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| When? | Content Domain | Topic | Reference | Learning Objectives | Hegarty Clip |
|---|---|---|---|---|---|
| Year 9 Half Term 1 | Number | Calculations, checking and rounding | 1a-1 | Multiply and divide decimals | 48 - 51 |
| 1a-2 | Four operations with negative numbers | 41 - 43 | |||
| 1a-3 | Related calculations | 135, 136 | |||
| 1a-4 | Use the product rule for counting | 671 - 673 | |||
| 1a-5 | Round to the nearest integer, to a given number of decimal places and to a given number of significant figures | 56, 130 | |||
| 1a-6 | Estimate complex calculations | 131 | |||
| Number | Indices, roots, reciprocals and order of operations | 1b-1 | Recognise powers of 2, 3, 4, 5 | 99 - 101 | |
| 1b-2 | Solve problems using index laws | 105 - 107 | |||
| 1b-3 | Find the value of calculations using negative indices | 104 | |||
| 1b-4 | Find the value of calculations using fractional indices | 108 - 110 | |||
| 1b-5 | Use the order of operations | 24, 44, 120, 150 | |||
| Number | Factors, multiples and primes | 1c-1 | Identify factors, multiples and prime numbers | 27, 28, 33 | |
| 1c-2 | Write positive integers as a product of prime factors | 29,30 | |||
| 1c-3 | Find the LCM and HCF of two numbers by listing and using prime factors. | 31 - 34 | |||
| 1c-4 | Solve problems using HCF and LCM | 36 | |||
| Number | Standard form and surds | 1d-1 | Convert large and small numbers into standard form and vice versa | 122 - 124 | |
| 1d-2 | Add and subtract numbers in standard form | 127 | |||
| 1d-3 | Multiply and divide numbers in standard form | 125, 126 | |||
| 1d-4 | Use a calculator to perform calculations in standard form | 128 | |||
| 1d-5 | Understand surd notation and simplify surd expressions involving squares | 111, 112, 115 | |||
| 1d-6 | Multiplication and division of surds | 113, 114 | |||
| 1d-7 | Brackets involving surds | 116, 117 | |||
| Year 9 Half Term 2 | Algebra | Algebra - the basics | 2a-1 | Know the difference between a term, expression, equation, formula and an identity | 154 |
| 2a-2 | Writing algebraic expressions | 151 - 153 | |||
| 2a-3 | Simplify and manipulate algebraic expressions by collecting like terms | 156, 157 | |||
| 2a-4 | Simplify and manipulate algebraic expressions by multiplying and cancelling terms | 158, 159 | |||
| 2a-5 | Simplify and manipulate algebraic expressions involving indices | 173 - 175 | |||
| 2a-6 | Substitute numerical values into formulae and expressions, including scientific formulae | 780 - 789 | |||
| 2a-7 | Expand single and double brackets | 160 - 165 | |||
| 2a-8 | Simplify expressions by factorising | 170, 171 | |||
| 2a-9 | Factorise quadratic expressions including using the difference of two squares | 223 - 227 | |||
| Algebra | Setting up, rearranging and solving equations | 2b-1 | Solve linear equations with one unknown | 178 - 183 | |
| 2b-2 | Solve linear equations with unknowns on both sides | 184 - 186 | |||
| 2b-3 | Set up and solve linear equations in context | 188 | |||
| 2b-4 | Change the subject of a formula | 280 - 284 | |||
| 2b-5 | Change the subject of a formula in cases where you need to factorise | 285, 286 | |||
| 2b-6 | Use iteration to find approximate solutions to equations | 322 | |||
| Algebra | Sequences | 2c-1 | Recognise simple sequences including triangular, square and cube numbers and Fibonacci sequences | 261, 263 | |
| 2c-2 | Generate specific terms in a sequence using the position-to-term rule and term-to-term rule including from pictures | 196 - 198 | |||
| 2c-3 | Identify and continue a quadratic sequence and use the nth term to generate terms | 247, 249 | |||
| 2c-4 | Find the nth term of quadratic sequences | 248 | |||
| 2c-5 | Recognise and use simple geometric sequences | 264 | |||
| Year 9 Half Term 3 | Statistics and Probability | Averages and Range | 3a-1 | Design and use two-way tables for discrete and grouped data | 422 - 424 |
