Course Content
A. Numbers and Counting
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A.01. Understand and identify different types of numbers (integers, rational, irrational)
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A.02. Represent numbers on a number line
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A.03. Convert fluently between decimals, fractions, and percentages
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A.04. Compare and order rational numbers
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A.05. Determine the prime factorization of a number
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A.06. Explore the properties of prime numbers
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A.07. Apply prime factorization to solve number theory problems
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A.08. Distinguish between rational and irrational numbers based on their decimal representations
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A.09. Prove that the square root of 2 is irrational
B. Scientific Notation
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B.01. Express numbers in standard form using scientific notation.
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B.02. Convert numbers from scientific notation to standard notation
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B.03. Compare numbers expressed in scientific notation
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B.04. Multiply numbers written in scientific notation
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B.05. Divide numbers written in scientific notation
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B.06. Apply scientific notation to solve real-world problems involving very large or very small numbers
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B.07. Perform addition and subtraction with numbers in scientific notation
C. Percentages and Consumer Maths
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C.01. Calculate the percentage of a number
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C.02. Determine a percentage given two numbers
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C.03. Solve multi-step percentage problems
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C.04. Calculate simple interest
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C.05. Calculate compound interest
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C.06. Calculate continuously compounded interest
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C.07. Apply percentages to calculate VAT, discounts and mark-ups
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C.08. Compare different investment options based on interest rates
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C.09. Analyze and compare loan options considering interest and repayment schedules
D. Solving Linear Equations and Inequalities
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D.01. Solve one-step linear equations
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D.02. Solve multi-step linear equations
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D.03. Solve linear equations involving fractions or decimals
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D.04. Solve linear equations: word problems
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D.05. Graph a linear inequality in one variable on a number line
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D.06. Solve linear inequalities
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D.07. Graph solutions to linear inequalities
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D.08. Write a linear inequality from a graph
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D.09. Write a linear inequality: word problems
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D.10. Translate real-world scenarios into linear equations and inequalities to find solutions.
E. Absolute Value Equations and Inequalities
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E.01. Define the absolute value of a number
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E.02. Solve absolute value equations
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E.03. Graph solutions to absolute value equations on a number line
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E.04. Solve absolute value inequalities
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E.05. Graph solutions to absolute value inequalities on a number line
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E.06. Interpret absolute value inequalities in real-world contexts
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E.07. Apply absolute value to solve problems involving tolerances and errors
F. Two-Dimensional Figures
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F.01. Define basic polygon vocabulary (e.g. vertices, sides, angles)
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F.02. Calculate the perimeter of various polygons
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F.03. Determine the area of triangles and quadrilaterals
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F.04. Calculate the area and circumference of circles
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F.05. Determine the area of compound figures
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F.06. Determine the area between two shapes
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F.07. Determine area and perimeter in the coordinate plane
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F.08. Solve problems involving perimeter, area, and circumference in real-world contexts.
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F.09. Solve problems involving areas of similar figures
G. Functions
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G.01. Define the domain and range of a function
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G.02. Identify whether a given relation is a function
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G.03. Evaluate functions for given input values
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G.04. Find values using function graphs
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G.05. Complete a table for a function given its graph or equation
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G.06. Find the slope of a linear function
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G.07. Graph a linear function
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G.08. Write the equation of a linear function in slope-intercept form
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G.09. Determine the equations of linear functions over unit intervals
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G.10. Write a function that describes a relationship between two quantities
H. Simultaneous Equations
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H.03. Solve simultaneous equations by graphing: word problems
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H.04. Determine the number of solutions (none, one, or infinite) to a system of simultaneous equations
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H.05. Solve systems of simultaneous equations using substitution
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H.06. Solve systems of simultaneous equations using substitution: word problems
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H.07. Solve systems of simultaneous equations using elimination
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H.08. Solve systems of simultaneous equations using elimination: word problems
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H.09. Solve systems of simultaneous equations using any appropriate method
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H.10. Solve systems of simultaneous equations using any appropriate method: word problems
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H.11. Solve systems of simultaneous equations in three variables using substitution
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H.12. Solve systems of simultaneous equations in three variables using elimination
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H.13. Determine the number of solutions to a system of equations in three variables
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H.14. Solve nonlinear simultaneous equations
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H.15. Model and solve real-world problems using systems of equations
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H.01. Determine if an ordered pair (x, y) is a solution to a system of simultaneous equations
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H.02. Solve systems of simultaneous equations by graphing
I. Inequalities and Linear Programming
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I.01. Determine if an ordered pair (x, y) is a solution to a system of inequalities
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I.02. Graph a linear inequality in the coordinate plane
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I.03. Solve systems of inequalities by graphing
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I.04. Find the vertices of a solution set for a system of inequalities
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I.05. Solve linear programming problems to find optimal solutions
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I.06. Formulate linear programming models from real-world scenarios
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I.07. Interpret the feasible region and corner points in linear programming problems
J. Factorising
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J.01. Factorise out a monomial from a polynomial
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J.02. Factorise quadratic polynomials
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J.03. Factorise quadratics using algebra tiles
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J.04. Factorise using a quadratic pattern (e.g., difference of squares, perfect square trinomials)
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J.05. Factorise by grouping
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J.06. Factorise sums and differences of cubes
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J.07. Factorise polynomials of higher degree
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J.08. Identify and apply appropriate factoring techniques based on the structure of the polynomial.
