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Walkthroughs

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Walkthroughs

Step-by-step interactive worked examples with practice questions — choose your year group below.

Year 7

Building core foundations — number, basic geometry, sequences, and data handling.

Ordering Integers and Decimals

Number lines · Comparing negatives

Decimal places · Nearest whole · Nearest 10

Negative Numbers

Adding and subtracting on a number line

Highest common factor · Lowest common multiple

Squares, Cubes and Roots

Square/cube numbers · Square/cube roots

Equivalent Fractions and Simplifying

Finding the HCF · Simplifying fractions

Adding and Subtracting Fractions

Common denominators

Fraction of an Amount

Divide then multiply

Percentages of Quantities

Finding and increasing by a percentage

Sharing in a Ratio

Dividing an amount into parts

Angles · Triangles · Basic shapes · Perimeter & area

Tally Charts and Frequency Tables

Counting and organising raw data

Reading Bar Charts

Interpreting bar chart data

Reading Pie Charts

Finding angles and proportions

Finding the Mean

Sum of values ÷ number of values

Median and Mode

Middle value and most common value

Range and Comparing Data Sets

Spread of data, mean vs range

Mean from a Frequency Table

Weighted average from grouped data

Stem-and-Leaf Diagrams

Reading and finding the median

Basic Probability

Simple probability from counters

Comparing Two Data Sets

Dual bar charts and comparisons

Term-to-term rules · nth term · Pattern recognition

Writing Algebraic Expressions

Turning words into expressions

Evaluating expressions with BIDMAS

Simplifying Expressions

Collecting like terms

Expanding Single Brackets

The rectangle method

One-Step Equations

The balance method

Two-Step Equations

Solving in stages

Forming Expressions

Real-life word problems

Simplifying with Negatives

Like terms with negative coefficients

nth Term of a Sequence

Finding the rule for a sequence

Forming and Solving Equations

Age and word problems

Common Misconceptions

Negatives · BIDMAS · Fractions · Angles · Area & perimeter

EOY Assessment of Competency

20 randomised questions across all Year 7 topics

Year 8

Extending number and algebra — index laws, formal equations, transformations and probability.

