Ages 12–15
Secondary maths
From working with numbers, directed numbers and algebra to linear equations, percentages, angles and parallel lines, coordinates, 3-D figures and statistical charts. Each topic lists its skills in order, each skill with its methods, worked examples, practice questions and answers.
Star Galaxy is open
The game's secondary world has a planet for each topic, each going from easy to hard. Start at any station you like.
Numbers and operations
5 topics- Working with numbersAges 12–13Divisibility by 4, 6, 8 and 9, Powers, Prime factorisation, H.C.F. and L.C.M., Brackets inside brackets, Fractions and decimals mixed
- Directed numbersAges 12–13Positive and negative numbers, Comparing directed numbers, Adding directed numbers, Subtracting directed numbers, Multiplying directed numbers, Dividing directed numbers, The four operations mixed, Using directed numbers
- Approximation & estimationAges 12–13Rounding off to a place value, Rounding to decimal places, Significant figures, Rounding up and rounding down, Estimation strategies, Estimating when shopping, Planning an estimate
- Laws of integral indicesAges 13–14Multiplying and dividing powers, Powers of powers, products and quotients, Zero and negative indices, Working with integral indices, Writing powers with the same base, Scientific notation, Binary numbers, Hexadecimal numbers
- Surds & irrational numbersAges 13–14Square, cube and nth roots, Rational and irrational numbers, Simplifying surds, Working with surds, Constructing lengths √n
Algebraic expressions
4 topics- Algebraic expressions & sequencesAges 12–13Words into algebra, Situations into algebra, Reading algebra as words, Substitution and input–output machines, Patterns in sequences, Growing patterns and the n-th term
- Polynomials & identitiesAges 13–14What a polynomial is, Adding and subtracting polynomials, A monomial times a polynomial, Multiplying polynomials, Identities and equations, Comparing coefficients, Expanding perfect squares, Expanding the difference of two squares, The sum and difference of two cubes
- FactorisationAges 13–14Taking out a common factor, Factorising a difference of two squares, Factorising perfect squares, Factorising by grouping, The cross method: leading coefficient 1, The cross method: other leading coefficients, Factorising sums and differences of cubes
- Formulae & algebraic fractionsAges 13–14Simplifying algebraic fractions, Multiplying and dividing algebraic fractions, Adding and subtracting algebraic fractions, Substituting into formulae, Changing the subject of a formula, A new subject on both sides or below the line
Equations and inequalities
3 topics- Linear equations in one unknownAges 12–13Equations and the balance, Unknowns on both sides, Equations with brackets, Fractions and decimals in equations, From words to an equation, Word problems with equations
- Simultaneous linear equationsAges 13–14Solutions of an equation in two unknowns, Solving by graphs, Solving by substitution, Solving by elimination, Simultaneous equations in other forms, From words to simultaneous equations, Word problems with simultaneous equations
- Linear inequalities in one unknownAges 14–15Inequalities and the number line, Properties of inequalities, Solving linear inequalities, Compound inequalities: and, or, Word problems with inequalities
Percentages and ratio
3 topics- Percentages (I)Ages 12–13Percentage increase and decrease, Back to the original value, One change after another, Profit and loss, Marked prices and discounts, Simple and compound interest, Tax, pay and commission
- Rates, ratios & proportionsAges 13–14Rates, Density, pressure and exchange rates, Ratios and proportions, Three-term ratios and sharing, Direct proportion, Inverse proportion, Average speed and mixtures, Scales on maps and plans
- Percentages (II)Ages 13–14Compound interest, Compounding periods, Growth and depreciation, Changes in the parts, Chains of sellers and offers, Salaries tax
Geometry and proof
7 topics- Angles & parallel linesAges 12–13Angles on a line and at a point, Vertically opposite angles, Angles with an unknown, Corresponding, alternate and interior angles, Telling parallel lines, Angles with parallel lines, Bends and reflex angles, Angles of a triangle, Isosceles triangles
