Student Date Topic Notes Examples Reference Resources · Angle symmetry properties of polygons...
Transcript of Student Date Topic Notes Examples Reference Resources · Angle symmetry properties of polygons...
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