Addition & Subtraction

Column method · Decimals · Negative integers · Borrowing & carrying

Grid method · Decimals · Powers of 10 · Long multiplication

Short & long division · Decimals · Fractions · Remainders

Mixed Operations

BODMAS · Brackets · Powers · Real-world problems

Integers, Powers & Roots

Negative integers · Index laws · HCF · LCM · Prime factors

Place Value & Rounding

Significant figures · Ordering · Standard form

Fractions, Percentages & Ratio

All fraction ops · % change · Reverse % · Ratio sharing

Expanding and Simplifying

Multiple brackets, then collect terms

Substituting into a Formula

Speed-distance-time and other formulae

Difference of Squares and Perfect Squares

Special product patterns

Forming Equations from Geometry

Angle facts turned into equations

Simplifying Expressions

Collecting like terms

Expanding Single Brackets

Distributing across every term

Substitution — Linear

Replacing letters with values

Substitution — Quadratic

Substituting into x² expressions

Expanding Double Brackets

FOIL: First, Outer, Inner, Last

Factorising — Common Factor

The reverse of expanding brackets

Solving Linear Equations

The balance method

Unknowns on Both Sides

Solving when x appears twice

Forming & Solving Equations

Word problems into equations

Multiplying, dividing, and raising powers

Arithmetic Sequences — nth Term

Finding the rule for a sequence

Geometric Sequences

Sequences that multiply by a ratio

Simultaneous Equations

Where two lines meet

Number lines and solving <, >, ≤, ≥

Special Sequences

Fibonacci, square, triangular, and cube numbers

Drawing Straight-Line Graphs

Table of values, plotting, and reading a line

Gradient and y-intercept

y = mx + c, and gradient from two points

Quadratic Graphs

Parabolas, roots, and turning points

Real-Life Graphs

Distance-time graphs and interpreting slopes

Parallel lines · Alternate & corresponding · Polygon angles

Shapes & Construction

Polygon properties · Symmetry · Bisectors

Perimeter, Area & Volume

Trapezium · Prisms · Compound shapes

Transformations

Reflection · Rotation · Translation · Enlargement

Units & Measurement

Conversions · Speed, distance, time · Scale drawings

Mean · Median · Mode · Range · Bar & pie charts

Probability scale · Simple probability · Experimental vs theoretical

Common Misconceptions

Decimals · Percentages · Algebra · Coordinates & graphs

🎯

EOY Assessment of Competency

20 randomised questions across all Year 8 topics

Coming Soon

Year 9

Cambridge Checkpoint Stage 9 — building towards IGCSE with number, algebra, geometry, statistics and probability.

Powers & roots · HCF & LCM · Standard form · Ratio & proportion · Compound interest

Double brackets · Factorising · Simultaneous equations · Inequalities · nth term

nth term · Quadratic sequences · Geometric sequences

Straight lines · Quadratic graphs · Distance-time · Speed-time

Parallel line angles · Polygon angles · Bearings · Similar & congruent triangles

Transformations

Reflection · Rotation · Enlargement · Translation · Describing transformations

Pythagoras & Trigonometry

Hypotenuse · Shorter side · Pythagorean triples · SOH-CAH-TOA

Arc & sector · Volume of prisms · Cylinders · Compound shapes

Scatter graphs · Mean from grouped data · Cumulative frequency · Box plots

Mutually exclusive · Tree diagrams · Independent events · Without replacement

Common Misconceptions

Equations · Inequalities · Probability · Ratio · Parallel lines · Reflections

EOY Assessment of Competency

30 questions · Indices · Sequences · Algebra · Geometry · Probability · Statistics and more

Year 10

Cambridge IGCSE 0580 — core and extended topics for the first year of the programme.

Indices · Standard form · Bounds · Percentages

Equations · Simultaneous · Inequalities · Functions

Area · Perimeter · Volume · Surface area

Angles · Symmetry · Bearings · Constructions

SOH-CAH-TOA · Sine & cosine rule · Bearings

Averages · Histograms · Cumulative frequency · Box plots

Linear · Quadratic · Distance-time · Speed-time

Constructions & Loci

Bisectors · Loci · Scale drawings

Calculus — Differentiation

Gradient · Turning points · Rates of change

Simplifying · Multiplying · Expanding brackets · Rationalising

Direct & Inverse Proportion

y∝x · y∝x² · y∝√x · y∝1/x · y∝1/x²

Scale factor · Area ratio · Volume ratio · Proving similarity

Rates, Speed & Density

Speed-distance-time · Density · Pressure · Exchange rates

Recurring Decimals

Converting to fractions · Stem & leaf · Box plots

Elevation & Depression

Angle of elevation · Angle of depression · Real-world trig problems

Common Misconceptions

Indices · Standard form · Rearranging · Trigonometry · Statistics

EOY Assessment of Competency

20 randomised questions across all Year 10 topics

Year 11

Cambridge IGCSE 0580 — completing the programme, exam-level extended content.

Quadratics · Factor theorem · Sequences · Functions

Cylinder · Cone · Sphere · Frustum · Arc & sector

Circle theorems · Pythagoras in 3D · Proof

Column vectors · Magnitude · Position vectors · Proof

Transformations

Rotation · Reflection · Enlargement · Combined

Differentiation

Gradient · Turning points · Rates of change

% of amount · Increase/decrease · Reverse % · Compound interest

Trig Graphs & Exact Values

y=sinx · y=cosx · y=tanx · Exact values · Solving trig equations

Advanced Sequences

Quadratic · Cubic · Exponential · nth term

Graphical Inequalities

Number line · Regions · Shading · Listing solutions

Frequency density · Unequal class widths · Reading & drawing

Advanced Transformations

Negative SF · Combined transformations · Invariant points

Conditional Probability

Without replacement · Tree diagrams · Venn · Two-way tables

Sets & Venn Diagrams

Set notation · 2-set & 3-set Venn · Union · Intersection · Complement

Exponential Growth & Decay

Compound interest · Depreciation · Population · Half-life

Common Misconceptions

Quadratics · Simultaneous equations · Circle theorems · Similarity · Probability trees

