Mathematics 4024
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Conquer Cambridge O Level Maths

Every topic on the syllabus — from number and algebra to circle theorems and probability — broken into clear, step-by-step lessons with worked examples and exam-focused practice, so you walk into the hall knowing exactly what to do.

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Mathematics 4024
This school is step 2 of Cambridge O Levels — a 13-school journey.See the whole path

My job isn't just to show you the answer — it's to make the reasoning so clear that next time, you don't need me.

Renstay College

What you'll learn

What you'll be able to do

  • Solve number, ratio, and proportion problems accurately using Cambridge syllabus methods
  • Apply algebraic techniques — equations, inequalities, and functions — to multi-step exam questions
  • Interpret and construct statistical diagrams, calculate measures of central tendency, and analyse data sets
  • Use geometric reasoning, circle theorems, and trigonometry to solve both straightforward and complex shape problems
  • Tackle transformation geometry, vectors, and coordinate geometry with confidence across all difficulty tiers
  • Approach any past-paper question with a proven exam strategy, manage time effectively, and maximise marks

How it works

A school that adapts to you

This isn't a set of static videos. Every lesson is generated live and tuned to where you actually are.

We learn your level

A quick placement check tailors your starting point so you're never bored or lost.

Lessons adapt as you go

Each lesson is written for your pace and your goal, adjusting as your skills grow.

Your AI coach keeps you moving

Checkpoints, feedback, and gentle nudges turn progress into a real result.

The curriculum

What's inside your school

50 modules · 145 lessons

1

Number, Ratio & Proportion

Builds fluency with the full range of number topics — integers, decimals, fractions, powers, and proportional reasoning — as tested in the Cambridge O Level examination.

  • 1.1Types of Number & the Number SystemIncluded
  • 1.2Fractions, Decimals & PercentagesIncluded
  • 1.3Powers, Roots & Standard FormIncluded
  • 1.4Ratio, Proportion & RatesIncluded
  • 1.5Estimation, Rounding & Limits of AccuracyIncluded
2

Algebra

Develops algebraic fluency from simplifying expressions through to solving equations, inequalities, and working with functions and sequences.

  • 2.1Algebraic Manipulation & SimplificationIncluded
  • 2.2Solving Linear Equations & InequalitiesIncluded
  • 2.3Simultaneous EquationsIncluded
  • 2.4Quadratic Equations & FactorisationIncluded
  • 2.5Sequences, Functions & GraphsIncluded
3

Geometry & Trigonometry

Covers angle properties, polygon and circle theorems, mensuration, and right-angled and non-right-angled trigonometry.

  • 3.1Angles, Lines & PolygonsIncluded
  • 3.2Circle TheoremsIncluded
  • 3.3Perimeter, Area & VolumeIncluded
  • 3.4Pythagoras' Theorem & Right-Angled TrigonometryIncluded
  • 3.5Sine & Cosine Rules and BearingsIncluded
4

Coordinate Geometry, Vectors & Transformations

Equips students to work with straight lines on the coordinate plane, describe and perform transformations, and solve problems using column vectors.

  • 4.1Coordinate Geometry & Straight-Line GraphsIncluded
  • 4.2Reflections, Rotations & TranslationsIncluded
  • 4.3Enlargements & Scale FactorsIncluded
  • 4.4Vectors & Vector GeometryIncluded
5

Statistics & Probability

Teaches students to collect, display, and analyse data and to calculate and compare probabilities using all methods required by the syllabus.

  • 5.1Statistical DiagramsIncluded
  • 5.2Measures of Central Tendency & SpreadIncluded
  • 5.3Cumulative Frequency & Box PlotsIncluded
  • 5.4Probability FundamentalsIncluded
  • 5.5Tree Diagrams & Conditional ProbabilityIncluded
6

Exam Preparation & Strategy

Consolidates the full syllabus through timed past-paper practice and equips students with exam strategies that maximise marks under pressure.

