Mathematics: 112 interactive topics
Numbers, algebra, geometry, trigonometry and statistics from first principles to exam level.
About Mathematics at secondary level
Mathematics on LearnViz SecondaryEdu has 112 interactive topics. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Every topic has a clear definition, key points written for secondary school, an animation you can control, and a three-question quiz. Topics are independent, so you can start anywhere.
How to study Mathematics with LearnViz
- Start with a topic you already know a little about, then move to one that is new to you.
- Use the animation before you read the key points. Predicting the result first makes the explanation easier to remember.
- Finish each quiz, then review the questions you got wrong. Mark a topic complete once you can explain it in your own words.
- Work one example by hand before you use the interactive to check it.
112 topics
1Natural Numbers and IntegersNatural numbers are the counting numbers 1, 2, 3 and so on, while…2Place ValuePlace value is the value a digit has because of its position in a…3Rounding and EstimationRounding replaces a number with a nearby simpler one, and…4Factors and MultiplesA factor divides a number exactly, and a multiple is the result of…5Prime NumbersA prime number has exactly two factors, itself and one, and cannot…6Prime FactorisationPrime factorisation writes a number as a product of prime numbers,…7Highest Common FactorThe highest common factor of two numbers is the largest number that…8Lowest Common MultipleThe lowest common multiple of two numbers is the smallest number…9Divisibility RulesDivisibility rules are quick tests that show whether a number…10Order of OperationsThe order of operations is the agreed sequence for evaluating an…11Negative NumbersNegative numbers are values less than zero, shown to the left of…12FractionsA fraction represents equal parts of a whole, written as a…13Equivalent FractionsEquivalent fractions look different but represent the same amount,…14Adding and Subtracting FractionsTo add or subtract fractions, first give them a common denominator,…15Multiplying and Dividing FractionsTo multiply fractions multiply the tops and the bottoms, and to…16Mixed Numbers and Improper FractionsA mixed number combines a whole number and a fraction, while an…17DecimalsA decimal is a number with a decimal point separating whole units…18Converting Fractions and DecimalsA fraction converts to a decimal by dividing the numerator by the…19PercentagesA percentage is a fraction out of one hundred, used to compare…20Percentage ChangePercentage change measures how much a quantity has increased or…21Simple and Compound InterestSimple interest is earned on the original amount only, whereas…22RatioA ratio compares two or more quantities of the same kind, showing…23ProportionTwo quantities are in direct proportion when one increases at the…24Rates and SpeedA rate compares two quantities with different units, and speed is…25Indices and PowersAn index or power shows how many times a number is multiplied by…26Laws of IndicesThe laws of indices are rules for simplifying expressions where the…27Negative and Fractional IndicesA negative index means a reciprocal, and a fractional index means a…28Square Roots and Cube RootsA square root is a number that multiplies by itself to give the…29Standard FormStandard form writes very large or very small numbers as a number…30SurdsA surd is a root that cannot be simplified to a whole number, such…31Rational and Irrational NumbersRational numbers can be written as a fraction of two integers,…32Significant FiguresSignificant figures count the meaningful digits in a number…33Bounds and ErrorBounds give the smallest and largest values a rounded measurement…34Sets and Venn DiagramsA set is a collection of distinct objects, and Venn diagrams show…35SequencesA sequence is an ordered list of numbers that follow a rule from…36Arithmetic SequencesAn arithmetic sequence has a constant difference between…37Geometric SequencesA geometric sequence has a constant ratio between consecutive…38Fibonacci and Special SequencesSpecial sequences such as square numbers, triangular numbers and…39Algebraic ExpressionsAn algebraic expression combines numbers, letters and operations…40SubstitutionSubstitution means replacing letters in an expression or formula…41Expanding BracketsExpanding brackets means multiplying each term inside by the term…42FactorisingFactorising is the reverse of expanding and writes an expression as…43Linear EquationsA linear equation has an unknown to the power one and is solved by…44Equations with Brackets and FractionsEquations that contain brackets or fractions are solved by…45Rearranging FormulaeChanging the subject of a formula means rearranging it so a…46Simultaneous EquationsSimultaneous equations are two or more equations with the same…47Quadratic EquationsA quadratic equation has the form ax squared plus bx plus c equals…48The Quadratic FormulaThe quadratic formula gives the solutions of any quadratic equation…49Completing the SquareCompleting the square rewrites a quadratic as a squared bracket…50The DiscriminantThe discriminant b squared minus 4ac tells you how many real roots…51InequalitiesAn inequality compares two expressions using less than or greater…52Coordinates and GraphsA coordinate pair gives the position of a point using its…53Gradient of a LineThe gradient measures how steep a line is, found as the change in y…54Equation of a Straight LineA straight line can be written as y equals mx plus c, where m is…55Midpoint and DistanceThe midpoint is the centre point of a line segment, and the…56Quadratic GraphsThe graph of a quadratic is a smooth symmetric curve called