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Chislehurst and Sidcup Grammar School Mathematics Department 1
KS4 Scheme of Work Edexcel GCSE 2017+ (Teacher Version)
Contents Key Information ................................................................................................................................................. 2
Module 1 – Indices and Surds ........................................................................................................................... 4
TOPIC 1 - Indices ............................................................................................................................................. 4
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
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
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
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
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
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*
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)
Interpret, analyse and compare distributions through graphical representations and measures of location and spread (averages, quartiles, IQR range and any outliers)
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
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
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
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