ks4 scheme of work edexcel gcse 2017+ (teacher version

Chislehurst and Sidcup Grammar School Mathematics Department 1

KS4 Scheme of Work Edexcel GCSE 2017+ (Teacher Version)

Contents Key Information ................................................................................................................................................. 2

Course Overview ............................................................................................................................................... 3

Module 1 – Indices and Surds ........................................................................................................................... 4

TOPIC 1 - Indices ............................................................................................................................................. 4

TOPIC 2 – Surds .............................................................................................................................................. 5

Module 2 – Equations and Coordinate Geometry ........................................................................................... 6

TOPIC 3 - Brackets, Equations and Formulae ................................................................................................ 6

TOPIC 4 – Coordinate Geometry ................................................................................................................... 7

Module 3 – 2D, 3D Shapes and Bounds ............................................................................................................ 8

TOPIC 5 – Measures, Perimeter, Area & Volume ......................................................................................... 8

TOPIC 6 – Estimation, Rounding, Approximation & Bounds ........................................................................ 9

Module 4 – Quadratics and Sequences .......................................................................................................... 10

TOPIC 7 – Quadratics & Algebraic Fractions ............................................................................................... 10

TOPIC 8 - Sequences ..................................................................................................................................... 11

Module 5 – Construction, Transformations and Similar Shapes ................................................................... 12

TOPIC 9 – Constructions, Angles, Lines & Planes ........................................................................................ 12

TOPIC 10 - Transformations ......................................................................................................................... 13

TOPIC 11 – Similar Shapes ........................................................................................................................... 14

Module 6 – Summary Statistics, Sampling and Number ............................................................................... 15

TOPIC 12 - Statistics 1 – Summary Statistics, Sampling and Time Series ................................................... 15

TOPIC 13 – Number, Percentage & Compound Measure ........................................................................... 16

Module 7 – Trigonometry and Circle Theorems ............................................................................................ 17

TOPIC 14 – Pythagoras & Trigonometry in 2D & 3D ................................................................................... 17

TOPIC 15 – Circle Theorems ......................................................................................................................... 19

Module 8 – Ratio, Proportion, Data representation and Probability ........................................................... 20

TOPIC 16 – Ratio & Proportion .................................................................................................................... 20

TOPIC 17 - Statistics 2 (Data Representation) ............................................................................................. 21

TOPIC 18 – Probability ................................................................................................................................. 22

Module 9 – Functions and Curved Graphs ..................................................................................................... 23

TOPIC 19 – Functions ................................................................................................................................... 23

TOPIC 20 – Curved Graphs & their Transformations .................................................................................. 24

Module 10 – Proof, Congruency and Vectors ................................................................................................ 26

Topic 21 – Proofs and Congruency .............................................................................................................. 26

TOPIC 22 - Vectors ........................................................................................................................................ 28


Key Information

Textbooks The scheme of work is based on the following textbooks:

Publisher Textbook Pearson Edexcel GCSE (9-1) Mathematics Higher, Student Book STP NC Mathematics Higher GCSE 10A

STP NC Mathematics Higher GCSE 11A

HegartyMaths Each section will have reference to exercises on HegartyMaths with video codes listed to complete as homework and revision where appropriate.

Prior Knowledge checks Each topic will include a prior knowledge exercise on HegartyMaths which should be completed as a homework before the topic is taught, the work is revision of knowledge gained at KS3.

Problem Solving The new style GCSE involves a lot more problem solving. It is therefore important that alongside every topic, you complete a variety of problem solving questions related to it. There are compulsory problem solving questions for each module and these can be found on the student drive. These problem solving exercises should be reviewed before the module assessment. In addition to this there will be a problem solving question in every test which is worth up to three merits for Communication, Mathematics and Correctly justified answers.

Testing Tests will happen frequently in year 10 and 11. Module tests will assess specific content and should be completed prior to each half term, 6 should be completed in year 10, with 4 completed in year 11. Two full papers will take place in the summer term of year 10 as end of year examinations covering modules 1 – 5. In year 11 two sets of mocks will be sat one in the winter term and one in the spring term, each consisting of full H1, H2 and H3 papers.


Course Overview

Module Topic

1

1. Indices

2. Surds

TEST 1 (By Autumn Half term)

2

3. Brackets, Equations and Formulae

4. Coordinate Geometry

TEST 2 (By end of Autumn term)

3

5. Measures, Perimeter, Area & Volume

6. Estimation, Rounding, Approximation and Bounds

TEST 3 (By Spring Half term)

4

7. Quadratics and Algebraic Fractions

8. Sequences TEST 4 (By end of Spring term)

5

9. Constructions, Angles, Lines & Planes

10. Transformations

11. Similar Shapes

TEST 5 (By Summer Half term)

End of Year Exams Summer Yr10

6

12. Statistics 1

13. Number, Percentage & Compound Measure

TEST 6 (By end of Summer term)

7

14. Pythagoras & Trigonometry in 2D & 3D

15. Circle Theorems

TEST 7 (By Autumn Half term)

8

16. Ratio and Proportion

17. Statistics 2 18. Probability

TEST 8 (By end of Autumn term)

9

19. Functions

20. Curved Graphs and their Transformations

TEST 9 (By Spring Half term)

10

21. Proofs, Congruency

22. Vectors

TEST 10 (By end of Spring term)


Module 1 – Indices and Surds

TOPIC 1 - Indices Topic 1 Prior Knowledge Check: HegartyMaths Task

Writing numbers in index notation 102 - Index form 1 (intro)

Estimate roots of any positive number 112 - Estimating a surd value

Standard form notation, converting between ordinary numbers to standard form and vice versa.

