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4579620112395Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics (1MA1)Higher tier diagnostic documentFor first teaching from September 2015Contents TOC \t "main-head,1,level-1-head,2,Head2,3,appendix,2" Introduction5Higher course overview6Higher units7IntroductionThis Higher tier diagnostic document is intended to support students in accessing the Higher tier of the new GCSE (9–1) Mathematics specification.This document lists the units in the Higher tier scheme of work, suggests questions to establish whether a student has the required prior knowledge, and provides a mapping of references to the Foundation scheme of work (and occasionally the Access to Foundation tier scheme of work) should the student need to refresh their understanding or develop a particular skill. Teachers can then turn to the relevant unit(s) in the Foundation scheme of work for additional support, including objectives, possible success criteria, opportunities for reasoning and problem-solving, and common misconceptions.For later Higher tier units, prior knowledge has sometimes not been covered in the Foundation scheme of work. In these instances, a reference to an earlier Higher tier unit is provided, along with diagnostic questions to check that this knowledge has been acquired.Our free support for the GCSE Mathematics specification (1MA1) can be found on the Edexcel mathematics website () and on the Emporium ().Unit Title1aCalculations, checking and roundingbIndices, roots, reciprocals and hierarchy of operationscFactors, multiples, primes, standard form and surds2aAlgebra: the basics, setting up, rearranging and solving equationsbSequences 3aAverages and rangebRepresenting and interpreting data and scatter graphs4aFractions and percentagesbRatio and proportion 5aPolygons, angles and parallel linesbPythagoras’ Theorem and trigonometry6aGraphs: the basics and real-life graphsbLinear graphs and coordinate geometrycQuadratic, cubic and other graphs7aPerimeter, area and circlesb3D forms and volume, cylinders, cones and spherescAccuracy and bounds8aTransformationsbConstructions, loci and bearings9aSolving quadratic and simultaneous equationsbInequalities10Probability11Multiplicative reasoning 12Similarity and congruence in 2D and 3D13aGraphs of trigonometric functionsbFurther trigonometry14aCollecting databCumulative frequency, box plots and histograms15Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics16aCircle theorems bCircle geometry17Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof18Vectors and geometric proof19aReciprocal and exponential graphs; Gradient and area under graphsbDirect and inverse proportionUNIT 1: Powers, decimals, HCF and LCM, positive and negative, roots, rounding, reciprocals, standard form, indices and surdsReturn to OverviewSUB-UNITSaCalculations, checking and roundingbIndices, roots, reciprocals and hierarchy of operationscFactors, multiples, primes, standard form and surdsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:understand place value, order integers and decimals and use the four operationsGiven the digits 2, 5, 7 and 9, make all the possible three-digit number with one decimal place and put them in order.Addition, subtraction, multiplication and division questions with up to three digits and one decimal placeFoundation Unit 1: Number, powers, decimals, HCF and LCM, roots and roundingfind integer complements to 10 and to 10046 + = 100Foundation Unit 1a: Integers and place valueSee also Access Unit 5: Addition and subtraction 2recall multiplication facts to 10 × 10Quick-fire multiplication and division questions. e.g.6 × 7 =8 × 9 =35 ÷ 5 =132 ÷ 12 =Foundation Unit 1a: Integers and place valuemultiply and divide by 10, 100 and 1000Multiply 24.75 by 10, 100, 1000Divide 72430 by 10, 100, 1000.Foundation Unit 1a: Integers and place valuerecall and identify squares, square roots, cubes and cube rootsWhich of these numbers is a square number? Which is a cube? Explain your answers.2, 5, 8, 12, 16, 20, 28Foundation Unit 1c: Indices, powers and rootsUNIT 2: Expressions, substituting into simple formulae, expanding and