| 3a-2 | Sort, classify and tabulate data, both discrete and continuous quantitative data, and qualitative data | 401 - 403 | |||
| 3a-3 | Calculate mean and range, find median and mode from small data set | 404 - 410 | |||
| 3a-4 | Recognise the advantages and disadvantages between measures of average | 413 | |||
| 3a-5 | Compare the mean and range of two distributions, or median or mode as appropriate | ||||
| 3a-6 | Interpret and find the median, mode and range from stem and leaf diagrams | 430 - 433 | |||
| 3a-7 | Interpret and find the median, mean and range from a (discrete) frequency table | 414 - 417 | |||
| 3a-8 | Interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table | 418 | |||
| Statistics and Probability | Representing and interpreting data | 3b-1 | Produce and interpret dual and composite bar charts | 425 | |
| 3b-2 | Produce and interpret pie charts | 427 - 429 | |||
| 3b-3 | Produce and interpret frequency polygons for grouped data | 441 | |||
| 3b-4 | Produce frequency diagrams for grouped discrete data | 402, 403 | |||
| 3b-5 | Construct and interpret time–series graphs, comment on trends | 450 - 452 | |||
| Statistics and Probability | Scatter Graphs | 3c-1 | Draw and interpret scatter graphs | 453 | |
| 3c-2 | Identify outliers and ignore them on scatter graphs | 453 | |||
| 3c-3 | Draw the line of best fit on a scatter diagram by eye and use the line of best fit to make predictions | 454 | |||
| 3c-4 | Distinguish between positive, negative and no correlation using lines of best fit | 453, 454 | |||
| 3c-5 | Use a line of best fit to predict values of a variable given values of the other variable | 453, 454 | |||
| Year 9 Half Term 4 | Number | Fractions | 4a-1 | Write a fraction in its simplest form and find equivalent fractions | 59, 61 |
| 4a-2 | Order fractions, by using a common denominator | 60 | |||
| 4a-3 | Convert between mixed numbers and improper fractions | 63, 64 | |||
| 4a-4 | Add and subtract fractions, including mixed numbers | 65, 66 | |||
| 4a-5 | Multiply and divide an integer by a fraction | 67 | |||
| 4a-6 | Understand and use reciprocals multiplicative inverses | 71, 72 | |||
| 4a-7 | Divide fractions by a whole number and fractions | 70 | |||
| 4a-7 | Find fraction of a quantity, including reverse fractions | 77 - 79 | |||
| 4a-8 | Convert between fractions and decimals, including recurring decimal | 73, 74, 55, 53, 54 | |||
| Number | Percentages | 4b-1 | Convert between fractions, decimals and percentages | 149 | |
| 4b-2 | Express a given number as a percentage of another number, including where the percentage is greater than 100% | 75, 76 | |||
| 4b-4 | Find a percentage of a quantity without a calculator | 84, 85 | |||
| 4b-5 | Find the new amount after a percentage increase or decrease | 88 | |||
| 4b-6 | Use 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-7 | Find a percentage of a quantity using a multiplier | 87 | |||
| 4b-8 | Use a multiplier to increase or decrease by a percentage in any scenario where percentages are used | 89, 90 | |||
| 4b-9 | Find the original amount given the final amount after a percentage increase or decrease (reverse percentages), including VAT | 96 | |||
| 4b-10 | Understand 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 proportion | 4c-1 | Write ratios in their simplest form | 329 | |
| 4c-2 | Write/interpret a ratio to describe a situation | 328 | |||
| 4c-3 | Write a ratio as a fraction | 330 | |||
| 4c-4 | Write ratios in form 1 : m or m : 1 | 331 | |||
| 4c-5 | Share a quantity in a given ratio including three-part ratios | 332 | |||
| 4c-6 | Use a ratio to find one quantity when the other is known | 333, 334 | |||
| 4c-7 | Use a ratio to convert between measures and currencies | 707 | |||
| 4c-8 | Use a ratio to compare a scale model to real-life object and solve problems involving scale diagrams. | 864 - 871 | |||