122 - Ordinary to standard form 123 - Standard form to ordinary

Teaching Objectives Pearson

Textbook STP

Textbook HegartyMaths

Multiplying/Dividing Nos. in index form including negative and fractional indices

Pg 9 Ex 1.4 Pg 31 Ex 2.1 Pg 11 Ex 1.5

Pg 65 Ex 2G

105 - Index form 4 (multiplying indices) 106 - Index form 5 (dividing indices) 107 - Index form 6 (power of power rule) 104 - Index form 3 (power of negative integers) 109 - Index form 8 (powers of non-unit fractions)

Combination of all index rules Pg 65 Ex 2G 110 - Index form 9 (combination of rules)

Changing the base to find a variable power 793 - Manipulating powers (4)

Calculate with standard form Pg 14 Ex 1.6 Pg 111 Ex 5B

125 - Multiplying with standard form 126 - Dividing with standard form 127 - Adding & subtracting with standard form


TOPIC 2 – Surds Topic 2 Prior Knowledge Check: HegartyMaths Task

Expanding single brackets 161 - Expand two single brackets & simplify

Multiply out two brackets 163 - Expand double brackets 2


Textbook STP


Manipulating Surds Simplifying, and expanding brackets with surds

Pg 16 Ex 1.7 Q3-14 Pg 27 Q12

Pg 60 Ex 2D

115 - Simplifying surds 116 - Brackets involving surds 1

Rationalising the denominator

Including: 𝑎

𝑐√𝑏 ,

𝑎

𝑐±√𝑏 ,

𝑎

√𝑐±√𝑏

Pg 18 Ex 1.7 Q15-18

Pg 60 Ex 2D

118 - Rationalising surds 1 119 - Rationalising surds 2


Module 2 – Equations and Coordinate Geometry

TOPIC 3 - Brackets, Equations and Formulae Topic 3 Prior Knowledge Check: HegartyMaths Task

Simple Factorising (single bracket) 169 - Factorise simple expressions 2

Solve linear equations 186 - Solve equations with x on both sides 3

Substitution of numerical values into formulae 787 - Substitution (8)

Understand equation, formula, identity, expression 154 - Expressions, equations, identities & formulae


Textbook STP


Multiply out triple brackets Pg 485 Ex 15.5 Q4-

166 - Expand triple brackets

Substitution of algebraic expressions into formulae

Pg 37 Ex 2.4 Pg 126 Ex 5H

Changing the subject of a formula including more challenging types

Pg 38 Ex 2.4 Q11-15

Pg 119 Ex 5E Pg 123 Ex 5G

284 - Change the subject of the formula 5 (x with powers) 285 - Change the subject of the formula 6 (x on both sides) 286 - Change the subject of the formula 7 (x on both sides/denominator)

Solve simultaneous linear equations algebraically including elimination and substitution

Pg 287 Ex 9.4 Pg 289 Ex 9.5

Pg 183 Q3-4

193 - Simultaneous equations by elimination 4 194 - Simultaneous equations by substitution

Form and solve worded simultaneous equations problems

Pg 287 Ex 9.4 Pg 289 Ex 9.5

195 - Simultaneous equations (in context)

Solve simultaneous equations graphically Pg 474 Ex 15.1

219 - Solving simultaneous equations using straight lines 2


TOPIC 4 – Coordinate Geometry Topic 4 Prior Knowledge Check: HegartyMaths Task

Understand notation of gradient and intercept 207 - Straight line graphs 2

Draw straight-line graphs using equation of line or gradient and intercept only.

208 - Straight line graphs 3 209 - Straight line graphs 4

Solving linear inequalities 271 - Solve single linear inequalities 3 (difficult)


Textbook STP


Find midpoint and length of line segment and parallel & perpendicular lines

Pg 164 Ex 6.2 Pg 174 Ex 6.5

200 - Midpoint of a line segment

Find gradient and y – intercept from graphs and equations not in the form 𝑦 = 𝑚𝑥 + 𝑐

Pg 161 Ex 6.1 208 - Straight line graphs 3 209 - Straight line graphs 4 210 - Straight line graphs 5

Finding the Equation (y = mx + c) given two points or one point and gradient

Pg 164 Ex 6.2 212 - Straight line graphs 7 213 - Straight line graphs 8

Interpret results in distance time graphs, velocity time graphs and graphs in financial contexts including rates of change

Pg 166 Ex 6.3, Pg 170

Ex 6.4

874 - Distance-time graphs (1) 876 - Distance-time graphs (3) 880 - Speed-time graphs (1) 881 - Speed-time graphs (2)

