Math Tutorial Contents

Click here for a tutorial on Numbers containing the following sections:

Natural counting and whole numbers, Negative numbers, Addition using negative numbers, Introducing brackets, Minus signs outside brackets, The number line, Number line question, Negative numbers on the calculator, Negative numbers on the calculator, Composite numbers, Factors and products, Prime numbers, Square numbers, Integers, Fractions, Writing fractions, Proper fractions, Equivalent fractions, Improper fractions, Mixed numbers, Reciprocals, Simplifying fractions, Greatest common factor, Greatest common factor question, Greatest common factor - one technique, Greatest common factor, Greatest common factor question, Fractions as percentages, Problems using percentages, Don't be a sucker at clearance sales, Commission, Doing calculations with fractions, Addition with fractions, Fraction addition problem, Subtraction with fractions, Fraction subtraction question, Multiplication with fractions, Multiplying with fractions, Fraction multiplication question, Dividing with fractions, Dividing with fractions, Fraction division question, Fractions on your calculator, Calculator fractions question, Fractions on your calculator, Decimal numbers, Rounding, Rounding to a number of decimal places, Rounding to decimal places, Rounding question, Tricky rounding, Rounding to a number of significant figures, What are significant digits?, Rounding to significant figures, Significant figures question, Significant figures question

Click here for a tutorial on Operations containing the following sections:

Order of operations, Order of operations, Other operations, Square operation, Cube operation, Square root, Using your calculator - square root, Square roots on the calculator, Inverse operations, Guesstimating or checking your answers make sense, Using memory on your calculator, Calculator memory instructions, Multiplying by hand, Checking multiplications, Division by hand - short division, Calculating using scientific notation or standard form, Adding and subtracting numbers in scientific notation

Click here for a tutorial on Algebra containing the following sections:

Introduction to algebra, Coefficients of variables, Multiplying and dividing variables, Expressions equations and terms, Like terms, Binomial and trinomial expressions, Algebraic addition and subtraction, Multiplication and division in algebra, Brackets in algebra, Factors in algebra, Highest common factor in algebra, Factorising algebra - using common factors to introduce brackets, Introducing brackets in algebra, Complex algebraic simplification problem, Fractions in algebra, Adding algebraic fractions, Algebraic fraction addition problem, Multiplying algebraic fractions, Multiplying algebraic fractions question, Dividing algebraic fractions, Dividing algebraic fractions question, Confusing ‘x' and ‘×', Translating problems into algebra, Algebraic translation question

Click here for a tutorial on Equations containing the following sections:

Simple equation question, More complex equation question, Checking equation solutions, Equations with brackets, The degree of an equation, Solving first degree equations, Celsius centigrade and fahrenheit, rearranging them to fit your needs

Click here for a tutorial on Inequations containing the following sections:

The larger than symbol: >, The smaller than symbol: <, The larger than or equals symbol: =, The smaller than or equals symbol: =, How to remember these symbols, Solving inequations, Inequation question, Choosing how to solve questions, Using set notation to solve inequations, Expressing solutions to inequations on a number line

Click here for a tutorial on Indices and powers containing the following sections:

Powers of negative numbers, Powers of negative numbers, Negative indices, Powers raised to another power, Exponential notation

Click here for a tutorial on Basic geometry containing the following sections:

Angles, Types of angles, Acute angles, Right angles, Obtuse angles, Straight angles, Reflex angles, 360 degrees, When not to simplify angles larger than 360 degrees, Complementary angles, Supplementary angles, Vertically opposite angles, Describing angles, Solving for angles in a diagram, Angle question, Triangles, Types of triangles, Angles within a triangle rule, Describing triangles using interior angles, Acute-angled triangles, Right-angled triangles, Obtuse-angled triangles, Describing triangles using sides, Equilateral triangles, Isosceles triangles, Scalene triangles, Exterior angles, Triangle angles question, Parallel lines, Transversal lines, Corresponding angles, Alternate angles, Co-interior angles, Parallel lines question, Angles of elevation and depression, Boat and lighthouse question, Making angles clear in diagrams, Symmetry, Multiple axes of symmetry, Symmetry and letters, Reflecting using x- and y-axes

Click here for a tutorial on 2D shapes containing the following sections:

