Edexcel GCSE Intermediate Scheme of Work
Edexcel GCSE Intermediate scheme
Using modules provided by Edexcel for:
GCSE Mathematics course with coursework (syllabus number1387)
Students in these groups will be issued with the text resources:
London GCSE Mathematics Intermediate Course (old version)
(Heinemann ISBN 0-435-53203-0)
London GCSE Revision and Practice Books in Spring Term Year 11
Exam Paper folders in Spring Term Year 11
The programme is referenced to:
- the modules provided by Edexcel for the GCSE Mathematics course with coursework (1387)
- the chapters of these books.
Whilst these are an important and useful resource, staff are reminded that they are only part of a variety of different materials that can be used in the teaching and learning programme. Where the text does not cover a particular topic this is referenced in the fifth column. For such topics worksheets and other resources are available in the mathematics staffroom.
Chapter / Chapter heading / Edexcel module / Edexcel objectives / Grade / Extra resources needed1. / Number / 1 / 1a
1b
1c / F
E
E / Order numbers of any size
Work with positive and negative temperatures
Work confidently without the aid of a calculator, including the four rules with negative numbers
2. / Simple Functions / 10 / 10a
10b
10c
10d / F
E
E
D / Continue sequences of diagrams
Continue linear and non-linear sequences of numbers
Generate sequences from given information
Investigate number patterns, describing them in words and using the nth term for linear expressions
3. / Probability 1 / 12 / 12a
12b
12c
12d
12e
12f / F
E
E
D
C
C / List outcomes of one or two events
Write down theoretical probabilities of a single event happening
Establish the estimated probability of an event happening
Find the probability of an event not happening given the probability of an event happening
Predict how many times an event may happened given the probability
Understand the concepts of exclusivity and independence
4. / 2D and 3D shapes / 2
6
11
30 / 2a
6a
6b
6b
6c
6g
11a
30a
30b
30c
30d / E
E
D
E
E
D
E
D
D
C
C / Use the angle sum for triangles and quadrilaterals to find other angles in the shapes
Plot and read co-ordinates in four quadrants
State the properties of each 2-D shape and classify a shape according to its symmetrical properties
Recognise congruency
Identify lines of symmetry or the order of rotational symmetry in 2-D shapes
Sketch plans of symmetry on simple shapes
Construct 2D and 3D shapes using ruler, pencil, protractor and compasses
Draw 2D representations of 3D objects, including the use of isometric paper
Use plans and elevations to answer questions
Draw nets of simple solids and use these to calculate surface areas of prisms, cylinders and shapes with rectangular and triangular faces
Solve problems involving volumes of prisms, cylinders and solids made from cuboids
5. / Measures 1 / 14 / 14h
14l / D
C / Convert between a variety of units using knowledge of metric equivalents of common imperial units
Calculate speed and other compound measures
6. / Approximation / 1
16 / 1d
16a
16d / D
C
C/D / Use a calculator to solve number problems and interpret the answers
Round numbers of any size to the nearest 10, 100, and 1000 or to any specified number of significant figures or decimal places
Use rounding methods to make estimates for simple and complex calculations
7. / Graphs of Linear Functions / 26 / 26a
26b
26c
26d
26e / D
C
C
B
B / Plot a straight line graph from a given set of values
Realise that an equation of the type y = mx + c represents a straight line graph, and plot this graph
Understand the relevance of m and c in the above equation
From a given graph, find the gradient and y-intercept and hence the equation of the graph
Draw a straight line graph without plotting points
8. / Collecting and Organising Data / 4 / 4a
4b
4c
4d
4e / D
C
F/E
E
E / Design a simple questionnaire, and appreciate deficiencies in a question
Understand the concept of sampling a population, what makes a fair sample, and explain deficiencies of sampling techniques