factorising, equations, sequences and inequalities, simple proofReturn to OverviewSUB-UNITSaAlgebra: the basics, setting up, rearranging and solving equationsbSequences PRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:use negative numbers with the four operations, recall and use the hierarchy of operations and understand inverse operations4 – (–6) =–6 × 3 =18 ÷ = –34 × 7 – 16 ÷ 2 = Foundation Unit 1a: Integers and place valueFoundation Unit 1c: Indices, powers and rootsdeal with decimals and negatives on a calculatorUse a calculator to calculate:–6.5 × –4.2 =Foundation Unit 1c: Indices, powers and rootsuse index laws numerically43 × 45 = 67 ÷ 62 = Foundation Unit 1c: Indices, powers and rootsUNIT 3: Averages and range, collecting data, representing dataReturn to OverviewSUB-UNITSaAverages and rangebRepresenting and interpreting data and scatter graphsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:read scales on graphs, draw circles, measure angles and plot coordinates in the first quadrantOn cm-squared paper, draw axes for x and y from 0 to 8. Plot these points: (1, 0), (2, 6), (7, 8). Join to make a triangle. Measure the angles.On the same coordinate grid, use a pair of compasses to draw a circle centre (5, 4), radius 4 cm. What are the coordinates of the point where the circle touches the x-axis?Foundation Unit 3a: Tables, charts and graphsFoundation Unit 3b: Pie chartsFoundation Unit 6a: Properties of shapes, parallel lines and angle factsFoundation Unit 15a: Plans and elevationsuse tally chartsWhat number does this represent?Write 24 in tallies.Foundation Unit 3: Drawing and interpreting graphs, tables and charts See also Access Unit 22: Data handling 2use inequality notationTake a pair of two-digit numbers and use < and > correctly. e.g. 46 and 78 or 62 and 35Foundation Unit 1a: Integers and place valuefind the midpoint of two numbersWhat number is in the middle of 3 and 9? 42 and 50?Foundation Unit 7: Statistics, sampling and the averages See also Access Unit 22: Data handling 2UNIT 4: Fractions, percentages, ratio and proportionReturn to OverviewSUB-UNITSaFractions and percentagesbRatio and proportion PRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:use the four operations of numberSee questions for Unit 1Foundation Unit 1a: Integers and place valuefind common factorsWhat factor is common to 8 and 12? To 14 and 35?Foundation Unit 1d: Factors, multiples and primesunderstand fractions as being ‘parts of a whole’Shade of ????????Shade of ??????Foundation Unit 4a: Fractions, decimals and percentages See also Access Unit 11: Fractions, decimals and percentages 2understand percentage as ‘number of parts per hundred’ and recognise that percentages are used in everyday lifeShannon got the questions in a test correct. What is as a percentage?In a sale, prices are reduced by 10%. What is 10% as a fraction?Foundation Unit 4b: PercentagesUNIT 5: Angles, polygons, parallel lines; Right-angled triangles: Pythagoras and trigonometryReturn to OverviewSUB-UNITSaPolygons, angles and parallel linesbPythagoras’ Theorem and trigonometryPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:rearrange simple formulae and equationsIf t = 6h – 3, write an expression for hFoundation Unit 2: Expressions, substituting into simple formulae, expanding and factorisingrecall basic angle factsOn squared paper, draw a right-angled triangle with one acute and one obtuse angle.Find the size of the angles marked x and y.30°x45°yFoundation Unit 6a: Properties of shapes, parallel lines and angle facts 6b - G3, G6understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents ≈ 0.3Which of the following give the most accurate answer? × 50 = 160.3 × 50 = 15Foundation Unit 4a: Fractions, decimals and percentagesUNIT 6: Real-life and algebraic linear graphs, quadratic and cubic graphs, the equation of a circle, plus rates of change and area under graphs made from straight linesReturn to OverviewSUB-UNITSaGraphs: the basics and real-life graphsbLinear graphs and coordinate geometrycQuadratic, cubic and other graphsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:identify coordinates of given points in