K. Polynomials
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K.01. Define polynomial vocabulary (degree, leading coefficient, etc.)
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K.02. Add and subtract polynomials
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K.03. Multiply polynomials
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K.04. Divide polynomials using long division
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K.05. Divide polynomials using synthetic division
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K.06. Evaluate polynomials using synthetic division (Remainder Theorem)
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K.07. Find the roots of factorised polynomials
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K.08. Solve polynomial equations by factoring
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K.09. Write a polynomial equation from its roots
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K.10. State and apply the Rational Root Theorem
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K.11. State and apply the Complex Conjugate Theorem
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K.12. State and apply Conjugate Root Theorems
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K.13. Sketch a polynomial from its roots
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K.14. Match polynomials and graphs
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K.15. Apply Pascal’s triangle to expand binomials
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K.16. State and apply the Binomial Theorem I
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K.17. State and apply the Binomial Theorem II
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K.18. Determine end behavior of polynomials.
L. Quadratic Functions
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L.01. Identify the characteristics of quadratic functions (vertex, axis of symmetry, intercepts)
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L.02. Complete a function table for quadratic functions
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L.03. Find a quadratic function given its graph or key features
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L.04. Graph a quadratic function in vertex form
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L.05. Match quadratic functions and graphs
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L.06. Solve a quadratic equation using square roots
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L.07. Solve a quadratic equation using the zero product property
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L.08. Solve a quadratic equation by factorising
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L.09. Complete the square to solve a quadratic equation
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L.10. Solve a quadratic equation using the quadratic formula
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L.11. Use the discriminant to determine the number and type of solutions to a quadratic equation
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L.12. Solve real world problems modeled by quadratic functions.
M. Radical Functions and Expressions
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M.01. Find the roots of integers
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M.02. Find the roots of rational numbers
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M.03. Find roots using a calculator
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M.04. Understand and apply Nth roots
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M.05. Simplify radical expressions with variables I
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M.06. Simplify radical expressions with variables II
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M.07. Multiply radical expressions
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M.08. Divide radical expressions
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M.09. Add and subtract radical expressions
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M.10. Simplify radical expressions using the distributive property
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M.11. Simplify radical expressions using conjugates
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M.12. Determine the domain and range of radical functions
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M.13. Solve radical equations
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M.14. Evaluate expressions involving radicals.
N. Rational Exponents
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N.01. Evaluate rational exponents
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N.02. Multiply expressions with rational exponents
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N.03. Divide expressions with rational exponents
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N.04. Apply the power rule to expressions with rational exponents
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N.05. Simplify expressions involving rational exponents I
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N.06. Simplify expressions involving rational exponents II
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N.07. Convert between radical expressions and expressions with rational exponents
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N.08. Use rational exponents to solve equations
O. Rational Functions and Expressions
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O.01. Identify asymptotes and excluded values of rational functions
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O.02. Evaluate rational expressions I
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O.03. Evaluate rational expressions II
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O.04. Simplify rational expressions
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O.05. Multiply and divide rational expressions
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O.06. Add and subtract rational expressions
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O.07. Solve rational equations
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O.08. Identify holes in the graphs of rational functions.