a…57Cubic and Reciprocal GraphsCubic graphs have an S-like shape from x cubed, while reciprocal…58Exponential GraphsAn exponential graph shows a quantity that multiplies by a fixed…59Transformations of GraphsGraph transformations shift, stretch or reflect a function without…60Distance-Time GraphsA distance-time graph shows how far an object has travelled over…61Speed-Time GraphsA speed-time graph plots speed against time, where gradient shows…62FunctionsA function is a rule that gives exactly one output for every input…63Composite and Inverse FunctionsA composite function applies one function after another, and an…64Angles on Lines and PointsAngles on a straight line add to 180 degrees, angles around a point…65Angles in Parallel LinesWhen a line crosses two parallel lines, it creates pairs of equal…66Angles in TrianglesThe three interior angles of any triangle always add up to 180…67Types of TriangleTriangles are classified by their sides as equilateral, isosceles…68QuadrilateralsQuadrilaterals are four-sided shapes whose interior angles always…69Polygons and Interior AnglesA polygon is a closed shape with straight sides, and the sum of its…70CongruenceTwo shapes are congruent when they are identical in shape and size,…71SimilaritySimilar shapes have the same angles and proportional sides, so one…72SymmetryA shape has symmetry if it looks the same after a reflection or a…73Perimeter and AreaPerimeter is the distance around a shape, and area is the amount of…74Area of Trapezium and ParallelogramThe area of a parallelogram is base times perpendicular height, and…75Circles and CircumferenceA circle is all points a fixed distance from its centre, and its…76Area of a CircleThe area of a circle is pi times the radius squared, showing how…77Arcs and SectorsAn arc is part of a circle's circumference, and a sector is the…78Circle TheoremsCircle theorems are rules about angles and lines in circles, such…79Pythagoras' TheoremIn a right-angled triangle, the square of the hypotenuse equals the…80Trigonometric RatiosSine, cosine and tangent are ratios of the sides of a right-angled…81The Unit CircleThe unit circle has radius one, and the coordinates of a point on…82Sine and Cosine RulesThe sine and cosine rules extend trigonometry to triangles that do…83Area of a Triangle Using SineThe area of any triangle can be found from two sides and the angle…84Trigonometric GraphsThe sine and cosine graphs are repeating waves with period 360…85BearingsA bearing gives a direction as an angle measured clockwise from…86Angles of Elevation and DepressionThe angle of elevation is measured upward from the horizontal, and…87Volume of PrismsVolume is the amount of space inside a 3D shape, and the volume of…88Surface AreaSurface area is the total area of all the faces of a 3D solid.89Pyramids, Cones and SpheresPyramids, cones and spheres have volumes found with a formula that…90Units and ConversionsUnits describe the size of a measurement, and conversions change a…91Transformations: Translation and ReflectionA translation slides a shape without turning it, and a reflection…92Rotation and EnlargementA rotation turns a shape about a centre by an angle, and an…93VectorsA vector is a quantity that has both a magnitude and a direction,…94Constructions and LociGeometric constructions use a compass and ruler to draw accurate…95Probability BasicsProbability measures how likely an event is, as a number from 0 for…96Tree Diagrams and Combined EventsA tree diagram lists every outcome of combined events, with…97Independent and Mutually Exclusive EventsIndependent events do not affect each other, while mutually…98Relative FrequencyRelative frequency is the proportion of times an event happened in…99Mean, Median and ModeThe mean, median and mode are three different averages that…100Range and SpreadThe range is the difference between the largest and smallest values…101Quartiles and Box PlotsQuartiles split ordered data into four equal parts, and a box plot…102Bar Charts and PictogramsBar charts and pictograms display categorical data using bars or…103Pie ChartsA pie chart shows how a whole is divided into parts, with each…104HistogramsA histogram displays continuous grouped data using touching bars,…105Scatter Graphs and CorrelationA scatter graph plots pairs of values to show whether two variables…106Cumulative FrequencyA cumulative frequency graph shows a running total of frequencies,…107Normal DistributionThe normal distribution is a symmetrical bell-shaped curve…108Sampling and BiasSampling means studying a small group to learn about a whole…109Counting PrinciplesCounting principles help find the number of possible arrangements…110Iteration and Number MethodsIteration is a method that repeats a calculation, using each answer…111Proof and ReasoningA proof is a logical argument that shows a statement is always…112Maths in Real LifeMathematics models everyday situations like budgets, travel,…
Mathematics: frequently asked questions
How many topics are in Mathematics?
Mathematics has 112 interactive topics on this site. Each one has its own page, so you can study them in any order.
Is Mathematics free to use?
Yes. Every topic, animation and quiz can be used in your browser without creating an account. Your progress is saved only on your own device.
Who is the Mathematics content for?
It is written for secondary school students studying Mathematics, and for teachers or parents who want a clear visual explanation. It supports your syllabus and your teacher rather than replacing them.
How do I move between topics?
Each topic page has Previous and Next links, a list of related topics, and a search box in the header. You can also filter the list on this page to find a topic by name.