Set 3 R = Recap level 6; C = Core level 7 (bold); E = Extension level 8 (italics) http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Y10 & 11 Higher GCSE SOW

Date Topic Notes Examples Student

Reference Resources 24th Jun – 23rd Jul Change of timetable. Summer Term of Y9

1. INDICES: STANDARD

FORM

R: Squares, cubes; square roots, and

cube roots

C: Index notation

Laws of indices

E: Standard form

Positive integers only

Positive integer powers only

With and without calculator including negative indices

Find 32 , 23, √ √

√

Find HCF of 216 and 240

Simplify a5 a3; m4 m2

Evaluate 2.762 1012 4.97 1021(cal.)

Evaluate 2.8 104 7 106 (no cal.)

Evaluate 2.8 104 7 106 (no cal.)

Ex 13, 14 p14-18 (HCF, LCM etc) Ex 13 p14 (roots) Ex1,2 p354-355 (indices) Ex18,19 p68-71 (standard form)

There is teacher support material for

each unit, including teaching notes,

mental tests, practice book answers, lesson plans, revision tests &

activities. The teacher support

material is available HERE

Clip 44 Factors, Multiples and

Primes

Clip 95 Product of Prime Factors

Clip 96 HCF & LCM

Clip 99 Four rules of Negatives

Clip 45 Evaluate Powers

Clip 46 Understanding Squares,

Cubes & Roots

Clip 111 Index Notation for

Multiplication. & Division

Clip 135 Standard Form Calculations

Clip 156 Fractional & Negative

Indices

23rd Jul – 4th Sept

SUMMER HOLIDAYS

9th Sept (Y10)

2. FORMULAE: ALGEBRAIC

FRACTIONS

R: Construct & use simple formulae

C: Substitution of any number into

simple formulae

E: More complex formulae:

C: Change of subject

E: More complex change of subject

E: Common term factorisation

Opportunity for revision of

negative numbers, decimals, simple fractions.

Subject appears only once

Find the perimeter of this rectangle given n = 5

Given q – 2, v 21, find the value of √v2 q2.

More complex formulae: Given u 2 , v 3, find f when 1 = 1 + 1

f u v

Simple: make x the subject of y = mx + c

Complex version: make L the subject of t = 2π√

Make v the subject of 1 = 1 + 1

f u v

Factorise x3y4 x4y3 x2y

Ex1 p96 (basic of algebra) Ex7 p104 (definitions) Ex24 p75-76 (substitution)

Clip 104 Factorising

Clip 107 Changing the subject of the

Formula

Clip 111 Index Notation for Mult. &

Division

Clip 163 Algebraic Fractions

Clip 164 Rearranging Difficult

Formulae

23rd Sept (Y10)

3. ANGLE GEOMETRY

R: Angle properties of straight lines,

points, triangles, quadrilaterals, parallel

lines

C: Angle symmetry & properties of

polygons

Symmetry properties of 3-D shapes

Compass bearings

E: Angle in a semi-circle Radius is perpendicular to the tangent

Radius is perpendicular bisector of

chord

Include line and rotational symmetry

Use standard convention for

labelling sides & angles of polygons

Easier to calculate the exterior

angle 1st then the interior

Include plane, axis and point Symmetry

8 compass points and 3 figure

bearings

Application of Pythagoras and

Trig. (after Unit 4 has been taught)

Calculate interior angle of a regular octagon/decagon

Describe fully the symmetries of this shape.

Scale drawings of 2-stage journeys

Ex1 p157-159 (angles) Ex4 p164-166 (angles in polygons) Ex23-25 p337-343 (circle theorems)

Clip 67 Alternate angles

Clip 68 Angle sum of a Triangle

Clip 69 Properties of Special

Triangles

Clip 70 Angles of Regular Polygons

Clip 150 Circle theorems

28TH Oct – 1st Nov

OCTOBER HALF TERM

4th Nov (Y10)

4. PYTHAGORAS THEOREM &

TRIGONOMETRY

R: Pythagoras Theorem

C: Trigonometry (sin, cos, tan)

Calculate a length & an unknown

angle

2D only

Angles of elevation and

depression

Bearings

2-D with right-angled triangles

only

SOH – CAH - TOA

Find x

Ship goes from A to B on a bearing 040Bearings for 20 km. How far north has it travelled?

