AQA · GCSE · Mathematics

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Handouts · IGCSE Mathematics (9)

Exercise sheets · IGCSE Mathematics (125)

Presentation slides · IGCSE Mathematics (9)

Course units and learning goals

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme.

Lessons →Vocabulary practice →

3.1 · Number

Exact arithmetic and estimation: A prime number that divides the integer exactly.
Indices, surds and standard form: The power to which a base is raised.
Accuracy, bounds and compound measures: The smallest possible value consistent with a stated rounding rule.
Signed numbers, place value and operation order: A number that multiplies a nonzero original number to give 1.
Exact fractions and mixed-number operations: A fraction whose numerator is at least as large as its positive denominator.
Systematic lists and the product rule: A list made in a fixed order so every allowed outcome appears exactly once.
Exact surds and rationalising denominators: An irrational root kept in exact form rather than replaced by a rounded decimal.
Terminating and recurring decimal conversions: A decimal with a digit or block of digits that repeats forever.
Metric and compound-unit conversions: The multiplier that expresses the same quantity in another unit.
Estimation, rounding and simple error intervals: A digit counted from the first nonzero digit when reporting numerical precision.
Ratio shares and fraction operators: A comparison that states the relative numbers of equal-sized parts.

prime factor: A prime number that divides the integer exactly.
index: The power to which a base is raised.
lower bound: The smallest possible value consistent with a stated rounding rule.
reciprocal: A number that multiplies a nonzero original number to give 1.
improper fraction: A fraction whose numerator is at least as large as its positive denominator.
systematic list: A list made in a fixed order so every allowed outcome appears exactly once.
surd: An irrational root kept in exact form rather than replaced by a rounded decimal.
recurring decimal: A decimal with a digit or block of digits that repeats forever.
conversion factor: The multiplier that expresses the same quantity in another unit.
significant figure: A digit counted from the first nonzero digit when reporting numerical precision.
ratio: A comparison that states the relative numbers of equal-sized parts.

3.2 · Algebra

Equations, identities and rearrangement: An equality that holds for every allowed value of its variable.
Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Simultaneous equations and feasible regions: Combining equations to remove one variable while retaining the same solutions.
Coordinate geometry and tangents: The change in y divided by the corresponding change in x.
Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
Algebraic notation, substitution and vocabulary: The numerical factor multiplying a variable term.
Collecting, expanding and factorising expressions: Rewrite an expression as a product of factors.
Rearranging formulae and checking the subject: The quantity written alone on one side of a formula.
Identities, equivalence and algebraic arguments: An expression with the same value as another for every allowed input.
Function machines and reversing operations: The value supplied to a rule before its operations are carried out.
Domains, inverses and composition: The set of allowed inputs to a function.
Coordinate quadrants and basic graph families: A line approached by a graph without a finite crossing in the stated example.
Exponential and degree-based trigonometric graphs: The input interval after which a repeating graph has the same values again.
Translations and reflections of function graphs: Move every point of a graph by the same horizontal and vertical displacement.
Distance-time graphs and contextual intersections: Not changing position over the time interval described.
Graphical gradients and area estimates: The slope of a tangent, used to estimate a curve’s rate at one input.
Origin-centred circles and tangent equations: The slope of a radius joining the centre to a point on the circle.
Numerical iteration for equation roots: Repeat a rule, using the previous output as the next input.
Linear inequalities and number-line solutions: All inputs that satisfy the stated condition.
Quadratic inequalities and two-variable regions: The equality line separating values that satisfy an inequality from those that do not.
Figurate, geometric and Fibonacci-type sequences: A rule that generates new terms from preceding terms.
Quadratic nth terms and surd-ratio progressions: The difference between consecutive first differences of a sequence.
Algebraic fractions and excluded values: An input for which an original denominator or divisor is zero.