Plane shapes, Quadrilaterals, Parallelograms, The rectangle, The square, The rhombus, Parallelogram problem, Closed shapes, Polygons, Regular polygons, Irregular polygons, Concave polygons, Convex polygons, Deriving the formula for the sum of the angles inside a polygon, Tessellations, Perimeters of 2d shapes, Length of an arc, Typical perimeter question, The running track perimeter question, Backwards perimeter question, Areas of plane shapes, Converting between different units of area, Imperial measurements of area, Areas of simple shapes, Area of a triangle, Area of a parallelogram, Area of a trapezium, Area of a circle, Area of a sector, Things to watch out for, Tied up dog question

Click here for a tutorial on 3D solid shapes containing the following sections:

Volume, Units of volume, Changing between units of volume, Solid shape terminology, Prisms, Cylinders, Practical prism questions, Pool volume question, Volumes of fluids, How big a cubic metre really is, Swimming pool fluid volume question

Click here for a tutorial on Basic interest containing the following sections:

Simple interest, Principal, Interest rate, Term length, Per annum, The simple interest formula, Simple interest question, How long will it take simple interest question

Click here for a tutorial on Bearings azimuths and symmetry containing the following sections:

Azimuths, Bearings, Clockwise and anti-clockwise, Using your protractor, Bearings question

Click here for a tutorial on Ratios containing the following sections:

Ratios and colons, Equivalent ratios, Simplifying ratios with zeroes, Splitting things up according to a ratio, Different units that measure the same thing, Using ratios to create models of the earth and the sun question, Ratios and geometry, Proportional or similar shapes, Congruent shapes, How to tell if two shapes are congruent, Congruent triangles, Similar triangles question, Similar triangles inside triangles, Similar triangles inside triangles question

Click here for a tutorial on Mathematical relations containing the following sections:

Domain, Range, Using tables to show a range and domain, Table range and domain question, The cartesian plane, Graphing relations, Fitting lines to graphs, Choosing a suitable scale for a graph, Specifying a relation, Working out the range and domain from a graph, Domain and range for horizontal and vertical lines, Straight line graphs, Gradient, Reading a gradient in the correct direction, Gradient types, Axis intercepts, Working out intercepts from the relation, Zero and undefined gradients, Intercepts, Quickly plotting straight line graphs, Graphing inequations, Using straight line graphs for real problems, Stretchy spring question

Click here for a tutorial on Simultaneous equations containing the following sections:

Picking the best equation to finish off a question with, Independent pieces of information, Working out whether you can find unique answers, Translating information into equations question, Methods for solving simultaneous equations, The substitution method, Picking the right equation to substitute into, The elimination method, Adding equations using the elimination method, Numbering equations, Graphical representations of simultaneous equations, Choosing whether to graph simultaneous equations, Simultaneous equations that produce parallel lines, Simultaneous equations application question

Click here for a tutorial on Rational numbers containing the following sections:

How many rational numbers?, Zero is a rational number, Operations with rational numbers, Multiplying rational numbers together, Dividing rational numbers, Adding and subtracting rational numbers, Using a dot instead of a multiplication symbol, Working with the number zero

Click here for a tutorial on Statistics containing the following sections:

Election surveying, Deciding what data to collect and how to collect it, Recording data, Presenting the data, The pie chart sector graph, Bar and column graphs, Bar graph, Line graphs, Drawing a line graph, Pictographs, Pictograph question, Trends, Extrapolating, There's more than one way to skin a cat, Averages middles and most frequent numbers, Mean, Median, Mode, The mean versus the median, Real estate housing values, Don't calculate averages of averages, Averages of averages question, Grouping data into classes, Grouping data question, Choosing classes, Be careful with trimming, Histograms, A continuous histogram, Frequency polygons, Data observation question, When can you compare frequency polygons, Finding means medians and modes of grouped data, Mean of grouped data, Median of grouped data, Cumulative frequency graphs, Mode of grouped data

Click here for a tutorial on Pythagoras' Theorem containing the following sections:

Pythagoras' theorem, Showing pythagoras' theorem working, Describing triangles, Specifying the hypotenuse side, Checking whether a triangle is right-angled, Proving pythagoras' theorem, Putting it all together, Using pythagoras' theorem to work out side lengths, Unknown hypotenuse triangle question, Known hypotenuse unknown side question, Significant figures and diagrams, Making an estimate of the side length, More complicated pythagoras' theorem questions, Complex pythagoras' theorem question, Pythagorean triples, Answering using a square root sign, Drawing a line exactly 29 units long, Practical pythagoras' theorem questions, ‘the race' question

Click here for a tutorial on Irrational numbers & surds containing the following sections:

Surds, Typical questions where you answer with a surd, Surd answer question, Simplifying bits out of square roots, Cube root surds, Roots of numbers smaller and larger than one, Adding and subtracting surds, Complex surd question, Multiplying and dividing surds, Going from a number back to a surd

Click here for a tutorial on Probability and set language containing the following sections:

Probability terminology, Trial experiment, Outcome, Outcome space, Event, Probability of an event occurring, Pack of cards probability question, Not probabilities, “not probability” question, Certainties and impossibilities, Impossibility statements, Set language, Subsets, ‘not' sets, Complementary sets, Venn diagrams, Overlapping areas, Venn diagram questions, Tv watching question, ‘and' probabilities, ‘or' probabilities

Click here for a tutorial on More algebra containing the following sections:

Multiplying binomial expressions together, Using areas to help visualise binomial multiplication, Factorised form and expanded form, Standard types of binomial multiplications, Difference of two squares, Mixing up the layout to fool you, Binomial perfect squares, Factorising perfect squares, Factorising trinomial expressions, Simplifying fractions involving algebraic expressions, Simplifying fractions, Simplifying fractions question

Click here for a tutorial on Exponentials and indices containing the following sections:

Index laws, Adding indices when you multiply, Subtracting indices when you divide, Raising powers to powers, The zero index or exponent, Negative indices or exponents, Evaluating versus simplifying, Indices and exponents that are fractions, Fractional indices with numerators larger than one, Common cube roots, Exponential relationships, Problems extending exponential graphs, Guessing the exponential relationship from a graph

Click here for a tutorial on Budgeting containing the following sections:

Typical budget questions, Living out of home question, weeks and months, Basic compound interest, Compound frequency, Interest calculated once per year, Interest calculated four times per year

Click here for a tutorial on Shapes inside circles containing the following sections:

Chords and segments, Arcs, Triangles inside circles, Triangles with a circle diameter as one side, Cyclic quadrilaterals, Can you draw a circle through the vertices of a quadrilateral?

Click here for a tutorial on More 3D shapes and shape nets containing the following sections:

Pyramids, Solid shape nets

Click here for a tutorial on Different forms of linear equations containing the following sections:

Gradients of straight line graphs, Graph to gradient-intercept form, Straight line graph equation question, Going between inequations and graphs, Going from an inequation graph to an inequation, Forming an inequation from a graph question, Practical simultaneous equations question

Click here for a tutorial on Trigonometry containing the following sections:

Triangle sides, Naming the sides, Ratios between the side lengths, Using actual values in trigonometric ratios, Using trigonometry to work out side lengths, Trigonometry on the calculator, Using pythagoras' theorem to check your triangle side lengths, Deciding whether you have enough information, finding the angle using trial and error, Finding angle question, Application problems in trigonometry, River rowing question

Click here for a tutorial on Quadratic equations 2 containing the following sections:

Quadratics with only a squared term and a number, Only one answer to the square root of a number by itself, Quadratics with a power 1 term but no number only term, Solving quadratic equations by plotting parabolas, The axis of symmetry, Parabolas of quadratic equations with no solution, Parabolas of quadratic equations with one unique solution, Solving simultaneous equations involving linear and quadratic equations, Balloon bullet games question, Using a graph, Simultaneous equations with quadratic equations, Solving them algebraically, Solving them using a graph, Milk lover question, Finding the value of a point using a ruler, Modelling car acceleration using quadratics, Car acceleration question, Parabolic inequations and finite differences, Solving it analytically, Watch the sign and there may not be a solution

Click here for a tutorial on Volumes and areas of irregular shapes and solids containing the following sections:

Using rectangular strips to measure area, Accuracy using grids and strips to measure areas, Working out prism cross sectional areas using water, Volumes and areas of more complicated shapes, The sphere, Dimensionality of formulas, The pyramid, Proving the volume of a pyramid formula, The cone, Martini glass question

Click here for a tutorial on Trip graphs containing the following sections:

Trip graphs, solving chase style questions, Burke and wills question

Click here for a tutorial on More Statistics containing the following sections:

Simple random sampling, Systematic or interval sampling, Stratified sampling, Cluster sampling, Stratified sampling question, Measures of spread, Range, Quarters and quartiles, Interquartile range, Deviations, Mean deviation, Standard deviation, Why do we divide by ‘n - 1'?, Using your calculator to find statistical measures, Changing into statistical mode, Changing your calculator into statistical mode, Clearing the statistical memory, Inputting the data, Finding statistical information

Click here for a tutorial on Using and abusing statistical information containing the following sections:

Interpolation, Extrapolation, Problems with extrapolation, How to get any result you want using statistics, Use a bad sample, Use too small a sample, Repeated small samples, Use loaded questions, Presentation tricks, Scales on graphs, Missing scales on graphs, Using the wrong measure, 3d graphs

Click here for a tutorial on Areas of composite shapes containing the following sections:

Composite area question, Surface areas of composite solid shapes, Surface area of a cylinder, Ice cream cone surface area question

Click here for a tutorial on Volumes of composite solid shapes containing the following sections:

Volumes of areas with a thickness, Volume of a tanker ship question

Click here for a tutorial on Working with errors and measurement containing the following sections:

Accuracy and precision, Precision in numbers, Error, Absolute error, Greatest possible error, Relative error, Percentage error, Calculations with numbers that have errors, Adding and subtracting numbers with errors, Adding or subtracting an exact number, Multiplication or division by an exact number, Multiplication of numbers with errors, Errors in multiplication - simple absolute error method, Errors in multiplication - simple relative error method, Multiplication of two numbers with large errors - long method, Division with two numbers with small errors - simple relative error method, Division with two numbers with large errors - long method, When is an error large enough to use the long method?, Land block sizing question

Click here for a tutorial on Equations using box stories containing the following sections:

Working backwards, Working backwards question, Rearranging to make something else the subject, Cake making question, Complicated equation rearrangement

Click here for a tutorial on the topic Water flow graphs

Click here for a tutorial on Finding polynomial relationships containing the following sections:

Finite differences, Using finite differences to find the actual relationship, Check the values of ‘x'

Click here for a tutorial on Linear programming containing the following sections:

A note about lines and areas on a graph, Translating linear programming questions, Storage of fighter jets question

Click here for a tutorial on Lines of best fit containing the following sections:

Visually finding a line of best fit, Line of best fit question

Click here for a tutorial on More set theory containing the following sections:

Union and intersection symbols with multiple sets, Combining in the other symbols, Combined venn diagram symbol question

Click here for a tutorial on More probability containing the following sections:

Tricky tree diagrams, Joining trees with different outcome spaces, Outcome spaces that change through trials, Independent events, Dependent events, Mutually exclusive events, Going to the movies question, Expected number for a certain outcome, Average run length of an outcome, Average run lengths for large numbers of trials, Gambling, Expected returns, Other types of roulette bets, Gambler's ruin, Doubling your bet each time, Blackjack, Card counting, You need capital though, Electronic components, Quality control question

Click here for a tutorial on Circle geometry containing the following sections:

Circle tangent lines, Arc angles, Chord multiplication, Angles for the same arc, Bridge building question

Click here for a tutorial on Similar figures and geometric constructions containing the following sections:

Scale factor, Geometric constructions using your compass and ruler, Bisecting an angle, Bisecting a line, Drawing a perpendicular from a point on a line, Drawing a perpendicular from a point to a line, Constructing shapes

Click here for a tutorial on Locus and loci - paths things travel containing the following sections:

Parabola, Projectile locus with air resistance, Locus of points on rolling objects, Rolling circle, Rolling square, Drawing an ellipse, Overlap points of loci

Click here for a tutorial on Three-dimensional trigonometry problems containing the following sections:

Thing in the tree question

Click here for a tutorial on Latitude and longitude containing the following sections:

Specifying a position on the surface, Finding distances along meridians of longitude, Finding distances along parallels of latitude

Click here for a tutorial on Proportional or direct relationships containing the following sections:

The proportional sign, Direct linear variation, From a graph, From an equation, From a table of data, Making cordial question, Higher order direct relationships, Graphs of higher order direct relationships, Tables of higher order direct relationships, Higher order direct relationship equations, The ‘x' people make ‘x' products problem, ‘x' people make ‘x' products question, Nuclear weapons effects, Nuclear weapons question

Click here for a tutorial on Inverse relationships containing the following sections:

Inverse relationships in graphs, Inverse relationships in tables, More than two variables in a relationship - joint variation, Fitting inverse relationships to data, Men's running speed in the 100 metre sprint, Sprint times question

Click here for a tutorial on Exponential graphs containing the following sections:

Line separation in graphs, Negative powers, Rabbit population question, The discussion bit about populations, Working out an exponential relationship's power, Exponential graphs as a tool, Multiplying using an exponential graph, Dividing using an exponential graph

Click here for a tutorial on Matrices containing the following sections:

The order of a matrix, Describing an element, Matrix operations, Adding and subtracting matrices, Multiplying matrices, Multiplying and dividing by a scalar, The identity matrix, The inverse of a matrix, Finding the matrix inverse

