Booklet review — 303 family samples

One representative question per family. All 23,000 question cards passed automated rendering checks. These samples make the methods review inspectable.

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FamilyTopicReference / coverage
F01-01Integer additionSupplementary GCSE method — not covered in this booklet
F01-02Integer subtractionSupplementary GCSE method — not covered in this booklet
F01-03Long multiplicationSupplementary GCSE method — not covered in this booklet
F01-04Division with remainderSupplementary GCSE method — not covered in this booklet
F01-05Capacity and minimum purchasesSupplementary GCSE method — not covered in this booklet
F02-01Ordering signed integersSupplementary GCSE method — not covered in this booklet
F02-02Adding and subtracting negativesApplication of related method — Booklet p. 27
F02-03Multiplying and dividing negativesApplication of related method — Booklet p. 3
F02-04Temperature changeSupplementary GCSE method — not covered in this booklet
F02-05Reasoning with signed calculationsApplication of related method — Booklet p. 27
F03-01Rounding decimal placesApplication of related method — Booklet p. 63
F03-02Significant figuresApplication of related method — Booklet p. 39 & p. 63
F03-03Estimating a calculationApplication of related method — Booklet p. 39
F03-04Checking an estimateApplication of related method — Booklet p. 39
F03-05Rounding to a given unitApplication of related method — Booklet p. 64
F04-01Squares and cubesApplication of related method — Booklet p. 17 & p. 45
F04-02Order of operationsApplication of related method — Booklet p. 32
F04-03Brackets and powersApplication of related method — Booklet p. 32
F04-04Inserting bracketsApplication of related method — Booklet p. 32
F04-05Square and cube rootsApplication of related method — Booklet p. 17 & p. 45
F05-01Collecting like termsBooklet p. 1
F05-02Expanding a single bracketBooklet p. 2
F05-03Factorising fullyBooklet p. 4
F05-04Expanding two bracketsBooklet p. 2
F05-05Expanding three bracketsBooklet p. 3
F06-01Substitution with negativesBooklet p. 30 & p. 78
F06-02Forming a cost expressionApplication of related method — Booklet p. 32
F06-03Substitution into a quadraticBooklet p. 30 & p. 78
F06-04Perimeter expressionApplication of related method — Booklet p. 1
F06-05Substitution into a formulaApplication of related method — Booklet p. 30
F07-01Two-step linear equationsBooklet p. 10
F07-02Equations with bracketsBooklet p. 2 & p. 10
F07-03Unknown on both sidesBooklet p. 10
F07-04Equations with fractional termsBooklet p. 11
F07-05Form and solve an equationBooklet p. 10
F08-01Integer solutionsBooklet p. 15
F08-02Linear inequalitiesBooklet p. 15
F08-03Negative coefficient inequalitiesBooklet p. 15
F08-04Integer constraintsBooklet p. 15
F08-05Quadratic inequalitiesBooklet p. 16
F09-01Prime factorisationBooklet p. 42
F09-02Highest common factorBooklet p. 42
F09-03Lowest common multipleBooklet p. 42
F09-04Repeated eventsBooklet p. 42
F09-05Square numbers from prime factorsBooklet p. 42
F10-01Simplifying fractionsApplication of related method — Booklet p. 7
F10-02Adding fractionsApplication of related method — Booklet p. 8 & p. 9
F10-03Multiplying mixed numbersApplication of related method — Booklet p. 8
F10-04Dividing fractionsApplication of related method — Booklet p. 8
F10-05Fraction of a remainderApplication of related method — Booklet p. 19
F10-06Reverse fractionsApplication of related method — Booklet p. 19 & p. 53