identity: An equality that holds for every allowed value of its variable.
discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
elimination: Combining equations to remove one variable while retaining the same solutions.
gradient: The change in y divided by the corresponding change in x.
common ratio: The constant multiplier between consecutive terms of a geometric sequence.
coefficient: The numerical factor multiplying a variable term.
factorise: Rewrite an expression as a product of factors.
subject: The quantity written alone on one side of a formula.
equivalent expression: An expression with the same value as another for every allowed input.
input: The value supplied to a rule before its operations are carried out.
domain: The set of allowed inputs to a function.
asymptote: A line approached by a graph without a finite crossing in the stated example.
period: The input interval after which a repeating graph has the same values again.
graph translation: Move every point of a graph by the same horizontal and vertical displacement.
stationary: Not changing position over the time interval described.
tangent gradient: The slope of a tangent, used to estimate a curve’s rate at one input.
radius gradient: The slope of a radius joining the centre to a point on the circle.
iteration: Repeat a rule, using the previous output as the next input.
solution set: All inputs that satisfy the stated condition.
boundary line: The equality line separating values that satisfy an inequality from those that do not.
recursive rule: A rule that generates new terms from preceding terms.
second difference: The difference between consecutive first differences of a sequence.
excluded value: An input for which an original denominator or divisor is zero.

3.3 · Ratio, proportion and rates of change

Percentages, ratio and proportional reasoning: A factor that performs a percentage change in one multiplication.
Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
Ratios, equivalent proportions and mixtures: A comparison of one share with the combined quantity.
Scale drawings and maps: The ratio of a drawing length to its corresponding real length.
Direct and inverse proportional relationships: The fixed multiplier in a stated proportional relationship.
Rates, unit prices, density and pressure: Mass per unit volume, with both units stated.
Length, area and volume scale factors: The squared length factor between similar shapes.
Simple interest, compound growth and decay: Interest calculated on the updated balance each period.
Iterative processes with repeated deposits: A rule obtaining a later value from the preceding value.

multiplier: A factor that performs a percentage change in one multiplication.
residual: The observed value minus the value predicted by a fitted model.
part-to-whole ratio: A comparison of one share with the combined quantity.
scale: The ratio of a drawing length to its corresponding real length.
constant of proportionality: The fixed multiplier in a stated proportional relationship.
density: Mass per unit volume, with both units stated.
area scale factor: The squared length factor between similar shapes.
compound interest: Interest calculated on the updated balance each period.
recurrence relation: A rule obtaining a later value from the preceding value.

3.4 · Geometry and measures

Angle reasoning, similarity and mensuration: The multiplier that relates corresponding lengths in similar shapes.
Right triangles and non-right triangles: The side opposite the right angle in a right-angled triangle.
Vectors and transformation geometry: The vector sum representing the combined displacement or force.
Reflections, rotations and enlargements: The point from which each point's displacement is multiplied by a scale factor.
Constructions, loci and geometric conditions: The set of all points satisfying a stated geometric condition.
Circle theorems and reasoned proofs: A quadrilateral whose four vertices lie on one circle.
Shape vocabulary, properties and symmetry: A mirror line that maps a whole shape onto itself.
Angle facts and polygon reasoning: Angles in matching positions at a transversal crossing two lines.
Triangle congruence and geometric proof: Equal shape and size, with matching lengths and angles.
Circle parts and geometric definitions: A region bounded by a chord and its corresponding arc.
Geometric reasoning on coordinate axes: The point halfway between the endpoints of a segment.
Solid properties, plans and elevations: An orthographic view from a stated horizontal direction.
Measuring angles and three-figure bearings: A direction measured clockwise from north at the starting point.
Combined isometries and invariants: A property preserved by a specified transformation.
Circle angles and proof chains: An angle formed by two radii meeting at the centre.
Tangents, chords and the alternate segment: The tangent–chord angle equals the angle subtended by that chord in the opposite segment.
Areas, perimeters and composite plane shapes: The distance between a base and its parallel opposite level, measured at right angles.
Prism volume and cylinder measurement: A slice perpendicular to a prism’s length that remains constant along it.
Circle lengths, areas and composite boundaries: The total length of a circle’s boundary.
Spheres, cones, pyramids and frustums: The remaining solid after a cone or pyramid is cut parallel to its base.
Arcs, sectors and reverse angle calculations: A circle region bounded by two radii and their intervening arc.
Exact trigonometric values from special triangles: A value retained as a fraction or surd rather than a rounded decimal.
Sine rule, cosine rule and triangle area: The angle between the two named sides.
Right triangles in three-dimensional shapes: The view or component of a spatial length on a selected plane.
Vector geometry and midpoint arguments: Lying on one straight line.

