Mathematics

Aims

Vision

To enable students to discover the joy and beauty of Mathematics and to be confident in applying Mathematics in the real world

Aims:

To create a positive attitude to mathematics and to develop, maintain and stimulate students’ curiosity, interest and enjoyment in mathematics.
To develop students’ familiarity with appropriate mathematical concepts, principles, methods and vocabulary.
To develop students’ understanding of mathematics in it’s widest context, to see how it relates to themselves outside school and to appreciate the purpose, power and relevance of mathematics.
To encourage students to develop personal qualities such as perseverance, initiative, self-confidence and independence.
To enable pupils to work independently and as part of a team.
To enable all students to have equal access to mathematics and to experience success in their work.
To allow students to develop transferable skills and informed opinions about mathematics and to be able to support them by reasoned arguments.

Staff

The Mathematics Department consists of the following staff:

Full-time

Mrs L Osborne Head of Department

Mrs G Bulloch Assistant Head

Mr G Dhillow

Mrs B Emmrich

Miss S Damaree

Mr P Crockford

Miss S Gilks

Mrs K Brady

Curriculum

Year 7

The reference book for this scheme of work is Essential Mathematics Book 7H and 8H
Work at National Curriculum Level 5 is consolidated and National Curriculum Level 6 is introduced.
Topics occur in the order suggested in the National Numeracy Strategy guide. The book is split into 6 Units corresponding to the six half-terms in the school year. There is appropriate revision material at the end of each Unit and many topics are reviewed later in the book, in line with the NNS guide.
Puzzle activities and mental arithmetic tasks can be found between the Units to be used as appropriate. Investigations occur at regular intervals.
Most work is broken down into two levels. ‘M’ exercises are aimed at all pupils at this level. ‘E’ exercises provide extension work. Some pupils will only complete the ‘M’ exercises. Pupils may move onto the ‘E’ work having completed some ‘M’ exercises. Other pupils may only need to tackle the ‘E’ exercises.
Pupil self-assessment is a very important part of assessment for learning. Regular ‘check yourself’ sections appear throughout the book. Answers to these exercises are provided at the back of the book for immediate feedback. Pupils can use these sections when revising for a test.
The class teacher will go through a number of examples on the board before pupils start the exercises.
At the end of each Unit there will be a summative test based on the work covered of 50 minutes duration. Each topic of work within the test will be marked separately, so that pupils can assess and identify in which techniques they are proficient and in which techniques they need to improve. Performance in each topic will be recorded by the pupil so individual targets may be set for improvement.
This scheme of work and the number of lessons for each topic would be adhered to where possible. However circumstances such as school closure due to snow etc, may mean that alterations are made at various points in the year.

Unit 1 (7 weeks )
Lesson No.	Topics & Learning Objectives	Textbook reference
1	1.1 Whole Number Arithmetic Use place value of digits in whole numbers Add, subtract and multiply with whole numbers including long multiplication	Use puzzles PowerPoint and other activities to cover basic numeracy work and also problem solving skills.
2	1.2 Decimals Add and subtract decimals	P22-23
3	Multiply decimals by a whole number Multiply decimals by a decimal	P25/26
4	Division of decimals by whole numbers	P28-30
5	1.4 Using a calculator BIDMAS without a calculator	P36 P37
6	Use a calculator with brackets and powers. Inserting brackets into expressions	P38-41
7	Find the next term in a sequence Use the term-to-term rule for a sequence	P45-48
8 + 9	1.6 Perimeter and area Find perimeters of shapes Find areas involving rectangles	P52-54
10	Find areas involving triangles Find areas of irregular shapes	P54-56 P57-58
11	BLH lesson using the investigation on p61 Reflect on group work	P 61
12	Area Problems ( word problems on area) Metric Units Revision	P58-59 P59-60
13	6.3 Metric and Imperial units Convert metric units Convert imperial units	P322 P322-323
14	Convert between metric and imperial units Change units in problems	P323-324 P325-327
15	Revision Lesson
16	Unit 1 test
17+18	Investigation on sequences, ice cream investigation, Fibonacci: Simple train journey

Part 2 (7 weeks)
Lesson No.	Topics & Learning Objectives	Textbook reference
1 + 2	2.1 Averages and range Find the mean, median and mode Find the range Comparing sets of data	P73-74
3	Averages and range from a frequency table	P78-80
4	Comparing data	P76-78
5	2.2 Fractions Find equivalent fractions Cancel fractions Proper, improper fractions and mixed numbers Find a fraction of a quantity	P87-89
6	Add and subtract fractions including mixed numbers	P87-89
7	2.3 Fractions, decimals, and percentages Convert between fractions and decimals	P89-90 P90-91 P92-93
8	Convert between fractions, decimals and percentages	Pg 93-94
9	2.4 Angles Label angles Measure and draw angles with a protractor	P97-98 P98-99
10	Calculate angles on a straight line and at a point	P100
11	Calculate angles in a triangle	P102
12	Calculate angles with parallel lines	P105
13	Calculate angles in a quadrilateral	P106-107
14	2.5 Rules of algebra Use of letters for numbers	P113
15	Collect together like terms	P115-116
16	Multiplying simple terms	P115-117
17	Substituting numbers into a formula	P118-119
18	3.1 Coordinates Use coordinates in four quadrants	P135-136 P136-137
19	Investigation

Unit 2 Test

Christmas investigation: Nrich website: Christmas trees, Christmas cards, Elf suits, Christmas boxes, More Christmas boxes, Family tree, Clever Santa (Search Christmas on Nrich)

Part 3 (6 weeks)
Lesson No.	Topics & Learning Objectives	Textbook reference
1	3.4 Properties of numbers Recognise prime numbers, factors of numbers, multiples of numbers.	P149-150 P150-151
2	Prime factors	P150-151
3	Least Common Multiple (LCM) Highest Common Factor (HCF)	P151-152
4	Recognise and use square and cube numbers Square root	P152-153 P154 P154-156
5	4.4 Proportion and ratio Use proportion in problems Use and simplify ratios Share in a given ratio	P226 P227-228 P229
6	4.5 Negative numbers Add and subtract negative numbers	P232-233
7	Multiply and divide negative numbers	P234
8	4.6 More algebra Substitution of negative numbers	P235 P236
9	3.5 Straight line graphs Equations of lines parallel to the axes	P160-161
10	Use points in a table to sketch the line	P163 P164
11	Use pie charts Calculate angles in pie charts	P176-178
12+13+14	Investigation on data handling (collect data to prove a hypothesis
15	3.7 Probability Use a probability scale Calculate experimental probability Calculate expected probability	P180-181 P181 P182
16	Equally likely outcomes and theoretical probability Calculate expected probability	P183-184 P185-187

Lesson 17+ 18 Revision & Part 3 Test

Part 4 (7 weeks )
Lesson No.	Topic & Learning Objectives	Textbook reference
1	4.1 Constructing triangles Construct triangles using ruler, protractor and compasses	P207-208
2	Construction using compasses	P209-210
3	4.2 2D shapes Recognise different quadrilaterals Recognise Polygons Identify symmetry properties of quadrilaterals	P211-212
4	Recognise line and rotational symmetry	P212-213 P214
5	Express one number as a percentage of another	P219-220
6	Calculate a percentage of a number Introduce idea of decimal equivalent to find % on calc.	P222-223 P224-225
7+8+9	Solve equations	P239 P240-241 P241-243
10+11	Expand brackets	P244-245
12+13	6.2 Sequence rules Find the rule for the nth term of a sequence	P315-317 P317-320
14	5.1 Rotation Rotation: 1 Rotating shapes 2 Rotational symmetry (revision)	P255-256 P256-257
15	5.2 Line symmetry Reflection Line symmetry Reflecting shapes	P260-265
16	5.3 Translation Translation Translate shapes	P266 P267
17	Revision lesson.
18	Unit 4 test
19+20	Investigation algebra: 4 consecutive numbers: pair products on Nrich website

Part 5 (9 weeks)
Lesson No.	Topics & Learning Objectives	Textbook Reference
1	5.4 Interpreting graphs Read information from line graphs Draw line graphs Interpret travel graphs	P283-289
2	5.5 Rounding numbers Round numbers to 10, 100, 100 Round to decimal places Round to 1sf Round numbers to estimate answers and check results using 1sf	P 292-296
3+4	Circles Find the circumference of a circle	P 299-300
5+6	Find the area of a circle	P301 P302
7+8	6.4 Construct bisectors Construct the perpendicular bisector Construct the angle bisector	P331-333
9+10	Count faces, edges and vertices Use nets to construct solids	P334-335 P336-338
11+12	Using Trial and improvement to solve problems	Other resources (SMP booklet)
	1 week revision before end of year exam START YEAR 8 SYLLABUS (year 8 textbook given)
13	6.4 Probability Find the expected number of outcomes for an event	P 330-331
14+15	Use two way tables to find the probability of two events Use simple Tree diagrams for two events	P 333 P 334
16	Use experimental results to estimate probability	P 336-337
17+18	Investigation on who is the richest?

