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Math and Geometry Tools

Master Year 10 Mathematics with Confidence

 Learning Journey

Build a solid foundation in key mathematical concepts and sharpen your problem-solving skills. Our Year 10 Maths program is developed and delivered by experienced educators, supported by comprehensive resources to help students excel in assessments and beyond.

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Course Structure

Targeted Academic Support Aligned with School Curriculum

While the course structure outlines the general topics covered each term, we go a step further by offering small group sessions made up of students from the same school. This allows us to align our support closely with the specific topics being taught in their classrooms. Our sessions reinforce school learning, help students stay on track, and build their confidence—especially as they prepare for exams. We also provide personalised guidance tailored to each student’s individual exam preparation needs.

Term 1 : Simultaneous Equations, Quadratic Techniques, Properties of Geometrical Figures

Lesson 1: Quadratic Techniques – Factoring with Common Factors, Grouping & Difference of Squares

Lesson 2: Trinomials Made Easy – Factorising Step-by-Step

Lesson 3: Perfect Squares & Mixed Methods – Advanced Factorisation

Lesson 4: Simplifying Algebraic Fractions – Techniques and Practice

Lesson 5: Understanding Similarity – Tests and Triangle Calculations

Lesson 6: Transformations & Enlargements – Similar Figures and 3D Solids

Lesson 7: Surface Area Basics – Accuracy and Prisms

Lesson 8: Surface Area of 3D Shapes – Pyramids, Cones & Spheres
Lesson 9: Revision

Lesson 10: Topic Test

Term 2 : Trigonometric Ratios and Further Trigonometry

Lesson 1: Trig Review – SOH CAH TOA and Complementary Angle Ratios

Lesson 2: Trig in All Quadrants – Angles of Any Magnitude

Lesson 3: Trigonometric Graphs – Sine, Cosine and Tangent Curves

Lesson 4: Solving Trig Equations – Simple Techniques and Practice

Lesson 5: Sine Rule – Including the Ambiguous Case

Lesson 6: Cosine Rule – Plus Area of a Triangle Using Trig

Lesson 7: Bearings – Real-World Applications of Trigonometry

Lesson 8: 3D Trigonometry – Applying Trig in Three Dimensions

Lesson 9: Revision

Lesson 10: Topic Test

Term 3 : Curve Sketching, Non-Linear Relationships, Functions

Lesson 1: Probability Basics – Experimental vs Theoretical & Compound Events

Lesson 2: Advanced Probability – Complementary Events & Multistage Problems

Lesson 3: Understanding Variation – Rates of Change in Context

Lesson 4: Introduction to Logarithms – Evaluating and Using Log Laws

Lesson 5: Logarithmic Rules – Power Laws and Change of Base

Lesson 6: Exploring Functions – Notation, Relations, Even & Odd Functions

Lesson 7: Sketching Parabolas – Vertex Form and Key Features

Lesson 8: Transforming Parabolas – General Form and Graphical Changes

Lesson 9: Revision

Lesson 10: Topic Test

Term 4 : Polynomials and Logarithms

Lesson 1: Reverse Engineering Parabolas – Finding the Equation from a Graph

Lesson 2: Sketching Cubic Functions – Key Features and Shapes

Lesson 3: Circles and Semi-Circles – Graphing and Understanding Their Equations

Lesson 4: Exploring Exponential Curves and Hyperbolas – Graphing Non-Linear Functions

Lesson 5: Hyperbolas in Depth – Features and Transformations

Lesson 6: Transforming Graphs – Shifts, Stretches and Reflections

Lesson 7: Introduction to Polynomials – Definitions and Operations

Lesson 8: Polynomial Division – Remainder and Factor Theorems Explained
Lesson 9: Revision

Lesson 10: Topic Test

 Syllabus 

🔢 Numbers

  • Real numbers and their properties

  • Scientific notation and significant figures (extended applications)

  • Index laws (including zero, negative, and fractional indices)

  • Operations with surds and rationalising denominators (5.3 pathway)

  • Financial mathematics (profit/loss, discounts, compound interest, loans)

📏 Measurement

  • Surface area and volume of composite solids

  • Time, rates, and unit conversions

  • Scale drawings, bearings, and map reading

  • Applications of Pythagoras’ Theorem

  • Trigonometry: solving right-angled triangles, angles of elevation/depression (extended in 5.3)

📊 Statistics

  • Data collection methods and reliability

  • Displaying and interpreting data (histograms, box plots, scatter plots)

  • Measures of central tendency and spread

  • Bivariate data, correlation, and line of best fit (5.2 and 5.3)

🧮 Algebra

  • Expanding, factorising, and simplifying algebraic expressions

  • Solving linear, quadratic, and simultaneous equations

  • Algebraic fractions and operations (5.2 and 5.3)

  • Quadratic expressions, equations, and factorisation techniques

  • Introduction to functions and their graphs

  • Patterns, sequences, and algebraic generalisation

📐 Geometry

  • Properties and classification of geometric figures

  • Angle relationships and geometric proofs

  • Congruence and similarity in two dimensions

  • Deductive reasoning and formal proofs (5.3 pathway)

🎲 Probability

  • Single and multi-step probability experiments

  • Theoretical vs. experimental probability

  • Venn diagrams, two-way tables, and probability rules

  • Tree diagrams and conditional probability (5.3)

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