Set 2 R = Recap (levels 6 & 7); C = Core level 8 (bold); E = Extension (italics)

http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm Y10 & 11 Higher GCSE SOW

Date Topic Notes Examples Student

Reference Resources 23rd Jun – 23rd Jul Start of new timetable end of Y9

1. INDICES: STANDARD FORM

R: Index notation Prime factors

Laws of indices

C: Indices (including negative &

fractional indices)

Standard form

N1 – N9

Positive integer powers only

With and without calculator

Simplify a5 a3; m4 m2

Prime factors Find HCF of 216 and 240

812/3 (without calculator); simplify (𝑚2

𝑛)–1

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 – 31st Aug

SUMMER HOLIDAYS

1st September (Y10)

2. FORMULAE: ALGEBRAIC

FRACTIONS

R: Formation, substitution, change of

subject in formulae

C: More complex formulae:

– substitution

– powers and roots

– change of subject with subject

in more than 1 term

Common term factorisation

E: Algebraic fractions – addition

and subtraction

A1 – A7

With and without calculator Opportunity for revision of

negative numbers, decimals,

simple fractions.

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

Make L the subject of t = 2π√𝐿𝐺

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

f u v

Make v the subject of 1 = 1 + 1

f u v

Factorise x3y4 x4y3 x2y

Simplify 𝑥

𝑥+1+

2𝑥

2𝑥+1

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

October (Y10)

3. ANGLE GEOMETRY

R: Angle properties of straight

lines, points, triangles, quadrilaterals,

parallel lines

G1, 3, 4, 6, 13

Include line and rotational

symmetry

Calculate interior angle of a regular octagon/decagon

Shade in the diagram so that it has rotational symmetry of

Ex1 p157-159 (angles) Ex4 p164-166 (angles in polygons)

Clip 67 Alternate angles

Clip 68 Angle sum of a Triangle

Clip 69 Properties of Special

Triangles

Clip 70 Angles of Regular Polygons

Angle symmetry properties

of polygons

Symmetry properties of 3-D shapes

Compass bearings

C: Angle in a semi-circle

Radius is perpendicular to the

tangent

Radius is perpendicular bisector of

chord

E: Angles in the same segment are

equal

Angle at the centre is twice the angle at the circumference.

Opposite angles of a cyclic

quadrilateral add up to 180 . Alternate segment theorem.

Tangents from an external point

are equal.

Intersecting chords

Tangent/secant

Include plane, axis and point

Symmetry 8 compass points and 3

figure bearings

Application of Pythagoras

and Trig.

Use standard convention for labelling sides & angles of

polygons

AX.BX CX.DX

PT2 PA.PB

Order 4 but no lines of symmetry.

Describe fully the symmetries of this shape.

Scale drawings of 2-stage journeys

Calculate angles: BDA, BOD, BAD & DBO

Ex23-25 p337-343 (circle theorems)

Clip 150 Circle theorems

28th Oct – 1st Nov

OCTOBER HALF TERM

4th November (Y10)

4. TRIGONOMETRY

R: Trigonometry (sin, cos, tan)

Know the exact values of sin, cos

and tan at key angles

G20 – G23

Angles of elevation and depression

Bearings

2-D with right-angled

triangles only

Ship goes from A to B on a bearing 040

Bearings for 20 km. How far north has it travelled?

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

Ex6-7 p294 (finding the length) Ex8 p297 (finding angles) Ex9 p299 (trig & bearing) Ex19-20 p328 (sine rule)

Clip 147 Trigonometry

Exact Trig Values resources

Clip 173 (sine & cosine)

C: Sine and cosine rules

E: Graphs of sin, cos, tan.

Solutions of trig equations

Including case with two

solutions

Angles of any size

Calculate length CB

Calculate angle x

Solve sin x 1

2or all x in range 0 x 720o.

Ex21 p331 (cosine rule) Ex22 (problem solving with sine & cosine rules) Ex17 p232 (graphs of trig fns) Ex18 p325 (solutions of trig equations)

Clip 168 Graphs of trig fns. (A/A*)

18th Nov (Y10)

5. PROBABILITY

R: Relative frequency experimental

probability and expected results

Appropriate methods of determining

probabilities

Probability of 2 events

Multiplication law for independent

events

C: Addition law for mutually

exclusive events

Conditional probability;

dependent events

E: Addition Law for non-mutually

exclusive events

C: Sets & Venn Diagrams

P1 – 9

Using symmetry, experiment

Simple tree diagrams

By listing, tabulation or tree

diagrams

Sampling without

replacement

Using Venn diagrams

Experiment to find probability of drawing pin landing point up.

pace4/52 = 1/13

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.

