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Higher Tier
R = Recap (levels 7 & 8); C = Core (bold); E = Extension to include AQA Further Maths (italics) Teacher support material available here: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm
Y10 & 11 GCSE SOW for Set 1
Date Topic Notes Examples Student
Reference Resources Mid-Jun – Jul (Y10)
1. INDICES: STANDARD FORM
R: Index notation
Prime factors Laws of indices
C: Negative / fractional Indices
Standard form
N1 – N9
N7: Positive integer powers only
N7: With and without calculator
N9: SF
Simplify a5 a3; m4 m2; (p2)5; (2xy2)3;
Prime factors Find HCF of 216 and 240
simplify 812/3
(without calculator);
Evaluate 2.762 10124.97 1021(cal.)
Evaluate 2.8 104 7 106 (no cal.)
Evaluate 2.8 104 7 106 (no cal.)
Starter:
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
Jul – Aug
SUMMER HOLIDAYS
September (Y10)
2. FORMULAE: ALGEBRAIC
FRACTIONS
R: Formation, substitution,
change of subject in formulae
More complex formulae:
– substitution
– powers and roots
– change of subject with subject in more
than 1 term
Common term factorisation
C: Algebraic fractions – addition
and subtraction
A1 – A7
With and without calculator Opportunity for revision of negative
numbers, decimals, simple fractions.
Including denominators with (i) numerical or single term
(ii) linear term
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 Angle symmetry properties
of polygons
Symmetry properties of 3-D shapes
G1, 3, 4, 6, 13
Include line and rotational symmetry Include plane, axis and point
Symmetry
Calculate interior angle of a regular octagon/decagon
Shade in the diagram so that it has rotational symmetry of
Order 4 but no lines of symmetry.
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
Clip 150 Circle theorems
Compass bearings
C: Angle in a semi-circle
Radius is perpendicular to the tangent
Radius is perpendicular bisector of
chord
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
8 compass points and 3 figure
bearings
Application of Pythagoras and Trig.
G9: identify and apply circle
definitions and properties, including:
centre, radius, chord, diameter, circumference, tangent, arc, sector and
segment
AX.BX CX.DX
PT2 PA.PB
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)
(Y10)
4. TRIGONOMETRY
R: Trigonometry (sin, cos, tan)
C: Sine and cosine rules
G20 – G23
Angles of elevation and depression
Bearings 2-D with right-angled triangles only
Including case with two solutions
Angles of any size
G21: know the exact values of sin θ
and cos θ for θ = 0°, 30°, 45°, 60° and
90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°
Ship goes from A to B on a bearing 040
Bearings for 20 km. How far north has it travelled?
Ex6-7 p294 (finding the length) Ex8 p297 (finding angles) Ex9 p299 (trig & bearing) Ex19-20 p328 (sine rule) Ex21 p331 (cosine rule)
Clip 147 Trigonometry
Exact Trig Values resources
Clip 173 (sine & cosine)
E: Graphs of sin, cos, tan.
Solutions of trig equations
find length CB
Solve sin x 1
2or all x in range 0 x 720o.
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*)
Oct – Nov
OCTOBER HALF TERM
November (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 (ME) events
Addition Law for non-
mutually exclusive events
Conditional probability;
dependent events
C: Sets & Venn Diagrams
Enumerate sets and combinations of sets systematically, using tables, grids, Venn
diagrams and tree diagrams."
"Calculate and interpret conditional probabilities through representation using
P1 – 9
Know that a better estimate for a
probability is achieved by increasing
the number of trials Using symmetry, experiment
Simple tree diagrams
By listing, tabulation or tree diagrams ME means both events cannot happen at the same time Non ME mean independent events = both can happen at same time.
Sampling without replacement
Using Venn diagrams (optional)
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.
Calculate the probability of obtaining 3 aces when dealt 3 cards from a deck of 52.
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.
Rayner: Ch9 p445 MEP Student book
Unit 5 Teachers Notes
MEP Text Book
Last One Standing Mathsland National Lottery Same Number! Who’s the Winner? Chances Are The Better Bet
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)
expected frequencies with two-way
tables, tree diagrams and Venn diagrams
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
(Y10)
6. NUMBER SYSTEM
R: Estimating answers Use of brackets and memory on a
calculator
C: Upper and lower bounds including
use in formulae
Irrational / rational numbers
Surds
Addition, subtraction, multiplication of
surds
N13 – N16
Use of ( ) button
Including area, density, speed
N10: Recurring decimals
N8: Surd form of sin, cos, tan of 30
45 60
N8: 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.
