# Maths Year 10 Higher Tier Learning Map

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When?Content DomainTopicReferenceLearning ObjectivesHegarty Clip
Year 9 Half Term 1NumberCalculations, checking and rounding1a-1Multiply and divide decimals 48 - 51
1a-2Four operations with negative numbers41 - 43
1a-3Related calculations135, 136
1a-4Use the product rule for counting 671 - 673
1a-5Round to the nearest integer, to a given number of decimal places and to a given number of significant figures56, 130
1a-6Estimate complex calculations131
NumberIndices, roots, reciprocals and order of operations1b-1Recognise powers of 2, 3, 4, 599 - 101
1b-2Solve problems using index laws105 - 107
1b-3Find the value of calculations using negative indices104
1b-4Find the value of calculations using fractional indices108 - 110
1b-5Use the order of operations24, 44, 120, 150
NumberFactors, multiples and primes1c-1Identify factors, multiples and prime numbers27, 28, 33
1c-2Write positive integers as a product of prime factors29,30
1c-3Find the LCM and HCF of two numbers by listing and using prime factors.31 - 34
1c-4Solve problems using HCF and LCM36
NumberStandard form and surds1d-1Convert large and small numbers into standard form and vice versa122 - 124
1d-2Add and subtract numbers in standard form127
1d-3Multiply and divide numbers in standard form125, 126
1d-4Use a calculator to perform calculations in standard form128
1d-5Understand surd notation and simplify surd expressions involving squares 111, 112, 115
1d-6Multiplication and division of surds113, 114
1d-7Brackets involving surds116, 117
Year 9 Half Term 2AlgebraAlgebra - the basics2a-1Know the difference between a term, expression, equation, formula and an identity154
2a-2Writing algebraic expressions151 - 153
2a-3Simplify and manipulate algebraic expressions by collecting like terms156, 157
2a-4Simplify and manipulate algebraic expressions by multiplying and cancelling terms158, 159
2a-5Simplify and manipulate algebraic expressions involving indices173 - 175
2a-6Substitute numerical values into formulae and expressions, including scientific formulae780 - 789
2a-7Expand single and double brackets160 - 165
2a-8Simplify expressions by factorising170, 171
2a-9Factorise quadratic expressions including using the difference of two squares223 - 227
AlgebraSetting up, rearranging and solving equations2b-1Solve linear equations with one unknown178 - 183
2b-2Solve linear equations with unknowns on both sides184 - 186
2b-3Set up and solve linear equations in context188
2b-4Change the subject of a formula280 - 284
2b-5Change the subject of a formula in cases where you need to factorise285, 286
2b-6Use iteration to find approximate solutions to equations322
AlgebraSequences2c-1Recognise simple sequences including triangular, square and cube numbers and Fibonacci sequences261, 263
2c-2Generate specific terms in a sequence using the position-to-term rule and term-to-term rule including from pictures196 - 198
2c-3Identify and continue a quadratic sequence and use the nth term to generate terms247, 249
2c-4Find the nth term of quadratic sequences248
2c-5Recognise and use simple geometric sequences 264
Year 9 Half Term 3Statistics and ProbabilityAverages and Range3a-1Design and use two-way tables for discrete and grouped data 422 - 424
3a-2Sort, classify and tabulate data, both discrete and continuous quantitative data, and qualitative data401 - 403
3a-3Calculate mean and range, find median and mode from small data set 404 - 410
3a-4Recognise the advantages and disadvantages between measures of average 413
3a-5Compare the mean and range of two distributions, or median or mode as appropriate
3a-6Interpret and find the median, mode and range from stem and leaf diagrams430 - 433
3a-7Interpret and find the median, mean and range from a (discrete) frequency table414 - 417
3a-8Interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table418
Statistics and ProbabilityRepresenting and interpreting data3b-1Produce and interpret dual and composite bar charts 425
3b-2Produce and interpret pie charts427 - 429
3b-3Produce and interpret frequency polygons for grouped data441
3b-4Produce frequency diagrams for grouped discrete data402, 403
3b-5Construct and interpret time–series graphs, comment on trends450 - 452
Statistics and ProbabilityScatter Graphs3c-1Draw and interpret scatter graphs453
3c-2Identify outliers and ignore them on scatter graphs453
3c-3Draw the line of best fit on a scatter diagram by eye and use the line of best fit to make predictions454
3c-4Distinguish between positive, negative and no correlation using lines of best fit453, 454
3c-5Use a line of best fit to predict values of a variable given values of the other variable453, 454
Year 9 Half Term 4NumberFractions4a-1Write a fraction in its simplest form and find equivalent fractions59, 61
4a-2Order fractions, by using a common denominator60
