Free International GCSE maths resource · Edexcel IGCSE 4MA1

Edexcel IGCSE maths worksheets by grade

204 free worksheets for Edexcel International GCSE maths (Specification A, 4MA1), from grade 1 to grade 9, with 2,839 original exam-style questions. Every topic has a printable worksheet, an answers sheet and a solutions sheet written out by hand, step by step, the way a tutor would write it next to you.

The International GCSE is a different qualification from the UK GCSE, with its own specification, so this list was built from the 4MA1 specification point by point rather than copied from the GCSE one. Of the 217 GCSE topics, 195 are on the International GCSE and 22 are not (they are listed at the bottom of this page with the reason). 9 topics are only on the International GCSE: Set notation: subsets and n(A), Arithmetic series: nth term and sum, Domain and range of a function, Proportion with square roots, Trigonometry with obtuse angles, Differentiation, Intersecting chords, Stationary points and turning points and Calculus in kinematics.

Pearson Edexcel International GCSE Mathematics A (4MA1) is sat as two papers of 2 hours, 100 marks each, and a calculator is allowed on both. Foundation covers grades 1 to 5 and Higher covers grades 4 to 9, as on the UK GCSE. The grade on each worksheet follows the Edexcel GCSE grade descriptors, which is a good guide to where a topic sits on an IGCSE paper. The International GCSE Foundation paper reaches a little further than the UK one, so a Foundation student should also work through these grade 6 topics: Compound growth and decay problems, Regions from inequalities on a graph, Combined transformations, Velocity-time graphs, Gradient as a rate of change, Similar shapes: lengths and Geometric and Fibonacci-type sequences.

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Grade 1 12 topics · Foundation

Place value of whole numbersReading the value of each digit up to thousands and millions
Ordering whole numbers and negative numbersPutting numbers in order on a number line
Adding and subtracting whole numbersColumn methods with carrying and borrowing
Multiplication tables and short multiplicationTimes tables to 10 x 10 and multiplying by a single digit
Continuing number sequencesSpotting the rule and finding the next terms
Naming 2D shapes and 3D solidsTriangles, quadrilaterals, polygons, cubes, cuboids, prisms, pyramids
Telling the time and reading timetables12-hour and 24-hour clock and finding durations
Reading scales and measuring with a rulerReading values from dials, jugs and rulers
Probability words and the probability scaleImpossible, unlikely, even chance, likely, certain
Reading tally charts and pictogramsCounting tallies and using a key
Reading bar chartsFinding and comparing values from bars
Simple money calculationsTotals, change and simple shopping problems

Grade 2 22 topics · Foundation

Rounding to the nearest 10, 100 and 1000Rounding whole numbers
Adding and subtracting decimalsLining up decimal points in column methods
Long multiplicationMultiplying by two-digit and three-digit numbers
Short divisionThe bus stop method including remainders
Multiples and factorsListing multiples and factor pairs
Prime numbersRecognising primes and listing them
Square numbers and cube numbersSquares to 15 x 15, cubes and their roots
Order of operations (BIDMAS)Brackets, indices, then division and multiplication, then addition and subtraction
Equivalent fractions and simplifying fractionsMultiplying or dividing top and bottom by the same number
Fractions of amountsFinding a unit fraction or simple fraction of a quantity
Finding 10%, 25% and 50% of an amountMental percentage methods without a calculator
Negative numbers in contextTemperatures, bank balances, adding and subtracting negatives
Function machines and simple formulae in wordsInput and output rules
Substituting into simple expressionsReplacing a letter with a positive number
Simple ratio notationWriting and simplifying ratios such as 4:6
Perimeter of rectangles and compound shapesAdding up all the sides
Area of rectanglesCounting squares and length times width
Types of angle and measuring with a protractorAcute, obtuse, reflex and measuring accurately
Lines of symmetryDrawing and counting mirror lines
Plotting coordinates in the first quadrantReading and plotting (x, y) points
Converting metric unitsmm, cm, m, km, g, kg, ml and litres
Mode, median and rangeAverages and spread from a small list

