IGCSE Mathematics · COVERAGE & GAPSIGCSE Mathematics: Coverage Map & Learning Gaps
Cambridge Mathematics 0580 Extended foundations for examination years 2025–2027
Official reference E1.1
Types of number
Partial practice2 linked question families · 10 variants. Variants are not separate syllabus objectives.
What still needs work
- Only HCF and LCM; classification, primes, reciprocals and irrational-number reasoning are missing.
Official reference E1.2
Sets
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Two-set union/intersection counts only; three sets, complements and set-builder notation missing.
Official reference E1.3
Powers and roots
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Square roots appear within right-triangle calculations; general powers and cube roots missing.
Official reference E1.4
Fractions, decimals and percentages
Partial practice2 linked question families · 9 variants. Variants are not separate syllabus objectives.
What still needs work
- Added two-digit pure recurring decimals converted exactly to fractions. Mixed recurring/terminating prefixes, mixed-number conversions and percentage–fraction equivalence remain incomplete.
Official reference E1.5
Ordering
Not yet coveredWhat still needs work
- No dedicated assessed family for ordering; adjacent lesson references do not count as coverage.
Official reference E1.6
The four operations
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- One fraction addition family only; broader four-operation combinations absent.
Official reference E1.7
Indices I
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- Added exact positive-base fractional-power evaluation. General negative indices, zero indices and broader index-law combinations remain unassessed.
Official reference E1.8
Standard form
Partial practice3 linked question families · 13 variants. Variants are not separate syllabus objectives.
What still needs work
- Added standard-form multiplication and division with normalization. Addition/subtraction across different exponents and extreme-scale contextual comparison remain missing.
Official reference E1.9
Estimation
Not yet coveredWhat still needs work
- No dedicated assessed family for estimation; adjacent lesson references do not count as coverage.
Official reference E1.10
Limits of accuracy
Partial practice4 linked question families · 20 variants. Variants are not separate syllabus objectives.
What still needs work
- Added upper/lower bounds for individual measures, area, differences and positive speed ratios. Different significant-figure precisions, intervals crossing zero and justified final rounding remain incomplete.
Official reference E1.11
Ratio and proportion
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- One ratio-part mixture family; sharing with unknown parts and complex proportions missing.
Official reference E1.12
Rates
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- Added speed as a quotient with measurement bounds. Other compound rates, unit conversions across rate contexts and rates from practical graphs remain missing.
Official reference E1.13
Percentages
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- One reverse-discount family; profit, compound interest and broader percentage applications missing.
Official reference E1.14
Using a calculator
Not yet coveredWhat still needs work
- No dedicated assessed family for using a calculator; adjacent lesson references do not count as coverage.
Official reference E1.15
Time
Not yet coveredWhat still needs work
- No dedicated assessed family for time; adjacent lesson references do not count as coverage.
Official reference E1.16
Money
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- One fee-free currency exchange family; financial arithmetic with fees and practical comparison missing.
Official reference E1.17
Exponential growth and decay
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added reversal of two-step compound growth. Forward decay, varying rates, population contexts and broader exponential problem solving remain incomplete.
Official reference E1.18
Surds
Partial practice3 linked question families · 15 variants. Variants are not separate syllabus objectives.
What still needs work
- Added like-surd addition, single-surd denominator rationalisation and conjugate multiplication. Rationalising binomial denominators and longer mixed surd expressions remain unassessed.
Official reference E2.1
Introduction to algebra
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Substitution and equation prerequisites only; general formula rearrangement and algebraic representation incomplete.
Official reference E2.2
Algebraic manipulation
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Expansion, selected factorisation and completed squares; broader products and identities incomplete.
Official reference E2.3
Algebraic fractions
Partial practice4 linked question families · 16 variants. Variants are not separate syllabus objectives.
What still needs work
- Added common-denominator addition, factor simplification, original exclusions and a rational equation. General multiplication/division of algebraic fractions, multi-factor denominators and complex combinations remain incomplete.
Official reference E2.4
Indices II
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- Added numerical fractional powers as a prerequisite. Algebraic index laws with variable bases, negative powers and simplifying composite powers remain missing.
Official reference E2.5
Equations
Partial practice5 linked question families · 20 variants. Variants are not separate syllabus objectives.
What still needs work
- Added reciprocal equations and quadratic–linear intersections. General rational equations, noninteger quadratic roots, exponential equations and multi-stage contexts remain incomplete.