4a-3Convert between mixed numbers and improper fractions63, 64
4a-4Add and subtract fractions, including mixed numbers65, 66
4a-5Multiply and divide an integer by a fraction67
4a-6Understand and use reciprocals multiplicative inverses71, 72
4a-7Divide fractions by a whole number and fractions70
4a-7Find fraction of a quantity, including reverse fractions77 - 79
4a-8Convert between fractions and decimals, including recurring decimal73, 74, 55, 53, 54
NumberPercentages4b-1Convert between fractions, decimals and percentages 149
4b-2Express a given number as a percentage of another number, including where the percentage is greater than 100%75, 76
4b-4Find a percentage of a quantity without a calculator84, 85
4b-5Find the new amount after a percentage increase or decrease 88
4b-6Use percentages in real-life situations
• Price after VAT (not price before VAT);
• Value of profit or loss;
• Simple interest;
• Income tax calculations
93, 759, 760
4b-7Find a percentage of a quantity using a multiplier 87
4b-8Use a multiplier to increase or decrease by a percentage in any scenario where percentages are used 89, 90
4b-9Find the original amount given the final amount after a percentage increase or decrease (reverse percentages), including VAT 96
4b-10Understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents, and choose fractions, decimals or percentages appropriately for calculations
Number Ratio and proportion4c-1Write ratios in their simplest form329
4c-2Write/interpret a ratio to describe a situation328
4c-3Write a ratio as a fraction330
4c-4Write ratios in form 1 : m or m : 1331
4c-5Share a quantity in a given ratio including three-part ratios332
4c-6Use a ratio to find one quantity when the other is known333, 334
4c-7Use a ratio to convert between measures and currencies707
4c-8Use a ratio to compare a scale model to real-life object and solve problems involving scale diagrams.864 - 871
4c-9Understand direct proportion and use this to scale up recipes 339, 340, 739 - 742
Year 9 Half Term 5Geometry and MeasurePolygons, angles and parallel lines5a-1Distinguish between scalene, equilateral, isosceles and right-angled triangles823
5a-2Find missing angles in a triangle using the angle sum in a triangle and the properties of an special triangles485 - 487
5a-3Recall the properties and definitions of special types of quadrilaterals824 - 826
5a-4Understand and use the angle properties of quadrilaterals and the fact that the angle sum of a quadrilateral is 360°560
5a-5Understand and use the angle properties of parallel lines and find missing angles using the properties of corresponding and alternate angles, giving reasons481 - 483
5a-6Solve problems involving interior and exterior angles of polygons, including algebraic problems561 - 565
Geometry and MeasurePythagoras theorem and trigonometry5b-1Understand, recall and use Pythagoras’ Theorem in 2D to find the hypotenuse or a shorter side in a right angled triangle, giving answers in surd form where appropriate497 - 499
5b-2Given 3 sides of a triangle, justify if it is right-angled or not497
5b-3Apply Pythagoras’ Theorem to solve various problems, including area problems500 - 504
5b-4Apply Pythagoras’ Theorem with a triangle drawn on a coordinate grid including calculating the length of a line segment AB given pairs of points
5b-5Understand and recall the trigonometric ratios sine, cosine and tan508
5b-6Use trigonometry to find missing sides of a right angled triangle509, 510
5b-7Use trigonometry to find missing angles in a right angled triangle511, 512
5b-8Use the trigonometric ratios to solve 2D problems513, 514
5b-9Find angles of elevation and depression515
5b-10Know the exact values for trigonometry845
Year 9 Half Term 6AlgebraGraphs, the basics and real life graphs6a-1Draw, label and scale axes and identify points with given coordinates199
6a-2Find the coordinates of the midpoint of a line segment from coordinates 200
6a-3Draw and interpret straight-line graphs for real-life situations, including ready reckoner graphs, conversion graphs, fuel bills, fixed charge and cost per item894, 895
6a-4Draw and interpret distance–time graphs 874 - 879
6a-5Draw and interpret velocity–time graphs 880 - 886
AlgebraLinear graphs and coordinate geometry6b-1Plot and draw graphs of y = a, x = a, y = x and y = –x205
6b-2Plot and draw graphs of straight lines of the form y = mx + c using a table of values and recognise that equations of the form y = mx + c correspond to straight-line graphs206 - 209
6b-3Identify and interpret gradient from an equation y = mx + c. Sketch a graph of a linear function, using the gradient and y-intercept210
6b-4Identify parallel lines from their equations214
6b-5Plot and draw graphs of straight lines in the form
ax + by = c
280, 281
6b-6Find the equation of a straight line from a graph210 - 211
6b-7Find the equation of the line through one point with a given gradient212
6b-8Find the equation of the line through two given points213