F11-01Ordering decimalsSupplementary GCSE method — not covered in this booklet
F11-02Subtracting decimalsSupplementary GCSE method — not covered in this booklet
F11-03Decimal multiplicationSupplementary GCSE method — not covered in this booklet
F11-04Decimal divisionSupplementary GCSE method — not covered in this booklet
F11-05Using a related calculationSupplementary GCSE method — not covered in this booklet
F12-01Length conversionApplication of related method — Booklet p. 40
F12-02Mass and capacityApplication of related method — Booklet p. 40
F12-03Journey timesApplication of related method — Booklet p. 54
F12-04Area unit conversionApplication of related method — Booklet p. 41
F12-05Volume unit conversionBooklet p. 40
F13-01Multiplying powersBooklet p. 1
F13-02Dividing powersBooklet p. 1
F13-03Power of a productBooklet p. 1
F13-04Negative indicesBooklet p. 17
F13-05Fractional indicesBooklet p. 17
F14-01Percentage of an amountRelated percentage arithmetic — Booklet p. 51
F14-02Percentage changeBooklet p. 51
F14-03Reverse percentageBooklet p. 53
F14-04Compound growthBooklet p. 52
F14-05Successive percentage changesBooklet p. 52
F14-06DepreciationBooklet p. 52
F15-01Decimal to fractionSupplementary GCSE method — not covered in this booklet
F15-02Fraction to percentageSupplementary GCSE method — not covered in this booklet
F15-03Comparing representationsSupplementary GCSE method — not covered in this booklet
F15-04Pure recurring decimalsBooklet p. 50
F15-05Mixed recurring decimalsBooklet p. 50
F16-01Simplifying ratiosApplication of related method — Booklet p. 18 & p. 21
F16-02Sharing in a ratioBooklet p. 18
F16-03Ratio with a differenceBooklet p. 18
F16-04Combining ratiosBooklet p. 21
F16-05Ratio and percentagesApplication of related method — Booklet p. 19
F16-06Changing ratiosBooklet p. 20
F17-01Unitary methodApplication of related method — Booklet p. 18 & p. 22
F17-02Recipe scalingApplication of related method — Booklet p. 18
F17-03Inverse proportion in contextBooklet p. 24
F17-04Direct proportion to a powerBooklet p. 23
F17-05Inverse square proportionBooklet p. 23
F17-06Scale drawingsApplication of related method — Booklet p. 18
F18-01Single-event probabilityApplication of related method — Booklet p. 60
F18-02Expected frequencyApplication of related method — Booklet p. 60
F18-03Venn diagram regionsBooklet p. 62
F18-04Two draws without replacementBooklet p. 60
F18-05Independent eventsApplication of related method — Booklet p. 60
F18-06Conditional probabilityBooklet p. 62
F18-07Two-way tablesApplication of related method — Booklet p. 60
F18-08Tree diagramsBooklet p. 60
F19-01Factorising quadratic equationsBooklet p. 5 & p. 12
F19-02Non-monic quadratic equationsBooklet p. 6 & p. 12
F19-03Quadratic formulaBooklet p. 13
F19-04Completing the squareBooklet p. 14
F19-05Quadratic modellingBooklet p. 12
F20-01Linear eliminationBooklet p. 27
F20-02Scaled eliminationBooklet p. 27
F20-03Simultaneous equations in contextBooklet p. 27
F20-04Linear and quadratic equationsBooklet p. 28
F20-05Intersections of a line and circleBooklet p. 28 & p. 83
F21-01Continuing arithmetic sequencesBooklet p. 25
F21-02Linear nth termBooklet p. 25
F21-03Sequence membershipBooklet p. 25
F21-04Quadratic nth termBooklet p. 26
F21-05Geometric sequencesSupplementary GCSE method — not covered in this booklet
F21-06Fibonacci-type sequencesSupplementary GCSE method — not covered in this booklet
F22-01Large numbers in standard formBooklet p. 44
