OCR GCSE maths worksheets by grade
215 free worksheets for OCR GCSE maths, from grade 1 to grade 9, with 3,007 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.
OCR GCSE Mathematics (J560) is sat as three papers of 1 hour 30 minutes, 100 marks each. Foundation sits Papers 1, 2 and 3 and Higher sits Papers 4, 5 and 6; Papers 2 and 5 are non-calculator. Foundation covers grades 1 to 5 and Higher covers grades 4 to 9.
OCR papers carry more marks in the same time than the other boards, so practise working at pace: time yourself on a worksheet, then mark it with the answers sheet. Grades 4 and 5 appear on both tiers, which is why those topics show for Foundation and Higher.
All three exam boards teach the same GCSE maths content, set by the Department for Education, so every topic below is on the OCR specification. The difference is in the style of the papers, not in what you need to know. The same sheets work for Edexcel and AQA too.
Open a topic to answer the questions online for an instant score, or print it for class or homework. Free to use, print and share, with no account needed.
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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 35 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
- Plotting scatter graphsDrawing points and describing correlation
Grade 4 43 topics · Foundation and Higher
- 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
- Plans and elevationsDrawing a solid from the front, side and top
- 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
- Stem and leaf diagramsDrawing, reading and finding the median
- Scatter graphs and the line of best fitDrawing a line and making predictions
- Comparing distributionsUsing an average and the range
Grade 5 34 topics · Foundation and Higher
- 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
- Product rule for countingCounting combinations by multiplying
- 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
- Trial and improvementSolving equations by successive approximation
- 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
- Frequency treesOrganising two-stage data
- Comparing data using averages and spreadWriting conclusions in context
- Sampling methodsRandom, stratified and bias
- Time series graphsDescribing trends and seasonality
Grade 6 27 topics · Higher
- 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
- Enlargement with a negative scale factorInverted enlargements
- Combined transformationsDescribing a single transformation equivalent to two
- Exact values of trigonometric ratiossin, cos and tan of 0, 30, 45, 60 and 90 degrees
- Congruent triangle proofsSSS, SAS, ASA and RHS
- 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
- Box plotsDrawing and comparing distributions
- Interquartile rangeMeasuring spread
- Recurring decimals as fractionsUsing algebra to convert
Grade 7 21 topics · Higher
- 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
- nth term of a quadratic sequenceUsing second differences
- Algebraic proofConsecutive numbers, odd and even
- Exponential graphsRecognising y = a^x
- 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
- Capture-recapture samplingEstimating population size
- Mean from a histogramUsing midpoints and frequencies
Grade 8 12 topics · Higher
- 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)
- Iterative methods for solving equationsUsing x(n+1) = g(x(n))
- Gradient of a curve and area under a curveTangents and trapezium estimates
- 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
- Equation of a circle centred at the originx^2 + y^2 = r^2
Grade 9 9 topics · Higher
- Algebraic proof with quadratics and identitiesMulti-step proofs
- Equation of a tangent to a circleRadius gradient then perpendicular gradient
- Turning points by completing the squareSketching and finding the minimum
- Probability with algebraUnknown probabilities leading to equations
- Exact value problems with surds and trigonometryAnswers kept as roots or fractions
- 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
Every question is original and written by Robinson Tuition; these are not OCR papers and are not endorsed by OCR. Other boards: Edexcel GCSE maths worksheets · AQA GCSE maths worksheets.