6b-9Explore the gradients of parallel lines and lines perpendicular to each other214 - 216
AlgebraQuadratic, cubic and other graphs6c-1Generate points and plot graphs of simple quadratic functions251
6c-2Identify and interpret roots, intercepts and turning points of quadratic graphs252 - 255
6c-3Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function 323
6c-4Interpret graphs of quadratic functions from real-life problems
6c-5Draw and interpret graphs of simple cubic functions using tables of values 298, 299
6c-6Draw graphs of the reciprocal function300, 301
6c-7Draw circles, centre the origin778, 779
6c-8Recognise a linear, quadratic, cubic, reciprocal and circle graph from its shape
Year 10 Half Term 1Geometry and MeasurePerimeter, area and circles7a-1Recall and use the formulae for the area of a triangle, rectangle, trapezium and parallelogram554, 556, 557, 559
7a-2Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms 555, 558
7a-3Find the perimeter of a rectangle, trapezium, parallelograms and compound shapes made from combinations of the above549 - 552
7a-4Recall the definition of a circle and name and draw parts of a circle592
7a-5Find the circumference of a circle, semi-circle and quarter circles, including giving your answers in terms of π534 - 538
7a-6Find the area of a circle, semi-circle and quarter circles, including giving your answers in terms of π539 - 543
7a-7Calculate arc lengths, angles and areas of sectors of circles544 - 547
Geometry and Measure3D forms and volume, cylinders, cones and spheres.7b-1Find the surface area of prisms using the formulae for triangles and rectangles584, 585
7b-2Draw sketches of 3D solids832
7b-3Find the volume of a prism570, 571
7b-4Convert between metric volume measures including volume and capacity668, 669, 702 - 704
7b-5Find the volume of a cylinder 572 - 575
7b-6Find the surface area of a cylinder 586
7b-7Recall and use the formula for volume of pyramid 579
7b-8Find the surface area of a pyramid
7b-9Use the formulae for volume and surface area of spheres580, 581, 588
7b-10Use the formulae for volume and surface area of cones576, 577, 587
7b-11Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones578,
7b-12Find the surface area and volumes of compound solids constructed from cubes, cuboids, cones, pyramids, spheres, hemispheres, cylinders 582, 583
Geometry and MeasureAccuracy and bounds in context7c-1Calculate the upper and lowers bounds of numbers given to varying degrees of accuracy 137 - 139
7c-2Find the upper and lower bounds of calculations involving perimeters, areas and volumes of 2D and 3D shapes
7c-3Use inequality notation to specify an error interval due to truncation or rounding774 - 777
Year 10 Half Term 2Geometry and MeasureTransformations8a-1Rotate a shape about the origin or any other point on a coordinate grid648, 649
8a-2Describe a rotation fully using the angle, direction of turn, and centre653, 654
8a-3Translate a given shape by a vector637, 638
8a-4Use column vectors to describe translations650
8a-5Transform 2D shapes using single reflections 639 - 641
8a-6Describe reflections on a coordinate grid652
8a-7Enlarge a shape using a scale factor only
8a-8Enlarge a given shape using positive, negative and fractional scale factors and a centre of enlargement642 - 647
8a-9Describe an enlargement using the scale factor and centre of enlargement651
8a-10Find areas after enlargement and compare with before enlargement, to deduce multiplicative relationship (area scale factor)615 - 617
8a-11Describe and transform 2D shapes using combined rotations, reflections, translations, or enlargements656 - 657
8a-12Describe the changes and invariance achieved by combinations of rotations, reflections and translations655
Geometry and MeasureConstructions, Loci and Bearings8b-1Understand and draw front and side elevations and plans of shapes made from simple solids837 - 840
8b-2Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid841 - 844
8b-3Estimate lengths using a scale diagram864 - 866
8b-4Make an accurate scale drawing from a diagram867, 868
8b-5Calculate bearings and solve bearings problems, including on scaled maps, and find/mark and measure bearings 492 - 496, 869
8b-6Use the standard ruler and compass constructions (bisect a given angle, construct a perpendicular to a given line from/at a given point, construct angles, perpendicular bisector of a line segment)659 - 669
8b-7Use constructions to solve a range of loci problems including with bearings674 - 679
AlgebraSolving quadratics and Simultaneous equations9a-1Factorise quadratic expressions in the form ax² + bx + c225 - 228
9a-2Solve quadratics by factorising230 - 233
9a-3Write quadratic expressions in vertex form (complete the square)235 - 237
9a-4Solve quadratic equations by completing the square238, 239
9a-5Set up and solve quadratic equations245
9a-6Solve quadratic equations by using the quadratic formula241 - 242