Grade 3 34 topics · Foundation

Rounding to decimal placesRounding to 1 or 2 decimal places
Multiplying and dividing decimalsUsing whole-number methods then placing the decimal point
Ordering fractions and decimalsComparing using common denominators or decimals
Adding and subtracting fractionsFinding a common denominator
Converting between fractions, decimals and percentagesSwitching between the three forms
Percentage of an amount with a calculatorUsing a decimal multiplier
Writing one amount as a percentage of anotherFraction then percentage, such as 18 out of 40
Multiplying and dividing negative numbersThe sign rules
Powers and rootsSquares, cubes, square roots and cube roots
Estimating answersRounding to one significant figure to check
Highest common factor and lowest common multiple (listing)Finding HCF and LCM by listing
Collecting like termsSimplifying expressions such as 3a + 2b + a
Expanding a single bracketMultiplying out 3(x + 4)
Substituting into expressions and formulaeIncluding negative numbers and squares
Solving one-step and two-step equationsUsing inverse operations
Continuing and describing sequencesTerm-to-term rules and sequence patterns
Plotting straight-line graphs from a tableMaking a table of values and drawing the line
Sharing in a ratioDividing an amount into given parts
Unitary method and simple direct proportionFinding the cost of one then scaling up
Best buysComparing value for money
Scale drawings and mapsUsing a scale such as 1 cm to 5 km
Angles on a line, around a point and vertically oppositeAngle facts and finding missing angles
Angles in triangles and quadrilateralsAngle sums of 180 and 360 degrees
Area of triangles and parallelogramsBase times height formulae
Circumference and area of a circleUsing pi, in terms of pi and as decimals
Volume of a cuboidLength times width times height
Nets and properties of 3D shapesFaces, edges, vertices and drawing nets
ReflectionReflecting shapes in mirror lines
TranslationMoving shapes using column vectors
Probability of a single eventProbability as a fraction, including the chance of an event not happening
Sample space diagramsListing all outcomes of two events
Mean from a listAdding and dividing
Two-way tablesCompleting and reading two-way tables
Reading pie chartsFinding frequencies from angles

Grade 4 40 topics · Foundation and Higher

Midpoint of a line segmentAveraging the x-coordinates and the y-coordinates of the two ends
Rounding to significant figuresRounding to 1, 2 or 3 significant figures
Mixed numbers and improper fractionsConverting between the two forms
Adding and subtracting mixed numbersFractions with whole-number parts
Multiplying fractionsMultiplying numerators and denominators
Prime factorisationWriting a number as a product of primes
HCF and LCM using prime factorsUsing prime factor decomposition
Writing numbers in standard formConverting large and small numbers to and from a x 10^n
Percentage increase and decreaseUsing multipliers such as 1.15 and 0.8
Simple interestInterest calculated on the original amount
Index laws with numbersMultiplying and dividing powers of the same base
Factorising into a single bracketTaking out a common factor
Solving equations with bracketsExpanding then solving
Solving equations with the unknown on both sidesCollecting terms on one side
Forming equations and formulae from wordsWriting an equation from a problem
Rearranging simple formulaeChanging the subject in one or two steps
Finding the nth term of a linear sequenceThe rule an + b
Gradient and y-intercept of a straight lineReading m and c from y = mx + c
Solving linear inequalities on a number lineSolving and showing the solution set
Plotting quadratic graphsTable of values and smooth curve
Distance-time graphsReading speed and stopping from the gradient
Algebraic index lawsSimplifying x^3 x x^4 and similar
Finding amounts from a ratio when one part is knownScaling a ratio to find the total or another part
Speed, distance and timeUsing the formula triangle and units
Exchange rates and currencyConverting between currencies
Percentage change in context (VAT, discounts, profit)Real-life percentage problems
Angles in parallel linesAlternate, corresponding and co-interior angles
Interior and exterior angles of polygonsAngle sums and regular polygons
BearingsThree-figure bearings and back bearings
Pythagoras' theorem: finding the hypotenuseSquaring, adding and square rooting
Volume of prismsCross-section area times length
Surface area of cuboids and prismsAdding the areas of every face
Area of compound shapesSplitting shapes into rectangles and triangles
Enlargement with a positive scale factorEnlarging from a centre
Constructions with compassesPerpendicular bisectors, angle bisectors and triangles
Congruent shapesSpotting congruent triangles and shapes
Relative frequencyEstimating probability from experiments
Expected number of outcomesProbability times number of trials
Venn diagrams and set notationSorting data and finding probabilities
Estimating the mean from a grouped frequency tableUsing class midpoints