Ex6-7 p294 (finding the length) Ex8 p297 (finding angles) Ex9 p299 (trig & bearing)

Clip 147 Trigonometry

E: Know the exact values of sin, cos

and tan at key angles

What are sin, cos and tan (0, 30, 45, 60, 90 degrees)?

(Y10)

5. PROBABILITY

R: Simple probability

Complimentary events

Listing combined outcomes of two events

C: Relative frequency experimental

probability and expected results

Appropriate methods of

determining probabilities

Probability of 2 events

Multiplication law for

independent events

E: Addition law for mutually exclusive

events

Conditional probability; dependent

Events

Use Venn Diagrams

pi 1; p p1

Use tree diagrams/ possibility

space diagram to find all

possible outcomes

Using symmetry/experiment

Tree diagrams

By listing, tabulation or tree diagrams

Sampling with replacement

Sampling without replacement

Using Venn diagrams

pheads on fair coin

If prain tomorrow

, what is pdry tomorrow?

Complete a possibility space diagram for the sum on two dice.

What is the probability of scoring a total of 7?

Do an experiment to find probability of drawing pin landing point up.

If p(rain)

, then we would expect

30 = 20 sunny days out of 30.

pace

=

There are 5 green, 3 red and 2 white balls in a bag. What is the probability of obtaining:

(a) a green ball (b) a red ball (c) a non-white ball?

Find the probability of obtaining a head on a coin and a 6 on a dice.

There are 3 blue and 5 red beads. Find the prob of picking a red then a blue with replacement.

If for a class, psize 6 feet0.2, psize 7 feet0.3

Calculate psize 6 or 7 feet

A bag contains 3 green, 5 red and 8 blue counters. 2 counters are taken from the bag.

Find the probability that

(i) both counters are the same colour (ii) one is green and the other red.

Examples of what pupils should know and be able to do for Venn

Diagrams:

Enumerate sets and unions /intersections of sets systematically, using tables, grids and Venn Diagrams. Very simple Venn diagrams previously KS2 content. Investigate – Venn Diagrams:

ξ = {numbers from 1- 15}; A = {odd numbers}; B = {multiples of 3} and C =

Rayner: Ch9 p445 MEP Student bk.

Unit 5 Teachers Notes

MEP Text Book NRich

Last One Standing

Mathsland National Lottery

Same Number!

Who’s the Winner?

Chances Are Clip 90 List Of Outcomes (Grade D) Clip 132 Experimental Probabilities (Grade C) Clip 154 Tree Diagrams (Grade B) Clip 182 Probability – And & Or Questions (Grade A* - A)

{square numbers}

(a) Draw a Venn diagram to show sets A, B & C. You’ll need 3 circles

(b) Which elements go in the overlap of

A & B

A & C

B & C

A, B & C

(c) Try and come up with three different sets where not all of the circles

overlap. How many different Venn diagrams with three circles that

overlap in different ways can you find?

20th Dec – 3rd Jan (Y10)

CHRISTMAS HOLIDAYS

6th Jan (Y10)

6. NUMBER SYSTEM

R: +, –, , whole numbers including

long multiplication and division

Multiplying and dividing by powers of

10

Rounding off

+, –, , decimals

C: Estimating answers

Use of brackets and memory on a

calculator

E: Upper and lower bounds including use in formulae

Without the use of a calculator

Decimal places and significant

figures

Including area, density, speed

127 23, 465 15

25.62 100, 216.2 10, 14 0.2

Round

to 2 d.p.; 39.96 to 3 s.f.

9.7 3.86; £3.36 7; £114.81 3

( )

9.7 means 9.65 x 9.75

100 metres (to nearest m) is run in 9.8 s (to nearest 0.1 s). Give the range of values within which the runner's speed must lie.

Ex19 p26-31 (estimating) Ex1 p49-50 Q21,22 (decimals to fractions) Ex3 p357 (surds)

Clip 101 Estimating (grade C)

Clip 125 & 160 Upper & lower bounds

Clip 98 & 155 Recurring Decimals to

Fractions

Clip 157 Surds (A)

Clip 158 Rationalising the

Denominator (A)

17th – 21st Feb

FEBRUARY HALF TERM

22ND February (Y10)

7. MENSURATION

R: Constructing nets of cuboids,

prisms, tetrahedrons

Appropriate degree of accuracy

Nets can be used (see below) for surface areas and volumes.