9a-7Find the exact solutions of two linear simultaneous equations in two unknowns using elimination190 - 193
9a-8Find the exact solutions of two linear simultaneous equations in two unknowns by substitution194
9a-9Solve simultaneous equations involving quadratics and circles.246, 259
Year 10 Half Term 3AlgebraInequalities9b-1Show inequalities on number lines265, 266
9b-2Write down whole number values that satisfy an inequality267
9b-3Solve simple linear inequalities in one variable, and represent the solution set on a number line269 - 271
9b-4Solve double linear inequalities in one variable, and represent the solution set on a number line272
Statistics and ProbabilityProbability10a-1Find the probability of an event happening using theoretical probability. Write the probabilities in fractions, decimals and percentages350 - 352
10a-2Find the probability of an event not happening353
10a-3List all outcomes for single events systematically670
10a-4Work out probabilities from two-way tables422, 423
10a-5Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1354
10a-6Find the probability of an event happening using relative frequency356
10a-7Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities355
10a-8Use and draw sample space diagrams358, 359
10a-9Use tree diagrams to calculate the probability of two independent events360 - 363
10a-10Use tree diagrams to calculate the probability of two dependent events364 - 367
10a-11Work out probabilities from Venn diagrams to represent real-life situations379, 380
10a-12Use set notation, including union and intersection370 - 378
10a-13Work out probabilities from Venn diagrams to represent abstract’ sets of numbers/values383 - 391
Year 10 Half Term 4Ratio and ProportionMultiplicative reasoning11a-1Understand what is meant by direct proportion339, 340
11a-2Solve word problems involving direct proportion, including using the unitary method, best buys and recipe problems341, 763 - 770, 739 - 742
11a-3Understand inverse proportion and solve word problems involving inverse proportion342
11a-4Work out which product is the better buy
11a-5Scale up recipes739 - 742
11a-6Convert between currencies707, 708
11a-7Solve simple interest problems93
11a-8Work out the multiplier for repeated proportional change as a single decimal number91, 92
11a-9Solve problems involving repeated percentage change. Including compound percentage problems94, 95
11a-10Perform calculations involving speed716 - 724
11a-11Perform calculations involving density725 - 733
11a-12Perform calculations involving pressure734 - 737
11a-13Calculate an unknown quantity from quantities that vary in direct or inverse proportion339 - 342
11a-14Recognise when values are in direct or inverse proportion by reference to the graph form348
Geometry and MeasureSimilarity and Congruence in 3D12a-1Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and to verify standard ruler and pair of compasses constructions682
12a-2Solve angle problems by first proving congruence684 - 689
12a-3Understand similarity of triangles and of other plane shapes, and use this to make geometric inferences608 - 610
12a-4Solve problems to find missing lengths in similar shapes610 - 614
12a-6Write the lengths, areas and volumes of two shapes as ratios in their simplest form
12a-7Know the relationships between linear, area and volume scale factors of mathematically similar shapes and solids615 - 621
12a-10Solve problems involving frustums of cones where you have to find missing lengths first using similar triangles578
Geometry and MeasureGraphs of trigonometric functions13a-1Recognise, sketch and interpret graphs of the trigonometric functions303 - 306
13a-2Know exact trig values and use these to solve non-calculator trigonometry problems845 - 853
13a-3Apply to the graph of y = f(x) the transformations y = –f(x), y = f(–x) for sine, cosine and tan functions f(x)311, 312
13a-4Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(x + a) for sine, cosine and tan functions f(x)307, 308
Year 10 Half Term 5Geometry and MeasureFurther Trigonometry13b-1Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle516 - 519
13b-2Use the sine rule to find missing lengths and angles520 - 525
13b-3Use the cosine rule to find missing lengths and angles526 - 530
13b-4Solve problems in 2D using the sine and cosine rules531 - 533
13b-5Use Pythagoras to solve 3D problems505 - 507
13b-6Use trigonometry to solve 3D problems854 - 862
13b-7Use the sine and cosine rules to solve 3D problems863
Statistics and ProbabilityCollecting data14a-1Distinguish between a census and a sample and understand how bias might arise394, 395
14a-2Carry out a stratified random sample396 - 398
14a-3Write questions to eliminate bias, and understand how the timing and location of a survey can ensure a sample is representative399 - 400
14a-4Solve problems involving capture re-capture872, 873
