Course Content
A. Numbers and Counting
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A.01. Understand roots of integers and rational numbers
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A.02. Find roots using a calculator
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A.03. Evaluate numerical expressions involving order of operations
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A.04. Understand and apply the properties of integers in addition, subtraction, multiplication, and division
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A.05. Convert between decimals, fractions, and percentages with precision
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A.06. Perform operations with rational numbers, including addition, subtraction, multiplication, and division
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A.07. Simplify complex numerical expressions involving rational numbers
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A.08. Estimate and approximate values of irrational numbers in decimal form
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A.09. Explore the historical significance and real-world applications of rational and irrational numbers
B. Scientific Notation
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B.01. Convert numbers between standard and scientific notation.
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B.02. Compare numbers expressed in scientific notation.
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B.03. Perform multiplication with numbers in scientific notation.
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B.04. Perform division with numbers in scientific notation.
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B.05. Solve real-world problems involving calculations with scientific notation.
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B.06. Apply scientific notation to simplify complex calculations in physics, chemistry, or astronomy.
C. Area and Perimeter
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C.01. Calculate the perimeter and circumference of basic shapes.
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C.02. Determine the area of polygons and circles using appropriate formulas.
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C.03. Calculate area and perimeter of figures in the coordinate plane.
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C.04. Solve practical problems involving area and perimeter.
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C.05. Apply concepts of area and perimeter to solve real-world design and construction problems.
D. Consumer Maths
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D.01. Calculate simple interest earned on an investment.
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D.02. Solve word problems involving compound interest calculations.
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D.03. Determine the amount resulting from continuously compounded interest.
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D.04. Calculate the percent of a number, including GST, discounts, and more.
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D.05. Calculate the percentage of discount and markup applied to an item.
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D.06. Solve multi-step problems involving percentage calculations.
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D.07. Compare different investment options based on interest rates and compounding periods.
E. Direct Variation
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E.01. Identify proportional relationships between variables.
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E.02. Find the constant of variation in a direct proportion.
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E.03. Graph a proportional relationship on the coordinate plane.
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E.04. Write equations representing direct variation.
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E.05. Write and solve direct variation equations for real-world scenarios.
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E.06. Analyse how changes in one variable affect the other in a direct variation relationship.
F. Coordinate Plane
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F.01. Review the fundamentals of the coordinate plane.
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F.02. Calculate the midpoint of a line segment.
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F.03. Determine the distance between two points.
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F.04. Apply coordinate geometry to solve geometric problems.
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F.05. Transform figures using translations, reflections, and rotations on the coordinate plane.
G. Functions
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G.01. Determine the domain and range of a function.
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G.02. Identify whether a relation represents 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 of values for a function given its graph.
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G.06. Find the slope of a linear function.
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G.07. Graph a linear function on the coordinate plane.
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G.08. Write the equation of a linear function given its graph or properties.
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G.09. Interpret linear functions over unit intervals.
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G.10. Analyse and compare different types of functions (linear, quadratic, exponential).
H. Equations and Inequalities
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H.01. Solve linear equations using algebraic techniques.
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H.02. Translate and solve linear equations presented as word problems.
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H.03. Graph a linear inequality on the number line.
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H.04. Graph a linear inequality on the coordinate plane.
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H.05. Write inequalities from their corresponding graphs.
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H.06. Formulate a linear inequality from a word problem.
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H.07. Solve linear inequalities and express the solution set.
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H.08. Graph the solutions to linear inequalities on the number line.
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H.09. Solve absolute value equations involving one variable.
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H.10. Graph solutions to quadratic inequalities on the number line.
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H.11. Solve quadratic inequalities using algebraic methods.
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H.12. Use equations and inequalities to model and solve real-world problems.
I. Simultaneous Equations
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I.01. Determine if a given point (x, y) is a solution to a system of simultaneous equations.
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I.02. Solve systems of simultaneous equations by graphing.
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I.03. Solve word problems involving systems of equations using graphical methods.
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I.04. Determine the number of solutions to a system of simultaneous equations.