F22-02Small numbers in standard formBooklet p. 44
F22-03Multiplying standard formBooklet p. 44
F22-04Dividing standard formBooklet p. 44
F22-05Adding standard formBooklet p. 44
F23-01MidpointsBooklet p. 81
F23-02Gradient between pointsBooklet p. 80
F23-03Equation of a straight lineBooklet p. 81
F23-04Perpendicular linesBooklet p. 81–82
F23-05Plotting a straight lineBooklet p. 78
F23-06Parallel linesBooklet p. 79 & p. 82
F24-01Plotting quadraticsBooklet p. 78 & p. 88
F24-02Cubic graphsApplication of related method — Booklet p. 88
F24-03Reciprocal graphsApplication of related method — Booklet p. 88
F24-04Real-life linear graphsApplication of related method — Booklet p. 79
F24-05Quadratic intercepts and turning pointsBooklet p. 12 & p. 14
F24-06Exponential modelsApplication of related method — Booklet p. 52 & p. 88
F24-07Trigonometric graphsBooklet p. 87 & p. 88
F24-08Gradient of a curveApplication of related method — Booklet p. 58 & p. 80
F25-01Triangle areaBooklet p. 37 & p. 94
F25-02Trapezium areaBooklet p. 58 & p. 94
F25-03Compound rectilinear areaBooklet p. 38
F25-04Shaded circular regionBooklet p. 38 & p. 83
F25-05Tiling and purchasesApplication of related method — Booklet p. 38
F25-06Algebraic perimeter and areaBooklet p. 10
F26-01Circle area and circumferenceBooklet p. 83 & p. 94
F26-02Circumference from diameterBooklet p. 83 & p. 94
F26-03Semicircle perimeterBooklet p. 38 & p. 83
F26-04Sector areaBooklet p. 38
F26-05Arc length and sector perimeterBooklet p. 38
F26-06Reverse circle areaBooklet p. 28 & p. 83
F27-01Cuboid surface areaBooklet p. 39 & p. 94
F27-02Prism volumeBooklet p. 39 & p. 40
F27-03Cylinder volumeBooklet p. 39 & p. 94
F27-04Cone volumeBooklet p. 39
F27-05Sphere and hemisphereBooklet p. 39
F27-06Volume and capacityBooklet p. 40
F27-07Plans and elevationsSupplementary GCSE method — not covered in this booklet
F27-08Pyramid volumeBooklet p. 94
F28-01Triangle anglesBooklet p. 73
F28-02Parallel-line anglesBooklet p. 73
F28-03Interior angle sumsBooklet p. 73
F28-04Regular polygonsBooklet p. 73
F28-05Algebraic anglesBooklet p. 10 & p. 73
F28-06Angles around a pointBooklet p. 73
F29-01Average speedBooklet p. 54
F29-02Speed unit conversionApplication of related method — Booklet p. 54
F29-03Density of a mixtureBooklet p. 54
F29-04PressureBooklet p. 56
F29-05Velocity–time graph areaBooklet p. 58
F29-06AccelerationBooklet p. 58
F30-01Stratified samplingBooklet p. 22
F30-02Sampling biasSupplementary GCSE method — not covered in this booklet
F30-03Questionnaire designSupplementary GCSE method — not covered in this booklet
F30-04Capture–recaptureBooklet p. 22
F30-05Systematic samplingSupplementary GCSE method — not covered in this booklet
F31-01Averages from a listBooklet p. 67 & p. 70
F31-02Missing value from meanBooklet p. 56
F31-03Mean from a frequency tableBooklet p. 67
F31-04Estimated mean of grouped dataBooklet p. 67
F31-05Combined meansBooklet p. 56
F31-06Comparing distributionsBooklet p. 71
F32-01Pie-chart anglesApplication of related method — Booklet p. 18
F32-02Histogram frequency densityBooklet p. 72
F32-03Box-plot comparisonBooklet p. 70 & p. 71
F32-04Scatter graphs and extrapolationSupplementary GCSE method — not covered in this booklet
F32-05Cumulative frequencyBooklet p. 69
F32-06Drawing a histogramBooklet p. 72
F32-07Stem-and-leaf diagramsSupplementary GCSE method — not covered in this booklet
F32-08Interpreting a bar chartSupplementary GCSE method — not covered in this booklet
F33-01Pythagoras hypotenuseBooklet p. 34