Worded inequality problems Double inequalities Represent solutions on a number line

Pg 293 Ex 9.7

268 - Multiple inequalities on a number line 272 - Solve double linear inequalities

Two variable inequalities, sketching graph to find regions

Pg 475 Ex 15.2

Pg 210 Ex 2.6

274 - Linear inequalities as graph regions 2 275 - Linear inequalities as graph regions 3 276 - Linear inequalities as graph regions 4


Module 3 – 2D, 3D Shapes and Bounds

TOPIC 5 – Measures, Perimeter, Area & Volume Topic 5 Prior Knowledge Check: HegartyMaths Task

Area of a trapezium 559 - Trapezium

Area and Circumference of a circle 536 - Circumference of a circle (3) 541 - Area of a circle (3)


Textbook STP


Converting between units of length, area and volume

Pg 207 Ex 7.2 Pg 235 Ex 3.1 Q1, 5 e) – j)

701 - Converting area units (2) 703 - Converting volume units (2) 698 - Converting capacity/volume (1)

Arc lengths, and areas of sectors Pg 216 Ex 7.5 Pg 244 Ex 10A

545 - Arc length (2) 547 - Area of a sector (2)

Volumes of Prisms and surface area including cylinders

Pg 210 Ex 7.3 Pg 220 Ex 7.6

Q1-9

Pg 249 - 251 Ex 10B to 10C

571 - Prisms (2) 573 - Cylinders (2) 574 - Cylinders (3) 585 - Surface area of prisms

Surface Area and volumes of Spheres, Pyramids and cones, including Frustums

Pg 220 Ex 7.6 Q10-16

Pg 222 Ex 7.7 Pg 231 Q1-4 Pg 233 Q2, 9,

10

Pg 251 – 259 Ex 10D to 10I

580 - Spheres (1) 581 - Spheres (2) 588 - Surface area of spheres 579 - Rectangular based pyramid 577 - Cones (2) 587 - Surface area of cones 578 - Frustums


TOPIC 6 – Estimation, Rounding, Approximation & Bounds Topic 6 Prior Knowledge Check: HegartyMaths Task

Carry out sensible estimations for calculations 131 - Estimate complex calculations


Textbook STP


Use and understand compound measures, including problems with unit conversions Density = Mass / Volume Speed = Distance / Time Pressure = Force / Area

Pg 344 Ex 11.2 Pg 346 Ex 11.3 Pg 352 Q5-10 Pg 357 Q2, 13

Pg 235 Ex 3.1 Q 8

727 - Density (3) 728 - Density (4) 729 - Density (5) 730 - Density (6) 718 - Speed (3) 720 - Speed (5) 735 - Pressure (2) 736 - Pressure (3)

Measurements and bounds

Pg 208 Ex 7.2 Q9-16

Pg 230 Q1-4 Pg 234 Q11-12

138 - Upper & lower bounds 2 (worded)

Calculations involving upper and lower bounds Solving problems giving answer to appropriate degree of accuracy (Via comparing upper and lower bounds).

Pg 400 EX 13.1

Pg 206 Ex 9A

139 - Upper & lower bounds 3 (calculations)


Module 4 – Quadratics and Sequences

TOPIC 7 – Quadratics & Algebraic Fractions Topic 7 Prior Knowledge Check: HegartyMaths Task

Factorise simple quadratic expressions ax2 + bx + c, where a = 1 223 - Factorise quadratic expressions 1


Textbook STP


Factorise quadratic expressions ax2 + bx + c where a ≠ 1 (via ac method of splitting bx term) Difference of two squares

Pg 75 - 76 Ex 3C to 3D

225 - Factorise quadratic expressions 3 226 - Factorise quadratic expressions 4 228 - Factorise quadratic expressions 6

Solve quadratic equations by factorisation Pg 281 Ex 9.1, Pg 282 Ex 9.2

Pg 80 – 87 Ex 3H to 3M

231 - Solving quadratic equations 2 (by factorising) 232 - Solving quadratic equations 3 (by factorising)

Understand and use the discriminant to determine the number of roots Solve quadratic equations by using the quadratic formula

Pg 284 Ex 9.2 Q13 - 16

Pg 95 - 99 Ex 4F to 4H

243 - Using the discriminant 242 - Solving using the quadratic formula 2

Solve quadratic equations by completing the square Pg 285 Ex 9.3 Pg 88 - 93 Ex 4A to 4E

236 - Completing the square 2 237 - Completing the square 3

Form and solve quadratic equations Pg 298 Q4-8 Pg 300 Q1-5 Pg 303 Q3-5

Pg 104 Ex 4J Q1-14

245 - Quadratic equations in context

Understand terminology of roots, intercepts and turning points of quadratic functions. Be able to sketch graphs of quadratic functions labelling roots and turning points (via CTS)

Pg 478 Ex 15.3 Pg 482 Ex 15.4

258 - The discriminant & quadratic graphs 257 - Sketch a fully labelled quadratic graph