Rounding sensibly for the

Which of these is the net of a cuboid?

Ex20 p28-29 (estimating measures) Ex13-15 p185-193

Clip 71 & 72 Circles

Clip 73 Area of compound shapes

Clip 120 & 121 surface area

Clip 122 & 177 Volume

Clip 178 Segments & Frustums

Conversion of units

Volume/capacity problems

Area and perimeter of squares,

rectangles, Triangles; Volumes of

cubes and cuboids

Area/ circumference of circles

Volumes of triangular prisms and

cylinders

C: 2-D representations of 3-D objects

Difference between discrete &

continuous measures

Areas of parallelograms, trapezia,

kites, rhombuses and composite

shapes

Volumes of prisms and composite

solids

Surface area of simple solids:

cubes, cuboids, cylinders

Volume/capacity problems

E: Upper and lower bounds

Volume of pyramid, cone and

sphere

range of measures used and the

context

Familiarity with mm, cm, m,

km, g, kg, tonne; inches, feet,

yards, miles, oz, lb, stones, litres, gallons

Include compound measures

such as density & pressure

These must be known 'by

heart'

A r2 , C D

V = Area of cross-section

length

V r2h

Use of isometric paper

To include estimation of measures

Volume of prism = Area of

cross-section length of prism

Include compound measures

such as density.

Use of isometric paper

A gallon is about 4

litres. How many litres will an 8 gallon petrol tank hold?

Use Pressure, P = Force ÷ Area and density = mass ÷ volume

Find the volume of this given base = 3cm, height =4cm & length = 12cm

Given the plan and side elevation, draw a 3D isometric diagram of the object.

Illustrate current postal rates; shoe sizes

Find the area of this kite.

l 9.57 m 9.565 l 9.575

Calculate the radius of a sphere which has the same volume as a

(area & perimeter) Ex23-25 p211-217 (Volume & surface area) Ex27-28 p79-82 (compound measures)

Clip 124 metric units

Clip 126 compound measures

Length of circular arc, areas of

sectors and segments of a circle

Dimensions of Formulae

Notation [L] [T] [M] for basic

dimensions

solid cylinder of base radius 5 cm and height 12 cm.

Calculate the shaded area given a = 5

Which of the following could be volumes?

rl, x3, ab+ cd, ( )

; where (r, l, x, a, b, c, d, are lengths)

7th – 21st April

EASTER HOLIDAYS

22ND April (Y10)

8. DATA HANDLING

R: Two-way tables including

timetables and mileage charts

Interpreting and constructing pie charts and line graphs

Questionnaires and surveys

C: Frequency graphs

Time series & Moving Averages

E: Construct and interpret histograms with unequal intervals

Frequency polygons

12 hour and 24 hour clock

Calculation of angles (total

frequency a factor or multiple of 360)

Fairness & bias

Identify trends in data over

time Calculate a moving average

Describe the trend in a time

series graph Use a time series graph to

predict futures (extrapolate)

For grouped data; equal

intervals. Include frequency polygons and Histograms

Understand and use frequency density

If a train arrives at a station at 13:26 and the connection leaves at 14:12, how long do you

have to wait?

2160 trees are planted. How many are oak?

Rayner p386-444 Unit 8 MEP

Unit 8 Teachers notes

Unit 8 MEP Text Clip 85 Two-Way Tables (Grade D) Clip 84 Questionnaires and Data Collection (Grade D) Clip 134 Designing Questionnaires (Grade C) Clip 153 Moving Averages (Grade B) Clip 181 Histograms (Grade A* - A)

9. DATA ANALYSIS

R: Mean for discrete data and tally

charts

C: Problems involving the mean

Mean, median, modal class for

grouped data

E: Cumulative frequency graphs;

median, quartiles

Box plots

Including discrete and

continuous data

Including percentiles

Inter-quartile and semi-interquartile range

Use box plots to compare sets

of data/distributions

Find the mean number of goals on these games.