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I.05. Solve systems of simultaneous equations using the substitution method.
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I.06. Solve word problems involving systems of equations using substitution.
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I.07. Solve systems of simultaneous equations using the elimination method.
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I.08. Solve word problems involving systems of equations using elimination.
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I.09. Solve systems of simultaneous equations using any appropriate method.
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I.10. Solve complex real-world problems using systems of simultaneous equations.
J. Inequalities and Linear Programming
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J.01. Determine if a given point (x, y) is a solution to a system of inequalities.
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J.02. Solve systems of inequalities by graphing the solution region.
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J.03. Identify the vertices of the feasible region (solution set) in a linear programming problem.
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J.04. Apply linear programming to solve optimization problems with constraints.
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J.05. Formulate a linear programming problem from a real-world scenario and solve graphically.
K. Matrices
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K.01. Understand and use matrix vocabulary (e.g., dimensions, elements, etc.).
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K.02. Apply matrix operation rules for addition, subtraction, and multiplication.
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K.03. Add and subtract matrices of compatible dimensions.
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K.04. Multiply a matrix by a scalar.
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K.05. Perform linear combinations of matrices.
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K.06. Multiply two matrices with compatible dimensions.
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K.07. Simplify expressions involving matrix operations.
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K.08. Understand and apply properties of matrices, such as the distributive property.
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K.09. Solve matrix equations using algebraic techniques.
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K.10. Calculate the determinant of a matrix.
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K.11. Determine if a matrix is invertible.
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K.12. Find the inverse of a matrix.
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K.13. Identify if two matrices are inverses of each other.
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K.14. Solve matrix equations using inverses.
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K.15. Apply matrices to solve systems of linear equations and real-world problems.
L. Complex Numbers
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L.04. Multiply complex numbers using the distributive property.
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L.05. Divide complex numbers by multiplying by the conjugate.
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L.06. Perform addition, subtraction, multiplication, and division of complex numbers.
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L.07. Calculate the absolute value (modulus) of a complex number.
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L.08. Simplify powers of i (the imaginary unit).
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L.09. Represent and interpret complex numbers on the complex plane.
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L.01. Define and understand the concept of complex numbers.
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L.02. Add and subtract complex numbers.
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L.03. Find the complex conjugate of a complex number.
M. Factorising
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M.01. Factorise out a monomial from a polynomial expression.
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M.02. Factorise quadratic expressions.
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M.03. Factorise quadratic expressions using algebra tiles.
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M.04. Factorise polynomials using a quadratic pattern.
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M.05. Factorise polynomials by grouping.
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M.06. Factorise sums and differences of cubes.
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M.07. Factorise general polynomials using various techniques.
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M.08. Apply factorization to simplify algebraic fractions and solve equations.
N. Quadratic Functions
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N.01. Identify the key characteristics of quadratic functions (vertex, axis of symmetry, etc.).
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N.02. Complete a function table for quadratic functions given an equation.
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N.03. Describe transformations of quadratic functions (shifts, stretches, reflections).
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N.04. Find a quadratic function given its graph, points, or properties.
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N.05. Graph a quadratic function on the coordinate plane.
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N.06. Match quadratic functions to their corresponding graphs.
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N.07. Solve a quadratic equation using square roots.
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N.08. Solve a quadratic equation using the zero product property.
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N.09. Solve a quadratic equation by factorising.
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N.10. Complete the square to rewrite a quadratic equation in vertex form.
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N.11. Solve a quadratic equation using the quadratic formula.
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N.12. Use the discriminant to determine the nature and number of solutions to a quadratic equation.
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N.13. Apply quadratic functions to model real-world scenarios and solve optimization problems.
O. Polynomials
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O.01. Understand polynomial vocabulary (degree, leading coefficient, etc.).
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O.02. Add and subtract polynomials.
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O.03. Multiply polynomials using the distributive property.
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O.04. Divide polynomials using long division.
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O.05. Divide polynomials using synthetic division.
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O.06. Evaluate polynomials using synthetic division.
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O.07. Write a polynomial equation from its roots.
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O.08. Find the roots of factorised polynomials.