Collect data from a variety of sources
Sort and collect data in a tally table and grouped frequency table
Design and use two-way tables / 4c extra resources needed to cover objective
9. / Using and Applying mathematics / 10 / 10d
32a / D
C / Investigate number patterns, describing them in words and using the nth term for linear expressions
Understand and apply the geometry rules included in the module content / 10d this is a coursework guide - it will need supplementing 32a extra resources needed to cover objective
10. / Angles / 2 / 2b
2c
2d
2e / D
C
D
C/D / Know how to work out the angle sum for any given polygon, use to find other angles relating to polygons and understand which shapes tessellate
Calculate angles on parallel lines, at a point and on a straight line
Understand the two proofs relating to angles in a triangle
Draw and measure three figure bearings accurately / 2d extra resources needed to cover objective
11. / Fractions / 7 / 7a
7b
7c
7d
7e
7f
7g
7h
7l / E
E
D
E
C/D
E
D
D/C
C / Equate one fraction with another, and simplify fractions to their lowest terms
Understand and change between improper fractions and mixed numbers
Understand the concept of a recurring decimal
Convert fractions into decimals and vice versa, including recurring decimals
Perform the four basic operations with fractions
Calculate a fraction of a quantity
Write one number as a fraction of another
Solve problems involving fractions
Order fractions using common denominators or decimal conversions
12. / Measure 2 / 16
14
29 / 16b
16c
14l
29f / C
C
C
B / Recognise the different types of numbers
Recognise the limitations of a measurement
Calculate speed and other compound measures
Use powers of scale factors to convert between units of area and volume
13. / Quadratic Functions / 5
25 / Only do pages 171 - 177
14. / Properties of numbers / 3
29
31
29 / 3a
3b
3c
3d
3e
3f
29a
29b
31a
31b
31c
29c
29d
29e / F
E
C
C
C
C
F
D
C
E/C
B
B
B
B / Recognise the different types of numbers
Calculate square and cube measures
Find square and cube roots of numbers including decimals by trial and improvement and by calculator methods
Calculate powers of whole numbers including negative numbers
Write numbers in terms of their factors/prime factors and use prime factors to find the HCF
Use lists of multiples to find the lowest common multiple
Recall the cubes of 2, 3, 4, 5 and 10
Recall integer squares and corresponding square roots to 15 x 15
Round large or small numbers to 1 significant figure to make estimates in standard form
BODMAS and standard form
Distance of planets from sun
Know the rules of indices (adding, subtracting and multiplying indices), and simplify expressions
Evaluate fractional and negative indices
Calculate exact answers by manipulating simple surds without a calculator / A lot of objectives covered here - allow more time for this chapter
29c, 29d and 29e extra resources needed to cover objective and include fractional and negative indices and A
manipulating surds
A*
15. / Pythagoras' Theorem / 20 / 20a
20d
20e
20c / C
C
C
C / Identify the hypotenuse of a right-angle triangle
Use Pythagoras' theorem to find the length of any side of a right-angled triangle
Use Pythagoras' theorem to solve problems such as bearings, areas of triangles, diagonals of rectangles etc
Pick out right-angled triangles from diagrams, (e.g. circles, isosceles triangles) / 20c extra resources needed to cover objective
16. / Averages and spread / 17
23 / 17a
17b
17c
17e
23a
23b
23c
23d / F
D
E
C
B
B
B
B / Calculate mode, mean, median and range for simple data
Calculate mean and modal class from a discrete or grouped frequency table
Justify the choice of a particular average
Calculate and interpret the meaning of a moving average
Design and complete a cumulative frequency table, identifying class boundaries where necessary
Plot a cumulative frequency curve using upper class boundaries
Solve problems using a cumulative frequency curve (e.g. How many _____ were more than …..)