No of goals 0 1 2 3 4 5 6 or more

Frequency 2 4 5 3 0 1 0

The mean of 6 numbers is 12.3. When an extra number is added, the mean changes to

11.9. What is the extra number?

Rayner p386-444

Unit 9 Teachers notes Clip 133 Averages From a Table (Grade C) Clip 151 Cumulative Frequency (Grade B) Clip 152 Boxplots (Grade B)

26th – 30th May (Y10)

MAY HALF TERM

2ND Jun (Y10)

10. EQUATIONS

R: Negative numbers in context

Number lines Ordering directed numbers

+, –, , directed numbers

Simplifying expressions Manipulating and solving

Simple linear equations

C: Linear equations

Trial and improvement methods

Expansion of brackets

E: Simultaneous linear equations

Factorisation of functions

Solve quadratic equations by factorising

Temperature problems

One fraction and/or one bracket

Algebraic solutions inc.

deriving from real-life

situations

Common terms, difference of

two squares

6oC 4oC ?

2a 3b a 2b ?

Expand 2 a 6?

Solve x 3 7; x 5 10; 3x 15

Solve 2x 3 7; 3x 4 x 18

Solve for x to 2 d.p. x3 7x 6 20 using trial & Improvement

Multiply out 2r 3s2r 5s

Solve: x 4y 7 and x + 2y = 16; Solve 2x y 5 and x 4y 7

Factorise (i) x2 1 (ii) x2 x

Solve (i) x2 1 (ii) x2 x

Ex20-24 p72-76 Ex1-6 p96-103 Ex6-8 p361-363 Ex15 p374

Clip 110 Trial & Improvement

Clip 105 Solving Equations

Clip 106 Forming Equations

Clip 115 Solving Simultaneous Eqs

Graphically

Clip 142 Simultaneous Linear

Equations

Clip 140 Solving Quadratic Eqs by

Factorising

Clip 141 Difference of Two Squares

Clip 161 Solving Quadratics using the

Formula

Clip 162 Solve Quadratics by

Completing the Square

11. FRACTIONS and

PERCENTAGES

R: Expressing quantities as a

percentage or a fraction

Finding fractions and percentages of

quantities

Discount, VAT, commission

30 out of 50; 17 out of 20 =

of 72 ? 13% of £97 =

20% VAT on hotel bill of £200?

Clip 47 Equivalent Fractions

Clip 48 Simplification of Fractions

Clip 49 Ordering Fractions

Clip 55 Find a Fraction of an Amount

Clip 56 & 57 arithmetic with

Fractions

Clip 58 Changing Fractions to

Decimals

Clip 139 Four Rules of Fractions

Clip 51 & 52 % of Amount

C: Percentage and fractional

changes

Manipulating fractions

E: Compound interest

Appreciation and depreciation

Reverse percentage problems

, , , with or without a

calculator

Repeated proportional change

;

Find the compound interest earned by £200 at 5% for 3 years.

A car costs £5,000. It depreciates at a rate of 5% per annum. What is its value after 3 years?

The price of a television is £79.90 including 17.5% VAT. What would have been the price with no VAT?

Clip 53 & 54 Change to a %

Clip 92 Overview of %

Clip 93 & 136 Increase/dec. by a %

Clip 137 Compound Interest

Clip 138 Reverse %

16TH June (Y10)

End of Year 10 Exams

23rd Jun 2014

START OF NEW TIMETABLE START OF YEAR 11

23rd Jun (Y11)

12. NUMBER PATTERNS and

SEQUENCES

R: recognise and continue number

patterns

C: Find the formula for the n th

term of a linear sequence.

Recognise & use sequences of

triangular, square, cube, Fibonacci,

quadratic & geometric sequences

E: Find a quadratic formula for the n

the term of a sequence

Explain the pattern in words If numbers ascend in 3’s, that’s the 3 x table = 3n. Then find the number before the 1st term (=5), so, nth term is 3n+5

Fibonacci – 1, 1, 2, 3, 5, ..., ...

1, 4, 7, 10, ..., ...

For sequence , the number of sides is 4, 7, 10, ...,

.... How many sides in the 100th member?

n th term in sequence 8, 11, 14, 17, ..., ..., ...