Statistics and ProbabilityCumulative frequency, box blots and histograms14b-1Construct and interpret cumulative frequency tables437 - 439
14b-2Compare the mean and range of two distributions, or median and interquartile range411, 412
14b-3Draw and interpret box plots to find median, quartiles, range and interquartile range and draw conclusions440, 434 - 436
14b-4Interpret histograms from class intervals with unequal width442, 443
14b-5Complete a grouped frequency table from a histogram.444
14b-6Use frequency density to draw a histogram445 - 449
14b-7Estimate the mean and median from a histogram
Year 10 Half Term 6AlgebraQuadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics15a-1Sketch a graph of a quadratic function, by factorising or by using the formula, identifying roots, y-intercept and turning point by completing the square257
15a-2Be able to identify from a graph if a quadratic equation has any real roots258
15a-3Find approximate solutions to quadratic equations using a graph259, 260
15a-4Expand the product of more than two linear expressions166
15a-5Solve simultaneous equations graphically, including quadratics and circles218, 219, 259
15a-6Solve quadratic inequalities by factorising and sketching the graph to find critical values277
15a-7Solve linear inequalities in two variables graphically and show the solution set of several inequalities in two variables on a graph273 - 276
15a-8Use iteration with simple converging sequences to find solutions to equations322
Geometry and MeasureCircle Theorems16a-1Recall the definition of a circle and draw parts of a circle, including sector, tangent, chord, segment592
16a-2Understand and use the following circle theorems:
• the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference;
• the angle in a semicircle is a right angle;
• the perpendicular from the centre of a circle to a chord bisects the chord;
• angles in the same segment are equal;
• alternate segment theorem;
• opposite angles of a cyclic quadrilateral sum to 180°;
• the tangent at any point on a circle is perpendicular to the radius at that point
594 - 602
16a-3Prove the above circle theorems816 - 820
16a-4Solve problems involving circle theorems595, 603 - 606
Geometry and MeasureCircle Geometry16b-1Find the equation of a tangent to a circle at a given point320
16b-2Recognise and construct the graph of a circle using x² + y² = r² for radius r centred at the origin of coordinates
Year 11AlgebraChanging the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof17a-1Rationalise the denominator involving surds118, 119
17a-2Multiply and divide algebraic fractions172
17a-3Simplify algebraic fractions (involving quadratics)229
17a-4Solve arising from algebraic fraction equations (including quadratics)187, 244
17a-5Change the subject of a formula, including cases where the subject occurs on both sides of the formula, or where a power of the subject appears283 - 286
17a-6Change the subject of a formula such as 1/f = 1/u + 1/v , where all variables are in the denominators
17a-7Solve ‘Show that’ and proof questions using consecutive integers (n, n + 1), squares a², b², even numbers 2n, odd numbers 2n +1325 - 327
17a-8Understand and use function notation288, 289
17a-9Find an expression for the output of composite functions293, 294
17a-10Find an expression for the output of inverse functions295, 296
17a-11Solve complex problems with functions297
AlgebraVectors and algebraic proof18a-1Understand and use vector notation622, 623
18a-4Calculate the sum of two vectors, the difference of two vectors and a scalar multiple of a vector using column vectors and represent these pictorially624 - 626
18a-5Find the magnitude (length) of a vector using Pythagoras’ Theorem627
18a-7Solve geometric problems involving vectors628 - 636
AlgebraReciprocal and exponential graphs; Gradient and area under graphs19a-1Recognise, sketch and interpret graphs of the reciprocal function300, 301
19a-2Recognise, sketch and interpret graphs of exponential functions302
19a-3Use calculators to explore exponential growth and decay 796 - 799
19a-4Recognise, sketch and interpret graphs of exponential functions800 - 803
19a-5Set up, solve and interpret the answers in growth and decay problems804 - 811
19a-6Apply to the graph of y = f(x) the transformations y = –f(x), y = f(–x) for linear, quadratic, cubic functions 311, 312
19a-7Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(x + a)
for linear, quadratic, cubic functions
307, 308
19a-8Estimate area under a quadratic or other graph by dividing it into trapezia891 - 893
19a-9Calculate the gradient at a point on a curve by drawing a tangent.889
19a-10Interpret the gradient of non-linear graph in real-life contexts888, 890
AlgebraDirect and inverse proportion19b-1Recognise and interpret graphs showing direct and inverse proportion348
19b-2Use y = kx to solve direct proportion problems343 - 345
19b-3Use y = k/x to solve inverse proportion problems346, 347