  • 6.1Understanding the Exam FormatIncluded
  • 6.2Exam Technique & Time ManagementIncluded
  • 6.3Tackling Multi-Step & Problem-Solving QuestionsIncluded
  • 6.4Past-Paper Practice & Mark-Scheme AnalysisIncluded
  • 6.5Targeted Revision & Final PreparationIncluded
7

Estimation

  • 7.1Round values to a specified degree of accuracy.Included
  • 7.2Make estimates for calculations involving numbers, quantities and measurements.Included
  • 7.3Round answers to a reasonable degree of accuracy in the context of a given problem.Included
8

Limits of accuracy

  • 8.1Give upper and lower bounds for data rounded to a specified accuracy.Included
  • 8.2Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracyIncluded
9

Ratio and proportion

  • 9.1Understand and use ratio and proportionIncluded
10

Rates

  • 10.1Use common measures of rateIncluded
  • 10.2Apply other measures of rate.Included
  • 10.3Solve problems involving average speed.Included
11

Percentages

  • 11.1Calculate a given percentage of a quantity.Included
  • 11.2Express one quantity as a percentage of anotherIncluded
  • 11.3Calculate percentage increase or decreaseIncluded
  • 11.4Calculate with simple and compound interest.Included
  • 11.5Calculate using reverse percentagesIncluded
12

Using a calculator

  • 12.1Use a calculator efficiently.Included
  • 12.2Enter values appropriately on a calculator.Included
  • 12.3Interpret the calculator display appropriately.Included
13

Time

  • 13.1Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between unitsIncluded
  • 13.2Calculate times in terms of the 24-hour and 12-hour clockIncluded
  • 13.3Read clocks and timetables.Included
14

Money

  • 14.1Calculate with money.Included
  • 14.2Convert from one currency to anotherIncluded
15

Exponential growth and decay

  • 15.1Use exponential growth and decay.Included
16

Surds

  • 16.1Understand and use surds, including simplifying expressions.Included
  • 16.2Rationalise the denominator.Included
17

Introduction to algebra

  • 17.1Know that letters can be used to represent generalised numbers.Included
  • 17.2Substitute numbers into expressions and formulasIncluded
18

Algebraic manipulation

  • 18.1Simplify expressions by collecting like terms.Included
  • 18.2Expand products of algebraic expressions.Included
  • 18.3Factorise by extracting common factors.Included
  • 18.4Factorise expressions of the formIncluded
  • 18.5Complete the square for expressions in the formIncluded
19

Algebraic fractions

  • 19.1Manipulate algebraic fractions.Included
  • 19.2Factorise and simplify rational expressions.Included
20

Indices II

  • 20.1Understand and use indices (positive, zero, negative and fractional).Included
  • 20.2Understand and use the rules of indices.Included
21

Equations

  • 21.1Construct expressions, equations and formulas.Included
  • 21.2Solve linear equations in one unknown.Included
  • 21.3Solve fractional equations with numerical and linear algebraic denominators.Included
  • 21.4Solve simultaneous linear equations in two unknowns.Included
  • 21.5Solve quadratic equations by factorisation, completing the square and by use of the quadratic formula.Included
  • 21.6Change the subject of formulas.Included
22

Inequalities

  • 22.1Represent and interpret inequalities, including on a number line.Included
  • 22.2Construct, solve and interpret linear inequalitiesIncluded
  • 22.3Represent and interpret linear inequalities in two variables graphically.Included
  • 22.4List inequalities that define a given region.Included
23

Sequences

  • 23.1Continue a given number sequence or pattern.Included
  • 23.2Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences.Included
  • 23.3Find and use the nth term of sequences.Included
24

Proportion

  • 24.1Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.Included
25

Graphs in practical situations

  • 25.1Use and interpret graphs in practical situations including travel graphs and conversion graphs.Included
  • 25.2Draw graphs from given dataIncluded
  • 25.3Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.Included
  • 25.4Calculate distance travelled as area under a speed–time graphIncluded
26