Grade 5 30 topics · Foundation and Higher

Set notation: subsets and n(A)Subsets, n(A), the empty and universal sets, complements and sets described by a rule
Dividing fractionsMultiplying by the reciprocal
Reverse percentagesFinding the original amount
Repeated percentage change and compound interestUsing a multiplier raised to a power
Negative indicesEvaluating and simplifying powers like 2^-3
Calculating with numbers in standard formMultiplying, dividing, adding and subtracting
Error intervals from roundingWriting 2.5 <= x < 3.5 style intervals
Expanding double bracketsExpanding (x + a)(x + b)
Factorising quadratics (x^2 + bx + c)Finding two numbers that multiply and add
Solving quadratic equations by factorisingFactorising then setting each bracket to zero
Solving simultaneous equations with eliminationLinear pairs of equations
Solving inequalities with more than one stepIncluding negative multipliers on Higher
Solving equations with algebraic fractionsClearing denominators first
Graphs of cubic and reciprocal functionsRecognising and sketching their shapes
Interpreting real-life graphsConversion graphs, filling containers, taxi fares
Inverse proportionQuantities that decrease as the other increases
PressureForce divided by area
Using multipliers for percentage changeSingle-step multiplier method
Ratio problems with algebraForming equations from ratio statements
Converting units of area and volumeWhy cm^2 and cm^3 conversions are not the same as lengths
Trigonometry: finding a sideSOHCAHTOA in right-angled triangles
Trigonometry: finding an angleUsing inverse sin, cos and tan
Pythagoras' theorem: finding a shorter sideSubtracting squares
LociRegions defined by distance rules
Volume of cylindersPi r squared times height
Similar shapes: finding lengthsUsing scale factors
Enlargement with a fractional scale factorShapes getting smaller
Tree diagrams for independent eventsMultiplying along branches and adding between
Venn diagrams for probabilityUsing set notation to find probabilities
Comparing data using averages and spreadWriting conclusions in context

Grade 6 24 topics · Higher

Expanding three bracketsMultiplying two brackets first, then the third
Upper and lower boundsBounds of measurements and in calculations
Compound growth and decay problemsPopulation, depreciation and exponential change
Difference of two squaresFactorising x^2 - a^2
Quadratic formulaSolving ax^2 + bx + c = 0
Equation of a line through two pointsFinding m then c
Parallel lines equationsLines with equal gradients
Regions from inequalities on a graphShading regions given by lines
Function notationUsing f(x) and evaluating functions
Geometric and Fibonacci-type sequencesCommon ratio and recurrence rules
Roots and turning points of quadratic graphsSketching and reading from a graph
Gradient as a rate of changeInterpreting a gradient in context
Velocity-time graphsAcceleration and distance from area
Setting up proportion equationsy proportional to x, x^2 or 1/x with a constant
Arc length and sector areaFractions of a circle
Volume of cones, spheres and pyramidsUsing the formulae provided
Surface area of cones and spheresCurved surface area formulae
Combined transformationsDescribing a single transformation equivalent to two
Vectors: notation and journeysColumn vectors and adding vectors
Similar shapes: lengthsRatios of corresponding sides in harder problems
Conditional probability with tree diagramsWithout replacement
Cumulative frequency graphsMedian and quartiles
Interquartile rangeMeasuring spread
Recurring decimals as fractionsUsing algebra to convert

Grade 7 22 topics · Higher

Arithmetic series: nth term and suma + (n - 1)d and the sum of the first n terms
Domain and range of a functionf: x maps to notation, values to exclude from the domain and the set of outputs
Proportion with square rootsy proportional to the square root of x, or inversely proportional to it
Trigonometry with obtuse anglessin (180 - x) = sin x, cos (180 - x) = -cos x and finding both angles
Simplifying surdsWriting root 50 as 5 root 2
Fractional indicesPowers such as 8^(2/3)
Factorising quadratics (ax^2 + bx + c)When a is not 1
Completing the squareWriting x^2 + bx + c as (x + p)^2 + q
Perpendicular linesGradients that multiply to -1
Algebraic fractionsSimplifying, adding and multiplying
Rearranging formulae where the subject appears twiceFactorising after collecting terms
Algebraic proofConsecutive numbers, odd and even
Composite and inverse functionsfg(x) and f^-1(x)
Inverse proportion equationsy = k/x problems
Sine ruleNon-right-angled triangles
Cosine ruleFinding sides and angles
Area of a triangle using 1/2 ab sin CUsing two sides and the included angle
Circle theoremsAngles in a semicircle, same segment, centre, tangent
Similar shapes: areas and volumesSquared and cubed scale factors
Conditional probability with Venn diagramsSet notation and intersections
Histograms with unequal class widthsFrequency density
Mean from a histogramUsing midpoints and frequencies