List some irrational numbers between 5 and 6.
Show that (i) 0.0˙9˙ (ii) 0.16˙ are rational.
Rationalise the denominator; 1
√3;
21
√7
expand 1√2 1√2
If p and q are different irrational numbers, is(i) p q (ii) p q 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)
December (Y10)
7. MENSURATION
R: Difference between discrete
and 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
G14: To include estimation of measures
G16: Area of cross-section x length of
prism
G17: Include compound measures
such as density.
Illustrate current postal rates; shoe sizes
G16: Find the area of this kite.
G17: Find the mass of water to fill this swimming pool.
Ex20 p28-29 (estimating measures) Ex13-15 p185-193 (area & perimeter) Ex23-25 p211-217 (Volume & surface area) Ex27-28 p79-82 (compound measures)
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
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 triangle 1
2 a b sinC
E: Area of triangle ss as bs c
where s 1
2a b c
Use of isometric paper
N13: Conversion between m and cm, m2 and cm2, m3 and cm3.
N15: Rounding sensibly for the context and the range of measures
used
N16: apply and interpret limits of
accuracy including UB & LB
G18: arcs & sectors
Notation [L] [T] [M] for basic dimensions
Heron's formula
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.
G18: 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)
Find the area of these triangles
Ex25-26 p77-78 (metric & imperial)
Dec – Jan
CHRISTMAS HOLIDAYS
January (Y10)
8. DATA HANDLING
R: Two-way tables including timetables
and mileage charts
Frequency graphs
12 hour and 24 hour clock
If a train arrives at a station at 13:26 and the connection leaves at 14:12, how long do you have to wait?
p386-444
Unit 8 Teachers notes
Clip 85 Two-Way Tables (Grade D)
Clip 84 Questionnaires and Data
Collection (Grade D)
Questionnaires and surveys
C: Construct and interpret histograms
with unequal intervals
Frequency polygons
Sampling
Select and justify a sampling method to
investigate a population.
Time series & Moving Averages
For grouped data; equal intervals.
Include frequency polygons and
Histograms
Fairness and bias
Understand and use frequency density Know Area of bar = frequency
Different methods: random, quota,
stratified
Effect of sample size; reliability of conclusions
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)
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
Year 7 8 9 10 11 Number 122 118 100 98 62
choose (5) (5) (4) (4) (2)
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)
Substitution Cipher
(Y10)
9. DATA ANALYSIS
R: Problems involving the mean
Mean, median, modal class for grouped
data
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
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?
p386-444
Unit 9 Teachers notes
Clip 133 Averages From a Table
Clip 151 Cumulative Frequency
Clip 152 Boxplots (Grade B)
Olympic Triathlon
February (Y10)
10. EQUATIONS (A17 – A21)
R: Linear equations
Trial and improvement methods
Expansion of brackets
C: Simultaneous linear equations
Factorisation of functions
A17: One fraction and/or one bracket
NB: Trial & Improvement will not be
assessed but we will continue to teach
it – now called: A20: find approximate solutions to equations numerically using iteration
A19: Algebraic solutions
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; and also 1 linear & 1 quadratic
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
Completing the square
Quadratic formula
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)
A4: Common terms, difference of two
squares, trinomials, compound
common factor
Including max/min values
A18: solving quadratics
𝑥 =−𝑏 ± √𝑏2 − 4𝑎𝑐
2𝑎
A4: Permissible cancelling
A21: translate simple situations or
procedures into algebraic expressions
or formulae; derive an equation (or two simultaneous equations), solve
the equation(s) and interpret the
solution - Including equations from additions or subtractions of algebraic
fractions
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. use the Formula
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
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
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
Mid-Feb
FEBRUARY HALF TERM
February (Y10)
11. FRACTIONS and
PERCENTAGES
R: Percentage and fractional changes
C: Compound interest
Appreciation and depreciation
Reverse percentage problems
(N10 – N12)
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 %
March (Y10)
12. NUMBER PATTERNS and
SEQUENCES
R: Find formula for the n th term of a linear sequence.
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
Find a quadratic formula for the n th
term of a sequence
C: Express general laws in
symbolic form
A23 – A25
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
A24: 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
A25: nth term of a quadratic sequence
n th term in sequence 8, 11, 14, 17, ..., ..., ... is 3n + 5
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
More resources on Sequences GP sort card GP worksheet
Geometric Series (from Don Steward)
March - April
EASTER HOLIDAYS
April (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
Equation of straight line
Graphical solution of simultaneous equations
Graphs of common functions
C: Solve equations by graphical
methods
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
A8 – A14
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)
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).