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O.09. Apply the Complex Conjugate Theorem.
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O.10. Identify conjugate roots of polynomial equations.
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O.11. Use Descartes’ Rule of Signs to determine the possible number of positive and negative real roots of a polynomial.
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O.12. State and apply the Fundamental Theorem of Algebra.
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O.13. Match polynomials to their corresponding graphs.
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O.14. Use the Factor Theorem and the Remainder Theorem to analyze polynomials.
P. Radical Functions and Expressions
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P.01. Find the roots of integers (square roots, cube roots, etc.).
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P.02. Find the roots of rational numbers.
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P.03. Find roots using a calculator.
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P.04. Understand and work with nth roots.
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P.05. Simplify radical expressions with variables I.
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P.06. Simplify radical expressions with variables II.
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P.07. Multiply radical expressions.
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P.08. Divide radical expressions.
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P.09. Add and subtract radical expressions.
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P.10. Simplify radical expressions using the distributive property.
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P.11. Simplify radical expressions using conjugates.
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P.12. Determine the domain and range of radical functions.
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P.13. Solve equations involving radical expressions.
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P.14. Graph radical functions and analyze their properties.
Q. Rational Exponents
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Q.01. Evaluate expressions involving rational exponents.
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Q.02. Simplify expressions with multiplication involving rational exponents.
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Q.03. Simplify expressions with division involving rational exponents.
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Q.04. Apply the power rule to expressions with rational exponents.
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Q.05. Simplify complex expressions involving rational exponents I.
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Q.06. Simplify complex expressions involving rational exponents II.
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Q.07. Convert between radical expressions and rational exponents.
R. Rational Functions and Expressions
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R.01. Identify asymptotes and excluded values of rational functions.
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R.02. Evaluate rational expressions I.
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R.03. Evaluate rational expressions II.
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R.04. Simplify rational expressions by canceling common factors.
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R.05. Multiply and divide rational expressions.
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R.06. Add and subtract rational expressions with like and unlike denominators.
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R.07. Solve equations involving rational expressions.
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R.08. Graph rational functions and analyze their behavior.
S. Logarithms
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S.01. Convert between exponential and logarithmic forms with rational bases.
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S.02. Evaluate logarithms.
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S.03. Apply the change of base formula to evaluate logarithms.
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S.04. Identify and use the properties of logarithms.
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S.05. Apply the product property of logarithms.
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S.06. Apply the quotient property of logarithms.
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S.07. Apply the power property of logarithms.
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S.08. Review and apply mixed properties of logarithms.
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S.09. Evaluate logarithms using a mixed review of properties.
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S.10. Use logarithms to solve exponential equations and model real-world phenomena.
T. Exponential and Logarithmic Functions
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T.01. Determine the domain and range of exponential and logarithmic functions.
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T.02. Evaluate exponential functions for given input values.
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T.03. Match exponential functions to their corresponding graphs.
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T.04. Solve exponential equations by rewriting the base.
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T.05. Solve exponential equations using common logarithms.
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T.06. Solve logarithmic equations I.
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T.07. Solve logarithmic equations II.
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T.08. Identify linear and exponential functions from tables, graphs, or equations.
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T.09. Interpret exponential functions over unit intervals.
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T.10. Describe linear and exponential growth and decay in real-world contexts.
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T.11. Solve exponential growth and decay word problems.
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T.12. Apply exponential and logarithmic functions to model financial, biological, and physical phenomena.
U. Parabolas
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U.01. Determine the direction a parabola opens.
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U.02. Find the vertex of a parabola.
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U.03. Find the focus and directrix of a parabola.
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U.04. Find the axis of symmetry of a parabola.
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U.05. Write equations of parabolas in vertex form from graphs.
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U.06. Write equations of parabolas in vertex form using given properties.
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U.07. Convert equations of parabolas from general to vertex form.
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U.08. Find properties of a parabola from equations in general form.
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U.09. Graph parabolas using key features.
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U.10. Solve real-world problems involving parabolic shapes and trajectories.
V. Hyperbolas
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V.01. Find the center of a hyperbola.