- PolygonsAges 13–14Regular polygons, Angle sum of a polygon, Exterior angles of a polygon, Tessellations, Equilateral triangles, squares and hexagons, Drawing a regular pentagon
- Congruent trianglesAges 13–14Congruent figures and transformations, Corresponding parts of congruent triangles, Conditions for congruent triangles, Proving triangles congruent, Properties of isosceles triangles, Proving a triangle isosceles, Bisecting an angle and a line segment, Angles compasses can draw
- Pythagoras' theoremAges 13–14Finding the hypotenuse, Finding a shorter side, The converse of Pythagoras' theorem, Using Pythagoras' theorem, Pythagorean triples
- Similar trianglesAges 14–15Corresponding sides of similar triangles, Conditions for similar triangles, Parallel lines and similar triangles, Proving triangles similar, Similar polygons, Areas of similar figures, The Sierpinski triangle
- QuadrilateralsAges 14–15Properties of a parallelogram, Rectangles and squares, Rhombuses, Conditions for a parallelogram, Proofs with quadrilaterals, The mid-point theorem, The intercept theorem, Congruent quadrilaterals
- Centres of a triangleAges 14–15The angle bisector's property, The perpendicular bisector's property, The incentre, The circumcentre, The centroid, The orthocentre, Telling the centres apart
Measures and solids
5 topics- 3-D figuresAges 12–13Prisms, pyramids and round solids, Cross-sections, Nets of solids, Drawing solids on paper, Three views, Euler's formula and regular polyhedra
- Prisms & cylindersAges 13–14Volume of a prism, Volume of a cylinder, Surface area of a prism, Surface area of a cylinder, Prisms and cylinders at work
- Errors in measurementAges 13–14Upper and lower limits, Absolute, relative and percentage errors, Errors in measurement at work, Planning a measurement
- Arc lengths & sectorsAges 14–15Arc length, Area of a sector, Perimeter of a sector, Segments and composite figures, Liu Hui's method for π
- Cones & spheresAges 14–15Volume of a pyramid, Volume of a cone, Surface area of pyramids and cones, Volume of a sphere, Surface area of a sphere, Similar figures and solids, Solids at work, Folding a box
Coordinates and trigonometry
3 topics- First steps in coordinatesAges 12–13Reading and plotting points, Quadrants and points on the axes, Distance along a horizontal or vertical line, Areas on the coordinate plane, Translation, Reflection, Rotation about the origin
- Coordinate geometryAges 14–15The distance formula, The mid-point formula, The section formula (internal division), Slope, Using slopes, Slopes of parallel and perpendicular lines, Proofs with coordinates, External division
- TrigonometryAges 14–15Sine, cosine and tangent, Finding a side, Finding an angle, How the ratios are related, Exact values at 30°, 45° and 60°, Trigonometry in plane figures, Gradient and inclination, Angles of elevation and depression, Bearings
Data and probability
4 topics- Organising data & statistical chartsAges 12–13Kinds of data, Frequency tables, Class limits, boundaries and marks, Grouped frequency tables, Stem-and-leaf diagrams, Histograms, Drawing stem-and-leaf diagrams and histograms, What the diagrams tell us, Back-to-back stem-and-leaf diagrams, Compound bar charts
- Cumulative frequency & chartsAges 14–15Frequency polygons, Cumulative frequency, Cumulative frequency polygons, Interpreting frequency polygons and curves, Choosing a statistical chart, Misleading statistical charts
- Measures of central tendencyAges 14–15Mean, median and mode, Finding an unknown from an average, Averages of grouped data, Choosing the mean, median or mode, How changing the data changes the averages, Weighted mean, Weighted mean word problems
- ProbabilityAges 14–15Certain, impossible and random events, What a probability means, Equally likely outcomes, Relative frequency and expected frequency, Listing outcomes in a table, Tree diagrams, Probability word problems, Expected value, Fair games and expected gain
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