| 4c-9 | Understand direct proportion and use this to scale up recipes | 339, 340, 739 - 742 | |||
| Year 9 Half Term 5 | Geometry and Measure | Polygons, angles and parallel lines | 5a-1 | Distinguish between scalene, equilateral, isosceles and right-angled triangles | 823 |
| 5a-2 | Find missing angles in a triangle using the angle sum in a triangle and the properties of an special triangles | 485 - 487 | |||
| 5a-3 | Recall the properties and definitions of special types of quadrilaterals | 824 - 826 | |||
| 5a-4 | Understand and use the angle properties of quadrilaterals and the fact that the angle sum of a quadrilateral is 360° | 560 | |||
| 5a-5 | Understand and use the angle properties of parallel lines and find missing angles using the properties of corresponding and alternate angles, giving reasons | 481 - 483 | |||
| 5a-6 | Solve problems involving interior and exterior angles of polygons, including algebraic problems | 561 - 565 | |||
| Geometry and Measure | Pythagoras theorem and trigonometry | 5b-1 | Understand, 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 appropriate | 497 - 499 | |
| 5b-2 | Given 3 sides of a triangle, justify if it is right-angled or not | 497 | |||
| 5b-3 | Apply Pythagoras’ Theorem to solve various problems, including area problems | 500 - 504 | |||
| 5b-4 | Apply Pythagoras’ Theorem with a triangle drawn on a coordinate grid including calculating the length of a line segment AB given pairs of points | ||||
| 5b-5 | Understand and recall the trigonometric ratios sine, cosine and tan | 508 | |||
| 5b-6 | Use trigonometry to find missing sides of a right angled triangle | 509, 510 | |||
| 5b-7 | Use trigonometry to find missing angles in a right angled triangle | 511, 512 | |||
| 5b-8 | Use the trigonometric ratios to solve 2D problems | 513, 514 | |||
| 5b-9 | Find angles of elevation and depression | 515 | |||
| 5b-10 | Know the exact values for trigonometry | 845 | |||
| Year 9 Half Term 6 | Algebra | Graphs, the basics and real life graphs | 6a-1 | Draw, label and scale axes and identify points with given coordinates | 199 |
| 6a-2 | Find the coordinates of the midpoint of a line segment from coordinates | 200 | |||
| 6a-3 | Draw and interpret straight-line graphs for real-life situations, including ready reckoner graphs, conversion graphs, fuel bills, fixed charge and cost per item | 894, 895 | |||
| 6a-4 | Draw and interpret distance–time graphs | 874 - 879 | |||
| 6a-5 | Draw and interpret velocity–time graphs | 880 - 886 | |||
| Algebra | Linear graphs and coordinate geometry | 6b-1 | Plot and draw graphs of y = a, x = a, y = x and y = –x | 205 | |
| 6b-2 | Plot 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 graphs | 206 - 209 | |||
| 6b-3 | Identify and interpret gradient from an equation y = mx + c. Sketch a graph of a linear function, using the gradient and y-intercept | 210 | |||
| 6b-4 | Identify parallel lines from their equations | 214 | |||
| 6b-5 | Plot and draw graphs of straight lines in the form ax + by = c | 280, 281 | |||
| 6b-6 | Find the equation of a straight line from a graph | 210 - 211 | |||
| 6b-7 | Find the equation of the line through one point with a given gradient | 212 | |||
| 6b-8 | Find the equation of the line through two given points | 213 | |||
| 6b-9 | Explore the gradients of parallel lines and lines perpendicular to each other | 214 - 216 | |||
| Algebra | Quadratic, cubic and other graphs | 6c-1 | Generate points and plot graphs of simple quadratic functions | 251 | |
| 6c-2 | Identify and interpret roots, intercepts and turning points of quadratic graphs | 252 - 255 | |||
| 6c-3 | Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function | 323 | |||
| 6c-4 | Interpret graphs of quadratic functions from real-life problems | ||||
| 6c-5 | Draw and interpret graphs of simple cubic functions using tables of values | 298, 299 | |||