Solve simultaneous equations one linear and one quadratic Pg 292 Ex 9.6 Q4-12

Pg 17 Ex 2C 246 - Simultaneous equations involving quadratics

Simplifying Algebraic Fractions Adding, Subtracting, Multiplying and Dividing Algebraic Fractions Solving Algebraic Fraction Equations

Pg 535 Ex 17.3 Pg 537 Ex 17.4 Pg 541 Ex 17.6

Pg 40 – 55 Ex 1A to 1J

172 - Expressions with algebraic fractions 229 - Simplify algebraic fractions (involving quadratics) 244 - Quadratic equations from algebraic fractions

Solve quadratic inequalities in one variable

Pg 477 Ex 15.2 Q10-14

Pg 495 Q7 Pg 497 Q15

Pg 137 - 141 Ex 6C to 6D

277 - Solving quadratic inequalities


TOPIC 8 - Sequences Topic 8 Prior Knowledge Check: HegartyMaths Task

Generate terms of a sequence via a term to term rule 197 - Linear sequences (term-to-term rule)


Textbook STP


Recognise arithmetic sequences, find nth term and solve problems

Pg 40 Ex 2.5 920 - Arithmetic sequences (2) 921 - Arithmetic sequences (3)

Deduce expressions to calculate the nth term of a quadratic sequence*

Pg 42 Ex 2.6 Q9-18

Pg 80 Ex 5A Q33-38

248 - Find the nth term of a quadratic sequence 250 - Use the nth term of a quadratic sequence 2

Recognise and use simple geometric sequences

Pg 41 Ex 2.6 Q4-8

264 - Geometric sequences

Special sequences with term to term rule, triangular*, square, cube and Fibonacci numbers

Pg 42 Ex 2.6 Q3

Pg 76 Ex 5A Q1-32, 39-50

263 - Fibonacci sequence


Module 5 – Construction, Transformations and Similar Shapes

TOPIC 9 – Constructions, Angles, Lines & Planes Topic 9 Prior Knowledge Check: HegartyMaths Task

Review all angle facts including angles in polygons (internal, external) 562 - Interior angles in polygons (2) 564 - Exterior angles in polygons (2)


Textbook STP


Carry out constructions of triangles, perpendicular bisector & angle bisector

Pg 256 Ex 8.6 Pg 259 Ex 8.7 Pg 267 Q9-11 Pg 272 Q1-6

Pg 188 – 189 Ex 8A to 8B

660 - Construct a perpendicular bisector 661 - Construct an angle bisector 662 - Construct a perpendicular from a point to a line 663 - Construct a perpendicular from a point on a line

Solve problems using constructions including loci problems

Pg 262 Ex 8.8 Pg 273 Q7-8

Pg 259 Ex 3.6

674 - Loci (1) 675 - Loci (2) 676 - Loci (3) 677 - Loci (4) 678 - Loci (5) 679 - Loci (problem solving)

Construct and interpret plans and elevations of 3D shapes*

Pg 240 Ex 8.1 Pg 267 Q5

Pg 270 Q1-2 Pg 275 Q12

837 - Plans and elevations (1) 838 - Plans and elevations (2) 840 - Plans and elevations (4) 842 - Plans and elevations (6)

Measure line segments and angles in geometric figures, interpret maps, scale drawings and bearings

Pg 253 Ex 8.5 Pg 267 Q6-8 Pg 271 Q2-6

495 - Bearings (4) 496 - Bearings (5) 869 - Scale diagrams with bearings


TOPIC 10 - Transformations Topic 10 Prior Knowledge Check: HegartyMaths Task

Recap Translation 637 - Translations (1)

Recap Enlargement 642 - Enlargements (1)

Recap Reflection 639 - Reflections (1)

Recap Rotation 648 - Rotations (1)


Textbook STP


Translations – via column vectors Pg 249 Ex 8.4 638 - Translations (2)

Reflections - Finding the mirror line Rotations - Finding the centre

Pg 242 Ex 8.2 640 - Reflections (2) 641 - Reflections (3) 649 - Rotations (2)

Enlargement Negative, fractional, finding the centre

Pg 245 Ex 8.3

643 - Enlargements (2) 645 - Enlargements (4) 646 - Enlargements (5) 647 - Enlargements (6)

Combinations of transformations

Pg 250 Ex 8.4 Pg 266 Q1-4

Pg 268 Q1-11 Pg 273 Q1-6,

13

656 - Combined transformations (1) 657 - Combined transformations (2)

Describe transformations & Invariance

653 - Describe transformations (4) 654 - Describe transformations (5) 655 - Invariance


TOPIC 11 – Similar Shapes Topic 11 Prior Knowledge Check: HegartyMaths Task


Textbook STP


Similar triangles and other plane shapes

Pg 370 Ex 12.3

Pg 374 Ex 12.4 Q1-6

Pg 383 Q3 – 9 Pg 387 Q1-11 Pg 390 Q1-4 Pg 392 Q10,

14

609 - Similar polygons (2) 610 - Similar polygons (3) 612 - Similar triangles (2) 613 - Similar triangles (3) 614 - Similar shapes (problem solving)

Areas and volumes of similar shapes (Classes should be taught both ratio method and fractional method)