If for class, psize 6 feet0.2, psize 7 feet0.3 pleft - handed0.15

(a) Calculate psize 6 or 7 feet

(b) Explain why psize 6 feet or left - handed0.2 0.15

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.

Using the class data given above, calculate

psize 6 feet or left - handedwhen psize 6 feet and left - handed0.05

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

Diagrams:

Rayner: Ch9 p445 MEP Examples

Unit 5 Teachers Notes

MEP Teacher Book Last One Standing Mathsland National Lottery Same Number! Who’s the Winner? Chances Are The Better Bet

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) Resources for Venn Diagrams Post on Frequency Trees Resources for Frequency Trees Prize Giving (NRich)

Enumerate sets and combinations of

sets systematically, using tables,

grids, Venn diagrams and tree

diagrams."

"Calculate and interpret conditional

probabilities through representation using expected frequencies with two-

way tables, tree diagrams and 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 = {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?

Example:

X is the set of students who enjoy science fiction Y is the set of students who enjoy comedy films The Venn diagrams shows the number of students in each set, work out:

(i) P(X ∩ Y) (ii) P(X U Y)

Example:

One of these 80 students is selected at random. (b) Find the probability that this student speaks German but not Spanish. Given that the student speaks German, (c) Find the probability that this student also speaks French

Frequency Trees

Record describe and analyse the

frequency of outcomes of probability experiments using tables and

frequency trees

December (Y10)

6. NUMBER SYSTEM

R: Estimating answers

Use of brackets and memory on a

calculator

C: Upper and lower bounds

including use in

formulae

E: Irrational / rational numbers

Surds

Addition, subtraction, multiplication

of surds

N13 – N16

Use of ( ) button

Including area, density, speed

Recurring decimals

Surd form of sin, cos, tan of

30 45 60

Division of surds using

conjugates

Expansion of two brackets

29.4 + 61.2

14.8 ≈

30 + 60

15 ≈ 6

2.5 × 14.3

7.8 + 2.95≈ 3.32558 (𝑡𝑜 5. 𝑑. 𝑝)

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.

Give examples of irrational numbers between 5 and 6. Discuss the 2 set-squares

(side lengths: 1,1,√2 and 1, √3, 2)

Show that (i) 0.0̇9̇ (ii) 0.16̇ are rational.

Rationalise the denominator; 1

√3;

21

√7

1√2 1√2

If p and q are different irrational numbers, is (i) p q (ii) pq

Rational / Irrational / Could be both?

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)

20th Dec – 3rd Jan

CHRISTMAS HOLIDAYS

6th January (Y10)

7. MENSURATION

R: Difference between discrete

and continuous measures

Areas of parallelograms, trapezia, kites, rhombuses

and composite shapes

G14-17

To include estimation of

measures

Illustrate current postal rates; shoe sizes

Find the area of this kite.

Ex20 p28-29 (estimating measures) Ex13-15 p185-193 (area & perimeter) Ex23-25 p211-217 (Volume & surface area)

Clip 71 & 72 Circles

Clip 73 Area of compound shapes

Clip 120 & 121 surface area

Clip 122 & 177 Volume

Clip 178 Segments & Frustums

Clip 124 metric units

Clip 126 compound measures

Clip 176 Area of a triangle using Sine

rule

Volumes of prisms and composite

solids

Surface area of simple solids:

cubes, cuboids, cylinders

Volume/capacity problems

2-D representations of 3-D objects

C: Units

Appropriate degree of accuracy

Upper and lower bounds

Volume and surface area pyramid,

cone and sphere and

combinations of these (composite

solids)

Length of circular arc, areas of

sectors and segments of a circle

Dimensions

Area of cross-section

length of prism

Include compound measures

such as density & Pressure

Use of isometric paper

Conversion between m and

cm, m2 and cm2, m3 and cm3.

Rounding sensibly for the context and the range of

measures used

Notation [L] [T] [M] for

basic dimensions

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

Find the mass of water required to fill this swimming pool.