P. Function Operations
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P.01. Add and subtract functions
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P.02. Multiply functions
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P.03. Divide functions
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P.04. Evaluate the composition of linear functions: find a value
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P.05. Determine the equation of the composition of linear functions: find an equation
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P.06. Evaluate the composition of linear and quadratic functions: find a value
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P.07. Determine the equation of the composition of linear and quadratic functions: find an equation
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P.08. Identify inverse functions
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P.09. Find values of inverse functions from tables
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P.10. Find values of inverse functions from graphs
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P.11. Find inverse functions and relations
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P.12. Verify that two functions are inverses of each other
Q. Logarithms
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Q.01. Convert between exponential and logarithmic form: rational bases
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Q.02. Convert between natural exponential and logarithmic form
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Q.03. Convert between exponential and logarithmic form: all bases
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Q.04. Evaluate logarithms
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Q.05. Evaluate natural logarithms
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Q.06. Apply the change of base formula to evaluate logarithms
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Q.07. Identify properties of logarithms
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Q.08. Apply the product property of logarithms
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Q.09. Apply the quotient property of logarithms
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Q.10. Apply the power property of logarithms
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Q.11. Apply properties of logarithms in mixed review problems
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Q.12. Evaluate logarithms in mixed review problems
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Q.13. Use logarithms to solve real world problems.
R. Exponential and Logarithmic Functions
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R.11. Describe linear and exponential growth and decay
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R.12. Solve exponential growth and decay word problems
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R.13. Graph exponential and logarithmic functions and identify key features.
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R.01. Determine the domain and range of exponential and logarithmic functions
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R.02. Evaluate exponential functions
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R.03. Match exponential functions and graphs
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R.04. Solve exponential equations by rewriting the base
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R.05. Solve exponential equations using common logarithms
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R.06. Solve exponential equations using natural logarithms
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R.07. Solve logarithmic equations I
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R.08. Solve logarithmic equations II
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R.09. Identify linear and exponential functions from tables and graphs
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R.10. Solve problems involving exponential functions over unit intervals
S. Complex Numbers
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S.01. Define the imaginary unit ‘i’ and complex numbers
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S.02. Add and subtract complex numbers
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S.03. Find the complex conjugate of a complex number
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S.04. Multiply complex numbers
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S.05. Divide complex numbers
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S.06. Perform all basic arithmetic operations (add, subtract, multiply, divide) with complex numbers
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S.07. Calculate the absolute value (modulus) of a complex number
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S.08. Calculate powers of i
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S.09. Solve quadratic equations with complex solutions.
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S.10. Simplify expressions with complex numbers.
T. Argand Plane
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T.01. Understand the Argand plane as a representation of complex numbers
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T.02. Graph complex numbers on the Argand plane
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T.03. Represent addition of complex numbers on the Argand plane
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T.04. Represent subtraction of complex numbers on the Argand plane
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T.05. Graph complex conjugates on the Argand plane
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T.06. Determine absolute value geometrically on the Argand plane
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T.07. Find the midpoint of two complex numbers on the Argand plane
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T.08. Calculate the distance between two complex numbers on the Argand plane
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T.09. Use the Argand Plane to visualise geometric transformations.
U. Angle Measures
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U.01. Convert between degrees and radians
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U.02. Calculate arc length using radians
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U.03. Identify the quadrant of an angle
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U.04. Draw and interpret graphs of angles
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U.05. Find coterminal angles
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U.06. Find reference angles
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U.07. Convert between angle units and real-world scenarios.
V. Trigonometry
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V.01. Apply Pythagoras’ Theorem and its converse
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V.02. Solve problems involving special right triangles (30-60-90 and 45-45-90)
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V.03. Define and calculate trigonometric ratios (sin, cos, tan)
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V.04. Define and calculate reciprocal trigonometric ratios (csc, sec, cot)
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V.05. Find trigonometric ratios in similar right triangles
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V.06. Find trigonometric ratios using the unit circle
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V.07. Determine the values of sin, cos, and tan for special angles (0, 30, 45, 60, 90 degrees)
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V.08. Determine the values of csc, sec, and cot for special angles
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V.09. Find trigonometric function values using a calculator
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V.10. Find the inverses of sin, cos and tan
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V.11. Find the inverses of csc, sec and cot
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V.12. Solve trigonometric equations I
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V.13. Solve trigonometric equations II
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V.14. Use trigonometric ratios to find a side length in a right triangle
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V.15. Use trigonometric ratios to find an angle measure in a right triangle
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V.16. Solve a right triangle
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V.17. Apply the Law of Sines
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V.18. Apply the Law of Cosines
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V.19. Solve a triangle using appropriate trigonometric laws
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V.20. Calculate the area of a triangle using the sine formula
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V.21. Calculate the area of a triangle using Heron’s Formula
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V.22. Model and solve real-world problems using trigonometry.