Year 8

The reference book is Essential Mathematics Book 8H and 9
Work at National Curriculum Level 6 is consolidated and National Curriculum Level 7 and 8 are introduced.
Topics occur in the order suggested in the National Numeracy Strategy guide. The book is split into 6 Units corresponding to the six half-terms in the school year. There is appropriate revision material at the end of each Unit and many topics are reviewed later in the book, in line with the NNS guide.
Puzzle activities and mental arithmetic tasks can be found between the Units to be used as appropriate. Investigations occur at regular intervals.
Most work is broken down into two levels. ‘M’ exercises are aimed at all pupils at this level. ‘E’ exercises provide extension work. Some pupils will only complete the ‘M’ exercises. Pupils may move onto the ‘E’ work having completed some ‘M’ exercises. Other pupils may only need to tackle the ‘E’ exercises.
Pupil self-assessment is a very important part of assessment for learning. Regular ‘check yourself’ sections appear throughout the book. Answers to these exercises are provided at the back of the book for immediate feedback. Pupils can use these sections when revising for a test.
The class teacher will go through a number of examples on the board before pupils start the exercises.
At the end of each Unit there will be a summative test based on the work covered of 50 minutes duration. Each topic of work within the test will be marked separately, so that pupils can assess and identify in which techniques they are proficient and in which techniques they need to improve. Performance in each topic will be recorded by the pupil so individual targets may be set for improvement.
This scheme of work and the number of lessons for each topic will be adhered to where possible. However circumstances such as school closure due to snow etc, may mean that alterations are made at various points in the year.

Unit 1 (6 weeks – complete before half term)
Lesson No.	Topics & Learning Objectives	Textbook reference
1	1.2 Fractions Use equivalent fractions Add and subtract fractions after finding a common denominator	P 9 P 10
2	Multiply two proper fractions including cancelling Multiply mixed numbers	P11 P12-13
3	Divide an integer by a fraction & vice-versa Divide a fraction by a fraction Divide one fraction by another	P15-16 P16-17 P16-17
4	1.3 Area and Perimeter Find the area of a parallelogram and a trapezium Find missing lengths given the area and some measurements Conversion of cm² to m²	P 17-19 P 19 P19
5	4.3 Handling data Draw and interpret scatter graphs	P 180
6+7	Interpret scatter diagrams in terms of positive and negative correlation Drawing lines of best fit.	P 182-183
8+9	5.2 Sequences and formulas Understand and use Mapping diagrams Use the n^th term to find terms Use differences to find the n^th term of a sequence	P247-248 P 249-250 P 251-255
10	5.5 Drawing and Using Graphs Use a computer graph plotter to draw graphs	P 275
11	Given coordinates or a graph, find the equation	P 276-277
12	Complete a table of points to draw a curved graph	P 278
13	Revision lesson for test
14	Unit 1 Test
15+16+17	BFG investigation in groups

Part 1 should be completed before half term

Part 2 (6 - 7 weeks – complete by Christmas)
Lesson No.	Topics & Learning Objectives	Textbook reference
1	2.1 Written calculation Read scales on a number line and interpret values Understand the value of each unit on a number line Multiply two decimal numbers Round numbers to approximate answers	P 63-67 P71
2	Divide by 0.1 and 0.2 Divide by any simple decimal number such as 0.3, 0.02	P 68
3	2.3 Geometrical reasoning Revise alternate, corresponding, vert. Opposite angles Revise angles at a point, on a straight line Use angle facts to prove results in geometry	P 84-85
4	2.4/4.7 Using Algebra Combine like terms Expand single brackets Multiply out brackets and collect like terms to simplify	P 86-88 P216-218
5	Writing expressions given instructions Simplify expressions	P 90-91
6+7	Use algebra to solve problems	P 92 P 93-95
8+9	Applying mathematics to solve a variety of problems in a range of contexts.	P 101-102 P 102-103
10+11	2.6 Circles Find the perimeter of shapes with semi-circles and quarter-circles Find the area of shapes with semi-circles and quarter-circles Find areas of more complicated shapes	P 110 P 111-112 P 113-114
12	5.4 Pythagoras’ Theorem Using squares to derive Pythagoras’ Theorem
13+14	Calculate the length of a side in a right angled triangle Solve problems using Pythagoras’ theorem	P 265-267 P 267-268 P 298-270
15	Revision lesson for test
16	Unit 2Test
17+18	9 Pegs circles investigation

Part 2 should be completed before Christmas.

Use Christmas Activities for any remaining lessons

Use Unit 2 Mixed Review for consolidation. Girls can also use this for revision prior to the test.

Part 3 (6 weeks – complete by Spring Half Term)
Lesson No.	Topics & Learning Objectives	Textbook reference
1	3.1 Reflection Draw reflections on squared paper Draw reflections using coordinates	P 127-128
2	Understand stem and leaf diagrams	P 139-140
3	3.4 Using formulas and expressions Substitute values into a range of formulas	P 147 - 150
4	Find the value of an expression	P 151-153
5+6	3.5 Construction and locus Describe and draw the locus of a point	P 156- 157
7	Construct various perpendicular bisectors of a line Construct the angle bisector	P 158-159 P 159-160
8+9	5.1 Enlargement Recognise enlargement and their properties Use the centre of enlargement and scale factor to enlarge shapes	P 242 P 243-245
10	5.6 Using ratios Use and simplify simple ratios Share quantities in a given ratio Use ratio in a range of contexts and problems	P 281-285
11+12	6.5 Drawing 3D objects Draw 3D objects in isometric view Draw three views of an object – front and side elevation and plan	P 339-341 P342
13	Revision lesson
14	Unit 3 Test
15+16+17	Investigation

Part 3 should be completed by the half term break.

Use Unit 3 Mixed Review for consolidation. Girls can also use this for revision prior to the test.

Part 4 (7 weeks – complete by Easter)
Lesson No.	Topic & Learning Objectives	Textbook reference
1	4.1 Bearings and scale drawing Learn about bearings Construct bearings	P 172-174
2+3	Understand scale Make scale drawings and use them to solve problems	P 175-176
4	4.4 Fractions, decimals and percentages Learn about recurring decimals Write fractions as recurring decimals using correct notation	P 195
5	Find percentage change without a calculator Find percentage change with a calculator	P 200-202
6	6.3 Percentages 2 Find percentage change without a calculator Find percentage change with a calculator	P 323-324 P 325-326
7+8	Combine two transformations in the correct order When possible fins a single transformation the same as the conbination	P 212-213 P 214-215
9	4.7 Brackets and equations Solve equations containing brackets Write down equations from word problems and solve	P 220
10+11	Use inverse operations to solve equations with the unknown on both sides	P 222-223
12	6.1 More Algebra Solve equations with one or more single brackets Formulate problems involving equations Solve a variety of problems with equations	P 304 P305
13	6.2 Volume of objects Find the volume of a cuboid Given the volume find lengths for cuboids	P 311-312 P 312-314
14+15	Find the volume of prisms Given the volume find missing lengths Use units for volume and units for liquids	P 315-316 P 316-317
16+17	Find the volume of cylinders	P 318-320
18	Revision lesson
19	Unit 4 Test
20 + 21	Investigation if time permits

Part 4 should be completed by Easter.

Part 5 (7 weeks – complete by Half Term)
Lesson No.	Topics & Learning Objectives	Textbook Reference
1+2	5.3 Applying maths in a range of contexts Use mathematics in a range of investigational and problem solving contexts	P 257-263
3	5.7 Congruent shapes and tessellation Understand and recognize congruent shapes Draw tessellations of congruent shapes	P 288-289 P 290
4	6.1 Continued More Algebra Solve a variety of problems with equations	P306-307
5	Book 9 1.3 Factors Factorise simple expressions by taking out common factors.	P 19
6+7	Book 9 1.4 Multiplying Brackets Expand brackets using FOIL Solve equations by removing brackets and collecting terms.	P 20 P 21
8+ 9	Book 9 2.6 Frequency distributions Use grouped frequency tables to calculate an estimate of the mean. Represent the data as a frequency polygon	P67-68 P69-71
10	Book 9 3.2 Rounding, errors and estimating Understand and round to a given number of significant figures. Understand measurements are not exact. Understand and write error bounds for given measurements. Problems involving error bounds	. P 85 P 87-88
11	Book 9 4.5 Simultaneous Equations Solve simultaneous equations using intersection of graphs.	P138-139
12+13	Use the algebraic method of elimination to solve simultaneous equations.	P141-143
14+15+16	Book 9 6.2 Listing possible outcomes Write down or calculate probability for two events. Use lists and two way tables. Understand the term independent events. Understand the term mutually exclusive events. Use tree diagrams for two events	P197-198 P 199
17+18+19	Revision for end of year exams

Part 5 should be completed by Summer half term.

Lesson No.	Topics & Learning Objectives	Textbook Reference
1+2+3	Review of end of year examination. Then investigation
4+5	Book 9 6.4 Inequalities Use notation for inequalities. Represent on a number line. Solve inequalities algebraically. Use inequalities in simple problems.	P205-206 P 207 P 208
6+ 7	Book 9 6.4 Inequalities in two variables Represent two inequalities in 2D space.	P 209
8+9	Book 9 5.3 Compound measures Recognise speed as Distance/Time Recognise density as Mass/Volume	P160-162 P162-163
10	Book 9 1.1 Index Laws Be able to multiply and divide using the rules for indices. Understand the meaning of negative indices.	P 1 - 2
11	Find a power of a power. Recognise and solve simple equations involving powers	P 3 – 5
12+13	Book 9 1.1 Standard Form Recognise and use numbers in standard form Perform calculations in standard form	P 7 P 8 – 9 P 10 P10 - 11
14	Book 9 5.5 Changing the subject of a formula Rearrange simple algebraic formulae.	P173-174
15	Book 9 5.5 Formulae involving fractions Rearrangement of formulae involving fractions.	P174-175
16	Book 9 5.5 Formulae with negative x terms Rearrangement of formulae containing negative x terms.	P 176
17 + 18	End of term activities/games

Part 6 should be completed by the end of term.