Pg 376 Ex 12.4 Q7-16

Pg 378 Ex 12.5

Pg 382 Q1-3 Pg 389 Q1-2 Pg 391 Q5-8 Pg 392 Q11-

12

Pg 352 – 364 Ex 14A to 14D

616 - Area of similar shapes (2) 617 - Area of similar shapes (3) 620 - Volume of similar shapes (3) 621 - Volume of similar shapes (4)


Module 6 – Summary Statistics, Sampling and Number

TOPIC 12 - Statistics 1 – Summary Statistics, Sampling and Time Series Topic 12 Prior Knowledge Check: HegartyMaths Task

Understand the terminology of mean, median, mode, range, and find averages for raw data

405 - Mean (1) 409 – Median 404 – Mode 410 - Range


Textbook STP


Find averages (mean, median and mode) for frequency table & grouped frequency tables

Pg 76 Ex 3.5

417 - Mean from frequency tables (1) 418 - Mean from frequency tables (2) 416 - Median from frequency tables 415 - Mode from frequency tables 420 - Averages & range (problem solving) (2)

Decide which average is best for a set of data 413 - Selecting appropriate averages

Calculate Quartiles and IQR via interpolation for grouped data

411 - Upper & lower quartiles 412 - Interquartile range

Interpret and construct frequency tables and line graphs for time series data.

Pg 78 Ex 3.6 Q 2-4

Pg 67 Ex 3.2 Q 4-9

451 - Time series charts (2) 452 - Time series charts (3)

Understand the difference between a population and sample and how to take a random sample including stratified sampling

Pg 440 Ex 14.1

Pg 458 Q 1-5 Pg 463 Q 2-5

Pg 110 - 119 Ex 7A to 7C

395 - Random sampling 397 - Stratified random sampling (2) 398 - Stratified random sampling (3)

Using sampling to estimate the size of a population ‘Peterson capture-recapture’ method*

Pg 442 Ex 14.1 Q10-11

872 - Capture-recapture (1) 873 - Capture-recapture (2)


TOPIC 13 – Number, Percentage & Compound Measure Topic 13 Prior Knowledge Check: HegartyMaths Task

Finding HCF and LCM for numerical values 32 - Highest common factor (prime factorisation) 35 - Lowest common multiple (prime factorisation)

Understand how to find one quantity as a percentage of another, increase and decrease percentages and reverse percentage problems

87 - Find percentages of amounts 4 (using calculator) 90 - Percentage increase or decrease 96 - Reverse percentages 97 - Percentage change


Textbook STP


Find the HCF of algebraic terms, and solve worded problems for LCM

167 - HCF of algebraic expressions 36 - LCM (worded problems)

Systematic Listing strategies Product rule for counting with / without repetitions allowed.

670 - Systematic Listing 672 - Product rule for counting (2) 673 - Product rule for counting (3)

Recurring Decimals

Pg 109 Ex 4.5 Q10, 12 – 13 Pg 99 Ex 4.1

Q5 - 6

Pg 59 Ex 2C

54 - Convert recurring decimals to fractions 2

Understand and use percentages including solving problems in real context and financial mathematics

Pg 105 Ex 4.4 Pg 161 Ex 1.4 Q 8 - 12

92 - Repeated percentage increase or decrease 2 98 - Percentages (worded problems) 760 - Profit and loss (2)

Set up, solve and interpret growth and decay problems including simple and compound interest

Pg 340 Ex 11.1

Pg 161 Ex 1.3 Q 9 - 16

93 - Simple interest 94 - Compound interest 753 - Money (problem solving 2) 754 - Money (problem solving 3)


Module 7 – Trigonometry and Circle Theorems

TOPIC 14 – Pythagoras & Trigonometry in 2D & 3D Topic 14 Prior Knowledge Check: HegartyMaths Task

Pythagoras in 2D

502 - Pythagoras (applied) (2) 504 - Pythagoras (multi-step) (2)

Trigonometry in 2D Right angled triangles, SohCahToa 510 - Trigonometry (find side) (2) 512 - Trigonometry (find angle) (2) 514 - Trigonometry (multi-step) (2)


Textbook STP


Know and use the Sine Rule Pg 411 Ex

13.5

Pg 268, Ex 11G Pg 272, Ex 11H

522 - Sine rule (find length) (2) 524 - Sine rule (find angle) (2) 525 - Sine rule (ambiguous case)

Know and use the Cosine Rule Pg 415 Ex

13.6 Pg 274, Ex 11I

528 - Cosine rule (find side) (2) 530 - Cosine rule (find angle) (2)

Calculate the area of a triangle using cabsin2

1

Pg 411 Ex 13.5

Pg 279, Ex 11K

518 - Area of triangle (1/2absinC) (2)

Pythagoras and Trigonometry in 3D for right angled triangles

Pg 418 Ex 13.7

506 - 3D Pythagoras (2) 507 - 3D Pythagoras (3) 856 - 3D trigonometry (3) 857 - 3D trigonometry (4) 858 - 3D trigonometry (5) 859 - 3D trigonometry (6) 860 - 3D trigonometry (7) 861 - 3D trigonometry (8) 862 - 3D trigonometry (9) 863 - 3D trigonometry (10)

Know the exact values of sin θ, cos θ & tan θ for θ = 0, 30, 45, 60, & 90.* (Two triangles should be covered, Equilateral side length 2, R-Angle Isosceles side length 1)

Pg 402 Ex 13.2, Pg 405 Ex 13.3, Pg 408 Ex 13.4

Pg 266, Ex 11F

846 - Non-calculator trigonometry (2) 847 - Non-calculator trigonometry (3) 850 - Non-calculator trigonometry (6) 851 - Non-calculator trigonometry (7)


Use the Sine Rule and Cosine Rule to solve problems in 2D and 3D.