W. Trigonometric Functions
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W.01. Find properties of sine functions (amplitude, period, phase shift, vertical shift)
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W.02. Write equations of sine functions from graphs
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W.03. Write equations of sine functions using given properties
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W.04. Graph sine functions
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W.05. Find properties of cosine functions (amplitude, period, phase shift, vertical shift)
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W.06. Write equations of cosine functions from graphs
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W.07. Write equations of cosine functions using given properties
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W.08. Graph cosine functions
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W.09. Graph sine and cosine functions on the same axes and compare their properties.
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W.10. Model periodic phenomena using trigonometric functions.
X. Trigonometric Identities
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X.01. Apply complementary angle identities
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X.02. Understand and apply symmetry and periodicity of trigonometric functions
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X.03. Find trigonometric ratios using a Pythagorean or reciprocal identity
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X.04. Find trigonometric ratios using multiple identities
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X.05. Verify trigonometric identities using algebraic manipulation
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X.06. Use trigonometric identities to simplify trigonometric expressions
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X.07. Use trigonometric identities to solve trigonometric equations.
Y. Triangles
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Y.01. Understand and apply the properties of midsegments of triangles
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Y.02. Understand and apply the properties of triangles and bisectors
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Y.03. Identify medians, altitudes, angle bisectors and perpendicular bisectors in a triangle
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Y.04. Understand and apply angle-side relationships in triangles
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Y.05. Apply the Triangle Inequality Theorem
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Y.06. Prove properties of triangles using geometric theorems.
Z. Similarity
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Z.01. Identify similar figures
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Z.02. Determine ratios in similar figures
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Z.03. Write similarity statements
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Z.04. Find side lengths and angle measures in similar figures
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Z.05. Solve problems involving similar triangles and indirect measurement
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Z.06. Compare perimeters of similar figures
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Z.07. Apply similarity rules for triangles (AA, SAS, SSS)
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Z.08. Understand the relationship between similar triangles and similarity transformations
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Z.09. Understand and explain the similarity of circles
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Z.10. Apply the Triangle Proportionality Theorem
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Z.11. Compare areas of similar figures
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Z.12. Determine relationships between side lengths and areas of similar shapes.
AA. Circles
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AA.01. Identify parts of a circle (centre, radius, diameter, chord, secant, tangent)
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AA.02. Understand and apply the properties of central angles
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AA.03. Calculate arc measure and arc length
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AA.04. Calculate the area of sectors
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AA.05. Solve circle measurement problems: mixed review
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AA.06. Understand and apply the relationship between arcs and chords
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AA.07. Understand and apply the properties of tangent lines
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AA.08. Calculate the perimeter of polygons with an inscribed circle
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AA.09. Understand and apply the properties of inscribed angles
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AA.10. Understand and apply the properties of angles in inscribed right triangles
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AA.11. Understand and apply the properties of angles in inscribed quadrilaterals
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AA.12. Apply geometric theorems to solve problems involving circles.
BB. Circles in the Coordinate Plane
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BB.01. Find the centre of a circle given its equation
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BB.02. Find the radius or diameter of a circle given its equation
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BB.03. Write equations of circles in standard form from graphs
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BB.04. Write equations of circles in standard form using given properties (centre and radius)
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BB.05. Convert equations of circles from general to standard form
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BB.06. Find properties of circles from equations in general form
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BB.07. Graph circles given their equations in standard form
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BB.08. Solve geometric problems using the equation of a circle.
CC. Surface Area and Volume
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CC.01. Understand the concepts of surface area and volume
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CC.02. Calculate the surface area of prisms and cylinders
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CC.03. Calculate the surface area of pyramids and cones
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CC.04. Calculate the volume of prisms and cylinders
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CC.05. Calculate the volume of pyramids and cones
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CC.06. Calculate the surface area and volume of spheres
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CC.07. Understand the concept of similar solids
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CC.08. Calculate the surface area and volume of similar solids
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CC.09. Solve surface area and volume review problems
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CC.10. Apply surface area and volume formulas to solve real-world problems.
