GCSE FOUNDATION TIER SYLLABUS
All of the topics listed below are in the Foundation tier of the
GCSE Mathematics course. They are divided into Number,
Algebra, Shape, Space
and Measures, and Handling Data. You will
sit two written papers which will test as much of this work as is
possible.
We hope this helps you with your revision and wish you good luck.
NUMBER
Place value in whole numbers and decimals. Writing figures in words.
Rounding to the nearest 10, 100, 1000 etc Rounding to the nearest
whole number and decimal places.
Decimals, fractions & percentages - equivalences & ordering.
Directed number.
Index notation - cubes & squares 8³=512.
Recognise that 2.53 08 on a calculator means 253 000 000.
Tables up to 10x10.
Odds, evens, primes, squares, factors & multiples.
Four rules of whole number without a calculator eg 321 x 23 etc.
Four rules of decimals & negative numbers.
Converting from fractions - decimals - percentages.
Percentages - finding 18% of £450, writing 30/40 as a %.
Increase and decrease by %.
Simple ratio and proportion. Dividing in a given ratio.
Correct use of a calculator & understanding the calculator display.
Estimation to find approximate answers eg 29 x 11 is about 30 x
10.
Metric system m, cm, km, mm, kg, g etc. Understand km/h, mpg,m/s.
Personal & household finance - bills, VAT, wages, tax etc.
Reading timetables - bus, train, TV, holiday tables.
Multiply by numbers between 0 and 1. Inverse operations.
Trial & Improvement methods to solve problems.
Checking the reasonableness of results.
ALGEBRA
Using letters to represent variables.
Number patterns & finding nth term - easy only.
Travel & conversion graphs.
Coordinates in 4 quadrants.
Drawing & understanding y=2, x=2, y-2x+1, y=3x²+1.
Substitution of positive & negative numbers, fractions &
decimals into formulae.
Simplifying by collecting like terms. Removing brackets. Understand
axaxa=a³ & a+a+a=3a.
Simple equations.
SHAPE, SPACE &
MEASURES
Right-angle, acute, obtuse, reflex, perpendicular, parallel, horizontal,
vertical.
Face, edge, vertex.
Vocabulary of triangles - isosceles, equilateral, scalene.
Exterior & interior angles.
Vocabulary of quadrilaterals -square, rectangle, rhombus, kite,
trapezium, diagonal.
Polygons - hexagon, pentagon, octagon.
Circle - radius, diameter, chord, tangent, arc, circumference, sector.
Cubes, cuboids, cylinders, triangular prisms, square pyramid, cone
& sphere.
Nets.
Use of a ruler, protractor, compasses. Construct triangles, quadrilaterals
& circles.
Symmetry reflection & rotation - order of rotational symmetry.
Angle facts - on a line, at a point, vertically opposite, 3 &
F and C angle.
Angles of polygons - exterior & interior.
Coordinates in 4 quadrants.
Rotation, reflection & enlargement - scale factor & centre
of rotation.
Tessellations.
Scale drawings & bearings.
24 hour clock.
Conversion between & imperial units km-miles, cm, m - inches,
feet.
Kg-lbs, litres-pints, gallons.
You must learn 8km ˜ 5 miles, 1 kg ˜ 2.2lbs, 1 litre ˜1.75
pints.
Perimeter & area - squares, rectangles, triangles, circles,
semi-circles etc.
Estimation of area by counting squares.
Volume of cubes, cuboids, and simple solids.
HANDLING DATA
Discrete & continuous data.
Tallying methods.
Questionnaires.
Pictograms, barcharts, pie charts, vertical line diagrams.
Grouped frequency diagrams & frequency polygons.
Scatter diagrams - correlation.
Mean, mode & medial and range.
Fair, evens, certain, likely, unlikely impossible.
Expected number of successes.
Relative frequency as estimate of probability.
Probability space, probability scale 0-1.
Simple single event probability. Sum of the probabilities is 1.
GCSE SYLLABUS INTERMEDIATE TIER MATHEMATICS
The topics you need to revise for GCSE Mathematics are listed below
divided into Number, Algebra,
Shape, Space and Measures, and
Handling Data. You could also be tested on work
covered in Years 1-9.
We hope this helps you with your revision and wish you the best
of luck.
NUMBER
Place value in whole numbers and decimals. Rounding to the nearest
10, 100 etc. Decimal places & significant figures.
Decimals, fractions & ratio - relationships between these.
Ordering whole numbers, decimals & fractions. Directed number.
Index notation & standard form.
Rules for indices - positive, negative and zero indices. Prime factors.
Odds, evens, primes, square numbers, factors, multiples, reciprocals,
powers & roots.
Four rules without calculator eg 324x24, 345(15 etc.
Four rules of decimals, fractions & negative numbers.
Percentages - finding % of, expressing as %, increase, decrease
by % or ratio.
Ratio & proportion. Divide in a given ratio.
Understand the effect of x & ( by numbers between 0 and 1.
Use of a calculator, memory, brackets, powers, roots keys etc.
Understand how calculators read operations.
Estimation to obtain approximate answers, mentally work out 0.04
x 300 etc.
Metric system, common imperial units, compound measures eg km hr-1.