Official reference E2.6
Inequalities
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Added integer counts within a strict quadratic sign interval. Continuous interval notation, nonstrict inequalities, compound regions and graphical inequality systems remain missing.
Official reference E2.7
Sequences
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Arithmetic term and quadratic term difference only; deriving unfamiliar nth terms incomplete.
Official reference E2.8
Proportion
Partial practice1 linked question families · 5 variants. Variants are not separate syllabus objectives.
What still needs work
- Single inverse-proportion worker-time context; powers and general proportional formulas missing.
Official reference E2.9
Graphs in practical situations
Not yet coveredWhat still needs work
- No dedicated assessed family for graphs in practical situations; adjacent lesson references do not count as coverage.
Official reference E2.10
Graphs of functions
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added intersections between a quadratic and a line. Drawing complete function graphs, estimating roots graphically and interpreting varied power/exponential functions remain missing.
Official reference E2.11
Sketching curves
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added the horizontal asymptote of a shifted reciprocal curve. Full sketching, vertical asymptotes across varied rational rules, and turning-point graph reconstruction remain incomplete.
Official reference E2.12
Differentiation
Partial practice4 linked question families · 16 variants. Variants are not separate syllabus objectives.
What still needs work
- Added polynomial gradients, stationary inputs, maximum heights and tangent intercepts. Gradient estimates from hand-drawn tangents, broader rational coefficients and full stationary classification across three-term cubics remain incomplete.
Official reference E2.13
Functions
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Added inversion of a domain-restricted shifted square. General inverse rules and domain/range analysis from graphs remain incomplete.
Official reference E3.1
Coordinates
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Coordinates used as prerequisites; quadrant and complete coordinate interpretation not separately assessed.
Official reference E3.2
Drawing linear graphs
Not yet coveredWhat still needs work
- No dedicated assessed family for drawing linear graphs; adjacent lesson references do not count as coverage.
Official reference E3.3
Gradient of linear graphs
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Gradient between labeled points; drawing tangent estimates and complex graphical contexts missing.
Official reference E3.4
Length and midpoint
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Only the midpoint x-coordinate; full midpoint and coordinate-distance tasks incomplete.
Official reference E3.5
Equations of linear graphs
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Intercept from known gradient and point; line construction from varied information incomplete.
Official reference E3.6
Parallel lines
Not yet coveredWhat still needs work
- No dedicated assessed family for parallel lines; adjacent lesson references do not count as coverage.
Official reference E3.7
Perpendicular lines
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Negative reciprocal gradient only; full perpendicular-line equations mostly lesson extension.
Official reference E4.1
Geometrical terms
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added reverse three-figure bearings. Broader geometric vocabulary, angle naming and bearing diagrams with several legs remain incomplete.
Official reference E4.2
Geometrical constructions
Not yet coveredWhat still needs work
- No dedicated assessed family for geometrical constructions; adjacent lesson references do not count as coverage.
Official reference E4.3
Scale drawings
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added converting a map scale into actual distance. Constructing scale drawings, measuring angles and interpreting multileg plans remain missing.
Official reference E4.4
Similarity
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Added conversion of a volume ratio into an area ratio. Similarity proofs, general unknown ratios and compound cross-sectional contexts remain incomplete.
Official reference E4.5
Symmetry
Not yet coveredWhat still needs work
- No dedicated assessed family for symmetry; adjacent lesson references do not count as coverage.
Official reference E4.6
Angles
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Regular polygons and straight-line angles only; parallel-line and complex angle reasoning missing.
Official reference E4.7
Circle theorems I
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Added same-arc centre/circumference angles, cyclic opposites and alternate-segment angle chains. Semicircle/tangent-radius configurations, multi-theorem diagrams and complete written proofs remain incomplete.
Official reference E4.8
Circle theorems II
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added chord length using perpendicular bisection and Pythagoras. Equal-chord symmetry, tangent-length equality and geometric construction/proof questions remain missing.
Official reference E5.1
Units of measure
Not yet coveredWhat still needs work
- No dedicated assessed family for units of measure; adjacent lesson references do not count as coverage.
Official reference E5.2
Area and perimeter
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Trapezium area only; broader plane-area and perimeter combinations missing.
Official reference E5.3
Circles, arcs and sectors
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Quarter-arc length only; general sectors, radians are not assumed, and mixed arc/perimeter questions missing.
