Post on 28-Dec-2021
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
Chislehurst and Sidcup Grammar School Mathematics Department 2
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.
Chislehurst and Sidcup Grammar School Mathematics Department 3
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)
Chislehurst and Sidcup Grammar School Mathematics Department 4
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
Chislehurst and Sidcup Grammar School Mathematics Department 5
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 6
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 7
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 8
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 9
TOPIC 6 – Estimation, Rounding, Approximation & Bounds Topic 6 Prior Knowledge Check: HegartyMaths Task
Carry out sensible estimations for calculations 131 - Estimate complex calculations
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 10
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 11
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 12
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 13
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 14
TOPIC 11 – Similar Shapes Topic 11 Prior Knowledge Check: HegartyMaths Task
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 15
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 16
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 17
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)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 18
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)
Chislehurst and Sidcup Grammar School Mathematics Department 19
TOPIC 15 – Circle Theorems Topic 15 Prior Knowledge Check: HegartyMaths Task
Terminology for parts of a circle 592 - Parts of the circle
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
596 - Circle theorem (3)
Alternate segment theorem
Pg 509 Ex 16.4
598 - Circle theorem (5)
External Tangents from a fixed point equal in length
Pg 512 Ex 16.5, Q1 – 8
600 - Circle theorem (7)
Tangent meets radius at 90o
Pg 523 Extend
Exercise
599 - Circle theorem (6)
Radius perpendicular to chord will bisect
601 - Circle theorem (8)
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)
Chislehurst and Sidcup Grammar School Mathematics Department 20
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 21
TOPIC 17 - Statistics 2 (Data Representation) Topic 17 Prior Knowledge Check: HegartyMaths Task
Pie Charts 428 - Pie charts (2)
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 22
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 23
Module 9 – Functions and Curved Graphs
TOPIC 19 – Functions Topic 19 Prior Knowledge Check: HegartyMaths Task
Substitution into Formulae 279 - Substitution into important formulae
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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
Chislehurst and Sidcup Grammar School Mathematics Department 24
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
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 25
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
Chislehurst and Sidcup Grammar School Mathematics Department 26
Module 10 – Proof, Congruency and Vectors
Topic 21 – Proofs and Congruency Topic 21 Prior Knowledge Check: HegartyMaths Task
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)
Chislehurst and Sidcup Grammar School Mathematics Department 27
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
Chislehurst and Sidcup Grammar School Mathematics Department 28
TOPIC 22 - Vectors Topic 22 Prior Knowledge Check: HegartyMaths Task
Teaching Objectives Pearson
Textbook STP
Textbook HegartyMaths
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)