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V.02. Find the vertices of a hyperbola.
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V.03. Find the length of the transverse and conjugate axes of a hyperbola.
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V.04. Find the equations for the asymptotes of a hyperbola.
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V.05. Find the foci of a hyperbola.
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V.06. Write equations of hyperbolas in standard form from graphs.
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V.07. Write equations of hyperbolas in standard form using given properties.
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V.08. Convert equations of hyperbolas from general to standard form.
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V.09. Find properties of hyperbolas from equations in general form.
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V.10. Graph hyperbolas using key features and asymptotes.
W. Angle Measures
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W.01. Convert angles between radians and degrees.
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W.02. Calculate radians and arc length.
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W.03. Identify the quadrant in which an angle lies.
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W.04. Represent angles graphically in standard position.
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W.05. Find coterminal angles.
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W.06. Determine the reference angle for a given angle.
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W.07. Apply angle measures to solve problems involving circular motion and geometry.
X. Trigonometry
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X.04. Calculate trigonometric ratios (csc, sec, cot) in right triangles.
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X.05. Find trigonometric ratios in similar right triangles.
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X.06. Find trigonometric ratios using the unit circle.
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X.07. Determine sin, cos, and tan of special angles (0, 30, 45, 60, 90 degrees).
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X.08. Determine csc, sec, and cot of special angles.
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X.09. Find trigonometric function values using a calculator.
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X.10. Find inverses of trigonometric functions (arcsin, arccos, arctan).
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X.11. Find inverses of csc, sec, and cot.
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X.12. Solve trigonometric equations I.
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X.13. Solve trigonometric equations II.
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X.14. Use trigonometric ratios to find a side length in a right triangle.
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X.15. Use trigonometric ratios to find an angle measure in a right triangle.
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X.16. Solve a right triangle given sufficient information.
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X.17. Apply the Law of Sines to solve triangles.
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X.18. Apply the Law of Cosines to solve triangles.
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X.19. Solve a general triangle given sufficient information.
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X.20. Calculate the area of a triangle using the sine formula.
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X.21. Calculate the area of a triangle using the Law of Sines.
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X.22. Apply trigonometric concepts to solve real-world problems in navigation, surveying, and physics.
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X.01. Apply Pythagoras’ Theorem and its converse to solve problems.
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X.02. Work with special right triangles (30-60-90 and 45-45-90).
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X.03. Calculate trigonometric ratios (sin, cos, tan) in right triangles.
Y. Trigonometric Functions
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Y.01. Identify properties of sine functions (amplitude, period, phase shift).
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Y.02. Write equations of sine functions from their graphs.
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Y.03. Write equations of sine functions using given properties.
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Y.04. Graph sine functions.
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Y.05. Identify properties of cosine functions (amplitude, period, phase shift).
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Y.06. Write equations of cosine functions from their graphs.
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Y.07. Write equations of cosine functions using given properties.
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Y.08. Graph cosine functions.
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Y.09. Graph both sine and cosine functions on the same coordinate plane.
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Y.10. Analyse and compare the properties of sine and cosine functions.
Z. Trigonometric Identities
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Z.01. Apply complementary angle identities.
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Z.02. Understand symmetry and periodicity of trigonometric functions.
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Z.03. Find trigonometric ratios using Pythagorean or reciprocal identities.
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Z.04. Find trigonometric ratios using multiple identities.
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Z.05. Apply trigonometric sum and difference identities.
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Z.06. Verify trigonometric identities using algebraic manipulation and known identities.
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Z.07. Use trigonometric identities to simplify expressions and solve equations.
AA. Surface Area and Volume
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AA.01. Understand the concepts of surface area and volume.
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AA.02. Calculate the surface area of prisms and cylinders.
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AA.03. Calculate the surface area of pyramids and cones.
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AA.04. Calculate the volume of prisms and cylinders.
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AA.05. Calculate the volume of pyramids and cones.
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AA.06. Calculate the surface area and volume of spheres.
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AA.07. Understand the concept of similar solids.