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

l 9.57 m 9.565 l 9.575

Calculate the radius of a sphere which has the same volume as a 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, (𝑎𝑏)2

7𝑏; where (r, l, x, a, b, c, d, are lengths)

Ex27-28 p79-82 (compound measures) Ex25-26 p77-78 (metric & imperial)

E: Area of triangle 1

2 a b sinC

E: Area of triangle ss as bs

c

where s 1

2a b c

Heron's formula

Find the area of these triangles

17TH – 21ST February

FEBRUARY HALF TERM

24th February (Y10)

8. DATA HANDLING

R: Two-way tables including timetables and

mileage charts

Frequency graphs

C: Construct and interpret

histograms with unequal intervals

Frequency polygons

Questionnaires and surveys

Time series & Moving Averages

E: Sampling Select and justify a sampling method

to investigate a population.

12 hour and 24 hour clock

For grouped data; equal

intervals. Include frequency

polygons and Histograms

Understand and use frequency density

Know that the Area of Bar =

Frequency

Fairness and 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)

Different methods: random,

quota, stratified, systematic

Understand how different methods of sampling and

different sample size can

affect reliability of conclusions.

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

do you have to wait?

Determine the number of pupils in each school year to represent their views when

the total representation is 20. The numbers of pupils in each year are

Year 7 8 9 10 11 Number 122 118 100 98 62

choose (5) (5) (4) (4) (2)

Rayner p386-444

Unit 8 Teachers notes Clip 85 Two-Way Tables (Grade D) Clip 84 Questionnaires and Data Collection (Grade D) Clip 134 Designing Questionnaires (Grade C) Clip 181 Histograms (Grade A* - A)

Clip 153 Moving Averages (Grade B) Clip 183 Stratified Sampling (Grade A* - A)

17th March (Y10)

9. DATA ANALYSIS

R: Problems involving the mean

Mean, median, modal class for grouped data

C: Cumulative frequency graphs;

median, quartiles

Including discrete and

continuous data

Including percentiles, Inter-

Quartile Range

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) Olympic Triathlon

Box plots

Use box plots to compare

sets of data/distributions

7th – 21st April

EASTER HOLIDAYS

22nd April (Y10)

10. EQUATIONS

R: Linear equations

Expansion of brackets

C: Simultaneous linear equations

Factorisation of functions

Completing the square

Quadratic formula

E: Multiplying and dividing

algebraic expressions

Equations leading to quadratics;

related problems

C: Iteration

Find approximate solutions to

equations numerically using

iteration

(NB: Trial and improvement is not

required)

One fraction and/or one

bracket

Algebraic solutions

Common terms, difference of two squares, trinomials,

compound common factor

Including max/min values

𝑥 =−𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎

Permissible cancelling

Including equations from additions or subtractions of

algebraic fractions

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) x4 1 (ii) x3 x2 x 1 (iii) 2x2 x 3

Solve (i) 4x2 – 1= 0 (ii) 4x2 9x 0 (iii) x2 x 6 (iv) x3 x2 x 1 0

By completing the square, find the minimum value of x2 4x 9.

Solve 5x2 x 3 0, giving answers to 2 d.p.

Simplify 𝑥2−9

𝑥2−𝑥−6

Solve 𝑥

𝑥+1+

2𝑥

2𝑥−1=

39

20

This iterative process can be used to find approximate solutions to x3 + 5x – 8 = 0

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

Clip 110 Trial & Improvement (X)

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 Post on Iteration by Colleen Young

(a) Use this iterative process to find a solution to 4 decimal places of x 3 +

5x – 8 = 0. Start with the value x = 1

(b) By substituting your answer to part (a) into x 3 + 5x − 8 and comment

on the accuracy of your solution to x 3 + 5x − 8 = 0

26th – 30th May

MAY HALF TERM

2ND Jun (Y10)

11. FRACTIONS and

PERCENTAGES

R: Percentage and fractional changes

C: Compound interest

Appreciation and depreciation

Reverse percentage problems

Discount, VAT, commission

Repeated proportional

change

VAT on hotel bill of £200?

