if and only if)
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W.09. Use logical reasoning to make valid inferences and deductions
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W.01. Identify hypotheses and conclusions in conditional statements
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W.02. Provide counterexamples to disprove statements
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W.03. Construct and interpret truth tables for logical statements
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W.04. Determine the truth values of logical statements
X. Probability
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X.01. Calculate theoretical probability of simple events
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X.02. Calculate experimental probability based on observed data
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X.03. Determine the number of outcomes for compound events
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X.04. Identify independent and dependent events
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X.05. Calculate the probability of independent and dependent events
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X.06. Calculate geometric probability
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X.07. Apply the counting principle to determine the number of possible arrangements or combinations
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X.08. Solve probability problems using tree diagrams and other visual aids
Y. Statistics
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Y.01. Calculate mean, median, mode, and range for a data set
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Y.02. Determine quartiles and interquartile range for a data set
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Y.03. Identify biased samples and their potential impact on statistical analysis
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Y.04. Create and interpret box-and-whisker plots to display data distributions
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Y.05. Apply statistical measures to compare and analyse different data sets
Z. Data and Graphs
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Z.01. Interpret histograms to understand data distributions
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Z.02. Create histograms from given data sets
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Z.03. Interpret stem-and-leaf plots to understand data distributions
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Z.04. Analyse and compare different types of graphs to represent data effectively
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Z.05. Identify trends and patterns in data from graphs
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Z.06. Recognize misleading graphs and their impact on interpretation
AA. Constructions
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AA.01. Construct a tangent line to a circle at a given point
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AA.02. Construct an equilateral triangle inscribed in a circle
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AA.03. Construct a regular hexagon inscribed in a circle
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AA.04. Construct the circumcenter and incenter of a triangle
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AA.05. Construct the inscribed and circumscribed circle of a triangle
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AA.06. Bisect a given angle using a compass and straightedge
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AA.07. Construct the perpendicular bisector of a line segment
