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 23 rd Jun – 23 rd Jul Start of new timetable end of Y9 Ch1.INDICES: STANDARD FORM R: Index notation Prime factors Laws of indices C: Indices (including negative & fractional indices) Standard form Positive integer powers only With and without calculator Simplify a 5 a 3 ; m 4 m 2 Prime factors Find HCF of 216 and 240 81 2/3 (without calculator); simplify ( ) –1 Evaluate 2.762 10 12 4.97 10 21 (cal.) Evaluate 2.8 10 4 7 10 6 (no cal.) Evaluate 2.8 10 4 7 10 6 (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 23 rd Jul – 31 st Aug SUMMER HOLIDAYS 1 st 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 With and without calculator Opportunity for revision of negative numbers, decimals, simple fractions. Given q – 2, v 21, find the value of √v 2 q 2 . Make L the subject of t = 2π√ 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 x 3 y 4 x 4 y 3 x 2 y Simplify 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 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
14
Embed
Student Date Topic Notes Examples Reference …side lengths: 1,1,√2 and 1, √3, 2) E: Irrational / rational numbers √Surds Addition, subtraction, multiplication of surds Use of
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Set 2 R = Recap (levels 6 & 7); C = Core level 8 (bold); E = Extension (italics)
rule) Ex21 p331 (cosine rule) Ex22 (problem solving with sine & cosine rules) Ex17 p232 (graphs of trig fns) Ex18 p325 (solutions of trig equations)
Clip 173 (sine & cosine)
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 Venn Diagrams
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)
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?
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
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
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. (ii) 0.1 are rational.
Rationalise the denominator;
√
√
1√2 1√2
If p and q are different irrational numbers, is (i) p q (ii) pq Rational / Irrational / Could be both?
Internal line ratio (BE:CD = 3:5) Draw 2 separate triangles and find scale factor/multiplier (=
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?
Ex31 p233(areas of similar shapes) Ex32 p237 (volumes of similar shapes)
Clip 123 Similar Shapes
Clip 124 Dimensions
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
y
y
y√ y
√
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: Graphical applications
Locating and describing
regions of graphs
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
December (Y11)
17. USING GRAPHS
C: Transformation of functions
E: Find the approximate area
y f x a, y f xa
y k f x, y f k x
Interpretation of area
For given shape of y f x, sketch
y f x2 , y
f x , y f x 1
Ex16-17 p378-381 Sections 17.2 (MEP practice book – area
See Core 1 LiveText for examples
Clip 167 Transformations of
functions
Clip 168 Graphs of trig fns (review)
Clip 169 Transformations of Trig fns
between a curve
and the horizontal axis.
Construct and use tangents to estimate rates
of change
Finding coefficients
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
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.
under graphs)
(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
Vector notation
( ), 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
E: Know and use commutative and associative properties of
vector addition
(Y11)
FEBRUARY HALF TERM
March (Y11)
20. AQA LEVEL 2 FURTHER
MATHEMATICS
Discussion to take place about how best to approach teaching FM – Parallel teaching (gcse & FM taught alongside) Versus Discrete (gcse in Y10 & FM in Y11) Most able 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 (payment to be collected beforehand) 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