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AA.08. Calculate the surface area and volume of similar solids using ratios.
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AA.09. Review and apply surface area and volume formulas.
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AA.10. Apply surface area and volume calculations to solve real-world problems in engineering and architecture.
BB. Quadrilaterals
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BB.01. Classify quadrilaterals based on their properties.
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BB.02. Graph quadrilaterals on the coordinate plane.
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BB.03. Understand and apply the properties of parallelograms.
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BB.04. Prove that a quadrilateral is a parallelogram using geometric theorems.
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BB.05. Understand and apply the properties of rhombuses.
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BB.06. Understand and apply the properties of squares and rectangles.
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BB.07. Understand and apply the properties of trapeziums.
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BB.08. Understand and apply the properties of kites.
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BB.09. Review and compare the properties of various quadrilaterals.
CC. Similarity
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CC.01. Understand and apply similarity ratios and statements.
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CC.02. Relate side lengths and angle measures in similar figures.
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CC.03. Compare perimeters of similar figures.
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CC.04. Compare areas of similar figures.
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CC.05. Apply similar triangles and similarity transformations.
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CC.06. Understand the concept of similarity of circles.
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CC.07. Apply similarity concepts to solve problems involving scale factors, maps, and models.
DD. Circles
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DD.01. Identify and define parts of a circle (radius, diameter, chord, etc.).
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DD.02. Understand and work with central angles in a circle.
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DD.03. Calculate arc measure and arc length.
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DD.04. Calculate the area of sectors in a circle.
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DD.05. Review and apply various circle measurements.
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DD.06. Understand and apply theorems related to arcs and chords.
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DD.07. Understand and apply theorems related to tangent lines to circles.
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DD.08. Calculate the perimeter of polygons with an inscribed circle.
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DD.09. Understand and apply theorems related to inscribed angles.
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DD.10. Understand and apply theorems related to angles in inscribed right triangles.
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DD.11. Understand and apply theorems related to angles in inscribed quadrilaterals.
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DD.12. Solve geometric problems using properties of circles and related figures.
EE. Circles in the Coordinate Plane
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EE.01. Find the center of a circle given its equation or graph.
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EE.02. Find the radius or diameter of a circle given its equation or graph.
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EE.03. Write equations of circles in standard form from graphs.
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EE.04. Write equations of circles in standard form using given properties.
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EE.05. Convert equations of circles from general to standard form.
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EE.06. Find properties of circles from equations in general form.
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EE.07. Graph circles using their equations.
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EE.08. Use coordinate geometry to solve problems involving circles.
FF. Logic
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FF.01. Identify hypotheses and conclusions in logical statements.
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FF.02. Provide counterexamples to disprove statements.
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FF.03. Construct and interpret truth tables.
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FF.04. Determine truth values of logical statements.
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FF.05. Understand and work with conditional statements.
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FF.06. Formulate negations of statements.
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FF.07. Understand and work with converses, inverses, and contrapositives.
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FF.08. Understand and work with biconditional statements.
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FF.09. Apply logical reasoning to solve problems and construct valid arguments.
GG. Sequences and Series
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GG.01. Classify formulas and sequences as arithmetic, geometric, or neither.
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GG.02. Find terms of an arithmetic sequence given a formula or pattern.
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GG.03. Find terms of a geometric sequence given a formula or pattern.
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GG.04. Find terms of a recursive sequence.
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GG.05. Evaluate formulas for sequences.
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GG.06. Write a formula for an arithmetic sequence.
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GG.07. Write a formula for a geometric sequence.
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GG.08. Write a formula for a recursive sequence.
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GG.09. Review and apply concepts related to sequences.
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GG.10. Understand and use sigma notation to represent series.
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GG.11. Identify arithmetic and geometric series.
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GG.12. Find the sum of a finite arithmetic or geometric series.
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GG.13. Understand and apply the concept of partial sums.
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GG.14. Calculate partial sums of arithmetic series.
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GG.15. Calculate partial sums of geometric series.
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GG.16. Review and apply concepts related to partial sums.
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GG.17. Determine if a geometric series is convergent or divergent.