DD. Constructions
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DD.07. Construct a square
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DD.08. Construct a tangent line to a circle
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DD.09. Construct the circumcenter or incenter of a triangle
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DD.10. Construct the inscribed or circumscribed circle of a triangle
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DD.11. Construct the centroid or orthocenter of a triangle
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DD.12. Explain the mathematical basis for each geometric construction.
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DD.01. Construct the midpoint or perpendicular bisector of a segment
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DD.02. Construct an angle bisector
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DD.03. Construct a congruent angle
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DD.04. Construct a perpendicular line
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DD.05. Construct parallel lines
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DD.06. Construct an equilateral triangle or regular hexagon
EE. Sequences and Series
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EE.01. Classify formulas and sequences (arithmetic, geometric, recursive)
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EE.02. Find terms of an arithmetic sequence
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EE.03. Find terms of a geometric sequence
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EE.04. Find terms of a recursive sequence
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EE.05. Evaluate formulas for sequences
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EE.06. Write a formula for an arithmetic sequence
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EE.07. Write a formula for a geometric sequence
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EE.08. Write a formula for a recursive sequence
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EE.09. Solve sequences mixed review problems
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EE.10. Understand and apply sigma notation
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EE.11. Identify arithmetic and geometric series
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EE.12. Find the sum of a finite arithmetic or geometric series
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EE.13. Understand the concept of partial sums
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EE.14. Calculate partial sums of arithmetic series
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EE.15. Calculate partial sums of geometric series
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EE.16. Solve partial sums mixed review problems
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EE.17. Determine whether a geometric series is convergent or divergent
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EE.18. Find the value of an infinite geometric series
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EE.19. Write a repeating decimal as a fraction using geometric series
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EE.20. Apply the concepts of sequences and series to model real-world phenomena.
FF. Logic
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FF.01. Identify hypotheses and conclusions in conditional statements
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FF.02. Provide counterexamples to disprove statements
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FF.03. Construct truth tables for logical statements
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FF.04. Determine truth values of logical statements
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FF.05. Understand and apply conditional statements (if-then)
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FF.06. Understand and apply negations
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FF.07. Understand and apply converses, inverses, and contrapositives
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FF.08. Understand and apply biconditionals (if and only if)
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FF.09. Use logical reasoning to solve problems.
GG. Probability
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GG.01. Understand the basic concepts of probability
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GG.02. Distinguish between theoretical and experimental probability
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GG.03. Calculate the number of outcomes for compound events
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GG.04. Calculate probabilities of events
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GG.05. Calculate permutations
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GG.06. Apply the counting principle
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GG.07. Understand and apply permutation and combination notation
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GG.08. Find probabilities using permutations and combinations
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GG.09. Find probabilities using two-way frequency tables
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GG.10. Identify independent events
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GG.11. Calculate probabilities of independent and dependent events
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GG.12. Solve geometric probability problems
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GG.13. Find conditional probabilities
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GG.14. Understand the relationship between independence and conditional probability
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GG.15. Find conditional probabilities using two-way frequency tables
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GG.16. Find probabilities using the addition rule
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GG.17. Calculate expected values of random variables
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GG.18. Write the probability distribution for a game of chance
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GG.19. Calculate expected values for a game of chance
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GG.20. Choose the better bet based on expected value
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GG.21. Find probabilities using the binomial distribution
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GG.22. Simulate probability experiments to estimate probabilities.
HH. Statistics
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HH.01. Calculate the mean, median, mode, and range of a data set
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HH.02. Determine quartiles of a data set
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HH.03. Identify biased samples
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HH.04. Calculate the mean absolute deviation of a data set
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HH.05. Calculate the variance and standard deviation of a data set
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HH.06. Interpret the meaning of statistical measures in real-world contexts.
II. Data and Graphs
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II.01. Interpret histograms
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II.02. Create histograms
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II.03. Interpret stem-and-leaf plots
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II.04. Interpret box-and-whisker plots
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II.05. Interpret a scatter plot
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II.06. Determine the line of best fit for a scatter plot
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II.07. Make predictions based on data displayed in graphs.