Use a cumulative frequency curve to estimate the median, lower quartile, and interquartile range / 17e extra resources needed to cover objective moving averages
17. / The tangent ratio / 21 / 21a
21b
21c / B
B
B / Identify appropriately the various sides of right-angles triangle as the Hypotenuse, Opposite and Adjacent
Recall the ratios for sine, cosine and tangent
Identify which of sine, cosine and tangent are required to solve a problem
18. / Graphs of more complex functions / 26
33 / 26f
26g
26h
33d
33e
33f
33g / C/B
D
B
B
B
B
B / Plot curves from given quadratic and cubic functions
Interpret and plot real-life graphs such as conversion graphs and distance/time graphs
Recognise graphs e.g. filling different shaped containers
Solve quadratics by constructing an appropriate graph
Solve cubics where the graph is given
Use terms like 'minimum point' maximum point' 'quadratic function'
Use graphical methods to find the maximum or minimum of a quadratic function
19. / Probability 2 / 24 / 24a
24b
24c
24d / C
B
C
B / Estimate probabilities and use relative frequencies to make predictions or test for bias
Complete tree diagrams as a means of showing outcomes for two successive events and related probabilities
Appreciate that a larger sample size will give a more accurate estimate
Know when to use the P(A) + P(B) 'OR' rule, and the P(A) x (B) 'AND' rule
20. / Lengths, areas and volumes / 11
13 / 11b
11c
11d
11e
13a
13b
13c
13d
29g / E
E
C
D
D
D
D
B
B / Find the perimeter and area of simple shapes, such as rectangles, squares, triangles, parallelograms, trapezia, kites and composites of rectangles and triangles
Know the formulae for area and volume of the shapes mentioned
Work confidently with 3D shapes and be able to calculate the volume of cuboids, prisms, solids made cuboids, and the surface area of solids with triangular and rectangular faces
Find how many boxes of a given size fit into a larger box
Use the vocabulary of a circle (circumference, radius, diameter, sector, segment, chord, tangent)
Recall and apply the formulae for the area and circumference of a circle given either the radius or diameter, using various approximations to or leaving as part of an irrational answer
Recognise that units of volume or area cannot be converted using linear conversion factors
Calculate angles within circles using rules relating to tangents and radii
Recognise the purpose of a formula by considering its dimensions / 13d extra resources needed to cover objective
21. / Algebraic expressions and formulae / 5
25 / 5a
5b
5c
19a
19c
19d
19e
25a
25b
25c
25d / E
E
D
D
C
B/C
B
C
B
B
B / Substitute positive and negative numbers into word formulae and algebraic formulae
Simplify algebra by collecting like terms - answers may involve negative coefficients
Remove and factorise a single pair of brackets - including cases where a variable is removed as a factor
Undertake simple substitution and substitution involving squaring
Generate algebraic formulae from information
Change the subject of formulae
Rearrange simple and complex formulae, including cases where the subject occurs more than once.
Expand and simplify two pairs of linear brackets, e.g. (x + 2) (x - 4), (3x + 2y) (4x + y), x + p) (a + g) etc
Factorise the trinomial, e.g. x2 - 5x + 6 = (x - 6) (x + 1)
Expand the square of a linear expression
Use a factorised trinomial in one variable to solve a quadratic equation
22. / Percentages / 9
27 / 9a
9b
9c
9d
9e
9f
27a
27b
27c
27d / D
E
D
C
C
D
C
B
B
B / Change between percentages, fractions and decimals
Find percentages of quantities, by both mental mathematics and calculator methods as appropriate
Increase and decrease quantities by a percentage, including within context of VAT, profit and loss
Find one quantity as a percentage of another, and calculate the percentage when an actual profit or loss is given
Calculate simple and compound interest
Solve problems using percentages e.g. taxation, bills
Recognise that an increase of e.g. 15% leads to 115% and decrease of e.g. 15% leads to 85%
Find the original amount e.g. price before a sale, price before VAT
Write down a decimal multiplier which is equivalent to an increase or decrease in percentage
Use multipliers to solve reverse percentage and compound interest problems
23. / Transformations / 6
18
34 / 6d
6e
6f
18a
18b
18c
18e
34a
34b
34c / D
D
D
C
C
D
C
C
B
C / Reflect a 2FD shape in a vertical, horizontal or diagonal line and state the equation of the line
Rotate a 2D shape about the origin or a point other than the origin, stating the angle, direction and centre of rotation
Translate a 2D shape and describe the translation in words