F33-02Pythagoras shorter sideBooklet p. 34
F33-03Right-angle trigonometryBooklet p. 34
F33-04Sine ruleBooklet p. 36
F33-05Cosine ruleBooklet p. 36
F33-06Area using sineBooklet p. 37
F33-07Three-dimensional PythagorasBooklet p. 34
F33-08Trigonometry to find an angleBooklet p. 34
F33-09Exact trigonometric valuesBooklet p. 35
F34-01Column-vector arithmeticBooklet p. 89
F34-02Vector between two pointsBooklet p. 75 & p. 89
F34-03Position vector dividing a lineBooklet p. 90
F34-04Parallel vector proofBooklet p. 90
F34-05Vector geometry proofBooklet p. 90
F35-01TranslationBooklet p. 75
F35-02ReflectionBooklet p. 76 & p. 77
F35-03RotationBooklet p. 75
F35-04Enlargement with a centreBooklet p. 76
F35-05Negative enlargementBooklet p. 76
F35-06Graph translationBooklet p. 87
F35-07Graph reflectionBooklet p. 87
F36-01Similar lengthsBooklet p. 41
F36-02Similar areasBooklet p. 41
F36-03Similar volumesBooklet p. 41
F36-04Reverse volume scale factorBooklet p. 41
F36-05Congruence proofBooklet p. 90
F36-06Area and length scale factorsBooklet p. 41
F37-01Reverse bearingsBooklet p. 91
F37-02Navigation with PythagorasBooklet p. 34 & p. 91
F37-03Perpendicular-bisector constructionSupplementary GCSE method — not covered in this booklet
F37-04Circle locusSupplementary GCSE method — not covered in this booklet
F37-05Intersecting lociApplication of related method — Booklet p. 34
F37-06Angle-bisector constructionSupplementary GCSE method — not covered in this booklet
F38-01Rounding error intervalsBooklet p. 63 & p. 64
F38-02Truncation intervalsBooklet p. 63
F38-03Upper bound of a productBooklet p. 64 & p. 65
F38-04Bounds on a quotientBooklet p. 65
F38-05Bounds on a differenceBooklet p. 65
F39-01Simplifying a surdBooklet p. 45
F39-02Combining surdsBooklet p. 46
F39-03Expanding surd bracketsBooklet p. 46 & p. 48
F39-04Rationalising a single surdBooklet p. 48
F39-05Rationalising a binomialBooklet p. 48
F40-01Cancelling algebraic factorsBooklet p. 6 & p. 7
F40-02Quadratic algebraic fractionsBooklet p. 5, p. 6 & p. 7
F40-03Adding algebraic fractionsBooklet p. 8 & p. 9
F40-04Multiplying algebraic fractionsBooklet p. 8
F40-05Solving rational equationsBooklet p. 11 & p. 12
F41-01Inverse functionsBooklet p. 31
F41-02Composite functionsBooklet p. 30
F41-03Rearranging a rational formulaBooklet p. 29
F41-04IterationBooklet p. 32
F41-05Algebraic divisibility proofBooklet p. 32–33
F41-06Rearranging with powersBooklet p. 28
F42-01Angles at centre and circumferenceBooklet p. 85 & p. 86
F42-02Cyclic quadrilateralBooklet p. 85 & p. 86
F42-03Tangent and radiusBooklet p. 85 & p. 86
F42-04Alternate segment theoremBooklet p. 85 & p. 86
F42-05Equation of a tangentBooklet p. 81 & p. 84
F42-06Equal tangentsBooklet p. 85 & p. 86
F43-01Budget and balanceSupplementary GCSE method — not covered in this booklet
F43-02Best valueApplication of related method — Booklet p. 18 & p. 22
F43-03Modelled income taxApplication of related method — Booklet p. 51
F43-04Comparing payment plansApplication of related method — Booklet p. 51
F43-05Simple and compound interestApplication of related method — Booklet p. 52
F43-06Currency conversionBooklet p. 22
X01Ratio, percentages and whole-pack purchasingApplication of booklet p. 18 & p. 51
X02Reverse percentage, VAT and profit marginBooklet p. 52 & p. 53
X03Fractions of remainders and reverse capacityBooklet p. 19 & p. 53
X04Density bounds for a cylindrical solidBooklet p. 39, p. 54 & p. 65
X05Quadratic modelling: rectangular borderBooklet p. 2, p. 6 & p. 12