the first quadrant or all four quadrantsDraw axes for values of x and y from –5 to +5.Plot the points (2, 3), (–3, 2) and (–2, –3), which form three corners of a square. What are the coordinates of the fourth corner?Foundation Unit 9a: Real-life graphsuse Pythagoras’ TheoremFind the length of the unknown side.12 cm5 cmx cmFoundation Unit 12: Right-angled triangles: Pythagoras and trigonometrycalculate the area of compound shapesFind the area of this shape.3 cm6 cm7 cmFoundation Unit 8: Perimeter, area and volumeuse and draw conversion graphs for common units5 miles ≈ 8 kilometresDraw axes with scales from 0 to 80 km on the horizontal axis and 0 to 50 miles on the vertical axis. Plot a line to show the relationship between miles and kilometres.Estimate 20 km in miles.Estimate 40 m in kilometres.Foundation Unit 9a: Real-life graphsuse function machines and inverse operations+5×2Find y when x = 3.x → → = y–4×3Find x when y = 11.x → → = yFoundation Unit 1a: Integers and place valueFoundation Unit 5a: Equations and inequalitiesUNIT 7: Perimeter, area and volume, plane shapes and prisms, circles, cylinders, spheres, cones; Accuracy and boundsReturn to OverviewSUB-UNITSaPerimeter, area and circlesb3D forms and volume, cylinders, cones and spherescAccuracy and boundsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:name and identify the properties of 3D formsSketch a cuboid, a cylinder and a square-based pyramid.How many faces does each shape have? How many vertices? How many edges?Foundation Unit 15a: Plans and elevationsfind perimeter and area by measuring lengths of sidesMeasure the sides of this rectangle. Find its perimeter and area.Foundation Unit 8: Perimeter, area and volumesubstitute numbers into an equation and give answers to an appropriate degree of accuracyUse the formula A = πr2 to find the area of this circle. Give your answer to an appropriate degree of accuracy.1.7 cmFoundation Unit 5a: Equations and inequalitiesFoundation Unit 1b: Decimalsunderstand the various metric unitsMatch each item to the most appropriate unit you could use to measure it.mmcapacity of an egg cupcmcapacity of a bathmlength of a pencil kmdiameter of a coin gmass of a horsekgjourney from London to Edinburghmlmass of a mousellength of a room Foundation Unit 8: Perimeter, area and volumeUNIT 8: Transformations; Constructions: triangles, nets, plan and elevation, loci, scale drawings and bearingsReturn to OverviewSUB-UNITSaTransformationsbConstructions, loci and bearingsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:recognise 2D shapesMake different shapes using two congruent right-angled triangles by matching equal sides, and name the shapes produced. (There are six: rectangle, kite, two parallelograms, two isosceles triangles.)Foundation Unit 6: Angles, polygons and parallel linesplot coordinates in four quadrantsSee questions for Unit 6.Foundation Unit 9a: Real-life graphsplot linear equations parallel to the coordinate axesOn cm-squared paper, draw axes for x and y from 0 to 8. Plot the lines x = 4 andy?=?–2.Foundation Unit 9b: Straight-line graphsUNIT 9: Algebra: Solving quadratic equations and inequalities, solving simultaneous equations algebraicallyReturn to OverviewSUB-UNITSaSolving quadratic and simultaneous equationsbInequalitiesPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:understand the ≥ and ≤ symbolsList the positive integers that satisfy the inequality 10?>?x?≥?6.List the integers that satisfy the inequality 10 < y ≤ 14.Foundation Unit 1a: Integers and place valuesubstitute into, solve and rearrange linear equationsWhat is the value of h in this formula, if C = 10?C = 5h + 20Foundation Unit 2b: Expressions and substitution into formulaefactorise simple quadratic expressionsFactorise x2 – x – 6,Foundation Unit 16a: Quadratic equations: expanding and factorisingrecognise the equation of a circleWhich of these equations is the equation of a circle?y = x2 + 16x2 + y2 = 52x + y = 25Higher Unit 6c: Quadratic, cubic and other graphsUNIT 10: ProbabilityReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:distinguish between events which are impossible, unlikely, even chance, likely, and