Personal & household finance, bills, HP, VAT, tax, wages, etc.
Simple & Compound Interest. Holiday booking tables, timetables
etc.
Trial & Improvement.
Inverse operations.
Appropriate degree of accuracy.
Recognising that measurement is approximate, giving upper &
lower bounds in calculations.
ALGEBRA
Letters to represent variables.
Number patterns, nth term linear or quadratic.
Travel graphs, average speed, graphs used in real-life.
Coordinates, drawing & interpreting graphs such as y=2, x=-2,
y=3x+2, y=2x²-1, y=8x3, y=8/x etc. Finding where lines/curves
and curves intersect.
Substitution of positive, negative, fractions, decimals & whole
numbers into formulae.
Form & solve equations or inequalities.
Simplification of expressions such as 2x² x 6x3 etc.
Expanding brackets, collecting like terms.
Factorising - taking out common factor, trinomials.
Change of subject.
Solving quadratic equations.
Simultaneous equations, equations with fractions & brackets.
Solving cubics eg y=3x3 +2 trial & improvement.
Inequalities & regions.
SHAPE, SPACE
& MEASURES
Right angle, obtuse, reflex, perpendicular, horizontal, vertical,
parallel.
Faces, edges & vertices.
Vocabulary of triangles, quadrilateral, and circles, Isosceles,
equilateral, scalene, exterior/interior angles.
Squares, rectangles, parallelogram, rhombus, kite, trapezium, polygon,
pentagon, hexagon, radius, diameter, chord, tangent, arc, circumference,
sector.
Simple solids - cube, cuboid, cylinder, prism, pyramid, tetrahedron,
cone & sphere.
Nets. Accurate use of ruler, compasses & protractor.
Congruence and similarity. Reflection & rotational symmetry.
Angles at a point on a line. Vertically opposite angles.
Corresponding & alternate angles. Angles of triangle, angles
of polygons interior & exterior.
Use of Pythagoras; theorem.
Trigonometry in a right-angles triangle.
Bearings, angles of elevation & depression.
Transformations including rotation, reflection, enlargement and
translation.
Tessellations.
Scale, similar figures.
Locus including given distance from point & line, equidistant.
24 hour clock.
Metric units of length, mass & capacity.
Conversions between metric units & imperial units. Km-miles,
cm-m,
inches-feet, kg-lbs, litres-pints, gallons.
8km=5 miles, 1km=2.2 lbs, 1 litre= 1.75 pints.
Understand discrete, continuous measure. Decimal scales, degree
of accuracy.
Compound measure m51, kmh-1, mph, mpg, density=kgm-3 (km¸m3).
Perimeter & area of squares, rectangles, triangles, circles
& composites.
Volume of cubes, cuboids, cylinder, prisms etc.
Distinguish between formulae by considering dimensions.
HANDLING DATA
Qualitative & quantitative data, discrete, continuous data and
class width.
Questionnaires. Testing hypotheses.
Pictograms, barcharts, pie charts.
Vertical line diagrams, line graph.
Grouped frequency diagrams & frequency polygons.
Cumulative frequency polygons. Scatter diagrams - correlation.
Mean, mode & median, range.
Median & Interquartile range from cumulative frequency diagram.
Comparing graphs - looking at measures of spread & central tendency.
Evaluate results critically.
Probability - fair evens, certain, likely, unlikely, impossible.
Probability of event not occurring is 1-probability of event occurring.
Expected number of successes.
Relative frequency as an estimate of probability.
Probability space, tree diagrams.
GCSE SYLLABUS EXTRA TOPICS FOR HIGHER
TIER
NUMBER
Direct & inverse proportion.
Rational & irrational numbers, converting recurring decimals
to fractions.
Upper & lower bounds in calculations involving x and ¸
Surds - simplification of surds.
Fractional indices - simplify 813/4, 8-?
ALGEBRA
Quadratics of type 5x²+3x+6=0 etc.
Harder change of subject eg 1/a+a/b=1/c etc.
Using the graph of one curve to solve another.
Tangents to curves, velocity in distance-time graphs, acceleration
in speed-time graphs.
Area under v-t graph = distance travelled. Use of trapezium rule.
Interpret functions such as y=f(x+a), y+f (kx), Y=f(x) =a applied
to y=f(x).
Select mathematical functions to fit sets of data.
Harder equations with fractions.
SHAPE, SPACE AND MEASURES
Congruent triangles - reasons SSS, SAS, ASA, RHS.
Enlargement with negative scale factor. Vector form required.
Volumes of sphere, cone and pyramids.
Length of arc, area of sectors and segment.
Volume of similar figures - relationship between length, area and
volume.
Vectors - magnitude of a vector =, - x by scalar. Vector notation.
Trigonometry in 3D. Sine, cosine rules. Area of triangle = 1/2 absinC.
Angle properties in a circle, tangents to a circle. Reasons may
be required.
Trigonometry for any size of angles, graphs of trigonometric functions.
HANDLING DATA
Histograms - frequency density.
Mean & dispersion.
Standard deviation - grouped & ungrouped data.
Sampling - random digits.
Simple random sampling, simple stratified sampling.
Probability - multiplication law for dependent events - without
replacement.
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