WAEC Topics

WAEC: Number Bases

Equations & basic operations · Binary · Octal · Base conversions

WAEC: Modulo Arithmetic

Operations in modulo tables · Clock arithmetic · Equations

Indicial equations · Laws of indices · Exponential equations

WAEC: Logarithms

Log tables · Substitution in logarithms · Laws of logs

Venn diagrams · 2-set & 3-set problems · Intersection & union

EOY Assessment of Competency

25 questions · Number Bases · Modulo · Indices · Logs · Sets · Percentages · Circle Theorems

Year 12

WAEC/NECO syllabus — including specialist topics and Cambridge A-Level bridging content.

Variation · Remainder & factor theorem · AP/GP · Indices · Logarithms

Earth geometry · Great circles · Latitude & longitude

Differentiation · Integration · Applications

Binary · Octal · Hexadecimal · Conversions · Equations

Modulo Arithmetic

Clock arithmetic · Modular operations · Tables

Binary Operations

Custom operations · Commutativity · Identity elements

Operations · Determinant · Inverse · Transformations

Venn diagrams · 2-set & 3-set problems · Complement · Set difference

🎯

EOY Assessment of Competency

20 randomised questions across all Year 12 topics

Coming Soon

Add Maths

Cambridge Additional Mathematics (0606) — extending IGCSE into pre-A-Level territory. All topics labelled by year group.

Year 10 — First Year Topics

f(x) notation · Composite · Inverse · Domain & range · Graph transformations

Simplifying · Rationalising denominators · Algebraic operations · Exact values

Quadratic Functions Y10

Roots · Turning points · Completing the square · Quadratic formula · Inequalities

Polynomials Y10

Remainder theorem · Factor theorem · Polynomial division · Higher-degree equations

Equations, Inequalities & Graphs Y10

Linear · Quadratic · Fractional equations · Inequalities algebraically & graphically

Simultaneous Equations Y10

Linear-linear · Linear-quadratic · Graphical interpretation · Number of solutions

Logarithmic & Exponential Functions Y10

Laws of logs · Solving exp/log equations · Growth & decay · Graph sketching

Straight Line Graphs Y10

Gradient & intercept · Parallel & perpendicular · Coordinate geometry · Linear models

Equation of a Circle Y10

(x−a)² + (y−b)² = r² · Centre & radius · Line-circle intersections

Circular Measure Y10

Degrees ⇄ radians · Arc length · Sector area · Segment area

Trigonometry Y10

Identities · Solving equations · Sine & cosine rules · Graphs · Radians · Proofs

Year 11 — Second Year Topics

Partial Fractions Y11

Proper & improper fractions · Repeated factors · Decomposition

Integration Y11

Indefinite & definite · Area under curve · Integration by substitution

Differentiation Y11

Chain · Product · Quotient rules · Tangents & normals · Stationary points

Polynomials (Advanced) Y11

Binomial theorem · Binomial series · General term

Functions (Advanced) Y11

Modulus functions · Graphs of |f(x)| · Solving modulus equations graphically

Arithmetic & geometric series · Sum to infinity · Sigma notation

Quadratics (Advanced) Y11

Maximum & minimum applications · Parametric equations · Further inequalities

Simultaneous Equations (Advanced) Y11

Non-linear systems · Three unknowns · Contextual problems

Circular Measure (Advanced) Y11

Sector & segment problems · Rates of change · Calculus with radians

Permutation & Combination Y11

ⁿPᵣ · ⁿCᵣ · Arrangements with restrictions · Probability applications

Trigonometric Identities Y11

Pythagorean · Double angle · R-form · Proving identities · Solving equations

🎯

EOY Assessment of Competency

Randomised questions across all Add Maths topics

Coming Soon

Further Maths

WAEC Further Mathematics — for our highest-attaining students in Year 12.

