Arithmetic and Order of Operations
Build accurate calculation habits and learn the rules that decide which operation happens first.
Mathematics
A progressive path through practical and foundational mathematics, from arithmetic to the first ideas of calculus, statistics and financial math.
Fractions and Ratios
Add, simplify and compare fractions, and use ratios to describe how quantities relate.
Percentages
Calculate percentages, percentage change and apply them to everyday money and data problems.
Basic Algebra and Equations
Translate word problems into algebraic expressions and solve simple linear equations.
Linear Equations and Graphing
Plot straight lines, read their slope and intercept, and write an equation from two points.
Exponents and Roots
Apply the laws of exponents and simplify square and cube roots with confidence.
The Pythagorean Theorem and Basic Geometry
Use the Pythagorean theorem and the properties of angles and triangles to solve practical problems.
Area and Volume
Calculate the area and volume of common shapes and solids for real measurement problems.
Coordinate Geometry
Find distances, midpoints and shapes using coordinates on the plane.
Sequences and Patterns
Recognise arithmetic and geometric sequences and predict their next terms.
Basic Statistics: Mean, Median, Mode and Range
Summarise a data set with the three measures of central tendency and understand their spread.
Probability Basics
Calculate the likelihood of simple and combined events using the rules of probability.
Quadratic Equations
Solve quadratic equations by factoring, completing the square and the quadratic formula.
Systems of Equations
Solve two linear equations together using substitution and elimination.
Inequalities
Solve and graph linear inequalities, and understand what happens when you multiply by a negative.
Functions and Graphs
Understand function notation, domain and range, and read information from a graph.
Trigonometry Basics: Sine, Cosine and Tangent
Use sine, cosine and tangent to find missing sides and angles in right triangles.
The Unit Circle
Extend sine and cosine beyond right triangles using the unit circle and radians.
Polynomials and Factoring
Add, multiply and factor polynomials using common patterns.
Exponential and Logarithmic Functions
Model growth and decay with exponential functions and use logarithms to undo them.
Combinatorics: Permutations and Combinations
Count the number of ways to arrange or choose items using permutations and combinations.
Standard Deviation and Variance
Measure how spread out a data set is using variance and standard deviation.
Introduction to Limits
Understand what a limit means and evaluate simple limits algebraically and graphically.
Introduction to Derivatives
Understand the derivative as an instantaneous rate of change and apply basic differentiation rules.
Basic Integration: Area Under a Curve
Understand integration as accumulated area and apply the power rule in reverse.
Matrices and Vectors Basics
Add, multiply and interpret matrices and vectors as tools for organising and transforming data.
Normal Distribution Basics
Recognise the bell curve and use the 68-95-99.7 rule and z-scores to interpret data.
Financial Math: Interest, Loans and Growth
Calculate simple and compound interest and understand how loans and investments grow over time.
Mathematical Proof and Logic Basics
Construct simple direct and contradiction proofs and use basic logical connectives correctly.
Problem Solving Strategies (Capstone)
Apply a structured problem-solving process to tackle unfamiliar, multi-step mathematics problems.