Grade 8 11 topics · Higher

DifferentiationDifferentiating powers of x and finding the gradient of a curve at a point
Intersecting chordsAX times XB = CX times XD for chords crossing inside or outside a circle
Rationalising the denominatorRemoving surds from fractions
Expanding and simplifying surd expressionsMultiplying brackets containing roots
Algebraic fractions: adding, subtracting and solvingEquations with algebraic denominators
Simultaneous equations: one linear and one quadraticSubstituting the linear into the quadratic
Quadratic inequalitiesSolving and showing the solution set
Transformations of graphsf(x) + a, f(x + a), -f(x), f(-x)
Pythagoras and trigonometry in 3DRight-angled triangles inside solids
Vector proofsShowing lines are parallel or points are collinear
Graphs of sin, cos and tanShape, period and solving equations

Grade 9 9 topics · Higher

Stationary points and turning pointsSolving dy/dx = 0 and deciding maximum or minimum from the shape of the graph
Calculus in kinematicsVelocity and acceleration by differentiating displacement, and greatest values
Algebraic proof with quadratics and identitiesMulti-step proofs
Turning points by completing the squareSketching and finding the minimum
Probability with algebraUnknown probabilities leading to equations
Multi-step circle theorem reasoningChains of reasons in geometry problems
Inverse of a composite functionCombining f, g and their inverses
Problems on similar shapes with algebraArea and volume ratios leading to equations
Rate of change and areas under graphsInterpreting gradient and area in context

GCSE topics not on the International GCSE (22)

These are on the UK GCSE but not in the 4MA1 specification, so they are left off the Edexcel IGCSE list. Each reason names the specification section checked.

Plotting scatter graphs scatter graphs are not in 4MA1; section 6.1 lists pictograms, bar charts, pie charts and two-way tables (Foundation) and histograms and cumulative frequency (Higher).
Plans and elevations plans and elevations are not in 4MA1 (section 4.10 covers names, faces, edges, vertices, surface area and volume of solids).
Stem and leaf diagrams stem and leaf diagrams are not in 4MA1 (section 6.1).
Scatter graphs and the line of best fit scatter graphs and lines of best fit are not in 4MA1 (section 6.1).
Comparing distributions half of this sheet uses stem and leaf diagrams, which are not in 4MA1; comparing with the mean and range is still examined under section 6.2.
Product rule for counting the product rule for counting is not in 4MA1.
Trial and improvement numerical methods are not in 4MA1.
Frequency trees frequency trees are not in 4MA1 (section 6.1).
Sampling methods sampling is not in 4MA1.
Time series graphs time series graphs are not in 4MA1 (section 6.1).
Enlargement with a negative scale factor section 5.2 limits enlargements to a positive scale factor, including fractions.
Exact values of trigonometric ratios exact values of sin, cos and tan are not in section 4.8, and a calculator is allowed on every 4MA1 paper.
Congruent triangle proofs 4MA1 asks only that congruence means the same shape and size (section 4.2 F and G); formal proofs are not required (Higher 4.1 note).
Box plots box plots are not in 4MA1; Higher section 6.1 has histograms and cumulative frequency diagrams, and 6.2 the interquartile range.
nth term of a quadratic sequence section 3.1 covers arithmetic sequences only (nth term, and the sum of an arithmetic series at Higher).
Exponential graphs section 3.3 lists the graphs to know (linear, quadratic, cubic, reciprocal, sine, cosine and tangent); y = a to the power x is not among them.
Capture-recapture sampling sampling is not in 4MA1.
Iterative methods for solving equations iteration is not in 4MA1.
Gradient of a curve and area under a curve estimating the area under a curve with trapezia is not in 4MA1; the gradient of a curve is covered on the Differentiation sheet.
Equation of a circle centred at the origin the equation of a circle is not in 4MA1 (x squared + y squared = 25 appears only as one of a pair of simultaneous equations, section 2.7).
Equation of a tangent to a circle the equation of a circle and its tangent are not in 4MA1.
Exact value problems with surds and trigonometry exact trigonometric values are not in 4MA1; surds themselves are covered by the surd sheets.

Every question is original and written by Robinson Tuition; these are not Pearson Edexcel papers and are not endorsed by Pearson. UK GCSE boards: Edexcel GCSE maths worksheets · AQA GCSE maths worksheets · OCR GCSE maths worksheets.