Year 9

The GCSE examinations in Summer 2014 will be linear. This means that all the written examination papers will be sat in the summer of 2014. The examination boards have not yet informed us as to how many papers there will be or how long they will be. As soon as we know this information we will update this section. At the moment we are following the GCSE course in year 9, 10 and 11.

Current year 9, 10 and 11

The course your daughter is following for GCSE is OCR Mathematic (code J562). It is split into three units in the following manner:
- Unit A503/02 Mathematics Unit C (Higher)
  - Written Paper
  - 2 Hours
  - 100 Marks
  - 50% of the qualification
  - Calculator Permitted
- Unit 502/02 Mathematics Unit B (Higher)
- - Written Paper
  - 1 Hours
  - 60 Marks
  - 25% of the qualification
  - Calculator not permitted
- Unit 501/02 Mathematics Unit A (Higher)
- - Written Paper
  - 1 Hours
  - 60 Marks
  - 25% of the qualification
  - Calculator permitted

There are 400 UMS marks in total, 100 each on unit A and B, 200 on unit C. The papers all cover material from grades A* - D. The overall grading is as follows:
- A* 360 A 320 B 280 C 240 D 200 E 160

Examinations take place November, January and June. (However the first sitting of unit C is June 2012, therefore there are no sittings prior to this one).
Unit A and B examinations are an hour each. The final Unit C is a two hour paper.
It should be noted that Unit B is a non-calculator examination and therefore will test basic calculation skills.
The reference book for this course used in school is the Essential Maths Higher GCSE Maths book published by Elmwood press. We also offer the accompanying homework text book.
The following is a brief outline of what will be covered accompanied by a approximate time line and order of course coverage.
As well as covering course content there are also lessons which will focus on functionality. That is the ability of students to apply their knowledge and generally problem solve. Another important feature is the quality of written communication. Both these areas are key foci of the new 2010 GCSE specifications.
We subscribe to the MyMaths website as well as sharing resources through the schools VLE – moodle. Your daughter has access to these and will find them invaluable in consolidating her learning.
Your daughter will need a scientific calculator for this course of study.

UNIT A

Chapter 1 Number and Problem Solving
Lesson No.	Learning Objectives			Main Activity Higher GCSE Maths *M_Grades B,C,D – E Grades A,A**
1	Developing problem solving strategies			Intermediate maths challenge 2011 (Q19,Q20).
2	Rounding numbers Appropriate accuracy – decimal places and significant figures. Estimate by first rounding to 1 s.f.			Unit 1 Number 1 Round off page 5
3	Understand prime numbers and factors. Write a number as the product of prime factors Find the HCF and LCM			Unit 5 Number 3 M5.2 page 118-119 M5.2 page 119-120
Chapter 2 Expressions
4	Expand simple expressions with brackets Collect together like terms to simplify			Unit 4 Algebra 1 M4.3 page 92 M4.3 page 93
5	Factorise simple expressions by taking out common factors			Unit 4 Algebra 1 M4.6 page 97
6	Simplify expressions with indices			Unit 2 Number 2 Expressions with indices M2.6 page 36 – 38
Chapter 3 – Statistics
7+8	Draw pie charts for simple sets of data Interpret pie charts Use tables of data to draw grouped frequency diagrams With grouped data draw frequency polygons Use tables of discrete data to draw stem-and-leaf diagrams Find the mode, median and range			Unit 11 Statistics 2 Draw pie charts M11.2 page 317 Q 1-3 Interpret pie charts M11.2 page 318 - 319 Draw and interpret frequency polygons M11.4 page 326 – 328 Unit 14 Statistics 3 Draw stem and leaf diagrams M14.5 page 431 - 432
Chapter 4 Linear Equations
9+10+11	Solve simple linear equations Solve simple equations involving exact square roots Solve simple linear equations with brackets Solve simple linear equations with fractions Solve simple linear equations with x on both sides			Unit 6 Algebra 2 Linear equations M6.1 page 148 Q 1 – 16 M6.1 page 149 Q 20 - 28 M6.2 page 149 Q 1 - 12 M 6.1 page 149 Q 38 – 47 M6.3 page 151 Q 1 – 9 M6.1 page 149 Q 29 – 37 M 6.2 page 150 Q 15 – 29
Chapter 5 Ratio
12+13		Understand and simplify ratio Simplify ratio with mixed units Write a ratio in the form 1:n Use ratio to solve problems including scale Share a quantity in a given ratio Solve problems on best value for money		Unit 2 Number 2 M2.5 page 34 – 35
Chapter 6 Statistics 2
14+15+ 16		Calculate the mean from a frequency table. Calculate mode, median and range Calculate the mean from a grouped frequency table – discrete data Calculate the mean from a grouped frequency table – continuous data		Unit 14 Statistics 3 M14.3 page 427 – 428 M14.4 page 429 Q 1-4 M14.4 page 430 Q 5 -6
Chapter 7 Geometry
17+18			Understand Pythagoras theorem in terms of area Calculate missing sides of triangles Solve problems using Pythagoras theorem	Unit 10 Geometry 3 M10.5 page 278-27 M10.6 page 280-283 Q1-10, Q16-20
19			Use Pythagoras theorem in 3D problems	Unit 18 Geometry 6 E18.4 page 546-548
20+21			Find gradient of lines on graphs Find the equation of a straight line (y=mx+c)	M6.10 – M6.12 p. 177
22			Calculate the length of line segments Find midpoints	Unit 10 Geometry 3 M10.5 page 281-282 Q11-15
Chapter 8 Algebra
23			Find the nth term for a linear sequence	M12.7 page 351-353
24			Substitution into expressions and formulas	Unit 4 Algebra 1 M4.1 page 89 M4.2 page 90-91 – higher sets
25			Using f(x) notation to substitute into an expression Solving f(x) = problems	Unit 6 Algebra 1 E6.2 pg 164-165
26+27			Rearrange formulas to change the subject EXTEND TO: Rearrange formulae where the new subject appears more than once Rearrange formulae where the new subject occurs as a root or power	Unit 6 Algebra 2 M6.6 page 157-159 M6.7 page 160-161 Unit 6 Algebra 2 E6.1 page 162-163 Mixed in with E6.1
Chapter 9 Measures
28+29			Convert between metric units Understand imperial units Convert between metric and imperial units Estimate length, mass, capacity of common objects standard form Perform standard form calculations by hand	Unit 10 Geometry 3 M10.1 page 268 Q2 – 5 M10.1 page 268-269 Q6 – Q10 M10.2 page 270-271
30			Construct: Perpendicular bisector of a line Perpendicular from a point on a line Perpendicular from a point to a line Angle bisector	Unit 17 Geometry 5 M17.2 page 494-495 M17.3 page 496-498
31+32			Understand and interpret loci Construct and draw simple loci Construct and draw intersecting loci	Unit 17 Geometry 5 M17.4 page 499-503
Chapter 10 Trigonometry
33+34+35+36			Understand the ratios SIN, COS, TAN Calculate the length of a side in a RA Triangle Calculate the hypotenuse in a RA Triangle Calculate the size of an angle in a RA Triangle	Unit 10 Geometry 3 M10.7 page 284-285 M10.8 page 286-287 M10.9 page 289-290
Chapter 11 Statistics
37+38			Interpret and construct cumulative frequency diagrams Interpret and construct Boxplots Calculate median and IQR to compare distributions	Unit 14 Statistics 3 M14.7 page 436-437 M14.8 page 439-440
39+40			Interpret and construct Histograms	E14.1 page 442
41+42+43+44			Understand and use the terms: Population, sample, bias, random, hypothesis Understand the good design of a questionnaire	E11.2 page 332-334

What your daughter will do in lessons.

Your daughter will cover the above content using a variety of activities. Lessons will be used to develop and explore new ideas and concepts. Your daughter will be expected to participate in whole class discussions as well as a variety of different group tasks. As well as covering subject content it is also the aim of lessons to develop the learning capacity of your daughter to progress her own ability to learn. Time will also be allocated for independent work and practice mainly using the text book named above, but also other sources. Much of the consolidation work will be expected to be done at home through two lots of 30 minutes homework a week. This is the minimum expectation. At different points in the year your daughter will also go through various revision programs close to assessment and examination periods.

How your daughter’s progress will be assessed.

The answers to all exercises from the textbook are at the back of the book. Your daughter will be expected to mark her ‘day to day’ exercises herself and to ask the teacher for further explanation for problems that are not correct. Your daughter’s homework exercises will be marked either by a peer or by her teacher on a regular basis. Homework’s often involve a self assessment as well as marker assessment. We also encourage your daughter to write a comment on how she found her homework. Your daughter will be given a summary assessment at regular intervals throughout the year covering the different modules of work. These assessments will be in the form of examination style tests to gauge the level she is currently working at, and to inform a prediction of her GCSE result. Nearer the examination, past paper will be completed and marked according to the examination board mark schemes. The tests and the past papers are used to produce the grades in the reviews and the predicted grades that we have to send to the examination board.