Pg 411 Ex 13.5, Pg 415

Ex 13.6

Pg 281, Ex 11L Pg 283, Ex 11M

532 - Sine & cosine rules (multi-step) (1) 533 - Sine & cosine rules (multi-step) (2) 852 - Non-calculator trigonometry (Problem solving 1) 853 - Non-calculator trigonometry (Problem solving 2)


TOPIC 15 – Circle Theorems Topic 15 Prior Knowledge Check: HegartyMaths Task

Terminology for parts of a circle 592 - Parts of the circle


Textbook STP


Angle at centre, twice angle at circumference

Pg 502 Ex 16.1

Pg 316 – 337 Ex 13E – 13R

594 - Circle theorem (1) 595 - Circle theorem (2)

Cyclic quadrilateral

Pg 504 Ex 16.2

597 - Circle theorem (4)

Angles in the same segment are equal

Pg 506 Ex 16.3


Alternate segment theorem

Pg 509 Ex 16.4


External Tangents from a fixed point equal in length

Pg 512 Ex 16.5, Q1 – 8


Tangent meets radius at 90o

Pg 523 Extend

Exercise


Radius perpendicular to chord will bisect


Problem solving with mixed circle theorems

603 - Circle theorems (using algebra) 604 - Circle theorems (multi-step) (1) 605 - Circle theorems (multi-step) (2) 606 - Circle theorems (multi-step) (3)


Module 8 – Ratio, Proportion, Data representation and Probability

TOPIC 16 – Ratio & Proportion Topic 16 Prior Knowledge Check: HegartyMaths Task

Understand ratio notation and simplify ratios 329 - Simplify ratios

Divide quantities by ratios 332 - Share in a given ratio 1 333 - Share in a given ratio 2

Write Ratio’s in the form 1:n or m:1 331 - Write ratios in the form 1:n or n:1


Textbook STP


Convert problems between ratio and fraction Pg 103 Ex 4.3 330 - Write ratios as fractions/proportions

Compare Ratios, including more complex problems

334 - Share in a given ratio 3 335 - Harder problems involving ratios 1 336 - Harder problems involving ratios 2 337 - Harder problems involving ratios 3

Solving Ratio Problems with Algebra 338 - Solve ratio problems using algebra

Solve problems involving direct proportion, using formula 𝑦 = 𝑘𝑥, including more complex problems such as powers and roots

Pg 588 Ex 19.1

Pg 590 Ex 19.2

Pg 613 Q4 – 7,

Pg 25, Ex 3B Pg 28, Ex 3C Pg 36, Ex 3F

343 - Algebraic direct proportion 1 344 - Algebraic direct proportion 2 345 - Algebraic direct proportion 3

Solve problems involving inverse proportion,

using formula 𝑦 =𝑘

𝑥, including more complex

problems such as powers and roots

Pg 592 Ex 19.3

Pg 32, Ex 3D Pg 34, Ex 3E Pg 36, Ex 3F

346 - Algebraic inverse proportion 1 347 - Algebraic inverse proportion 2

Represent direct and inverse proportion graphically

Pg 588 Ex 19.1, Pg 590 Ex 19.2, Pg 592 Ex 19.3

348 - Graphs & algebraic proportion


TOPIC 17 - Statistics 2 (Data Representation) Topic 17 Prior Knowledge Check: HegartyMaths Task

Pie Charts 428 - Pie charts (2)


Textbook STP


Draw and interpret Frequency Polygons and Cumulative Frequency Diagrams

Pg 443 Ex 14.2, Pg 446

Ex 14.3

Pg 126 Ex 8A

441 - Frequency polygons 438 - Cumulative frequency diagrams (2)

Draw and interpret Box plots and Stem and Leaf Diagrams.

435 - Box plots (2) 440 - Box plots (4) 431 - Stem & leaf diagrams (2)

Solve advanced questions involving Pie Charts

429 - Pie charts (3)

Identify diagrams of skewed data sets matching cumulative frequency to box plot.