scale factor: The multiplier that relates corresponding lengths in similar shapes.
hypotenuse: The side opposite the right angle in a right-angled triangle.
resultant: The vector sum representing the combined displacement or force.
centre of enlargement: The point from which each point's displacement is multiplied by a scale factor.
locus: The set of all points satisfying a stated geometric condition.
cyclic quadrilateral: A quadrilateral whose four vertices lie on one circle.
line of symmetry: A mirror line that maps a whole shape onto itself.
corresponding angles: Angles in matching positions at a transversal crossing two lines.
congruence: Equal shape and size, with matching lengths and angles.
segment: A region bounded by a chord and its corresponding arc.
midpoint: The point halfway between the endpoints of a segment.
elevation: An orthographic view from a stated horizontal direction.
bearing: A direction measured clockwise from north at the starting point.
invariant: A property preserved by a specified transformation.
angle at the centre: An angle formed by two radii meeting at the centre.
alternate segment theorem: The tangent–chord angle equals the angle subtended by that chord in the opposite segment.
perpendicular height: The distance between a base and its parallel opposite level, measured at right angles.
cross-section: A slice perpendicular to a prism’s length that remains constant along it.
circumference: The total length of a circle’s boundary.
frustum: The remaining solid after a cone or pyramid is cut parallel to its base.
sector: A circle region bounded by two radii and their intervening arc.
exact value: A value retained as a fraction or surd rather than a rounded decimal.
included angle: The angle between the two named sides.
projection: The view or component of a spatial length on a selected plane.
collinear: Lying on one straight line.

3.5 · Probability

Probability, trees and conditional reasoning: The probability of an event after restricting the sample space to a stated condition.
Experimental probability, fairness and expected outcomes: The observed count of an outcome divided by the number of trials.
Systematic possibilities and equally likely outcomes: The complete set of outcomes in an experiment.
Venn diagrams, unions and two-way counts: The outcomes belonging to both named sets.
Conditional probability with tables and expected frequencies: A probability within the group selected by given information.

conditional probability: A probability within the group selected by given information.
relative frequency: The observed count of an outcome divided by the number of trials.
sample space: The complete set of outcomes in an experiment.
intersection: The outcomes belonging to both named sets.

3.6 · Statistics

Data summaries, histograms and interpretation: Frequency divided by class width, used as histogram height.
Cumulative frequency and box plots: The difference between the upper and lower quartiles.
Samples, populations and justified comparisons: The complete group about which a statistical claim is made.
Choosing displays, pie charts and time series: Measurements recorded in time order.
Frequency summaries and grouped estimates: The class interval containing the greatest frequency.
Scatter graphs, correlation and cautious predictions: A pattern of association between two measured variables.
Histogram density and cumulative-frequency construction: Frequency divided by class width, used as histogram height.
Quartiles, box plots and distribution comparisons: The upper quartile minus the lower quartile.

frequency density: Frequency divided by class width, used as histogram height.
interquartile range: The upper quartile minus the lower quartile.
population: The complete group about which a statistical claim is made.
time series: Measurements recorded in time order.
modal class: The class interval containing the greatest frequency.
correlation: A pattern of association between two measured variables.

Preparing for this qualification

Choose one tier for all three papers. Foundation targets grades 1–5; Higher targets grades 4–9, with a possible grade 3 award.
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Teaching coverage still needed

Official question-bank boundaries, scheme alignment and all objective-level teaching coverage require the recorded review; no practice registry promotion.
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