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
May (Y11)
14. LOCI and TRANSFORMATIONS:
CONGRUENCE and SIMILARITY
R: Constructions of loci
Translation
Enlargements
G2: use the standard ruler and
compass constructions (perpendicular
bisector of a line segment, constructing a perpendicular to a
given line from/at a given point,
bisecting a given angle); use these to construct given figures and solve loci
problems; know that the perpendicular
distance from a point to a line is the shortest distance to the line
G7: About point(s) and line(s)
Using vector notation
Construct the locus of points equidistant from both lines
Draw image after translation (−32
)
Ex2-3 p171-176 (simple construction) Ex13 p310 (Translation & enlargement)
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
C: Enlargements
Reflections
Rotations
Combination of two transformations
Congruence – conditions for triangles
Similarity – similar triangles, line, area
and volume ratio
G7: Positive integers and simple
fractions for scale factor
G7: 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
G5: SSS SAS AAS RHS
G19: apply the concepts of
congruence and similarity, including
the relationships between lengths, areas and volumes in similar figures
Enlarge diagram by scale factor 1
3 ,
centre A (inside triangle)
Find the Equations of the mirror lines
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 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?
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 shapes0
Clip 123 Similar Shapes
Clip 124 Dimensions
Clip 149 Similar Shapes
Clip 179 Congruent Triangles
May END OF YEAR 10 EXAMS This will be used to help set for Y11
May – Jun
MAY HALF-TERM
Mid-June (Y11)
15. VARIATION: DIRECT and
INVERSE
R: Direct and inverse variation
C: Functional representation
Graphical representation
R13 – R14
y x , y x2 , y x3 , y 1
𝑥;
y 1
𝑥2 y 1
𝑥3y√𝑥y 1
√𝑥
𝑦 ∝ 1
√𝑥𝑛
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)
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
E: Linear programming
A22: 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
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
Jun
START NEW TIMETABLE
Year 11
Mid-June- July (Y11)
17. USING GRAPHS
C: Transformation of functions
C: Find the approximate area between
a curve and the horizontal axis.
C: Construct and use tangents to
estimate rates of change & Interpret
the gradient at a point on a curve as
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
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
Ex16-17 p378-381 Sections 17.2 (MEP practice book – area under graphs)
See Core 1 LiveText for examples
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
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
C: 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
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
E: Use of logarithms to produce straight line 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
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.
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.
July – Aug
SUMMER HOLIDAYS
September (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.
October (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
G24 – G25
G24: Use Vector notation (𝑎𝑏), 𝐴𝐵⃗⃗⃗⃗ ⃗ or
a
Students should think of Vectors as
making a journey from A to B and finding alternative routes.
G25: apply addition and subtraction of
vectors, multiplication of vectors by 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)
See Mechanics 1 Chapter 1_LiveText for examples
Clip 180 Vecors
methods to 2-dimensional
geometry
E: Know and use commutative
and associative properties of
vector addition
scalar, and diagrammatic and column
representations of vectors and use
vectors to construct geometric
arguments and proofs
Ex16 (vector geometry)
Mid-Oct
OCTOBER HALF TERM
November
20. AQA Level 2 Further Maths
Ch8. Calculus
Hand out the Level 2 Further maths
Workbooks which they work
through. The workbook stays in class
See AQA Level 2 FM specification
Collins Text
(AQA) & the OCR Text for
Add Maths
Collins Text (AQA) & the
OCR Text for Additional Maths Buy each student a CGP Workbook (to
write in)
December Ch1. Number and Algebra I
Ch2, Algebra II
Ch3. Algebra III
December CHRISTMAS HOLIDAYS
January &
February Ch4. Algebra IV
Ch5. Coordinate Geometry
Ch6. Geometry I
Mid-February
FEBRUARY HALF TERM
March Ch7. Geometry II
Ch9. Matrices Start setting Past Papers as
homework
Mar EASTER HOLIDAYS
Intervention Set 4 x Past Papers as homework over Easter & get them to complete their Level 2 Workbooks and their GCSE Maths Workbooks
April Revision & Intervention Past Papers & Intervention
Review all work for both Edexcel GCSE Mathematics & AQA Level 2
Mathematics
Level 2 Past Papers
May Study Leave Intervention & Revision
June
EXAMS, EXAMS, EXAMS Revision Sessions on-going
NOTES FOR THE TEACHER
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 your students at all times – refer to
the diagram. This means stretching the least able as much as the most able. No exceptions.
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