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GG.18. Find the value of an infinite geometric series.
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GG.19. Write a repeating decimal as a fraction using geometric series.
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GG.20. Apply sequences and series to solve problems involving patterns, growth, and decay.
HH. Probability
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HH.13. Understand and apply geometric probability.
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HH.14. Find conditional probabilities.
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HH.15. Understand the relationship between independence and conditional probability.
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HH.16. Find conditional probabilities using two-way frequency tables.
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HH.17. Find probabilities using the addition rule.
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HH.18. Find probabilities using the normal distribution.
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HH.19. Use probability concepts to analyze and interpret data in real-world scenarios.
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HH.01. Understand the basic concepts of probability.
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HH.02. Calculate theoretical and experimental probabilities.
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HH.03. Calculate the number of outcomes in compound events.
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HH.04. Calculate probabilities of events.
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HH.05. Understand and use factorials.
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HH.06. Understand and use permutations.
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HH.07. Apply the counting principle to calculate probabilities.
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HH.08. Use permutation and combination notation.
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HH.09. Find probabilities using permutations and combinations.
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HH.10. Find probabilities using two-way frequency tables.
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HH.11. Identify independent events.
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HH.12. Calculate probabilities of independent and dependent events.
II. Statistics
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II.01. Calculate the mean, median, mode, and range of a data set.
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II.02. Determine quartiles of a data set.
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II.03. Identify biased samples.
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II.04. Calculate the mean absolute deviation of a data set.
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II.05. Calculate the variance and standard deviation of a data set.
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II.06. Interpret statistical measures to analyze and compare different data sets.
JJ. Introduction to Limits
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JJ.01. Find limits using graphs.
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JJ.02. Find one-sided limits using graphs.
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JJ.03. Determine if a limit exists based on graphical analysis.
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JJ.04. Understand the concept of a limit and its role in calculus.
KK. Calculate Limits
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KK.01. Find limits using addition, subtraction, and multiplication laws.
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KK.02. Find limits using the division law.
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KK.03. Find limits using power and root laws.
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KK.04. Find limits using limit laws.
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KK.05. Find limits of polynomials and rational functions.
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KK.06. Find limits involving factorisation and rationalisation.
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KK.07. Find limits involving absolute value functions.
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KK.08. Find limits involving trigonometric functions.
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KK.09. Apply limit laws to evaluate complex limits and analyze function behavior.
LL. Limits and Rational Functions
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LL.01. Find limits at vertical asymptotes using graphs.
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LL.02. Determine end behavior of functions using graphs.
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LL.03. Determine end behavior of polynomial and rational functions.
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LL.04. Find the limit at a vertical asymptote of a rational function I.
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LL.05. Find the limit at a vertical asymptote of a rational function II.
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LL.06. Analyze the behavior of rational functions near asymptotes and at infinity.
MM. Continuity
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MM.01. Identify graphs of continuous functions.
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MM.02. Determine continuity using graphs.
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MM.03. Determine one-sided continuity using graphs.
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MM.04. Find and analyze points of discontinuity using graphs.
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MM.05. Determine continuity on an interval using graphs.
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MM.06. Determine the continuity of a piecewise function at a point.
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MM.07. Make a piecewise function continuous by adjusting parameters.
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MM.08. Apply the Intermediate Value Theorem.
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MM.09. Understand the relationship between limits, continuity, and differentiability.
NN. Introduction to Derivatives
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NN.01. Calculate the average rate of change of a function I.
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NN.02. Calculate the average rate of change of a function II.
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NN.03. Find instantaneous rates of change using limits.
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NN.04. Understand velocity as a rate of change.
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NN.05. Find values of derivatives using limits.
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NN.06. Find the gradient of a tangent line using limits.
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NN.07. Find equations of tangent lines using limits.
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NN.08. Apply the sum and difference rules to find derivatives.
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NN.09. Apply the power rule to find derivatives I.
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NN.10. Apply the power rule to find derivatives II.
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NN.11. Find derivatives of polynomials.
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NN.12. Apply derivatives to solve optimization and related rates problems.