| 6c-6 | Draw graphs of the reciprocal function | 300, 301 | |||
| 6c-7 | Draw circles, centre the origin | 778, 779 | |||
| 6c-8 | Recognise a linear, quadratic, cubic, reciprocal and circle graph from its shape | ||||
| Year 10 Half Term 1 | Geometry and Measure | Perimeter, area and circles | 7a-1 | Recall and use the formulae for the area of a triangle, rectangle, trapezium and parallelogram | 554, 556, 557, 559 |
| 7a-2 | Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms | 555, 558 | |||
| 7a-3 | Find the perimeter of a rectangle, trapezium, parallelograms and compound shapes made from combinations of the above | 549 - 552 | |||
| 7a-4 | Recall the definition of a circle and name and draw parts of a circle | 592 | |||
| 7a-5 | Find the circumference of a circle, semi-circle and quarter circles, including giving your answers in terms of π | 534 - 538 | |||
| 7a-6 | Find the area of a circle, semi-circle and quarter circles, including giving your answers in terms of π | 539 - 543 | |||
| 7a-7 | Calculate arc lengths, angles and areas of sectors of circles | 544 - 547 | |||
| Geometry and Measure | 3D forms and volume, cylinders, cones and spheres. | 7b-1 | Find the surface area of prisms using the formulae for triangles and rectangles | 584, 585 | |
| 7b-2 | Draw sketches of 3D solids | 832 | |||
| 7b-3 | Find the volume of a prism | 570, 571 | |||
| 7b-4 | Convert between metric volume measures including volume and capacity | 668, 669, 702 - 704 | |||
| 7b-5 | Find the volume of a cylinder | 572 - 575 | |||
| 7b-6 | Find the surface area of a cylinder | 586 | |||
| 7b-7 | Recall and use the formula for volume of pyramid | 579 | |||
| 7b-8 | Find the surface area of a pyramid | ||||
| 7b-9 | Use the formulae for volume and surface area of spheres | 580, 581, 588 | |||
| 7b-10 | Use the formulae for volume and surface area of cones | 576, 577, 587 | |||
| 7b-11 | Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones | 578, | |||
| 7b-12 | Find the surface area and volumes of compound solids constructed from cubes, cuboids, cones, pyramids, spheres, hemispheres, cylinders | 582, 583 | |||
| Geometry and Measure | Accuracy and bounds in context | 7c-1 | Calculate the upper and lowers bounds of numbers given to varying degrees of accuracy | 137 - 139 | |
| 7c-2 | Find the upper and lower bounds of calculations involving perimeters, areas and volumes of 2D and 3D shapes | ||||
| 7c-3 | Use inequality notation to specify an error interval due to truncation or rounding | 774 - 777 | |||
| Year 10 Half Term 2 | Geometry and Measure | Transformations | 8a-1 | Rotate a shape about the origin or any other point on a coordinate grid | 648, 649 |
| 8a-2 | Describe a rotation fully using the angle, direction of turn, and centre | 653, 654 | |||
| 8a-3 | Translate a given shape by a vector | 637, 638 | |||
| 8a-4 | Use column vectors to describe translations | 650 | |||
| 8a-5 | Transform 2D shapes using single reflections | 639 - 641 | |||
| 8a-6 | Describe reflections on a coordinate grid | 652 | |||
| 8a-7 | Enlarge a shape using a scale factor only | ||||
| 8a-8 | Enlarge a given shape using positive, negative and fractional scale factors and a centre of enlargement | 642 - 647 | |||
| 8a-9 | Describe an enlargement using the scale factor and centre of enlargement | 651 | |||
| 8a-10 | Find areas after enlargement and compare with before enlargement, to deduce multiplicative relationship (area scale factor) | 615 - 617 | |||
| 8a-11 | Describe and transform 2D shapes using combined rotations, reflections, translations, or enlargements | 656 - 657 | |||
| 8a-12 | Describe the changes and invariance achieved by combinations of rotations, reflections and translations | 655 | |||
| Geometry and Measure | Constructions, Loci and Bearings | 8b-1 | Understand and draw front and side elevations and plans of shapes made from simple solids | 837 - 840 | |