Official reference E5.4
Surface area and volume
Partial practice5 linked question families · 20 variants. Variants are not separate syllabus objectives.
What still needs work
- Added cone volume, sphere surface area and hemisphere-plus-cylinder volume. Cone slant surface area, exposed-area composites, pyramids and reverse-dimension problems remain incomplete.
Official reference E5.5
Compound shapes and parts of shapes
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added volume of a cylinder joined to a hemisphere. Exposed surface areas, cut-out solids and other compound cross-sections remain missing.
Official reference E6.1
Pythagoras’ theorem
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Integer Pythagorean triples only; irrational and contextual distances missing.
Official reference E6.2
Right-angled triangles
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- One cosine ratio family only; unknown-angle and broader side-solving tasks missing.
Official reference E6.3
Exact trigonometric values
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Only tan45 in a height context; complete exact sine/cosine/tangent value set missing.
Official reference E6.4
Trigonometric functions
Not yet coveredWhat still needs work
- No dedicated assessed family for trigonometric functions; adjacent lesson references do not count as coverage.
Official reference E6.5
Non-right-angled triangles
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Added cosine-rule squared side, sine-rule exact side ratio and included-angle area. Unknown-angle solving, obtuse/ambiguous sine-rule cases and calculator rounding contexts remain missing.
Official reference E6.6
Pythagoras’ theorem and trigonometry in three dimensions
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added recovery of a missing cuboid edge from its space diagonal and two known perpendicular edges. Angle between line and plane, non-cuboid spatial contexts and selecting spatial right triangles from diagrams remain missing.
Official reference E7.1
Transformations
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- One translation, reflection and rotation rule each; enlargement and complete descriptions incomplete.
Official reference E7.2
Vectors in two dimensions
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Only one vector component in a linear combination; full vector and geometric interpretation incomplete.
Official reference E7.3
Magnitude of a vector
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added exact magnitude of a two-component vector as representation transfer of Pythagoras, not a new algorithm. Magnitudes with irrational outcomes and unknown-component equations remain incomplete.
Official reference E7.4
Vector geometry
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added a segment fraction through collinear displacement vectors. General vector proofs of parallelism, position-vector expressions and multi-segment geometry remain missing.
Official reference E8.1
Introduction to probability
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Simple event proportions as prerequisites; probability scale/complements not directly assessed across representations.
Official reference E8.2
Relative and expected frequencies
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Expected count only; empirical relative frequency and bias interpretation missing.
Official reference E8.3
Probability of combined events
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Two-success paths; exactly-one and multiple-path reasoning only in manual extension and article.
Official reference E8.4
Conditional probability
Partial practice2 linked question families · 8 variants. Variants are not separate syllabus objectives.
What still needs work
- Selected group and without-replacement examples; Venn/table conditional probability breadth incomplete.
Official reference E9.1
Classifying statistical data
Not yet coveredWhat still needs work
- No dedicated assessed family for classifying statistical data; adjacent lesson references do not count as coverage.
Official reference E9.2
Interpreting statistical data
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- A frequency-table mean and simple summaries; comparisons and limits of inference missing.
Official reference E9.3
Averages and measures of spread
Partial practice7 linked question families · 28 variants. Variants are not separate syllabus objectives.
What still needs work
- Added grouped-mean estimates and quartile/IQR interpretation. Modal classes, comparisons of distributions and quartiles requiring graph interpolation remain incomplete.
Official reference E9.4
Statistical charts and diagrams
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- One simple frequency table; bar/pie/stem-and-leaf and pictogram reading/drawing missing.
Official reference E9.5
Scatter diagrams
Partial practice1 linked question families · 4 variants. Variants are not separate syllabus objectives.
What still needs work
- Added reading a supplied fitted line and computing a residual as an original extension. Drawing scatter plots and a best-fit line by eye, correlation classification and deciding safe extrapolation remain unassessed.
Official reference E9.6
Cumulative frequency diagrams
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Added cumulative-count differences, quartile ranks and IQR from supplied quartiles. Drawing cumulative curves and reading interpolated quartiles/percentiles from a full curve remain missing.
Official reference E9.7
Histograms
Partial practice3 linked question families · 12 variants. Variants are not separate syllabus objectives.
What still needs work
- Added density, area-to-frequency and within-class estimated counts. Full histogram drawing, missing-scale recovery and comparisons across complete unequal-width distributions remain incomplete.