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 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

Clip 53 & 54 Change to a %

Clip 92 Overview of %

Clip 93 & 136 Increase/dec. by a %

Clip 137 Compound Interest

Clip 138 Reverse %

12. NUMBER PATTERNS and

SEQUENCES

R: Find formula for the n th term of a

linear sequence.

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

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

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

Clip 65 Generate a Sequence from

Nth term

Clip 112 Finding the nth term More resources on Sequences GP sort card

C: Recognise and use sequences of

triangular, square and cube

numbers, simple arithmetic

progressions, Fibonacci type

sequences, quadratic sequences,

and simple geometric progressions

(rn where n is an integer, and r is a

rational number > 0 or a surd) and

other sequences

C: Find a quadratic formula for

the n th term of a sequence

E: Express general laws in symbolic

form

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

GP worksheet Geometric Series (from Don Steward)

16TH June (Y10)

End of Year 10 Exams

23rd Jun 2014

START OF NEW TIMETABLE START OF YEAR 11

23rd Jun (Y11)

13. GRAPHS

R: 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

C: 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

Quadratic, cubic, reciprocal

and exponential equations

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.

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.

Use the graphs of y x2 5x and y 2x 3 to solve x2 7x 3 0.

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 Geogebra File for the equation of a Tangent to a Circle

Tangent to a Circle

Recognise and use the equation of a circle with centre at the origin; find

the equation of a tangent to a circle

at a given point

(Y11)

SUMMER HOLIDAYS

September (Y11)

14. LOCI and

TRANSFORMATIONS:

CONGRUENCE and

SIMILARITY

R: Constructions of loci

Translation

Enlargements

C: Enlargements

Reflections

Rotations

Combination of two

transformations

Congruence – conditions for

triangles

Similarity – similar triangles, line,

area and volume ratio

About point(s) and line(s)

Using vector notation

Positive integers and simple fractions for scale factor

Negative scale factor

Finding the centre of

enlargement

Reflection in y = x, y = – x, y

= c, x = c

Finding the axis of symmetry

Rotation about any point 90o , 180o in

a given direction

Finding the centre of rotation

by inspection

Use the criteria to prove

congruence: SSS SAS AAS

RHS Internal line ratio (BE:CD = 3:5)

Construct the locus of points equidistant from both lines

Draw image after translation (−32

)

Enlarge diagram by scale factor 1

3 , centre A (inside triangle)

Find the Equations of the mirror lines and reflect the shape in the

line y = 0, y = -3, y = x

Prove that ▲ABX & ▲CDX are congruent

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

ABE and BCDE

Ex2-3 p171-176 (simple construction) 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 (volumes of similar shapes)

Clip 127 bisecting a line

Clip 128 perpendicular to a line

Clip 129 bisecting an angle

Clip 130 Loci

Clip 74-77 Transformation

Clip 171 Negative scale factor

Clip 123 Similar Shapes

Clip 124 Dimensions

Draw 2 separate triangles and find scale factor/multiplier (= 5

3)

Two similar cones have heights 100cm & 50cm.

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

E.g. Sudso 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?

Clip 149 Similar Shapes

Clip 179 Congruent Triangles

(Y11)

15. VARIATION: DIRECT and

INVERSE

R: Direct and inverse variation

C: Functional representation

Graphical representation

E: further functional representation

Mathswatch leads into this topic in a very easy way

y x , y x2 , y x3 , y 1

𝑥;

y 1

𝑥2

y 1

𝑥3y√𝑥y

1

√𝑥

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

(Y11)

OCTOBER HALF TERM

November (Y11)

16. INEQUALITIES

R: Solution of linear inequalities and simple quadratic inequalities

C: Solve linear inequalities in one

or two variable(s), and quadratic

inequalities in one variable;

represent the solution set on a

number line, using set notation

and on a graph

C: Graphical applications

Locating and describing regions of graphs

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

Find the range of values of x for which x2 - 3x - 10 ≤ 0

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 Post on Inequalities Collection of Resources

ICT tools for Inequalities: Geogebra 1 / Geogebra 2 / Desmos /

echalk

December (Y11)