| 8b-2 | Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid | 841 - 844 | |||
| 8b-3 | Estimate lengths using a scale diagram | 864 - 866 | |||
| 8b-4 | Make an accurate scale drawing from a diagram | 867, 868 | |||
| 8b-5 | Calculate bearings and solve bearings problems, including on scaled maps, and find/mark and measure bearings | 492 - 496, 869 | |||
| 8b-6 | Use 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-7 | Use constructions to solve a range of loci problems including with bearings | 674 - 679 | |||
| Algebra | Solving quadratics and Simultaneous equations | 9a-1 | Factorise quadratic expressions in the form ax² + bx + c | 225 - 228 | |
| 9a-2 | Solve quadratics by factorising | 230 - 233 | |||
| 9a-3 | Write quadratic expressions in vertex form (complete the square) | 235 - 237 | |||
| 9a-4 | Solve quadratic equations by completing the square | 238, 239 | |||
| 9a-5 | Set up and solve quadratic equations | 245 | |||
| 9a-6 | Solve quadratic equations by using the quadratic formula | 241 - 242 | |||
| 9a-7 | Find the exact solutions of two linear simultaneous equations in two unknowns using elimination | 190 - 193 | |||
| 9a-8 | Find the exact solutions of two linear simultaneous equations in two unknowns by substitution | 194 | |||
| 9a-9 | Solve simultaneous equations involving quadratics and circles. | 246, 259 | |||
| Year 10 Half Term 3 | Algebra | Inequalities | 9b-1 | Show inequalities on number lines | 265, 266 |
| 9b-2 | Write down whole number values that satisfy an inequality | 267 | |||
| 9b-3 | Solve simple linear inequalities in one variable, and represent the solution set on a number line | 269 - 271 | |||
| 9b-4 | Solve double linear inequalities in one variable, and represent the solution set on a number line | 272 | |||
| Statistics and Probability | Probability | 10a-1 | Find the probability of an event happening using theoretical probability. Write the probabilities in fractions, decimals and percentages | 350 - 352 | |
| 10a-2 | Find the probability of an event not happening | 353 | |||
| 10a-3 | List all outcomes for single events systematically | 670 | |||
| 10a-4 | Work out probabilities from two-way tables | 422, 423 | |||
| 10a-5 | Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1 | 354 | |||
| 10a-6 | Find the probability of an event happening using relative frequency | 356 | |||
| 10a-7 | Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities | 355 | |||
| 10a-8 | Use and draw sample space diagrams | 358, 359 | |||
| 10a-9 | Use tree diagrams to calculate the probability of two independent events | 360 - 363 | |||
| 10a-10 | Use tree diagrams to calculate the probability of two dependent events | 364 - 367 | |||
| 10a-11 | Work out probabilities from Venn diagrams to represent real-life situations | 379, 380 | |||
| 10a-12 | Use set notation, including union and intersection | 370 - 378 | |||
| 10a-13 | Work out probabilities from Venn diagrams to represent abstract’ sets of numbers/values | 383 - 391 | |||
| Year 10 Half Term 4 | Ratio and Proportion | Multiplicative reasoning | 11a-1 | Understand what is meant by direct proportion | 339, 340 |
| 11a-2 | Solve word problems involving direct proportion, including using the unitary method, best buys and recipe problems | 341, 763 - 770, 739 - 742 | |||
| 11a-3 | Understand inverse proportion and solve word problems involving inverse proportion | 342 | |||
| 11a-4 | Work out which product is the better buy | ||||
| 11a-5 | Scale up recipes | 739 - 742 | |||
| 11a-6 | Convert between currencies | 707, 708 | |||
| 11a-7 | Solve simple interest problems | 93 | |||
| 11a-8 | Work out the multiplier for repeated proportional change as a single decimal number | 91, 92 | |||
| 11a-9 | Solve problems involving repeated percentage change. Including compound percentage problems | 94, 95 | |||
| 11a-10 | Perform calculations involving speed | 716 - 724 | |||