Draw and interpret Histograms Including problem solving with Histograms

Pg 449 Ex 14.4, Pg 450

Ex 14.5

Pg 134 – 145 Ex 8C to 8E

444 - Histograms (3) 443 - Histograms (2) 445 - Histograms (4) 447 - Histograms (6) 448 - Histograms (7) 449 - Histograms (8)

Interpret, analyse and compare distributions through graphical representations and measures of location and spread (averages, quartiles, IQR range and any outliers)

Pg 453 Ex 14.6

439 - Cumulative frequency diagrams (3) 433 - Stem & leaf diagrams (4) 436 - Box plots (3)

Use and interpret Scatter Graphs of bivariate data recognising correlation

Pg 70 Ex 3.3 Pg 379 Ex 15D

453 - Scatter diagrams (1) 454 - Scatter diagrams (2)

Draw lines of best fit and use to extrapolate recognising the dangers of doing so

Pg 72 Ex 3.4 Pg 384 Ex 15E


TOPIC 18 – Probability Topic 18 Prior Knowledge Check: HegartyMaths Task

Understand probability notation, including not probabilities P(A) – probability of event A

351 - Probability of single events (1) 352 - Probability of single events (2)

353 - Probability of an event not happening

Relative frequency and estimates of expected outcomes 356 - Experimental probability & relative frequency 357 - Relative frequency & testing for bias


Textbook STP


Mutually Exclusive and Independent Events. AND and OR rules for two events

Pg 310 Ex 10.2

Pg 387 Ex 16A Pg 388 Ex 16B

Use of two way tables to solve problems 422 - Two-way tables (1) 423 - Two-way tables (2) 424 - Two-way tables (3)

Use of Venn Diagrams to solve problems Construct and complete Venn diagrams including cases where intersect isn’t known Conditional and given probability problems

Pg 321 Ex 10.6

Pg 332, Q 9, 11

Pg 337, Q8, 9

375 - Shading sets in Venn diagrams (2) 376 - Shading sets in Venn diagrams (3) 383 - Venn diagrams for probability (1) 384 - Venn diagrams for probability (2) 385 - Venn diagrams for probability (3) 386 - Venn diagrams for probability (4) 387 - Venn diagrams for probability (5) 388 - Venn diagrams for probability (6) 391 - Venn diagrams & conditional probability (combined)

Use tree diagrams to solve independent and dependent events, conditional probabilities.

Pg 314 Ex 10.4

Pg 318 Ex 10.5

Pg 392 Ex 16C Pg 398 Ex 16D

361 - Independent events & probability trees (1) 362 - Independent events & probability trees (2) 364 - Conditional probability (1) 365 - Conditional probability (2) 366 - Conditional probability (3) 367 - Conditional probability (4)


Module 9 – Functions and Curved Graphs

TOPIC 19 – Functions Topic 19 Prior Knowledge Check: HegartyMaths Task

Substitution into Formulae 279 - Substitution into important formulae


Textbook STP


Interpret simple expressions as functions with inputs and outputs Solving problems e.g. f(x) = 5, and f(4) = n

Pg 543 Ex 17.7

Pg 43, Ex 4A Pg 46, Ex 4B

288 - Function notation 1 289 - Function notation 2

Understand and find the inverse function through algebraic rearrangement

Pg 543 Ex 17.7

295 - Inverse functions 1 296 - Inverse functions 2

Interpret the succession of two functions as a ‘composite function’

Pg 543 Ex 17.7

293 - Composite functions 1 294 - Composite functions 2

Solving Complex problems with Functions, including terminology of range and domain

297 - Complex problems with functions 290 - Domain & range of functions 1 291 - Domain & range of functions 2

Solve approximate solutions to equations numerically using iteration Finding location of solution by change of sign Acquiring the iteration formula by rearrangement.

Pg 484 Q12 Pg 489 Q 14 & 15 Pg 492

Q5 Pg 496 Q11-

12 Pg 500 Q 11

322 - Iteration


TOPIC 20 – Curved Graphs & their Transformations Topic 20 Prior Knowledge Check: HegartyMaths Task

Sketch graphs of quadratic functions and find turning point 257 - Sketch a fully labelled quadratic graph


Textbook STP


Plot and recognise shapes of quadratic, cubic, reciprocal and exponential graphs, trigonometric graphs

Pg 176 Ex 6.6, Pg 180 Ex 6.7, Pg

182 Ex 6.8, Pg 595 Ex

19.4, Pg 402 Ex 13.2, Pg

405 Ex 13.3, Pg 408 Ex

13.4

Pg 133, Ex 6B Pg 53 – 69 Ex 4D - I

298 - Cubic graphs (from a table of values) 302 - Exponential graph 303 - Sine graph 304 - Cosine graph 305 - Tangent graph

Use quadratic graphs to solve new functions by drawing equation of straight line on graph. Use graphs to solve simultaneous equations, one linear, one quadratic

Pg 472, Ex 15.1

Pg 142, Ex 6E

260 - Using a quadratic graph to solve a related quadratic equation 259 - Simultaneous equations using graphs (quadratic & linear)

Apply transformations y = f(x) + a, y = f(x + a), y = af(x), y = f(ax) including applying these to Sine and Cosine Graphs

Pg 602 Ex 19.6

Pg 605 Ex 19.7

Pg 50, Ex 4C

307 - Graph transformations 1 f(x)±a 308 - Graph transformations 2 f(x±a) 309 - Graph transformations 3 af(x) 310 - Graph transformations 4 f(ax) 311 - Graph transformations 5 -f(x) 312 - Graph transformations 6 f(-x) 313 - Graph transformations 7 (combined)