certain to occurMatch to events to how likely they are to occur.1Christmas will fall on 25 December this year.2The sun will rise at midnight tonight.3You will score an even number if you roll an ordinary, fair dice.4The next person you meet likes chocolate.5If you buy a lottery ticket, you will win the jackpot.A ImpossibleB UnlikelyC Even chanceD LikelyE CertainFoundation Unit 13: Probabilityunderstand that a probability is a number between 0 and 1 and mark events and/or probabilities on a probability scale of 0 to 1A bag contains 20 marbles. Tessa picks a marble at random.Mark these probabilities on the number line. P(blue) = P(red) = P(green) = P(pink) = P(black) = 0P(marble) = 101Foundation Unit 13: Probabilityadd and multiply fractions and decimals + = × = 0.35 + 1.7 =0.2 × 0.6 = Foundation Unit 4a: Fractions, decimals and percentagesexpress one number as a fraction of another numberWhat is 15 as a fraction of 25?Foundation Unit 4a: Fractions, decimals and percentagesUNIT 11: Multiplicative reasoning: direct and inverse proportion, relating to graph form for direct, compound measures, repeated proportional changeReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:find a percentage of an amount and relate percentages to decimalsWhat is 45% of 300?What is the decimal equivalent of 6%?Foundation Unit 4b: Fractions and percentagesrearrange equations and use these to solve problemsA square has sides of d + 3. A rectangle has sides of 3d + 1 and d – 3. They have the same length perimeter. Find d.Foundation Unit 5a: Equations and inequalitiesunderstand speed = distance/time, density = mass/volumeA car travels 70 miles in 2 hours. What is its average speed?Cobalt has a density of 8.9 gm/cm3. What is the mass of a cm cube of cobalt?Foundation Unit 14: Multiplicative reasoningUNIT 12: Similarity and congruence in 2D and 3DReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:recognise and enlarge shapes and calculate scale factorsEnlarge this triangle by a scale factor of 2.Shape B is an enlargement of shape A. What is the scale factor?BAFoundation Unit 10: Transformationscalculate area and volume in various metric measuresWhat is the area of a rectangle that measures 4.5 m by 6 m?What is the volume of a cuboid that measures 2 mm by 5 mm by 7 mm?Foundation Unit 8: Perimeter, area and volumemeasure lines and angles and use compasses, ruler and protractor to construct standard constructionsUse compasses and a ruler to construct this triangle accurately.6 cm40°35°xyaMeasure the length of sides x and y and the size of angle a.Foundation Unit 3b: Pie charts Foundation Unit 6a: Properties of shapes, parallel lines and angle factsFoundation Unit 8: Perimeter, area and volumeFoundation Unit 15b: Constructions, loci and bearingsUNIT 13: Sine and cosine rules, ab sin C, trigonometry and Pythagoras’ Theorem in 3D, trigonometric graphs, and accuracy and boundsReturn to OverviewSUB-UNITSaGraphs of trigonometric functionsbFurther trigonometryPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:use axes and coordinates to specify points in all four quadrantsSee questions for Unit 6.Foundation Unit 9a: Real-life graphsrecall and apply Pythagoras’ Theorem and trigonometric ratiosSee questions for Unit 6.Use the cosine rule to find the value of a.a cm32°11 cmFoundation Unit 12: Right-angled triangles: Pythagoras and trigonometrysubstitute into formulaeSee questions for Unit 9.Foundation Unit 5a: Equations and inequalitiesUNIT 14: Statistics and sampling, cumulative frequency and histogramsReturn to OverviewSUB-UNITSaCollecting databCumulative frequency, box plots and histogramsPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:understand the different types of data: discrete/continuousSort the following data into two groups: discrete and continuous.AHeights of 10 studentsBNumber of pets owned by 30 studentsCFavourite colours of 15 studentsDMass of 20 applesFoundation Unit 3a: Tables, charts and graphsuse inequality notation?See questions for Unit 3.Foundation Unit 1a: Integers and place valuemultiply a fraction by a numberWhat is of 48?Foundation Unit 4a: Fractions, decimals and percentagesunderstand