| 11a-11 | Perform calculations involving density | 725 - 733 | |||
| 11a-12 | Perform calculations involving pressure | 734 - 737 | |||
| 11a-13 | Calculate an unknown quantity from quantities that vary in direct or inverse proportion | 339 - 342 | |||
| 11a-14 | Recognise when values are in direct or inverse proportion by reference to the graph form | 348 | |||
| Geometry and Measure | Similarity and Congruence in 3D | 12a-1 | Understand 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 constructions | 682 | |
| 12a-2 | Solve angle problems by first proving congruence | 684 - 689 | |||
| 12a-3 | Understand similarity of triangles and of other plane shapes, and use this to make geometric inferences | 608 - 610 | |||
| 12a-4 | Solve problems to find missing lengths in similar shapes | 610 - 614 | |||
| 12a-6 | Write the lengths, areas and volumes of two shapes as ratios in their simplest form | ||||
| 12a-7 | Know the relationships between linear, area and volume scale factors of mathematically similar shapes and solids | 615 - 621 | |||
| 12a-10 | Solve problems involving frustums of cones where you have to find missing lengths first using similar triangles | 578 | |||
| Geometry and Measure | Graphs of trigonometric functions | 13a-1 | Recognise, sketch and interpret graphs of the trigonometric functions | 303 - 306 | |
| 13a-2 | Know exact trig values and use these to solve non-calculator trigonometry problems | 845 - 853 | |||
| 13a-3 | Apply 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-4 | Apply 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 5 | Geometry and Measure | Further Trigonometry | 13b-1 | Know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle | 516 - 519 |
| 13b-2 | Use the sine rule to find missing lengths and angles | 520 - 525 | |||
| 13b-3 | Use the cosine rule to find missing lengths and angles | 526 - 530 | |||
| 13b-4 | Solve problems in 2D using the sine and cosine rules | 531 - 533 | |||
| 13b-5 | Use Pythagoras to solve 3D problems | 505 - 507 | |||
| 13b-6 | Use trigonometry to solve 3D problems | 854 - 862 | |||
| 13b-7 | Use the sine and cosine rules to solve 3D problems | 863 | |||
| Statistics and Probability | Collecting data | 14a-1 | Distinguish between a census and a sample and understand how bias might arise | 394, 395 | |
| 14a-2 | Carry out a stratified random sample | 396 - 398 | |||
| 14a-3 | Write questions to eliminate bias, and understand how the timing and location of a survey can ensure a sample is representative | 399 - 400 | |||
| 14a-4 | Solve problems involving capture re-capture | 872, 873 | |||
| Statistics and Probability | Cumulative frequency, box blots and histograms | 14b-1 | Construct and interpret cumulative frequency tables | 437 - 439 | |
| 14b-2 | Compare the mean and range of two distributions, or median and interquartile range | 411, 412 | |||
| 14b-3 | Draw and interpret box plots to find median, quartiles, range and interquartile range and draw conclusions | 440, 434 - 436 | |||
| 14b-4 | Interpret histograms from class intervals with unequal width | 442, 443 | |||
| 14b-5 | Complete a grouped frequency table from a histogram. | 444 | |||
| 14b-6 | Use frequency density to draw a histogram | 445 - 449 | |||
| 14b-7 | Estimate the mean and median from a histogram | ||||
| Year 10 Half Term 6 | Algebra | Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics | 15a-1 | Sketch a graph of a quadratic function, by factorising or by using the formula, identifying roots, y-intercept and turning point by completing the square | 257 |
| 15a-2 | Be able to identify from a graph if a quadratic equation has any real roots | 258 | |||
| 15a-3 | Find approximate solutions to quadratic equations using a graph | 259, 260 | |||
| 15a-4 | Expand the product of more than two linear expressions | 166 | |||