Recognise translations as sliding movements, and translate simple 2D shapes within a plane using words or vector notation
Understand which are the invariant properties of enlargements
Enlarge shapes using a variety of positive scale factors
Work on tasks involving these transformations
Use co-ordinates in 3 dimensions and use these to solve problems such as mid-points of lines
Solve problems involving similar polygons
Use and describe fully the four types of transformations in a variety of combinations / 34a, 34b extra resources needed to cover objective 34c - link back to transformations
24 / Presenting Data / 15 / 15a
15b
15c
15d
15e
15f
22a
22b
22c
22d / E
E
E
E
D
B
D
D
D
C / Sort and collect data in a tally table and grouped frequency table
Use a pie chart to display data as appropriate
Interpret given pie charts
Construct and interpret line graphs for all types of data
Construct and interpret ordered and unordered stem and leaf diagrams
Construct box plots
Plot and use a scatter graph to describe correlation
Describe a relationship between two variables as illustrated by a scatter diagram
Describe correlation in terms of the two variables, and as positive, weak, negative, or strong
Draw a line of best fit where possible "by eye", and use this to make predictions / 15e, 15f extra resources needed to cover objective and include box and whisker, B
stem and leaf diagrams D
25. / Ratio and Proportion / 14 / 14a / E / Recognise a ratio as a way of showing the relationship between two numbers
26. / Accurate drawings, scales and loci / 18
28 / 18d
18f
28a
28b
28c
28d / C
E
E
C
C
C / Recognise translations as sliding movements, and translate simple 2D shapes within a plane using words or vector notation
Use scale to interpret maths and complete scale drawings
Construct shapes from given information using only compasses and a ruler
Construct perpendicular bisectors, and angle bisectors using only compasses and a ruler
Construct LOCI in terms of distance from a point, equidistance from two points, distance from a line, equidistance from two lines and line of sight
Shade regions using LOCI to solve problems e.g. vicinity to lighthouse/port / For loci - extra resources needed to cover objective i.e. past exam papers
C
27 / The sine and cosine ratios / 21 / 21d
21e
21f
21g
21h / B
B
B
B
B / Use information given to write down the sine, cosine and tangent of an angle
Use information given to find angles using the appropriate ratio
Use the appropriate ration to find the lengths of sides in a right-angles triangle
Find angles of elevation and depression using the appropriate ratio
Apply trigonometric ratios and Pythagoras' Theorem to solve assorted problems, including those involving bearings
28. / Equations and inequalities / 8
33 / 8a
8b
8c
8d
33a
33b
33c
33h / D
B
C
B
B
B
B
B / Solve problems requiring inverse operations
Solve linear equations including those with an unknown on both sides, those that require prior simplification (e.g. brackets), fractional equations, and those where the answers are either negative or a fraction
Derive algebraic expressions from information given and extend this to derive equations
Solve linear inequalities through both algebraic methods and listing possible integer values
Factorise using the difference of two squares and use this to solve problems
Use factorising methods to simplify algebraic fractions
Solve simultaneous equations by eliminating a variable and by graphical methods, using them to solve problems
Use regions on a graph to solve inequality problems in two variables
29 / Interpreting data / 17 / 17d / D / Compare distributions using averages and range
30 / Calculators and computers / 3
7
9 / 16e
19b / D
C / Use a calculator correctly and efficiently for complex calculations (possibly involving powers and roots) and round the answers appropriately
Use trial and improvement methods to solve non-trivial equations such as cubics, usually to 1 d.p. / Revision - will cover many more objectives Calculator and spreadsheet work needs supplementing
35 / Module 35 not covered in the book - extra resources needed to cover objectives
Comments
This scheme is matched to the new syllabus
The need for extra resources to cover some objectives is identified
A time scale is provided in the accompanying two-year scheme
Objectives can be shared with pupils
We recommend you buy one copy of the new version textbook, as there is an extra section on handling data for coursework, which would cover module 35
Edexcel modules matched to books by Fiona Mapp and Heather Boyce
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