UNIT B

Chapter 1 Properties of shapes
Lesson No.		Learning Objectives	Main Activity Higher GCSE Maths *M_Grades B,C,D – E Grades A,A**
1		Use the angle properties associated with parallel lines: Corresponding angles Alternate angles Allied angles	Unit 3 Geometry 1 M3.2 page 55-57
2		Angles in triangles and quadrilaterals Properties of special quadrilaterals: Square, rectangle, parallelogram, rhombus, kite, trapezium, Isosceles trapezium
3+4		Calculate the angles in polygons. Interior and exterior angles of regular polygons	M3.3 page 59-60 M3.4 page61-62
Chapter 2 Fractions, decimals and percentages
5		Compare fractions Four rules of fractions to include mixed numbers Four rules for decimals	Unit 1 Number 1 M1.2 page 3-5 M1.1 page 2 Q7
6+7		Calculate percentage increase and decrease Calculate a percentage change	Unit 2 Number 2 M2.1 page 24-26 M2.2 page 27-28
Chapter 3 Indices, decimals and surds
8+9		Use the rules of indices Understand and use fractional and negative indices	Unit 2 Number 2 M2.6 page 36-38 E2.1 page 39-40 E2.2 page 41-42
10		Convert fractions to terminating or recurring decimals Represent recurring decimals as fractions	Unit 1 Number 1 M1.4 page 9 E1.1 page 10-11
11+12+13		Use surds in variety of contexts Rationalise a denominator that has a surd	E1.2 page 12-13 E1.3 page 15 Q1-3, 5 E1.3 page 15-16 Q4, 6-10
Chapter 4 Straight-line Graphs
14+15		Gradient and intercept of a straight line graph Equation in the form y=mx+c Gradients of parallel and perpendicular lines	Unit 6 Algebra 2 M6.8 page 167 M6.10 page 177-178 M6.12 page 180-181 E6.5 page 182 E6.6 page 184
Chapter 5 Transformations
16+17	Transform shapes by: Reflection, Rotation and Translations. Reflective symmetry		Unit 9 Geometry 2 M9.4 page 239-241 M9.5 page 243-245 M9.3 page 237-238
18+19	Transform shapes by enlargement, including fractional and Negative scale factors		M9.2 page 247-249 E9.1 page 250-251
20	Combine a mixture of transformations		E9.2 page 252-254
Chapter 6 Inequalities
21	Solve inequalities with one unknown Represent inequalities with one unknown on a number line		Unit 16 Algebra 4 M16.1 page 465-466
22+23	Solve inequalities with two unknowns Represent inequalities with two unknowns on a graph		M16.3 page 468-469
Chapter 7 Similarity
24+25	Recognise similar shapes Use similarity in a variety of problems		Unit 13 Geometry 4 M13.3 pg 402 M13.4 pg 404
Chapter 8 Congruency
26+27	Recognise congruent triangles SSS, SAS, ASA and RHS Use congruency in a variety of problems		Unit 9 Geometry 2 E9.3 page 256-258
Chapter 9 Simultaneous Equations
28	Solve simultaneous equations graphically		Unit 12 Algebra 3 M12.2 page 343
29	Solve simultaneous equations algebraically using addition or subtraction		M12.3 page 344-345
30+31	Solve simultaneous equations algebraically by multiplying one or both equations Form simultaneous equations and solve		M12.4 page 346 M12.5 page 347-348
Chapter 10 Vectors
32	Column vectors and translation Understand idea of magnitude and direction Addition and subtraction of vectors Multiplication by a scalar		Unit 10 Geometry 3
33	Column vectors and translation Understand idea of magnitude and direction Addition and subtraction of vectors Multiplication by a scalar		E10.1 page 296-297 E10.2 page 299-302
34+35	Use vector methods to solve geometrical problems		E10.3 page 304-307
Chapter 11 Circle Theorems
36+37	Understand all terms relating to a circle: Radius, diameter, arc, chord, tangent, sector, segment, circumference Angle properties: Angle in a semi-circle is a right angle Angle at centre is twice that at circumference Angles on the same arc are equal		Unit 3 Geometry 1 E3.1 page 67-68
38	Understand cyclic quadrilaterals Angle properties: Opposite angles are supplementary Exterior angle is equal to the interior opposite angle		E3.2 page 70-71
39	Recognise tangents Angle properties: Angle between tangent and radius is a right angle Tangents from point to a circle are equal length		E3.3 page 72-74
40	Angle properties: The perpendicular bisector of a chord passes through the centre The alternate segment theorem		E3.4 page 76-77
Chapter 12 Scatter diagrams and time series
41	Interpret and draw scatter diagrams Understand and use correlation Draw a line of best fit		Unit 11 Statistics 2
42+43	Draw and interpret time series Calculate moving averages

What your daughter will do in lessons.

Your daughter will cover the above content using a variety of activities. Lessons will be used to develop and explore new ideas and concepts. Your daughter will be expected to participate in whole class discussions as well as a variety of different group tasks. As well as covering subject content it is also the aim of lessons to develop the learning capacity of your daughter to progress her own ability to learn. Time will also be allocated for independent work and practice mainly using the text book named above, but also other sources. Much of the consolidation work will be expected to be done at home through two lots of 40 minutes homework a week. This is the minimum expectation. At different points in the year your daughter will also go through various revision programs close to assessment and examination periods.

How your daughter’s progress will be assessed.

UNIT C

Chapter 1 Algebraic Manipulation
Lesson No.	Learning Objectives		Main Activity Higher GCSE Maths *M_Grades B,C,D – E Grades A,A**
1	Expand two bracket		Unit 4 Algebra 1 M4.5 page 95
2	Expand brackets involving surds		Unit 1 Number 1 E1.3 page 15-16 Q 1-7
Chapter 2 Perimeter, area, volume and 2-D representation
3	Area of triangle, parallelogram and complex shapes		Unit 13 Geometry 4 M13.1 page379-381
4	The circumference and area of a circle
5 6	Volume of prisms, including a cylinder Surface area of a cylinder		M13.2 page 392-395
7	Understand plans and elevations		Unit 18 Geometry 6 M18.1 page527
Chapter 3 – Trial and Improvement
8+9	Use trial and improvement to find solutions to problems		Unit 6 Algebra 2 M6.5 page 155-156
Chapter 4 Probability 1
10	Understand basic idea of probability P(A) + P(A’) =1		Unit 8 Statistics 1
11+12	Calculate expected frequency Calculate relative frequency		M8.1 page 202-203
Chapter 5 Graphs 1
13		Draw and interpret graphs of real life situations	Unit 6 Algebra 2 E6.4 page 174-176
14		Draw and interpret velocity time graphs
15+16		Draw graphs of quadratic functions	M6.9 page 169-170
17+18		Use quadratic graphs to solve equations	Unit 12 Algebra 3 E12.7 page 369-371
Chapter 6 Measures
20		Convert between measures, especially area and volume	Unit 10 Geometry 3 M10.1 page 268-269
21+22		Accuracy of measurement – upper and lower bounds Calculations involving accuracy and giving answers to a sensible degree of accuracy	Unit 5 Number 3 M5.6 page 128-129 E5.1 page 130-132
23+24		Use compound measures such as speed and density	Unit 10 Geometry 3 M10.3 page 273274 M10.4 page 276
Chapter 7 Percentage and Proportional change
25	Repeated percentage and proportional change		Unit 2 Number 2 M2.1 page 24-26
26+27	Reverse percentage problems		M2.4 page 32-33
28+29	Solve real life problems on percentage and proportional change, including compound interest Index numbers – retail price index		M2.3 page 29-31
Chapter 8 Standard form and using a calculator
30+31	Representing very large and small numbers in standard form Perform standard form calculations by hand		Unit 5 Number 3 M5.3 page 121-122 M5.4 page 123-124
32	Use a calculator to perform more complex calculations		M5.5 page 125-126
33+34	Explore examples of exponential growth and decay		Unit 12 Algebra 3 E12.6 page 366-368
Chapter 9 Similarity
35+36	Recognise the properties of similar shapes, particularly similar triangles Calculate length of sides in similar shapes		Unit 13 Geometry 4 M13.3 page 402-403 M13.3 page 404-406
37+38	Understand area and volume scale factors Calculate the area and volume of similar shapes		Bottles Investigation
Chapter 10 Factorising
39	Factorise by common factor		Unit 4 Algebra 1 M4.6 page 97
40+41	Factorise quadratics with single square term		M4.7 page 98-99
42	Factorise the difference of two squares		E4.1 page 100
43	Factorise quadratics with multiple square term		E4.3 page 102-103
44+45	Simplify algebraic fractions		Unit 16 Algebra 4 E16.1 page 476 E16.2 page 477
Chapter 11 Three dimensional geometry
47	Use coordinates in 3 dimensions		Unit 18 Geometry 6 M18.4 page 534-535
48+49	Use right angled triangles to find lengths and angles in 3D		E18.4 page 546-548
50	Find the angle between a line and a plane		E18.5 page 550-551
Chapter 12 Proportion and variation
51+52	Solve problems using direct proportion		Unit 5 Number 3 E5.2 page 134-135
53	Solve problems involving more complicated forms of direct proportion – square, cube, square root		E5.3 page 135-137
54+55	Solve problems using inverse proportion, including square, cube, square root etc		E5.4 page 138-139
Chapter 13 Graphs 2
56+57	Solve simultaneous equations graphically – one linear, one a curve		Unit 12 Algebra 3 E12.5 page 364 E12.7 page 369-371
58+58	Drawing the graphs of simple functions – cubic, reciprocal and exponential functions		Unit 6 Algebra 2 E6.3 page171-173 Unit 12 Algebra 3 E12.6 page 366-368
Chapter 14 Quadratic equations
59+60	Solve quadratic equations by factorisation		Unit 4 Algebra 1 E4.4 page 104-106
61	Solve quadratic equations by completing the square		Unit 12 Algebra 3 E12.2 page 358-359
62+63	Solve quadratic equations using the formula		E12.3 page 360-361
Chapter 15 Simultaneous equations
64+65	Solve simultaneous equations by substitution Solve simultaneous equations where one is linear and the other quadratic		Unit 12 Algebra 3 E12.5 page 364
Chapter 16 Trigonometry
67	Find angles and lengths in non-right angle triangles Use the sine rule		Unit 18 Geometry 6 E18.1 page 539
68	Use the cosine rule		E18.2 page 541-542
69+70	Solve problems using sine and cosine rule, including bearing problems and angle of elevation or depression		E18.3 page 543-544
71	Area of triangle using trigonometry		Unit 13 Geometry 4 E13.1 page 382-383
72	Draw the graphs of the trig functions Draw graphs for related trig functions eg 4sinx, cos4x
Chapter 17 Functions
73	Understand and use function notation		Unit 6 Algebra 2 E6.2 page 164-166
74	Transform graphs – translation parallel to axes and reflection in axes		Unit 17 Geometry 5 E17.3 page 511-512
75	Transform graphs – stretches parallel to both axes		E17.4 page 514-515
Chapter 18 Length, area and volume
76	Find the length of arc in a circle Find the area of a sector		Unit 13 Geometry 4 E13.2 page 384-386 E13.3 page 387-389
77+78	Calculate the surface area and volume of cones, pyramids and spheres		E13.4 page 396-399 E13.5 page 400-401
79	Compound shape problems		Included in E13.4 and E13.5
Chapter 19 Probability 2
80	Addition rule for mutually exclusive events		Unit 8 Statistics 1 M8.5 page 210-212
81	Multiplication rule for independent events		M8.6 page 213-214
82	Use tree diagrams for independent events		M8.7 page 216-218
83	Use tree diagrams for conditional probability		E8.1 page 220-222
Chapter 20 Algebraic fractions
84	Factorising and simplifying algebraic fractions		Unit 16 Algebra 4 E16.1 page 476-477
85	Add and subtract algebraic fractions		E16.3 page 479-480
86+87	Solving equations involving algebraic fractions		E16.4 page 481-482