X06Line–parabola intersections and distanceBooklet p. 28 & p. 80
X07Rational equation with two solutionsBooklet p. 12 & p. 13
X08Intersecting quadratic and linear inequalitiesBooklet p. 15 & p. 16
X09Quadratic sequence and membership testBooklet p. 12, p. 25 & p. 26
X10Combined proportion and percentage changeBooklet p. 23 & p. 52
X11Conditional probability without replacementBooklet p. 60 & p. 62
X12Histogram frequencies, proportion and estimated meanBooklet p. 67 & p. 72
X13Combined means and an unknown group sizeBooklet p. 10 & p. 56
X14Velocity–time graph: distance and average speedBooklet p. 54 & p. 58
X15Segment area and perimeter from a sectorBooklet p. 37 & p. 38
X16Composite stadium: reverse perimeter and surfacing costBooklet p. 38, p. 51 & p. 83
X17Chord geometry and a minor segmentBooklet p. 34, p. 37 & p. 38
X18Two tangents: length and quadrilateral areaBooklet p. 34, p. 85 & p. 86
X19Circle theorem chain with an exterior angleBooklet p. 38, p. 85 & p. 86
X20Coordinate circle, tangent intercepts and triangle areaBooklet p. 37 & p. 84
X21Cone transfer, cylinder capacity and overflowBooklet p. 39 & p. 40
X22Connected triangles: angle and shortest distanceBooklet p. 34 & p. 37
X23Similar solids: volumes, surface areas and coating costBooklet p. 41
X24Vector division and a parallel-line proofBooklet p. 90
R01Double-bracket factorising: paired monic quadraticsBooklet p. 5
R02Double-bracket factorising: non-monic quadraticsBooklet p. 6
R03Common factor followed by double bracketsBooklet p. 4 & p. 5
R04Difference of squares with an error explanationBooklet p. 2 & p. 6
R05Area equality with algebraic side lengthsBooklet p. 2 & p. 10
R06Budget inequalities and admissible whole numbersBooklet p. 15
R07Fraction mixture and a target concentrationBooklet p. 18 & p. 19
R08Changing a ratio by transferring quantitiesBooklet p. 20
R09Successive percentages and a reverse comparisonBooklet p. 51, p. 52 & p. 53
R10Compound growth followed by a fixed withdrawalBooklet p. 52
R11Standard form, area conversion and densityBooklet p. 41, p. 44 & p. 54
R12Repeating schedules and simultaneous eventsBooklet p. 42 & p. 54
R13Bounds on journey speed and a decisionBooklet p. 54, p. 64 & p. 65
R14Inverse-square model and a changed conditionBooklet p. 23
R15Conditional probability from two production linesBooklet p. 60 & p. 62
R16Two-way table: conditional selection without replacementBooklet p. 60 & p. 62
R17Frequency table with an unknown countBooklet p. 11 & p. 67
R18Histogram: recover the total and estimate a percentileBooklet p. 67 & p. 72
R19Cumulative frequency: compare distributionsBooklet p. 69 & p. 71
R20Quadratic graph: factorisation, vertex and intersectionBooklet p. 5, p. 12 & p. 14
R21Simultaneous equations from bundles and a discountBooklet p. 27 & p. 51
R22Sequence: consecutive terms and a limiting conditionBooklet p. 10, p. 15 & p. 25
R23Circle chord: reverse radius and exact areaBooklet p. 34, p. 37 & p. 85
R24Coordinate tangent and distance from the centreBooklet p. 80, p. 82 & p. 84
R25Sector: derive the angle and compare areasBooklet p. 38 & p. 51
R26Similar cones: frustum capacity and materialBooklet p. 39, p. 40 & p. 41
R27Polygon exterior angles and a perimeter comparisonBooklet p. 18 & p. 73
R28Triangle area, unknown side and obtuse angleBooklet p. 36 & p. 37
R29Two transformations and an invariant areaBooklet p. 75, p. 76 & p. 87
R30Surd dimensions: exact perimeter, area and diagonalBooklet p. 34 & p. 46