List (i) 12 – 162 (ii) 13 – 53 (iii) the 1st 10 triangular numbers

Continue the sequence: 1, 1, 2, 3 … Continue the sequence: 1, 2, 4…

Find n th term for

(i) 3, 6, 11, 18, ..., n2 2(ii) 6, 7, 10, 15, ..., n2 2n 7

Ex19 p119-122 (sequences) Ex20 p123-125 (nth term)

Clip 65 Generate a Sequence from

Nth term

Clip 112 Finding the nth term

13. GRAPHS

R: Coordinates Plotting straight lines and curves given

values

C: Graphs in context, including

conversion

and travel graphs (s – t and v – t)

and an

understanding of speed as a

compound unit

Scatter graphs and lines of best fit

E: Equation of straight line

Graphical solution of simultaneous

equations

Draw & recognise Graphs of common

functions

Solve equations by graphical methods

Draw and interpret

Gradient and area under graph

a for polygon graphs only

Opportunities for use of ICT

(Excel can find equation for

line of best fit)

Use y = mx + c to identify

parallel lines

Quadratic, cubic, reciprocal and

exponential equations

Identify coordinates of points in the xy-plane. Plot graph for values x –3 –2 –1 0 1 2 3

y 9 4 1 0 1 4 9

Calculate the speed for each part of the journey

Name the type of correlations illustrated below

Find equation of straight line joining points (1, 2) and (4, 11).

Find equation of straight line going through points (1, 3) and gradient 4.

Which lines are parallel? y = 3x = 1, 2y = 6x – 8, -3x + y = 7 etc.

Solve graphically: (i) y = x + 5 and y = 7 – x (ii) x + y = 4and 2x + y = 10

Use the graph of y x2 5x to solve x2 5x 7.

Draw graphs of y x2 5x and y x3 to solve x2 5x x3.

Solve graphically 2x 5.

Ex21 p126 Ex23 p129 Q1-4 (straight line graphs) Ex 24 p131 (y = mx + c) Ex23 p129 Q5-8 (gradients)

Clip 87 Scatter Graphs (Grade D)

Clip 113 Drawing straight line graphs

Clip 114 Finding the Equation of a

straight line

Clip 116 Drawing Quadratic Graphs

Clip 117 Real-life Graphs

Clip 143 Understanding y=mx+c

Clip 145 Graphs of Cubes &

Reciprocal Functions

Clip 166 Gradients of Parallel and

Perpendicular Lines

July (Y11)

SUMMER HOLIDAYS

September (Y11)

14. LOCI and

TRANSFORMATIONS:

CONGRUENCE and SIMILARITY

R: Scale drawings

Notation 1 : 200, etc.

Make scale drawing of garden or playground

Ex2-3 p171-176 (simple construction)

Clip 127 bisecting a line

Clip 128 perpendicular to a line

Clip 129 bisecting an angle

Clip 130 Loci

Construction using protractor

and compasses

Simple enlargements and reflections

C: Constructions of loci

Enlargements

Reflections

Rotations

Translation

E: Combination of two transformations

Congruence – conditions for triangles

Similarity – similar triangles, line, area

and volume ratio

Triangle and other shapes

About point(s) and line(s)

Positive integers and simple

fractions for scale factor

Reflect lines in oblique lines

Describe the mirror line using

simple equations

Rotation about any point 90

o ,

180o in a given direction

Finding the centre of rotation

by inspection.

Using vector notation

SSS SAS AAS RHS

Internal line ratio (BE:CD = 3:5) Draw 2 separate triangles and

find scale factor/multiplier (=

)

Construct the locus of points equidistant from both lines

Enlarge diagram by scale factor

, centre A (inside triangle)

Find the Equations of the mirror lines and reflect the shape in the line y =

0, y = -3, y = x

Draw image after translation ( )

Prove that ▲ABX & ▲CDX are congruent

Calculate (i) x and y (ii) ratio of areas ABE

and BCDE

Two similar cones have heights 100cm & 50cm. The

Ex13 p310 (Translation & enlargement) Ex12 p308 (reflection & rotation) Ex14 p313 (combined transformations) Ex6 p169 (congruence) Ex29-30 p227 (lengths & similarity) Ex31 p233(areas of similar shapes) Ex32 p237

Clip 74-77 Transformation

Clip 171 Negative scale factor

Clip 123 Similar Shapes

Clip 124 Dimensions

Clip 149 Similar Shapes

Clip 179 Congruent Triangles

volume of the smaller cone is 1000cm3, what is the volume of the larger cone?