17. USING GRAPHS

C: Transformation of functions

E: Find the approximate area

between a curve and the horizontal axis. Calculate or estimate gradients

of graphs and areas under graphs

(including quadratic and other non-linear graphs), and interpret results

in cases such as distance-time

graphs, velocity-time graphs and graphs in financial contexts

C: Construct and use tangents to

estimate rates of change

Interpret the gradient at a point on a

curve as the instantaneous rate of

change; apply the concepts of average and instantaneous rate of

change (gradients of chords and

tangents) in numerical, algebraic and graphical contexts

E: Finding coefficients

E: Quadratic Graphs

Identify and interpret roots,

intercepts, turning points of quadratic functions graphically;

deduce roots algebraically and

turning points by completing the square

y f x a, y f xa

y k f x, y f k x

Interpretation of area

Drawing trapezia; trapezium rule

Including max/min points

Applications to travel graphs

Speed from a distance/time

graph. Acceleration and distance

from a velocity/time graph.

Find values of a and b in y

ax2 b by plotting y against x2.

Find values of p and q from

the graph of y= pqx

For given shape of y f x, sketch

y f x2 , y 1

2 f x , y f x 1

Estimate the area between the curve y x2 1, the x-axis and the lines x 1 and x

3.

A car accelerates so that its velocity is given by the formula

v 10 0.3t2 . Sketch the velocity/ time graph for t 0 to t 10, and estimate the

v distance travelled by the car. Also estimate the acceleration when t 5.

Ex16-17 p378-381 Sections 17.2 (MEP practice book – area under graphs)

See Core 1 LiveText for examples on Transformations of curves

Clip 167 Transformations of

functions

Clip 168 Graphs of trig fns (review)

Clip 169 Transformations of Trig fns Quadratic Graphs Resources Functions resources Heinemann Live Textbook C3_Ch2 Functions Audit

E: Functions

Interpret simple expressions as

functions with inputs and outputs; interpret the reverse process as the

‘inverse function’; interpret the

succession of two functions as a ‘composite function

The functions f and g are such that: f(x) = 1 – 5x and g(x) = 1 + 5x

(a) Show that gf(1) = – 19

(b) Prove that f–1(x) + g–1(x) = 0 for all values of x.

(Y11)

CHRISTMAS HOLIDAYS

January (Y11)

18. 3-D GEOMETRY

C: Length of slant edge of pyramid

Diagonal of a cuboid Angles

between two lines, a line and a

plane, two planes

Producing 2-D diagrams from 3-D problems

Pythagoras, sine and cosine

rules

ABCDE is a regular square-based pyramid of vertical height 10 cm and base, BCDE, of side 4 cm. Calculate:

(i) the slant height of the pyramid

(ii) the angle between the line AB and the base (iii) the angle between one of the triangular faces and the square base.

February (Y11)

19. VECTORS

C: Vectors and scalars

Sum and difference of vectors

Resultant vectors

Components

Multiplication of a vector by a

scalar

Applications of vector methods

to 2-dimensional geometry

E: Know and use commutative

and associative properties of vector addition

Vector notation

(𝑎𝑏), 𝐴𝐵⃗⃗⃗⃗ ⃗ or a

A plane is flying at 80 m/s on a heading of 030However, a wind of 15 m/s is

blowing from the west. Determine the actual velocity (speed and bearing) of the

plane.

𝑂𝐴⃗⃗⃗⃗ ⃗ = a and 𝐴𝐵⃗⃗⃗⃗ ⃗ = b

Write down, in terms of a and b,

(i) 𝑂𝐵⃗⃗ ⃗⃗ ⃗, (ii) 𝑂𝐶⃗⃗⃗⃗ ⃗, (iii) 𝐴𝐶⃗⃗⃗⃗ ⃗, (iv) 𝐶𝐵⃗⃗⃗⃗ ⃗

Ex15 p317 (addition & scalar multiplication) Ex16 (vector geometry)

See Heinemann M1 Live Text book Ch1 for examples

Clip 180 Vecors

(Y11)

FEBRUARY HALF TERM

March (Y11)

20. AQA LEVEL 2 FURTHER

MATHEMATICS (Optional)

Most able in Set 2 may have chance to sit AQA Level 2 Further mathematics.

Extra topics: Algebra, Geometry, Calculus, Matrices, Trigonometry, Functions, Graphs. See AQA Level 2 FM specification

Collins Text

Mar EASTER HOLIDAYS

April Revision & Intervention Linear (A) Past paper booklets to be prepared in-house. Revision Workbooks to be ordered. 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

at2

v2 = u2 + 2as