What your daughter will do in lessons.

Your daughter will cover the above content using a variety of activities. Lessons will be used to develop and explore new ideas and concepts. Your daughter will be expected to participate in whole class discussions as well as a variety of different group tasks. As well as covering subject content it is also the aim of lessons to develop the learning capacity of your daughter to progress her own ability to learn. Time will also be allocated for independent work and practice mainly using the text book named above, but also other sources. Much of the consolidation work will be expected to be done at home through two lots of 40 minutes homework a week. This is the minimum expectation. At different points in the year your daughter will also go through various revision programs close to assessment and examination periods.

How your daughter’s progress will be assessed.

Post 16 (A Level Mathematics)

AS level mathematics

The course your daughter is following in the L6 is OCR MEI Mathematic AS(code 3895). The Mathematics AS that your daughter is studying is made up of three units Core 1(code 4751), Core 2 (code 4752) and Statistics 1(code 4766). They are all equal weighting (UMS mark out of 100) and the UMS marks for each are added up to give a total out of 300. The grade boundaries are A-240, B-210, C-180, D-150, E-120, U- less than 120.
The Core 1 examination will be taken in the January Series and Core 2 and Statistics 1 will be taken in the Summer Series.
All 3 units consist of a written exam 1h 30min (100% of marks). The examination consists of two parts. Section A is worth 36 marks and consists of shorter questions – approximately 10 questions. Section B is worth 36 marks and consists of longer questions- approximately 3 questions.
Candidates may not use any calculator in Core 1 but may in Core 2 and Statistics1
The reference book for Core 1 and Core 2 is ‘Core 1 and 2’ and for Statistics 1 is ‘Statistics 1. Your daughter will be given her own copy of these books.
The following is a brief outline of what will be covered each lesson. Quite a few of the topics and techniques Core 1 have been covered as part of the GCSE course and may be covered quite quickly. These will be marked with * in the first column. Extra lessons to consolidate/deepen learning may be added when the teacher judges it is necessary.
‘My Maths’and the MEI website are both software packages that your daughter has access to and will find invaluable in consolidating her learning.
We also strongly recommend the purchase of a graphical calculator as it is invaluable in helping consolidate learning but also in all of the A level units except Core 1.

Core 1

Time scale

Lessons Number

Topic and Learning Objectives

Chapter and Pages

Basic Algebra

*Equations

* Change of subject

Ch 1 P7-11

Ex 1B

Ch 1 P11-13

Ex 1C

Basic Algebra

*Quadratic Equations

Ch 1 P 13-17

Ex 1D Q1-7

Basic Algebra

Quadratic Functions and Equations

Ch 1 P 18-27

Ex 1D Q8-16

Basic Algebra

*Simultaneous Equations.

Ch 1 P 28-33

Ex 1E.

7+8+9

Co-ordinate Geometry.

*Gradient of a line.

*Parallel lines: m_{1 =} m₂

Perpendicular lines m_{1 X} m₂ = -1 :

* Distance between two points.

Midpoint between two points.

The equation of a straight line:

*Drawing a line, given its equation

(a) Lines parallel to the axes

(b) y=mx+c

Ch 2 P34-41

Ex 2A,B

Co-ordinate Geometry.

Finding the equation of a line

Different techniques to solve practical problems

*Intersection of two lines.

Ch 2 P 46-54

Ex 2C,D

11+12

Co-ordinate Geometry.

Curves:

The circle

Co-ordinate Geometry.

Intersection of a line and a curve.

Intersection of two curves.

Ch 2 P 68-75

Ex 2F Ch 3 P

Polynomials.

Definition of a polynomial.

Order of a polynomial.

Operations with polynomials

Ch 3 P 77- 82

Ex 3A

Polynomials.

Polynomial curves:

Ch 3 P 82-87

Ex 3B

Polynomials.

Polynomial Equations

Factor theorem

Spotting a root of a polynomial equation

Ch 3 P 88-92

Ex 3C Q1-8

Polynomials.

Remainder theorem

Ch 3 P 92-97.

Ex 3C Q9-

Polynomials.

The graphs of quadratic functions

Ch 3 P 97-100

Ex 3D

Polynomials.

*Using transformations to sketch the curves of functions

Ch 3 P101-108

Ex 3E

20+21

Polynomials.

Binomial expansions.

Show relationship with Pascal’s Triangle.

The formula for a binomial coefficient

The expansion of (1 +x)ⁿ

Application to numerical approximations.

Ch 3 P 108-117

Ex 3C

Uncertainty

Errors and inequalities

Variability

The Accuracy of given stored information

absolute error

percentage error

Uncertainty

The algebra of inequalities

*Linear inequalities

Quadratic inequalities

Ch4 P119-122

Activity 4.1

Ch4 P122-126

Ex 4A

Indices

Working with square roots

Ch 5 P127-130

Ex 5A

24+25

Indices

*Negative and fractional indices

Multiplication

Division

Index zero

Negative indices

Fractional indices

Power of a power

Mixed bases

Simplifying sums and differences of fractional powers

Ch 5 P130-137

Ex 5 B

The Language of Mathematics

Types of numbers

counting numbers

natural numbers

integers

rational numbers

real numbers

The Language of Mathematics

‘Necessary’ and ‘sufficient’

The converse of a theorem

The Language of Mathematics

Proof

a) disproving a conjecture by counter-example

b) by exhaustion

c) by deduction

d) by contradiction

Ch 6 P144-148

Ex 6A

Ch6 P 149-154

Ex 6B

Ex 6C

Ch 7 P 154-158

Ex 6D

Core 2

Time Scale

Lessons Number

Topic and Learning Objectives

Chapter and Pages

Sequences and Series.

Definitions and notation

Patterns in sequences

Arithmetic sequences

Geometric sequences

Periodic sequences

Oscillating sequences

Sequences with other patterns

Ch 7 P 160-168

Ex 7A

Sequences and Series.

Arithmetic Sequences and Series:

Notation

General Term

Sum of the terms of an arithmetic sequence

Ch 7 P 169-176

Ex 7B

3+4

Sequences and Series.

Notation

Geometric Sequences and Series:

General Term.

Sum of the terms of a geometric sequence.

Sum of Infinite Sequence

Ch 7 P 176-

Ex 7C

Differentiation.

The gradient of a curve.

Drawing tangents.

Finding the gradient of a curve.

Finding the gradient from first principles.

The gradient function

Ch 8 P 191-161.

Ex 8A

Differentiation.

Differentiating using standard results.

Sums and differences of functions.

Ch 8 P 199-205.

Ex 8B

Ex 8C

7+8

Differentiation.

Tangents and Normals.

Ch 8 P 206-210.

Ex 8D

Differentiation.

Turning points:

Maximum and minimum

Increasing and decreasing functions

Ch 8 P 210-217.

Ex 8E.

Differentiation.

Stationary Points

Points of inflection

Ch 8 P 217-221

Differentiation.

Higher Derivatives.