Plot & interpret graphs of non-standard functions in real contexts to find approximate solutions to problems eg for kinematic problems

Pg 182 Ex 6.8 Pg 171 Ex 6.4

Pg 168 – 184 Ex 7D - J

899 - Sketch graphs for water flows (1) 900 - Sketch graphs for water flows (2) 901 - Sketch graphs for water flows (3) 902 - Sketch graphs for water flows (4) 883 - Speed-time graphs (4)


Interpret the gradient at a point on a curve as the instantaneous rate of change, in numerical, algebraic & graphical contexts

Pg 166 Ex 6.3, Pg 170 Ex 6.4, Pg

598 Ex 19.5

889 - Gradient at a point on a curve

Calculate or estimate gradients of graphs and areas under curves. Interpret this for distance-time, velocity -time and financial contexts.

Pg 163, Ex 7B

891 - Area under a curve (1) 892 - Area under a curve (2) 893 - Area under a curve (3) 876 - Distance-time graphs (3) 877 - Distance-time graphs (4) 881 - Speed-time graphs (2) 882 - Speed-time graphs (3) 884 - Speed-time graphs (5) 885 - Speed-time graphs (6) 886 - Speed-time graphs (7)

Recognise and use the equation of a circle centre at origin and find equation of a tangent to a circle at a given point

Pg 185, Ex 6.8 Q 10

Pg 514, Q 9 - 12

Pg 518, Q 6

314 - Equation of a circle 1 315 - Equation of a circle 2 316 - Equation of a circle 3 317 - Equation of a circle 4 320 - Circles, normals & tangents


Module 10 – Proof, Congruency and Vectors

Topic 21 – Proofs and Congruency Topic 21 Prior Knowledge Check: HegartyMaths Task


Textbook STP


Use algebra to construct arguments and proofs, including counterexamples Represent using algebra: odd numbers, even numbers, sum of digits.

Pg 545 Ex 17.8

Pg 549, Q13, 14, 16

Pg 553, Q 1, 2

325 - Direct algebraic proof 1 326 - Direct algebraic proof 2 327 - Direct algebraic proof 3 (quadratics) 324 - Proof & counterexamples

Understand what it means for shapes to be Congruent, and use of rules for congruent triangles

Pg 364 Ex 12.1, Pg 367

Ex 12.2 Pg 391, Q 9

Pg 393, Q 13

680 - Congruence (1) 681 - Congruence (2) 682 - Congruent triangles

Congruency Proofs

684 - Congruent triangles (problem solving 1) 685 - Congruent triangles (problem solving 2) 686 - Congruent triangles (problem solving 3) 687 - Congruent triangles (problem solving 4) 688 - Congruent triangles (problem solving 5) 689 - Congruent triangles (problem solving 6)

Similarity Proofs

Pg 374 Ex 12.4

Q 2 – 5 Pg 390, Q 1

Pg 393, Q 14

Proof of circle theorems Should be

covered with top sets

816 - Proof of Circle Theorem (1) 817 - Proof of Circle Theorem (2) 818 - Proof of Circle Theorem (3)


819 - Proof of Circle Theorem (4) 820 - Proof of Circle Theorem (5)

Proof of Sine, Cosine and Area rules for triangles

520 - Sine rule (proof) 526 - Cosine rule (proof) 516 - Area of triangle (1/2absinC) (proof)

Proofs of angle sum of triangle, external opp. angle of triangle equals sum of opp. interior angles

Extension in class if you have time

484 - Proof - angles in triangles

Proof of quadratic formula from general form via complete the square

Extension in class if you have time

240 - Proof of the quadratic formula


TOPIC 22 - Vectors Topic 22 Prior Knowledge Check: HegartyMaths Task


Textbook STP


Sum, difference, scalar multiple, vector addition, column vectors, Magnitude

Pg 558 Ex 18.1, Pg 560 Ex 18.2, Pg 563 Ex 18.3

Pg 85 – 93 Ex 6A – 6C

622 - Vectors (1) - vectors & scalars 623 - Vectors (2) - column vectors 624 - Vectors (3) - negative vectors 625 - Vectors (4) - combining vectors 626 - Vectors (5) - multiplying by scalars 627 - Vectors (6) - magnitude of a vector

Solve simple geometric problems in 2D, including ratio problems

Pg 566 Ex 18.4

Pg 94 - 102 Ex 6D – 6E

628 - Vectors - geometry problems (1) 629 - Vectors - geometry problems (2) 630 - Vectors - geometry problems (3) 631 - Vectors - geometry problems (4)

Use vectors to construct geometric arguments & proofs, including proof of straight line, proof of parallel.

Pg 568 Ex 18.5

Pg 580 Q6, 7 - 13

Pg 103 – 107 Ex 6F

632 - Vectors - geometry problems (5) 633 - Vectors - geometry problems (6) 634 - Vectors - geometry problems (7) 635 - Vectors - geometry problems (8) 636 - Vectors - geometry problems (9)

ks4 scheme of work edexcel gcse 2017+ (teacher version

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