Graphs of functions

  • 26.1Construct tables of values, and draw, recognise and interpret graphs for functionsIncluded
  • 26.2Solve associated equations graphically, including finding and interpreting roots by graphical methods.Included
  • 26.3Draw and interpret graphs representing exponential growth and decay problems.Included
  • 26.4Estimate gradients of curves by drawing tangents.Included
27

Sketching curves

  • 27.1Recognise, sketch and interpret graphs of the linear functionsIncluded
  • 27.2Recognise, sketch and interpret graphs of the quadratic functionsIncluded
  • 27.3Recognise, sketch and interpret graphs of the cubic functionsIncluded
  • 27.4Recognise, sketch and interpret graphs of the reciprocal functionsIncluded
  • 27.5Recognise, sketch and interpret graphs of the exponential functionsIncluded
28

Functions

  • 28.1Understand and find inverse functionsIncluded
  • 28.2Form composite functionsIncluded
29

Coordinates

  • 29.1Use and interpret Cartesian coordinates in two dimensionsIncluded
30

Drawing linear graphs

  • 30.1Draw straight-line graphs for linear equations.Included
31

Gradient of linear graphs

  • 31.1Find the gradient of a straight line.Included
  • 31.2Calculate the gradient of a straight line from the coordinates of two points on itIncluded
32

Length and midpoint

  • 32.1Calculate the length of a line segment.Included
  • 32.2Find the coordinates of the midpoint of a line segment.Included
33

Parallel lines

  • 33.1Find the gradient and equation of a straight line parallel to a given lineIncluded
34

Perpendicular lines

  • 34.1Find the gradient and equation of a straight line perpendicular to a given line.Included
35

Geometrical terms

  • 35.1Use and interpret the following geometrical terms: • point • vertex • line • plane • parallel • perpendicular • perpendicular bisector • bearing • right angle • acute, obtuse and reflex angles • interior and exterior angles • similar • congruent • scale factorIncluded
  • 35.2Use and interpret the vocabulary of: • triangles • special quadrilaterals • polygons • nets • solids.Included
  • 35.3Use and interpret the vocabulary of a circle.Included
36

Geometrical constructions

  • 36.1Measure and draw lines and angles.Included
  • 36.2Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only.Included
  • 36.3Draw, use and interpret netsIncluded
37

Scale drawings

  • 37.1Draw and interpret scale drawings.Included
  • 37.2Use and interpret three-figure bearings.Included
38

Similarity

  • 38.1Calculate lengths of similar shapes.Included
  • 38.2Use the relationships between lengths and areas of similar shapes and lengths, surface areas and volumes of similar solidIncluded
  • 38.3Solve problems and give simple explanations involving similarityIncluded
39

Symmetry

  • 39.1Recognise line symmetry and order of rotational symmetry in two dimensions.Included
  • 39.2Recognise symmetry properties of prisms, cylinders, pyramids and cones.Included
40

Angles

  • 40.1Calculate unknown angles and give simple explanationsIncluded
  • 40.2Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior angles sum to 180° (supplementary).Included
  • 40.3Know and use angle properties of regular and irregular polygonsIncluded
41

Circle theorems

  • 41.1Calculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90° • angle at the centre is twice the angle at the circumference • angles in the same segment are equal • opposite angles of a cyclic quadrilateral sum to 180° (supplementary) • alternate segment theorem.Included
  • 41.2Use the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the centre • tangents from an external point are equal in lengthIncluded
42

Units of measure

  • 42.1Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units.Included
43

Area and perimeter

  • 43.1Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium.Included
44

Circles, arcs and sectors

  • 44.1Carry out calculations involving the circumference and area of a circleIncluded
  • 44.2Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle.Included
45

Surface area and volume

  • 45.1Carry out calculations and solve problems involving the surface area and volume of a: • cuboid • prism • cylinder • sphere • pyramid • cone.Included
46

Compound shapes and parts of shapes

  • 46.1Carry out calculations and solve problems involving perimeters and areas of: • compound shapes • parts of shapes.Included
  • 46.2Carry out calculations and solve problems involving surface areas and volumes of: • compound solids • parts of solids.Included
47