Using Second Derivative to Determine Nature of Stationary Points.

Points of inflection

Ch 8 P 221-227

Ex 8G

Differentiation.

Applications.

Ch 8 P 227-232.

Ex 8H.

Integration.

Reversing differentiation

Particular solutions

Integration as the opposite to

differentiation.ie. indefinite integration.

Ch 9 P 234-238.

Ex 9A

14+15

Integration.

Finding the area under a curve ie definite integration.

Standardising the procedure

Area as the limit of a sum

Notation

Definite integrals

Indefinite integrals

Ch 9 P 239-250.

Integration.

Area below the x axis..

Ch 9 P 250-253

Ex 9C

Integration.

Area between two curves

Ch 9 P254-258

Ex 9D

Integration.

Numerical integration:

Trapezium Rule.

Ch 9 P 260-266.

Ex 9F

Trigonometry.

*Angles of elevation and depression

*Bearing

*Trigonometrical functions

definitions

*Special Cases

Exact trig values of

*Positive and negative angles

Sin q = cos (90⁰- q)

cos q = sin (90⁰- q)

*Trigonometrical functions for angles of any size

. Ch 10 P 270-276

Ex10A Q 1, 5, 6

Trigonometry.

Identities involving sinq, cosq and tanq

tanq = sinq/cosq

sin²q + cos²q = 1

The sine and cosine graphs

The tangent graph

Solution of equations using graphs of trigonometrical functions

Ch 10 P 276-285

Ex 10A

Only teach this if enough time

Trigonometry.

Triangles without right angles

*The sine rule

Using the sine rule to find an angle

Ch 10 P286-288

Ex 10B

Only teach this if enough time

Trigonometry.

*The cosine rule

Ch 10 P289-288

Ex 10C

Trigonometry.

Using the sine and cosine rules together

Ch 10 P292-295

Ex 10D

Only teach this if enough time

Trigonometry.

*Area of a triangle.

Ch 10 P296-299

Ex 10E

Trigonometry.

Circular Measure:

Radians

Ch 10 P 299-303

Ex 10F

23+24

Trigonometry.

The length of an arc of a circle

The area of a sector of a circle

Ch 10 P 303-309

Ex 10G

Trigonometry.

More trigonometric graphs

Translations

One way stretches

Ch 10 P 311-317

Ex 10H

26+27

Logarithms and Exponentials

Logarithms

Logarithms to the base 10

The laws of logarithms

Multiplication

Division

Power zero

Indices

Roots

The logarithm of a number to its own base

Reciprocals

Graphs of logarithms

Exponential functions

Ch11 P319-326

Ex 11A

28+29

Logarithms and Exponentials

Modelling Curves

Reducing to linear form the relationships of the form y=kxn and exponential relationships y=kax

Ch11 P326-337

Ex 11B

Further Differentiation and Integration

Differentiation with negative and fractional indices

Ch 12 P339-347

Ex 12A

Further Differentiation and Integration

Integration with negative and fractional indices

Ch 12 P347-352

Ex 12A

Statistics 1

Time Scale

Lesson Number

Topic and Learning Objectives

Chapter and Pages

Exploring Data.

Looking at Data

Shape of distribution

*Stem and Leaf diag

Exploring Data.

*Numerical/quantative data

*Discrete/continuous data

*Measures of central tendency of single data and

frequency distributions (not grouped data)

Ch 1 P 1-11

Ex 1A P9

Ch 1 P 12-19

Ex 1B P17

Ex 1C P20

Exploring Data.

*Grouped data

Ch 1 P 22-31

Ex 1D P29

3+4

Exploring Data.

Measures of spread

*Range

Mean absolute deviation

The mean square deviation - msd

The root mean square deviation-rmsd

Variance and standard deviation-s

The standard deviation and outliers

Ch 1 P 31-45

Ex 1E P42

Q1-10

Exploring Data.

Measures of spread cont. Combining distributions.

Ch 1 P42

Ex 1E Q11-14

Exploring Data.

Coding:

If x = ay + b

then

Mean: x = ay + b

Variance: s_x² =a²s_y²

Standard Dev:

s_x =as_y

Ch 1 P 46-48

Ex 1F P48

Data presentation and related measures of centre and spread

*Bar charts and vertical line charts

*Pie charts

*Histograms

Ch 2 P56-70

Ex 2A P60

Ex 2B P69

Only teach if enough time, set as HWK

Data presentation and related measures of centre and spread

Measures of central tendency and of spread using quartiles

Quartiles for small data sets

*Interquartile range

Box and Whisker plots

Outliers

*Cumulative frequency curves

Box and Whisker plots for grouped data

Ch 2 P 71-84

Ex 2C P78

8+9

Probability.

Venn diagrams.

* Experimental estimation of probability

*Probability of one event.

*Expectation

Mutually Exclusive Events.

Ch 3 P 86-98

Ex 3A P96

Probability.

*Probability of Events from Two Trials.

Tree diagrams

Possibility spaces.

P(at least one) = 1-P(none)

Ch 3 P98-106

Ex 3B P 103

11+12

Probability.

Conditional Probability.

Definition of independent events.

Ch 3 P 107-117

Ex 3C P 113

Discrete Random Variables

Discrete Random Variables

Notation and conditions

Diagrams of discrete random variables

Ch 4 P118-126

Ex 4A P124

Discrete Random Variables

Expectation and variance

Ch 4 P126-133

Ex 4B P131

Discrete Random Variables

Mixed exercise of above techniques

Ch 4 P133-136

Ex 4C P133

Further Probability

Arrangements n!

Factorials

Ch 5 P138-141

Ex 5A P141

17+18

Further Probability

Permutations nPr

Combinations nCr several events

Ch 5 142-151

Ex 5B P149

19+20

The Binomial Distribution.

The binomial distribution

P (X = r) = nCr prqn-r where q = 1-p.

recognising questions modelled by Binomial distribution.

Ch 6 P153-146

Ex 6A P157

The Binomial Distribution.

The expectation of B(n,p)

Using the binomial distribution

Ch 6 P158-166

Ex 6B P163

Hypothesis Testing Using the Binomial Distribution.

Hypothesis H0

Alternate hypothesis H1

Hypothesis Testing Check List.

Choosing the significance level.

Cumulative Binomial Probability tables.

Critical Value and Critical Region

Ch 7 P167-174

Hypothesis Testing Using the Binomial Distribution.

The Smarties Experiment.

The Mind Reading Experiment.

Ch 7 P 179

Hypothesis Testing Using the Binomial Distribution.

Applying hypothesis test technique

Ch 7 P175-177

Ex 7A P175

Hypothesis Testing Using the Binomial Distribution.

Critical values and critical regions

Ch 7 P 180-181

Ex 7B P180

Hypothesis Testing Using the Binomial Distribution.

1-tail and 2-tail tests.

Asymmetrical Cases.

Ch 7 P182-186

Ex 7C P185

What your daughter will do in lessons.

When a new technique is introduced your daughter’s teacher will usually go through several examples on the board with the class interacting in the production of the solutions. Your daughter will then be asked to start practicing applying the technique to the questions found in the exercises. She will need to then finish these exercises at home. An hour a day is the usual amount of work that your daughter will be expected to spend on her exercises(outside of lessons).

At regular intervals more interactive activities will take place which aim to deepen your daughter’s understanding.

How your daughter’s progress will be assessed.

The answers to all exercises from the textbook are at the back of the book. Your daughter will be expected to mark her ‘day to day’ exercises herself and to ask the teacher for further explanation for problems that are not correct. At the end of each chapter your daughter will be given an assessment sheet which has questions based on the entire chapter. She will be given approximately a week in which to do this before she hands it into her teacher to be marked. There will also be a test approximately once per half term. Nearer the examination, past paper will be completed and marked according to the examination board mark schemes. The tests and the past papers are used to produce the grades in the reviews and the predicted grades that we have to send to the examination board.

A2 level mathematics

The course your daughter is following in the U6 is OCR MEI Mathematic A2(7895). The Mathematics A2 that your daughter is studying is made up of three units Core 3(code 4753), Core 4 (code 4754) and Statistics 2(code 4767). They are all equal weighting (UMS mark out of 100) and the UMS marks for each are added up to give a total out of 300. The grade boundaries for the final A level take into account all six module UMS marks. The grade boundaries are A-480, B-420, C-180, D-300, E-240, U- less than 240. To achieve an A*, students need to get an A overall and score more than 90 UMS marks in Core 3 and Core 4.
The Core 3 and Statistics 2 examination will be taken in the January Series and Core 4 will be taken in the Summer Series.
All 3 units consist of a written exam 1h 30min (100% of marks). The examination consists of two parts. Section A is worth 36 marks and consists of shorter questions – approximately 10 questions. Section B is worth 36 marks and consists of longer questions- approximately 3 questions. Core 3 also has a coursework element on “numerical solutions of equations”, which is worth 20% of the Core 3 score. Core 4 has a second paper which is a comprehension paper on a mathematical text, worth 20% of the Core 4 score.
At the end of year 12, after the students have taken the AS level examination, we start with Core 3 coursework (2 weeks). After two weeks of coursework we then start with Statistics 2, lesson 22 (chapter 4 in the textbook).
The reference book for Core 3 and Core 4 is ‘Core 3 and 4’ and for Statistics 2 is ‘Statistics 2. Your daughter will be given her own copy of these books.
The following is a brief outline of what will be covered each lesson.
‘My Maths’ and the MEI website are both software packages that your daughter has access to and will find invaluable in consolidating her learning.
We also strongly recommend the purchase of a graphical calculator as it is invaluable in helping consolidate learning but also in all of the A level units except Core 1.