E.g. Persil is available in 800 g and 2.7 kg boxes which are similar in shape. The smaller

box uses 150 cm3 of card. How much card is needed for the larger box?

(volumes of similar shapes)

Combining Transformations: Play ‘TranStar’ http://www.mangahigh.com/en_gb/games/

(Y11)

OCTOBER HALF TERM

November (Y11)

15. VARIATION: DIRECT and

INVERSE

R: Unitary ratios; direct and inverse

variation

Map scales / ratios

C: Proportional division

Direct and inverse variation

E: Functional representation

Graphical representation

Recipes Mixed units Mathswatch leads into this topic in a very easy way

y x , y x2 , y x3 ,

y

y

If 5 books cost £15, what is the cost of 8 books? If 8 people take 3 days to paint some

railings, how long would 6 people take?

e.g. 1:20 00; 1 cm to 2 km

If the map scale is 1:250 000, what is the actual distance between two churches 3 cm apart on

the map?

Share £30 in the ratio 2:3.

For the following data, is y proportional to x?

x 3 4 5 6 y 8 10 12 14

If y is proportional to the square of x and y 9 when x 4, find the positive value of x for

which y 25.

Ex12-13 p263-267 P267-269 (common curves to discuss)

Clip 159 Direct & Inverse Proportion

December (Y11)

16. INEQUALITIES

R: Solution if inequalities on a number

line

C: Solution of linear inequalities and

simple quadratic inequalities

E: Graphical applications

Notation: or , < or >,

● or ○

Locating and describing regions of graphs

List whole numbers n which satisfy 4 n 2

List whole numbers n which satisfy

Solve for x: (a) 5x 2 x 16 (b) x2 25

Sketch lines y x 1, y 3 x and x 2; hence, shade the region for which

y x 1, y 3 x and x 2.

Ex9-10 p255-258 (solving) Ex11 p259-260 (regions)

See Core 1 LiveText for examples

Clip 108 Inequalities

Clip 109 Solving Inequalities

Clip 144 Regions

(Y11)

CHRISTMAS HOLIDAYS

January (Y11)

REVISION

Linear (A) Past paper booklets to be prepared in-house. Revision Workbooks to be ordered (payment to be collected beforehand) Intervention to be organised by teachers.

Review the entire SOW again from Year 10.

(Y11)

FEBRUARY HALF TERM

March (Y11)

REVISION

Review the entire SOW again –

March EASTER HOLIDAYS

April Revision & Intervention Past Papers on the shared area

Linear (A) Past paper booklets to be prepared in-house. Revision Workbooks to be ordered (payment to be collected beforehand)

Level 2 Past Papers – see fronter

Intervention to be organised by teachers.

May Study Leave

June EXAMS, EXAMS, EXAMS

NOTES FOR THE TEACHER

There is teacher support material for each unit, including teaching notes, mental tests, practice book answers, lesson plans, revision tests, overhead slides and additional activities. The teacher

support material is only available online.

Resources: Teacher support material for each unit, inc. teaching notes, mental tests, answers, lesson plans, revision tests and

additional activities is available online on the MEP website: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Homework: a variety of tasks can be set ranging from short Q&A to extended pieces of investigation work. When you set

homework – you MUST mark it and record it. You could also ask students to make summary notes of each topic to lay foundations

for independent study. Fronter has been loaded with a wealth of homework practice which students should be directed to by you.

Lesson planning & Expectations: You are expected to have extremely high expectations of all you students at all times – refer to

the diagram

Closing the Gap: Know your students, Plan effectively, Enthuse & Inspire, Engage & Guide, Feedback appropriately & Evaluate

together

FORMULAE SHEET

Perimeter, area, surface area and volume formulae

Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone:

Curved surface area of a cone = rl

Surface area of a sphere = 4 r 2

Volume of a sphere = 3

4 r

3

Volume of a cone = 3

1 r

2h

Kinematics formulae

Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken:

v = u + at

s = ut + 21 at

2

v2 = u

2 + 2as