🧮

Sets and Venn Diagrams

Set notation · Unions · Intersections · De Morgan’s laws

√

Surds

Simplify · Add & subtract · Rationalise · Solve surd equations

💬

Logical Reasoning

Propositions · AND/OR/NOT · Implication · Truth tables · Tautology

📈

Functions

Composite · Inverse · Domain & range · One-to-one · Reflection in y=x

Coming Soon

𝐴

Partial Fractions

Linear factors · Repeated roots · Improper fractions · Verification

Coming Soon

𝑥

Indices & Logarithms

Index laws · Log laws · Solving exponential equations · Graphs

Coming Soon

📊

Binomial Theorem

Pascal’s triangle · Expanding (a+bx)^n · Specific terms · Approximation

…

Sequences & Series

AP & GP · nth term · Sum formulas · Sum to infinity

🔁

Permutations & Combinations

Factorials · nPr · nCr · Restrictions · Complement method

Coming Soon

📐

Trigonometry

Special angles · Identities · Sine & cosine rules · Solving equations

📉

Statistics

Mean · Variance · Frequency tables · Normal distribution · Z-scores

🎲

Probability

Addition & multiplication rules · Conditional · Tree diagrams · Binomial distribution

📏

Vectors

Position vectors · Magnitude · Dot product · Applications

Coming Soon

∫

Integration

Standard integrals · Definite integrals · Area under curve · Integration by parts

Coming Soon

⚖️

Statics

Forces · Equilibrium · Moments · Friction

Coming Soon

🏎️

Dynamics

Newton’s laws · Momentum · Connected particles · Work & energy

Coming Soon

Year 7

Cambridge Lower Secondary Science (0893) — Biology, Chemistry, Physics and Science in Context.

Cell structure · Animal & plant cells · Specialised cells · Microscopy

Classifying Life

Five kingdoms · Vertebrates · Invertebrates · Dichotomous keys

Classifying Matter

Elements · Compounds · Mixtures · Atoms & Periodic Table

Properties of Matter

Density · Diffusion · Pressure · Changes of state

Chemical Changes

Word equations · Combustion · Acids & alkalis · Reactivity series

Forces · Gravity · Solar system · Speed · Friction

Energy stores & transfers · Sound waves · Light · Thermal transfer

Static electricity · Current & circuits · Magnets · Ohm’s Law

Science in Context

Scientific method · Data & graphs · Lab safety · Measurement

End of Year Review

Mixed review across Biology, Chemistry and Physics

Year 8

Cambridge Lower Secondary Science (0893) — Biology, Chemistry, Physics and Earth Science.

Aerobic & anaerobic respiration · Breathing system · Photosynthesis · Enzymes

Health, Disease & the Body

Pathogens · Immune system · Reproduction · Inheritance · Evolution

Atmosphere · Greenhouse effect · Reactions of acids · Gas tests

Liquids & Solutions

Solubility · Rates of reaction · Energy changes · Periodic Table groups

Atomic Structure

Electron shells · Ionic bonding · Covalent bonding · Metallic bonding

Applications of Science

Materials science · Fertilisers · Industrial processes · Sustainability

EM spectrum · Colour & filters · Lenses & the eye · Sound & the ear

Speed, Motion & Forces

Newton’s laws · Velocity & acceleration · Work, energy & power · Waves

Earth & Solar System

Earth’s structure · Solar system · Day, night & seasons · Weather & climate

Science in Context

Science & technology · Data analysis · Ethics in science · Engineering

End of Year Review

Mixed review across Biology, Chemistry, Physics and Earth Science

Year 9

Cambridge Lower Secondary Science (0893) Checkpoint — Biology, Chemistry, Physics and Earth Science.