Click here for a tutorial on Vectors containing the following sections:

Vector magnitudes, Equal vectors, Taking the negative of a vector, Multiplying a vector by a scalar, Vector addition and subtraction, Adding vectors, Subtracting vectors, The vector coordinate frame, Unit vectors

Click here for a tutorial on Logic containing the following sections:

Logic connectors, Or connector, And connector, Implies connector, Equivalence connector, Not connector, Truth tables, Logic circuits and symbols, Not symbol, Or symbol, And symbol, Analysing logic circuits, Evaluating the final output

Click here for a tutorial on Box and whisker plots containing the following sections:

Outliers in box and whisker plots

Click here for a tutorial on Quadratic equations containing the following sections:

The quadratic formula, Solving by factorising, Picking the ‘correct' solution, Rocket launching question, Quadratic equation summary, Getting ‘good' with the quadratic formula, Plotting quadratic functions, Turning points, Axis intercepts, Solving by completing the square

Click here for a tutorial on the topic Turning recurring decimals into fractions

Click here for a tutorial on Logarithms containing the following sections:

Index laws revision, Common logarithms, Natural logarithms, Logarithm laws, Change of base theorem

Click here for a tutorial on the topic Rates of change

Click here for a tutorial on Derivatives containing the following sections:

Differentiation rules, The chain rule, Chain rule question, Chain rule question, The product rule, Product rule question, Writing letters in calculus, The quotient rule, Quotient rule question, Starting the question, Product or quotient rule

Click here for a tutorial on Solving polynomial equations containing the following sections:

General approach to solving polynomials

Click here for a tutorial on More triangles containing the following sections:

Finding the area of a triangle, Triangle area question, Units, The cosine rule, Cosine rule question, The sine rule, Problems with the sine rule

Click here for a tutorial on The unit circle containing the following sections:

Radians, Exact trigonometric ratios, Exact trigonometric ratios question, Another exact trigonometric ratios question, Unit circle angle question, Another unit circle angle question

Click here for a tutorial on Finance and interest containing the following sections:

Interest terms revision, Common terms, Simple interest question, Compound interest formula, Effective interest rates, Effective interest rate question, Present and future values, Present value question, Depreciation, Straight-line depreciation, Diminishing-value method, Scrap value, Annuities, Annuity question, Present values of annuities, Present value annuity question

Click here for a tutorial on More simultaneous equations containing the following sections:

Rearranging simultaneous equations, Solving three or more simultaneous equations, Store fractions in your calculator

Click here for a tutorial on Integration containing the following sections:

The constant of integration, Integration rules, Definite integrals, Some physical meanings of integration, Practical integration question, Integration and graphs, Curves that pass below the x-axis, Calculating areas between curves, Areas between curves question, Graphs that intersect multiple times

Click here for a tutorial on Numerical integration methods containing the following sections:

Riemann sums, Trapezoidal rule, Trapezoidal rule question, General tips for both rules

Click here for a tutorial on Probability containing the following sections:

Relative frequency, Probabilities, Tree diagrams, Tree probability question, Another tree probability question, Mutually exclusive events, Picking card at random question, Addition rule, Probability distributions, Binomial distributions, Binomial distribution question, Pascal's triangle, Coin tossing question

Click here for a tutorial on Solving dy dx=ky containing the following sections:

Water flow question, Approximate derivatives, Approximate derivative question

Click here for a tutorial on Hypothesis testing containing the following sections:

Hypothesis testing terms, Sample, Census, Survey, Parameter, Statistic, Bias in sampling, Hypothesis testing, The null hypothesis h0, The alternative hypothesis h1, Level of significance, Significance level question, The sign test, Sign test question, Small sample hypothesis testing, Small sample hypothesis question, Large sample hypothesis testing, Large sample size question, Small sample confidence intervals, Upper confidence limits, Small sample confidence interval question, Lower confidence limits, Large sample confidence intervals, Large sample confidence interval question

Click here for a tutorial on Plotting graphs containing the following sections:

Periodic functions, Graph transformations, Amplitude transformations, Sideways movement, Horizontal squashing or stretching, Vertical displacements, Sign changes, Putting it all together, Periodic graph plotting question, Sketching general graphs, Graph sketching question, Managing your time, Asymptotes and discontinuous graphs, Plotting complex asymptote functions, Asymptote plotting question, Find graph characteristics first

Click here for a tutorial on the topic General tips for maths tests