the data handling cyclePut these four steps in the correct order.AAnalyse the data.BDraw ollect data.DSpecify the problem and plan an investigation.Foundation Unit 7: Statistics, sampling and the averagesUNIT 15: Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadraticsReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:solve quadratics and linear equationsSolve these equations.3(x – 6) = 6x2 – 3x – 28 = 0Foundation Unit 5a: Equations and inequalities Foundation Unit 16: Algebra: quadratic equations and graphssolve simultaneous equations algebraicallySolve these simultaneous equations:3x – y = 232x + y = 7Foundation Unit 20: Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equationsUNIT 16: Circle theorems and circle geometryReturn to OverviewSUB-UNITSaCircle theorems bCircle geometryPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:draw circles with compasses?See questions for Unit 3.Foundation Unit 15a: Plans and elevationsrecall the words, centre, radius, diameter and circumferenceUse the following words to fill in the gaps.centre circumference diameter radiusThe ___ of a circle is a straight line from the ___ to the ___. It is half the length of the ___. Foundation Unit 17: Circles, cylinders, cones and spheresrecall the relationship of the gradient between two perpendicular linesLine A has gradient 2.Line B is perpendicular to Line A.Write down the gradient of Line B.Higher Unit 6b: Linear graphs and coordinate geometryfind the equation of the straight line, given a gradient and a coordinateFind the equation of the line with gradient 3 that passes through the point (2, 4).Foundation Unit 20: Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equationsUNIT 17: Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proofReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:simplify surds?Simplify .Higher Unit 1c: Factors, multiples, primes, standard form and surdsuse negative numbers with all four operations?See questions for Unit 2.Foundation Unit 1a: Integers and place valuerecall and use the hierarchy of operations?See questions for Unit 2.Foundation Unit 1a: Integers and place valueFoundation Unit 1c: Indices, powers and rootsUNIT 18: Vectors and geometric proofReturn to OverviewPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:use vectors to describe translationsWrite as a column vector the transformation that maps shape A onto shape B.Foundation Unit 10: Transformationsuse Pythagoras’ Theorem?See questions for Unit 6.Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometryidentify properties of triangles and quadrilaterals?See questions for Unit 8.Foundation Unit 6a: Properties of shapes, parallel lines and angle factsUNIT 19: Direct and indirect proportion: using statements of proportionality, reciprocal and exponential graphs, rates of change in graphs, functions, transformations of graphsReturn to OverviewSUB-UNITSaReciprocal and exponential graphs; Gradient and area under graphsbDirect and inverse proportionPRIOR KNOWLEDGEStudents will be able to:Possible diagnostic questionsStudents will need to work on the objectives covered in:draw linear and quadratic graphsSketch the following graphs.y = 2x – 3y = x2Foundation Unit 9: Real-life and algebraic linear graphsFoundation Unit 16b: Quadratic equations: graphscalculate the gradient of a linear function between two pointsA line passes through the points (1, 2) and (7, 5).Find the gradient of the line.Foundation Unit 9a: Real-life graphsrecall transformations of trigonometric functionsSketch the graph of y = sin x.On the same axes, sketch the graph of y = 2 sin x.Higher Unit 13a: Graphs of trigonometric functionswrite statements of direct proportion and form an equation to find valuesa is directly proportional to b.a = 18 when b = 1.5.Form an equation involving a and b and solve it to find the value of a when b = 7.Foundation Unit 11b: Proportion444886199213Issue 1 – April 2016For more information on Edexcel and BTEC qualifications pleasevisit our websites: and btec.co.ukEdexcel is a registered trademark of Pearson Education LimitedPearson Education Limited. 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