Photosynthesis in depth · Transport in plants · Plant hormones · Adaptations · Reproduction

Circulatory system · Homeostasis · Nervous system · Hormones & reproduction · Immunity

Species & Environments

Ecosystems & habitats · Adaptation & survival · Population dynamics · Biodiversity & conservation

Chemical Bonding

Ionic bonding · Covalent bonding · Metallic bonding · Comparing bond types

Chemical Structures

States & particle model · Nanoparticles · Polymers in detail

Chemical Reactions

Balanced equations · Calculating masses · Reversible reactions · Electrolysis

Sound waves in depth · Energy resources · Efficiency & power

Series & parallel circuits · Electrical power · Static electricity · Generators & transformers

🌌

Earth & Beyond

Universe · stars · space exploration

Coming Soon

🔬

Science in Context

Scientific method · data analysis · ethics

Coming Soon

🎯

End of Year Checkpoint

Mixed review across Biology, Chemistry and Physics

Coming Soon

Physics Y10

Cambridge IGCSE Physics (0625) — Year 10 topics: measurements, motion, forces, energy, thermal physics.

Physical Quantities

SI units · Scalars & vectors · Measurement · Significant figures

Speed · Velocity · Acceleration · Distance-time graphs · SUVAT

Mass, Weight & Density

Mass vs weight · Gravitational field strength · Density calculations

Newton's laws · Friction · Resultant forces · Free body diagrams

p = mv · Conservation of momentum · Impulse · Collisions

KE · GPE · Work done · Power · Efficiency

P = F/A · Pressure in fluids · Atmospheric pressure · Hydraulics

States of matter · Kinetic theory · Gas pressure · Brownian motion

Thermal Physics

Specific heat capacity · Specific latent heat · Conduction · Convection · Radiation

Physics Y11

Cambridge IGCSE Physics (0625) — Year 11 topics: waves, electricity, magnetism, nuclear physics and space.

