Fundamentals of Mathematics Course

Lesson 1 • Fractions and Rational Numbers

Develops conceptual and procedural mastery of fractions, mixed numbers, and rational arithmetic. Provides the foundation for ratio, proportion, and algebraic fraction work ahead.

Lesson 2 • Decimals and Percents

Teaches decimal place value, rounding, and percent conversions. Connects these skills to estimation and percentage-based calculations used in everyday professional tasks.

Lesson 3 • Understanding the Number System

Introduces natural numbers, integers, rationals, and irrationals within a unified framework. Establishes the vocabulary and structure needed for all subsequent arithmetic work.

Lesson 4 • Estimation and Mental Math Strategies

Introduces front-end estimation, compatible numbers, and mental computation techniques. Reinforces number sense as a check on calculator and written computation results.

Lesson 1 • Proportional Relationships

Examines direct proportion, constant of proportionality, and proportional tables and graphs. Connects proportional reasoning to scaling and prediction tasks.

Lesson 2 • Ratios and Rates

Defines ratios and unit rates and distinguishes part-to-part from part-to-whole relationships. Builds the conceptual base for proportional reasoning throughout the chapter.

Lesson 3 • Scale, Similarity, and Indirect Measurement

Uses proportional reasoning to interpret scale drawings and solve indirect measurement problems. Extends ratio skills to geometric and spatial applications.

Lesson 1 • Inequalities and Their Solutions

Extends equation-solving techniques to linear inequalities and introduces interval notation. Connects inequality solutions to real-world constraints and decision-making.

Lesson 2 • Solving One-Variable Linear Equations

Develops systematic methods for isolating a variable using inverse operations. Provides the core equation-solving skill applied in every subsequent algebraic topic.

Lesson 3 • Properties of Real Numbers

Covers commutative, associative, distributive, and identity properties as tools for simplification. Connects these properties to efficient algebraic manipulation.

Lesson 4 • Variables and Algebraic Expressions

Introduces variables, constants, coefficients, and terms within algebraic expressions. Establishes the symbolic language used throughout the remaining core chapters.

Lesson 1 • Systems of Linear Equations

Introduces graphical, substitution, and elimination methods for solving two-equation systems. Applies systems to break-even, mixture, and comparison problems.

Lesson 2 • The Coordinate Plane

Introduces the Cartesian coordinate system, quadrants, and ordered-pair plotting. Provides the graphical foundation for representing all functions and data relationships.

Lesson 3 • Slope and Rate of Change

Defines slope as a ratio of vertical to horizontal change and connects it to rate of change. Distinguishes positive, negative, zero, and undefined slopes through graphical analysis.

Lesson 4 • Forms of Linear Equations

Presents slope-intercept, point-slope, and standard forms and the conversions among them. Builds flexibility in writing and interpreting linear equations for varied applications.

Lesson 1 • Introduction to Polynomials

Defines polynomials by degree, leading coefficient, and standard form. Builds vocabulary and classification skills needed for polynomial arithmetic and factoring.

Lesson 2 • Exponent Rules and Scientific Notation

Establishes product, quotient, power, zero, and negative exponent rules. Applies these rules to scientific notation for very large and very small quantities.

Lesson 3 • Factoring Polynomials

Develops GCF factoring, trinomial factoring, and grouping as systematic decomposition strategies. Factoring is the essential prerequisite for solving quadratic equations.

Lesson 4 • Polynomial Division

Introduces long division and synthetic division of polynomials and the remainder theorem. Connects division to factoring and prepares students for rational expressions.

Lesson 1 • Quadratic Modelling and Optimisation

Uses quadratic functions to model real-world scenarios and find maximum or minimum values. Applies vertex interpretation to area, revenue, and projectile motion problems.

Lesson 2 • Completing the Square

Develops completing the square as both a solving technique and a method for converting to vertex form. Provides the algebraic derivation of the quadratic formula.

Lesson 3 • Solving Quadratics by Factoring and Roots

Applies zero-product property and square root method to solve quadratic equations. Reinforces factoring skills from the previous chapter in an equation-solving context.

Lesson 4 • Graphing Quadratic Functions

Analyses vertex, axis of symmetry, direction of opening, and intercepts of parabolas. Connects the graph's features to the coefficients of the standard and vertex forms.

Lesson 1 • Perimeter and Area of Plane Figures

Derives and applies formulas for triangles, quadrilaterals, and circles. Connects area and perimeter to material estimation and layout planning tasks.

Lesson 2 • The Theorem of Pythagoras

Proves and applies the Theorem of Pythagoras to find missing side lengths in right triangles. Extends to distance calculations and diagonal measurements in practical contexts.

Lesson 3 • Angles, Lines, and Geometric Relationships

Defines angle types, parallel and perpendicular lines, and transversal angle relationships. Establishes the geometric vocabulary and reasoning used throughout the chapter.

Lesson 4 • Volume of Three-Dimensional Figures

Derives and applies volume formulas for prisms, cylinders, pyramids, cones, and spheres. Connects volume to capacity, storage, and fluid-quantity calculations.

Lesson 1 • Correlation and Linear Regression

Identifies correlation direction and strength using scatter plots and the correlation coefficient. Fits a line of best fit and uses it to make predictions within the data range.

Lesson 2 • Measures of Centre and Spread

Calculates mean, median, mode, range, variance, and standard deviation for data sets. Distinguishes when each measure best represents a distribution's centre and variability.

Lesson 3 • Compound and Conditional Probability

Applies addition and multiplication rules to compound events and introduces conditional probability. Connects probability reasoning to risk assessment and decision-making scenarios.

Lesson 4 • Basic Probability Concepts

Defines probability, sample space, and events using classical and experimental approaches. Builds the conceptual framework for compound and conditional probability.