Core 3

Time scale

Topic and Learning Objectives

Chapter and Pages

1+2

Proof

Proof by direct argument

Proof by exhaustion

Proof by contradiction

Disproof by the use of a counter-example

Ch 1 P1-7

Ex 1A P 6

3+4

Natural Logarthims and Exponentials.

Definition of the exponential function

Definition of Natural logarithms

Ch 2 P 8-18

Ex 2A

P 15

Functions.

The language of functions

Mappings.

Functions.

Ch 3 P 19-24

Ex 3A P23

Functions.

Using Transformations to Sketch Curves of functions:

Combinations of translations and one-way stretches.

Ch 3 P 25-30.

Ex3B P28

Functions.

Reflections.

The General Quadratic Curve.

Ch 3 P 30-36

Ex 3C P 34

8+9

Functions.

Composite Functions.

Inverse Functions:

The graph of a function and its inverse.

Finding the algebraic form of the inverse function.

Inverse Trig Functions.

Ch 3 P 36-49

Ex 3D P 47

Functions.

Even, Odd and Periodic Functions.

Ch 3 P 49-55.

Ex 3E P 53.

Functions

The modulus function

Ch 3 P 56-60

Ex 3F P59

Functions.

Curve Sketching

Ch 3 P60-61.

Activity 3.5 P60

Techniques For Differentiation.

The Chain Rule.

Differentiating a composite function

Differentiation with respect to different

variables

Ch 4 P 63-68

Ex 4A P 67

14+15

Techniques For Differentiation.

The Product Rule.

The Quotient Rule.

Ch 4 P 68-77

Ex 4B P 73

16+17

Techniques For Differentiation.

Differentiating an inverse function.

Ch 4 P 77

Ex 4C P 80

18+19

Techniques For Differentiation.

Differentiating natural logarithms and exponentials

Ch 4 P 82

Ex 4D P86

20+21

Techniques For Differentiation.

Differentiating sin x and cos x (and tan x)

Ch 4 P 91-96

Ex 4E P96

22+22

Techniques For Differentiation.

Differentiating functions defined implicitly

Stationary points

Types of stationary points

Ch 4 P 96-101

Ex 4F P101

23+24

Techniques For Integration:

Calculus Techniques.

Integration by Substitution.

Ch 5 P 103-110.

Ex 5A P 107

Techniques For Integration:

Integrals involving the exponential function

Ch 5 P 110-111.

Ex 5B P114 Q 2-5

26+27+28

Techniques For Integration:

Integrals involving the natural logarithm function

Extending the domain for the logarithmic function

Ch 5 P 111-121.

Ex 5B P114 Q1,6 on

29+30

Techniques For Integration:

Integrating sin x and cos x

Ch 5 P 123-125

Ex 5C P125

31+32

Techniques For Integration:

Integration by Parts

Using integration by parts twice

Ch 5 P 125-131

Ex 5D P130

33+34

Techniques For Integration:

Definite integration by parts

Ch 5 P 131-134

Ex 5D P130

Numerical Solution Of Equations.

This is coursework

Introduction to coursework.

Criteria on which coursework is marked.

Change of Sign Methods:

Decimal Search.

Ch 6 P135

Ex 6A P 142

Do an example finding one root together. Then get them to find the other roots.

Numerical Solution Of Equations.

Failures with Change of Sign Methods.

No need to do Interval Bisection or Linear Interpolation.

Ch 6 P 143

37+38

Numerical Solution Of Equations.

Fixed Point Estimation.

Rearranging the equation f(x)=0 into the form x=g(x).

Using different arrangements of the equation

The choice of g(x)

Accuracy of method of rearranging equation

Ch 6 P 166-171

Ex 6B P149

Numerical Solution Of Equations.

Failure of this method and dependence on the gradient

Ch 6 P 171

Ex 6B P149

Numerical Solution Of Equations.

The Newton-Raphson Method.

Ch 6 P 150

Ex 6C P152

41+42+43

Numerical Solution Of Equations.

Failure of Newton-Raphson

Poor choice of starting point

The function is discontinuous

The function is not defined over the whole of the real nos.

Ch 6 P 174

Ex 6C P152

Core 4

Time scale

Topic and Learning Objectives

Chapter and Pages

1+2

Algebra

The General Binomial Expansion

Ch 7 pp 156-165

Ex 7A pp164

Algebra

*Review of Algebraic Fractions

simplifying fractions

multiplication and division of fractions

addition and subtraction of fractions

Ch 7 pp 166-168

Ex 7B pp 168

Algebra

*Review of Algebraic Fractions

Equations involving algebraic fractions

Ch 7 pp 169-173

Ex 7B pp 171

Algebra

Partial Fractions

Denominators of form (ax + b)(cx+d)

Ch 1 pp 173-176

Ex 7D pp176

Algebra

Partial Fractions

Denominators of form (ax + b)(cx2+d)

Ch 1 pp 176

Ex 7E pp 178 Q1 (ii) (iv) (v) (vii) (viii)

Algebra

Partial Fractions

Denominators of form (ax + b)(cx +d)2

Ch 7 pp 177

Ex 7E pp 178 Q1 (i) (iii) (vi) (ix)

2,3

Algebra

Using Partial Fractions With the Binomial Expansion.

Ch 7 pp 179-181

Ex 7F pp 180

Trigonometry

Reciprocal trigonometry

functions

Ch 8 pp 183-187

Ex8A pp 186

10+11

Trigonometry

Compound Angle Formulae

Ch 8 pp 187-192

Ex8B pp 190

Trigonometry

Double Angle Formulae

Ch 8 pp 192-197

Ex 8C p196

Trigonometry

The Factor Formulae

Ch 8 pp 197-200

Ex 8D pp 200

14+15+16

Trigonometry

The Forms

rcos()

rsin()

Ch 8 pp 201-208

Ex 8E pp 204

Trigonometry

Consolidation of the above

Ch 8 pp 209-210

Ex 8F pp 209

18+19

Trigonometry

Small-angle approximations

Ch 8 pp 210-215

Ex 8G pp 215

Trigonometry

The General Solution of Trig Equations

Ch 8 pp 218-220

Using trig identities in integration

Ch 8 pp 220-22

Parametric Co-ordinates

Graphs from parametric equations.

Finding the equation by eliminating the parameter; algebraic and trigonometric equations

Ch 9 pp 224-231

Ex 9A pp 234

22+23

Parametric Co-ordinates

Parametric equations of a circle.

Parametric equations of other standard curves.

Ch 9 pp 231

Ex 9A pp 234

24+25+26

Parametric Co-ordinates

Parametric differentiation

Turning points

Ch 9 pp 238-251

Ex 9B pp 242

27+28

Further techniques for integration.

Finding Volumes by integration

Solids formed by rotation about the x axis

Rotation about the y axis.

Ch 10 pp 253-261

Ex 10A pp258

29+30

Further techniques for integration.

The use of partial fractions in integration

A repeated factor in the denominator

A quadratic factor in the denominator

Ch 10 pp 261-265

Ex 10B pp 264

30+31

Further techniques for integration.

General Integration

Ch 10 pp 266-269

Ex 10C pp 268

Further techniques for integration.

Integrals you cannot do

Ch 10 pp 269-269-274

Ex 10D pp 273

Vector Geometry

Vectors (2D)

Terminology

Equal vectors

Position vectors

Multiplying a vector by a scalar

The negative of a vector

Adding vectors

Subtracting vectors

Unit vectors

Ch 11 pp 275-118

Ex 11A pp 281 and Ex 11B pp287

Vector Geometry

Co-ordinate geometry using vectors : 2D

Vector joining 2 points.

Vector equation of a line

Direction

Location

Vector and Cartesians form of the equation of a line

Ch 11 pp 289-295

Ex 11C pp297

Q 1,2,3,4

Vector Geometry

The intersection of 2 lines

Ch 11 pp 295-299

Ex 11C pp 297

Q 5,6,7

Vector Geometry

The angle between two vectors

Scalar Product

Perpendicular vectors

Ch 11 pp 299-302

Ex 11D P302

Vector Geometry

Coordinate geometry using vectors: 3D

Right handed screw for axes

Length of a vector

Vector equation of line

Cartesian equation of a line

Special cases of the Cartesian form

Ch 11 pp 303-

309

Ex 11E pp311

Q 1-3

38+39

Vector Geometry

Angle between 2 directions

Ch 11 pp 309

Ex 11E pp 311

Q 4-7

Vector Geometry

The equation of a plane given 3 points on it.

The equation of a plane given a vector perpendicular to the plane and one point on the plane.

Ch 11 pp 315-319

Ex 11 F pp322

Q 1-5

41+42+43

Vector Geometry

The intersection of a line and a plane.

The distance of a point from a plane-general formula.

Ch 11 pp 320-331

Ex 11F pp 322

Q 6-

Differential Equations

Forming differential equations from rates of change

Ch 12 pp 335-340

Ex 12A pp339

Differential Equations Solving differential equations

The general solution of the differential equation

The method of separating the variables

Ch 12 pp 341-344

Ex 12B pp344

46+47+48

Differential Equations

Particular solutions

Ch 12 pp 344-357

Ex 12C pp 348

Statistics 2

Time scale

Topic and Learning Objectives

Chapter and Pages

1+2

The Poisson Distribution.