| 15a-5 | Solve simultaneous equations graphically, including quadratics and circles | 218, 219, 259 | |||
| 15a-6 | Solve quadratic inequalities by factorising and sketching the graph to find critical values | 277 | |||
| 15a-7 | Solve linear inequalities in two variables graphically and show the solution set of several inequalities in two variables on a graph | 273 - 276 | |||
| 15a-8 | Use iteration with simple converging sequences to find solutions to equations | 322 | |||
| Geometry and Measure | Circle Theorems | 16a-1 | Recall the definition of a circle and draw parts of a circle, including sector, tangent, chord, segment | 592 | |
| 16a-2 | Understand 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-3 | Prove the above circle theorems | 816 - 820 | |||
| 16a-4 | Solve problems involving circle theorems | 595, 603 - 606 | |||
| Geometry and Measure | Circle Geometry | 16b-1 | Find the equation of a tangent to a circle at a given point | 320 | |
| 16b-2 | Recognise and construct the graph of a circle using x² + y² = r² for radius r centred at the origin of coordinates | ||||
| Year 11 | Algebra | Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof | 17a-1 | Rationalise the denominator involving surds | 118, 119 |
| 17a-2 | Multiply and divide algebraic fractions | 172 | |||
| 17a-3 | Simplify algebraic fractions (involving quadratics) | 229 | |||
| 17a-4 | Solve arising from algebraic fraction equations (including quadratics) | 187, 244 | |||
| 17a-5 | Change the subject of a formula, including cases where the subject occurs on both sides of the formula, or where a power of the subject appears | 283 - 286 | |||
| 17a-6 | Change the subject of a formula such as 1/f = 1/u + 1/v , where all variables are in the denominators | ||||
| 17a-7 | Solve ‘Show that’ and proof questions using consecutive integers (n, n + 1), squares a², b², even numbers 2n, odd numbers 2n +1 | 325 - 327 | |||
| 17a-8 | Understand and use function notation | 288, 289 | |||
| 17a-9 | Find an expression for the output of composite functions | 293, 294 | |||
| 17a-10 | Find an expression for the output of inverse functions | 295, 296 | |||
| 17a-11 | Solve complex problems with functions | 297 | |||
| Algebra | Vectors and algebraic proof | 18a-1 | Understand and use vector notation | 622, 623 | |
| 18a-4 | Calculate the sum of two vectors, the difference of two vectors and a scalar multiple of a vector using column vectors and represent these pictorially | 624 - 626 | |||
| 18a-5 | Find the magnitude (length) of a vector using Pythagoras’ Theorem | 627 | |||
| 18a-7 | Solve geometric problems involving vectors | 628 - 636 | |||
| Algebra | Reciprocal and exponential graphs; Gradient and area under graphs | 19a-1 | Recognise, sketch and interpret graphs of the reciprocal function | 300, 301 | |
| 19a-2 | Recognise, sketch and interpret graphs of exponential functions | 302 | |||
| 19a-3 | Use calculators to explore exponential growth and decay | 796 - 799 | |||
| 19a-4 | Recognise, sketch and interpret graphs of exponential functions | 800 - 803 | |||
| 19a-5 | Set up, solve and interpret the answers in growth and decay problems | 804 - 811 | |||
| 19a-6 | Apply to the graph of y = f(x) the transformations y = –f(x), y = f(–x) for linear, quadratic, cubic functions | 311, 312 | |||
| 19a-7 | Apply 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-8 | Estimate area under a quadratic or other graph by dividing it into trapezia | 891 - 893 | |||
| 19a-9 | Calculate the gradient at a point on a curve by drawing a tangent. | 889 | |||
| 19a-10 | Interpret the gradient of non-linear graph in real-life contexts | 888, 890 | |||
| Algebra | Direct and inverse proportion | 19b-1 | Recognise and interpret graphs showing direct and inverse proportion | 348 | |
| 19b-2 | Use y = kx to solve direct proportion problems | 343 - 345 | |||
| 19b-3 | Use y = k/x to solve inverse proportion problems | 346, 347 |