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Revision — Cambridge Mathematics (without Coursework) (0580) — EC2 Excel

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Cambridge Mathematics (without Coursework) (0580) — key learnings, examiner-sourced common mistakes, flashcards and practice questions, organised by the 0580 syllabus.

Section 1 · Number

E1.1Types of number — primes, HCF, LCM, squares and cubesView →
E1.2Sets — set language, notation and Venn diagramsView →
E1.4aFractions, decimals and percentages — equivalence and convertingView →
E1.4bFractions, decimals and percentages — recurring decimals, ordering and place valueView →
E1.7Indices I — positive, zero, negative and fractional indicesView →
E1.8Standard form — A × 10ⁿ, converting and calculatingView →
E1.9Estimation — rounding to dp/sf and estimating calculationsView →
E1.10Limits of accuracy — upper and lower boundsView →
E1.11Ratio and proportion — simplest form, dividing in a ratio, best valueView →
E1.12Rates — pay, exchange, flow, fuel, pressure, density, average speedView →
E1.13Percentages — increase/decrease, reverse %, simple and compound interestView →
E1.15Time — units, 12/24-hour clock, timetables, time zonesView →
E1.16Money — calculate with money, convert between currenciesView →
E1.17Exponential growth and decayView →
E1.18Surds — simplifying expressions and rationalising the denominatorView →

Section 2 · Algebra and graphs

E2.1Introduction to algebra — notation, collecting like terms and substitutionView →
E2.2Algebraic manipulation — expanding and factorisingView →
E2.3Algebraic fractions — manipulate, factorise and simplify rational expressionsView →
E2.5aEquations — solving linear equations in one unknownView →
E2.5bEquations — simultaneous equations (linear; and one linear, one non-linear)

Section 3 · Coordinate geometry

E3.5Coordinate geometry — straight-line graphs, gradient, parallel and perpendicularView →

Section 4 · Geometry

E4.2Geometrical constructions — measure/draw, SSS triangle, netsView →
E4.3Scale drawings — three-figure bearings (measured clockwise from north)View →
E4.4Similarity — length, area and volume scale factors; showing triangles similarView →
E4.5Symmetry — line and rotational symmetry; symmetry of solidsView →
E4.6aAngles — at a point/line, vertically opposite, triangles, parallel lines

Section 5 · Mensuration

E5.2/E5.3Area and perimeter — rectangle, triangle, parallelogram, trapezium (E5.2) and circles (E5.3)View →
E5.3Circles, arcs and sectors — arc length and sector areaView →
E5.4Surface area and volume — cuboid, prism, cylinder, sphere, pyramid, coneView →

Section 6 · Trigonometry

E6.1/E6.6Pythagoras' theorem — in 2D (E6.1) and in 3D (E6.6)View →
E6.2/E6.6Right-angled trigonometry — sine, cosine, tangent; elevation/depression (E6.2) and in 3D (E6.6)View →
E6.3Exact trigonometric valuesView →
E6.4Trigonometric functions — graphs of sin/cos/tan and solving trig equationsView →
E6.5

Section 7 · Transformations and vectors

E7.1Transformations — reflection, rotation, enlargement, translationView →
E7.2Vectors in two dimensionsView →
E7.4Vector geometry — position vectors, parallel/collinear, ratio proofsView →

Section 8 · Probability

E8.1Probability of single and combined eventsView →
E8.3Probability from Venn diagrams — set notationView →
E8.4Tree diagrams and conditional probabilityView →

Section 9 · Statistics

E9.3Averages and measures of spread — mean, median, mode, rangeView →
E9.5Scatter diagrams — correlation and line of best fitView →
E9.6Cumulative frequency diagrams — median, quartiles, IQRView →
E9.7Histograms — frequency density and unequal widthsView →

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E2.5cEquations — changing the subject of a formulaView →

E2.7Sequences — nth term (linear, quadratic, cubic, exponential)View →

E2.5dEquations — quadratic expressions and equationsView →

E2.9Graphs in practical situations — travel graphs and kinematicsView →

E2.6Inequalities — linear inequalities, number lines and graphical regionsView →

E2.12Differentiation — derivatives of ax^n, stationary/turning pointsView →

E2.8Proportion — direct and inverse proportion in algebraic termsView →

E2.13Functions — domain and range with function notationView →

E2.11aGraphs of functions — quadratic graphs (sketch, solve, turning point)View →

E2.11bGraphs of functions — cubic, reciprocal and exponential graphsView →

E2.13aFunctions — f(x), composite gf(x), inverse and domain/rangeView →

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E4.6bAngles — properties of regular and irregular polygonsView →

E4.1/E4.8Circle vocabulary (E4.1) and chord/tangent symmetry properties (E4.8)View →

E4.7Circle theorems — semicircle, centre/circumference, same segment, cyclic quadrilateral, tangent/radiusView →

Non-right-angled triangles — sine rule, cosine rule and area = ½ab·sin C

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