Trigonometry

  • 47.1Pythagoras’ theoremIncluded
  • 47.2Right-angled trianglesIncluded
  • 47.3Non-right-angled trianglesIncluded
  • 47.4Pythagoras’ theorem and trigonometry in 3DIncluded
48

Transformations and vectors

  • 48.1TransformationsIncluded
  • 48.2Vectors in two dimensionsIncluded
  • 48.3Magnitude of a vectorIncluded
  • 48.4Vector geometryIncluded
49

Probability

  • 49.1Introduction to probabilityIncluded
  • 49.2Relative and expected frequenciesIncluded
  • 49.3Probability of combined eventsIncluded
50

Statistics

  • 50.1Classifying statistical dataIncluded
  • 50.2Interpreting statistical dataIncluded
  • 50.3Averages and measures of spreadIncluded
  • 50.4Statistical charts and diagramsIncluded
  • 50.5Scatter diagramsIncluded
  • 50.6Cumulative frequency diagramsIncluded
  • 50.7HistogramsIncluded

Who it's for

Is this you?

The Exam Candidate

A Year 10 or 11 student working through the Cambridge O Level syllabus who wants structured, reliable lessons covering every topic that could appear on the paper.

The Algebra Avoider

A student who freezes at quadratics or simultaneous equations and needs patient, step-by-step worked examples to build real algebraic confidence.

The Last-Minute Reviser

A student with weeks — not months — to go who needs a fast, targeted route through syllabus gaps and a clear exam strategy to maximise their marks.

The Supportive Parent

A parent who wants to understand what their child is studying so they can offer meaningful help at home, especially with tricky topics like circle theorems or vectors.

The Private Tutor

A tutor looking for a well-sequenced, syllabus-aligned resource to anchor their sessions and show students exactly how to write answers that earn full marks.

The Geometry Struggler

A student who can handle number and algebra but loses marks on circle theorems, trigonometry, and geometric reasoning — the topics this school unpacks with particular care.

Questions

Frequently asked

Your teacher

A note from your teacher

Renstay College

Renstay College

I know exactly what it feels like to stare at a past paper and have no idea where to begin. Maybe you look at a circle-theorem question and the logic just won't click. Maybe algebra made sense in class but falls apart the moment the problem has more than two steps. Maybe you understand each topic in isolation but can't see how it all fits together — and the exam is getting closer.

That feeling is not a sign that you're bad at mathematics. It's a sign that you haven't yet had someone sit beside you and walk you through each idea one careful step at a time — showing you not just the answer, but the reasoning behind it, so that the next similar question feels familiar rather than frightening. That is exactly what I've built this school to do.

Every lesson in this school follows the same simple rhythm: I explain the concept clearly, I work through an example in front of you — narrating every decision along the way — and then I give you the chance to try it yourself before we move on. Nothing is left as a mystery. Whether we're working through ratio problems, factorising quadratics, applying the sine rule, or constructing a cumulative frequency diagram, you'll always know why each step is taken, not just what the step is. That 'why' is what makes knowledge stick under exam pressure.

I've also taken care to build the school in the order that matters. Number and proportion lay the foundation for algebra. Algebra supports coordinate geometry and functions. Geometry builds towards trigonometry. By the time you reach vectors and transformations, you'll have the tools you need — and you'll recognise the connection. Learning maths this way means you're not carrying around a bag of disconnected tricks; you're building a structure that holds together.

The final part of the school is something I'm especially proud of: a dedicated exam preparation and strategy section that teaches you how to actually perform on the day. Understanding the content is only half the battle. Knowing how to read a multi-step question, where to look for method marks, how to pace yourself across both papers, and how to use the mark scheme as a revision tool — these are skills that can meaningfully shift your grade, and they're taught here explicitly.

If you're a student preparing for Cambridge O Level Mathematics, a parent wanting to support your child with confidence, or a tutor looking for a structured resource you can rely on — this school is for you. Come in, take it one step at a time, and let's get you ready.

Renstay College

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  • 50 modules, 145 lessons
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