Definition of a Poison Distribution:

X~Poisson (l)

P(X=r) = e^-^ll^r

Conditions for use:

(i) random

(ii) independent

(iii) the events occur with uniform likelihood over the interval

Cumulative Poisson Probability tables and Recurrence Relationships.

Mean = Variance = l

Ch1 P1-12

Ex 1A P7

The Poisson Distribution.

The sum of two or more Poisson distributions.

If V=X+Y and X and Y are independent and X~Poisson (l) and Y ~Poisson (m) Þ

V~Poisson (l+m)

Ch 1 12-18

Ex 1B P15

3.5

Using and applying mathematics

The phone call problem MSV 13

The Poisson Distribution.

Poisson as an approximation for Binomial Distribution

Conditions for use:

p is small (ie rare event) and n is large and np is not too large. Also trials are random and independent.

Ch1 P18-25

Ex 1C P23

5+6

The Poisson Distribution.

Mixed techniques

Ch1 P26-31

Ex 1D P26

7+8+9

The Normal Distribution.

The curve for the Normal Distribution with mean m and standard deviation s is j(x)-formula P39 Notation N (m,s²) Shape of Normal Distribution

Using Normal Distribution tables.

Where z = x-m

Ch2 P32-48

MEI resources: interactive tables activity

Ex 2A P44

The Normal Distribution.

Normal approximation to model discrete situations.

Continuity Corrections.

The Normal distribution as an approximation for the binomial distribution.

Conditions:

(i) n is large

(ii) p is not too close to 0 or 1.

Mean: l= np

Variance: s² = npq

Ch2 P49-56

Ex 2B P54 Q1-8

11+12

The Normal Distribution.

The Normal Distribution as an approximation for the Poisson distribution.

Conditions:

Large mean: l>10 so that distribution is reasonably symmetrical.

Mean must roughly equal the variance. Therefore N(l,l)

Ch2 P52-67

Ex 2B P 54-58 Q9-18.

13+14

The Normal Distribution

Mixture of questions

Ch 3 P59-67

Ex 2C P 59

15+16

Samples and Hypothesis Testing

Interpreting sample data using the Normal Distribution

Estimating the population mean, m

The distribution of sample means

A hypothesis test for the mean using the Normal distribution

Known and estimated standard deviation

Ch 3 P68-80

Ex 3A

17+18+19

Samples and Hypothesis Testing

Contingency tables

What is the significance level of the test?

How many degrees of freedom are involved?

The C² test for independence in a contingency table

Ch 3 P81-96

Ex 3B P92

20+21

Samples and Hypothesis Testing

Mixed exercise

Ch 3 P97-103

Ex 3C P97

Bivariate Data.

Describing variables: independent/dependent, random/non-random

Scatter graphs:

positive correlation

negative correlation

no correlation.

Lines of best fit

Ch4 P104-109

Dice investigation P109.

23+24

Bivariate Data.

Product Moment Correlation.

Covariance.

Pearson’s Moment Correlation Coefficient.

Ch4 P110-118

Ex 4A P116

25+26

Bivariate Data.

The meaning of a correlation coefficient.

Hypothesis testing

Critical values

Degrees of freedom

Correlation does not imply causation

Non- linear correlation

Extrapolation.

Ch4 P118-131.

Ex 4B P125

27+28

Bivariate Data.

Rank Correlation.

Spearman’s Coefficient of Rank Coefficient.

Hypothesis Test.

Tied Ranks.

When to use rank correlation

Ch4 P132-124.

Ex 4C p137

Bivariate Data.

The Least Squares Regression Line.

Residuals.

Ch 4 P142-151

Ex4D P148

30+31

Bivariate Data.

Mixed exercise

Ch4 P151

Ex 4E

What your daughter will do in lessons.

At regular intervals more interactive activities will take place which aim to deepen your daughter’s understanding.

How your daughter’s progress will be assessed.

The answers to all exercises from the textbook are at the back of the book. Your daughter will be expected to mark her ‘day to day’ exercises herself and to ask the teacher for further explanation for problems that are not correct. At the end of each chapter your daughter will be given an assessment sheet which has questions based on the entire chapter. She will be given approximately a week in which to do this before she hands it into her teacher to be marked. There will also be a test approximately once per half term. Nearer the examination, past paper will be completed and marked according to the examination board mark schemes. The tests and the past papers are used to produce the grades in the reviews and the predicted grades that we have to send to the examination board.

AS Further Mathematics

Having achieved the full A level mathematics in L6, your daughter will start her AS level in Further Mathematics at the end of year 12.
The course your daughter is following in the U6 is OCR MEI Further Mathematic AS (code 3898). The Mathematics AS that your daughter is studying is made up of three units, two applied units (usually Mechanics 1 and Decision 1) and one core unit (further Pure 1). They are all equal weighting (UMS mark out of 100) and the UMS marks for each are added up to give a total out of 300. The grade boundaries are A-240, B-210, C-180, D-150, E-120, U- less than 120.
All three units will be examined in the January Series.
All 3 units consist of a written exam 1h 30min (100% of marks). The examination consists of two parts. Section A is worth 36 marks and consists of shorter questions – approximately 10 questions. Section B is worth 36 marks and consists of longer questions- approximately 3 questions.
‘My Maths’ and the MEI website are both software packages that your daughter has access to and will find invaluable in consolidating her learning.

A2 Further Mathematics

The course your daughter is following in the U6 is OCR MEI Further Mathematic A (code 7898). The Mathematics A2 that your daughter is studying is made up of three units, two applied units (usually Mechanics 2 and Statististics 3) and one core unit (further Pure 2). They are all equal weighting (UMS mark out of 100) and the UMS marks for each are added up to give a total out of 300. The grade boundaries are A-240, B-210, C-180, D-150, E-120, U- less than 120. To achieve the A* as A level Further Mathematics your daughter will have to achieve a grade A overall and score at least 90 UMS in all four applied modules.
One applied unit will be examined in the January series, FP2 and the other applied unit will be examined in the June Series.
All 3 units consist of a written exam 1h 30min (100% of marks). The examination consists of two parts. Section A is worth 36 marks and consists of shorter questions – approximately 10 questions. Section B is worth 36 marks and consists of longer questions- approximately 3 questions.
‘My Maths’ and the MEI website are both software packages that your daughter has access to and will find invaluable in consolidating her learning.

How to improve

Read the teacher comments and where relevant act on them.
Follow the advice given in your assessment folder.
Refer to the level or grade descriptors for your age group
Use the text book to read ahead to be ready for new topics.
Make revision materials at the end of each topic
Review your work frequently
Use the text book to consolidate classroom learning
Use the internet sites like mymaths or the MEI website to consolidate your learning
Explain your lessons to your parents
Ask your teacher for a more detailed explanation

Extracurricular opportunities out of lessons

Jaguar Cars competition
Maths Challenge at all levels
Team challenge and Senior Team Challenge
Cipher Challenge
Further Maths Conference
Maths trip to Drayton Manor in year 10

Learning opportunities parents can provide

Talk about Mathematics – there is plenty of maths around us: Finance, shopping, changing cooking recipes...

Mathematics

Aims

Staff

Curriculum

KS3

Year 7

Year 8

KS4 (GCSE, year 9, 10 and 11)

Year 9

Current year 9, 10 and 11

UNIT A

Chapter 1 Number and Problem Solving

Chapter 2 Expressions

Chapter 3 – Statistics

Chapter 4 Linear Equations

Chapter 5 Ratio

Chapter 6 Statistics 2

Chapter 7 Geometry

Chapter 8 Algebra

Chapter 9 Measures

Chapter 10 Trigonometry

Chapter 11 Statistics

How your daughter’s progress will be assessed.

UNIT B

Chapter 1 Properties of shapes

Chapter 2 Fractions, decimals and percentages

Chapter 3 Indices, decimals and surds

Chapter 4 Straight-line Graphs

Chapter 5 Transformations

Chapter 6 Inequalities

Chapter 7 Similarity

Chapter 8 Congruency

Chapter 9 Simultaneous Equations

Chapter 10 Vectors

Chapter 11 Circle Theorems

Chapter 12 Scatter diagrams and time series

How your daughter’s progress will be assessed.

UNIT C

Chapter 1 Algebraic Manipulation

Chapter 2 Perimeter, area, volume and 2-D representation

Chapter 3 – Trial and Improvement

Chapter 4 Probability 1

11+12

Chapter 5 Graphs 1

Chapter 6 Measures

Chapter 7 Percentage and Proportional change

Chapter 8 Standard form and using a calculator

Chapter 9 Similarity

Chapter 10 Factorising

Chapter 11 Three dimensional geometry

Chapter 12 Proportion and variation

Chapter 13 Graphs 2

Chapter 14 Quadratic equations

Chapter 15 Simultaneous equations

Chapter 16 Trigonometry

Chapter 17 Functions

Chapter 18 Length, area and volume

Chapter 19 Probability 2

Chapter 20 Algebraic fractions

How your daughter’s progress will be assessed.

Post 16 (A Level Mathematics)

AS level mathematics

How your daughter’s progress will be assessed.

A2 level mathematics

How your daughter’s progress will be assessed.

AS Further Mathematics

A2 Further Mathematics

How to improve

Extracurricular opportunities out of lessons

Learning opportunities parents can provide