v=fλ · Transverse & longitudinal · Reflection · Refraction · Diffraction

Lenses · 1/f=1/v+1/u · Dispersion · TIR · The eye

Electromagnetic Spectrum

EM wave order · Uses · Dangers · c=fλ

Longitudinal waves · Speed · Pitch & loudness · Echoes · Ultrasound

Field lines · Electromagnets · F=BIL · Transformers · National Grid

I=Q/t · V=IR · Power · LDRs · Thermistors · Diodes

Electric Circuits

Series · Parallel · Potential divider · Internal resistance · Kirchhoff

Electrical Safety

3-pin plug · Fuses · RCDs · Earthing · Double insulation · AC vs DC

Electromagnetism

Motor effect · Fleming's LHR · Generators · Transformers · Grid

Nuclear Physics

Alpha · Beta · Gamma · Half-life · Fission · Fusion

Solar system · Star lifecycle · Big Bang · Redshift · Hubble's Law

⚗️ Chemistry Year 10

States of Matter

Solids, liquids, gases · Kinetic theory · Changes of state

Atoms and Elements

Atomic structure · Protons, neutrons, electrons · Isotopes

Chemical Bonding

Ionic · Covalent · Metallic bonding · Structure and properties

Moles · Molar mass · Calculations from equations

Electrochemistry

Electrolysis · Electrode products · Applications

Chemical Energetics

Exothermic · Endothermic · Energy profiles · Bond energies

Rates of Reaction

Factors affecting rate · Collision theory · Catalysts

Redox Reactions

Oxidation · Reduction · OIL RIG · Oxidation states

⚗️ Chemistry Year 11

The Periodic Table

Groups 1, 7, 0 · Transition metals · Trends

Acids, Bases and Salts

pH · Neutralisation · Making salts · Titration

Reactivity series · Extraction · Rusting · Alloys

Organic Chemistry

Alkanes · Alkenes · Crude oil · Polymers · Alcohols

Chemistry of the Environment

Atmosphere · Greenhouse effect · Acid rain · Water treatment

Experimental Techniques and Analysis

Separation · Ion tests · Titration · Rf values · Gas tests

Practical Skills

% yield · Atom economy · Errors · Graphs · Safe handling

🌿 Biology Year 10

Five kingdoms · Binomial nomenclature · Keys

Cell Organisation

Cell structure · Organelles · Prokaryotes vs eukaryotes

Diffusion · Osmosis · Active transport

Biological Molecules

Carbohydrates · Proteins · Lipids · DNA

Active site · Factors · Lock and key · Induced fit

Plant Nutrition

Photosynthesis · Limiting factors · Leaf structure

Human Nutrition

Nutrients · Digestion · Absorption · Alimentary canal

Transport in Plants

Xylem · Phloem · Transpiration · Translocation

Transport in Animals

Heart · Blood vessels · Blood · Circulation

Disease and Immunity

Pathogens · Immune system · Vaccines · Antibodies

Lungs · Alveoli · Breathing · Fish gills · Leaves

Aerobic · Anaerobic · ATP · Fermentation

Kidneys · Urine · Liver · Osmoregulation

Coordination and Response

Nervous system · Hormones · Reflex arc · Sense organs

Medicinal · Recreational · Effects on body · Addiction

🌿 Biology Year 11

Reproduction — Asexual and Sexual

Mitosis · Meiosis · Gametes · Cloning · IVF

Sexual Reproduction in Humans

Reproductive system · Menstrual cycle · Hormones · Pregnancy

Sexual Reproduction in Plants

Flower structure · Pollination · Fertilisation · Seed dispersal

Genes · Alleles · Punnett squares · Co-dominance · X-linked

Variation and Selection

Continuous/discontinuous · Natural selection · Mutation · Evolution

Organisms and Their Environment

Ecosystems · Food webs · Abiotic/biotic factors · Cycles

Human Influences on Ecosystems

Deforestation · Climate change · Eutrophication · Conservation

Biotechnology and Genetic Modification

Genetic engineering · GM crops · Monoclonal antibodies · PCR

Year 7

JS1 — Introduction to Digital Technologies, hardware, operating systems, data, algorithms and first steps in programming.

Introduction to Digital Technologies

Computer Hardware

Operating Systems

Digital Devices

Data and Information

Basic Algorithms

Computational Thinking

Introduction to Programming

Computational Thinking

Productivity Software

Productivity & Internet

Internet Fundamentals

Productivity & Internet

Year 8

JS2 — Networking, file management, cybersecurity basics, data representation, programming concepts and multimedia.

Computer Networking Basics

Internet Services

File Management

Cybersecurity Basics

Data Representation

Data & Programming

Programming Concepts

Computational Thinking

Computational Thinking

Scratch / Block Programming

Computational Thinking

Introduction to Databases

Data & Programming

Multimedia Creation

Data & Programming

Year 9

JS3 — Computational thinking, Python, web technologies, AI/robotics/IoT awareness, entrepreneurship and digital ethics.

Computational Thinking

Computational Thinking

Python / Text-Based Programming

Computational Thinking

Web Technologies

Computational Thinking

Artificial Intelligence Awareness

Emerging Technology

Robotics & IoT Concepts

Emerging Technology

Digital Entrepreneurship

Emerging Technology

Ethics & Responsible Use of Technology

Emerging Technology

Year 10

SS1 — Computer architecture, operating systems and networks (extended), Python, algorithms & data structures, SQL, web development, cybersecurity and cloud computing.

Computer Architecture

Architecture & OS

Operating Systems (Extended)

Architecture & OS

Networks (Extended)

Networks & Cybersecurity

Python Programming

Programming & Algorithms

Algorithms & Data Structures

Programming & Algorithms

Databases & SQL

Data & Databases

Web Development

Cybersecurity (Extended)

Networks & Cybersecurity

Cloud Computing

Year 11

SS2 — Object-oriented programming, advanced SQL, full-stack web & mobile development, advanced networking, data analysis, AI/ML and digital communication.

Object-Oriented Programming

Programming & Software

SQL Databases (Advanced)

Data & Databases

Website Development (Advanced)

Mobile Application Development

Computer Networking (Advanced)

Networks & Cybersecurity

Data & Analysis

AI & Machine Learning

Emerging Technology

Digital Communication

Emerging Technology

Year 12

SS3 — Software development project, systems analysis, emerging technologies, blockchain & cloud, cybersecurity management, entrepreneurship and careers.

Software Development Project

Software Engineering

Systems Analysis

Software Engineering

Emerging Technologies

Emerging Technology

Blockchain & Cloud Services

Emerging Technology

Cybersecurity Management

Software Engineering

Digital Entrepreneurship (Advanced)

Business & Careers

Project Management & Careers in Computing

Business & Careers