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AS & A2 Maths Scheme of Work 2014 2016

DateTopic & page ref in Heinemann

Live Text NotesSkills developed & Examples students should be able to answer the end

of each section Homework Resources

1stSeptember2014

Core 1: p1-14Ch1. ALGEBRA & FUNCTIONS

1.1 Simplifying terms by collectinglike terms

1.2 Rules of Indices1.3 Expanding an expression1.4 Factorising expressions1.5 Factorising quadratic expressions1.6 Rules of Indices for all R1.7 Surds (p10)1.8 Rationalising the denominator

Teachers are free touse whatever resourcesthey wish but mustadhere to the timingsof the SOW. It issuggested that in classuse the LiveText CDROM to go throughexamples.

Students should learn the squares from 12to 162; cube numbers from 13to 63which will

help them solve fractional indices problems.

Examples:

Fractional Indices: if 81is 9 then 25is .?Simplify a5 a3; m4 m2; (p2)5; (2xy2)3; solve 2n=16; solve 32x-1= 27

Simplify:

Rationalise the denominator;

; ;

Expand

Factorise and solve : x2+ 8x + 15 = 0; 2x2+ 7x + 6 = 0 ; 4x2-1 = 0;

And worth at this stage pointing out how to find the roots (or solutions) and the critical

values which can be used to sketch a curve of the fn.

Staff should tryto explicitlydifferentiatehomework tomeet the needsof all learners.

Heinemann C1 Live Text onCD to use in lessons to

support explanations.

Tarsias available:

Manipulating Surds

Standards Unit N11Surds

Standards Unit N12usingindices

Solomon worksheetsavailable as PDF.

These can be used as

homework to stretch allstudents. There are alsoTESTS that can be flashed in

lessons on the IWB.

September Core 1: p1526Ch2. QUDARATIC FUNCTIONS

2.1 plotting graphs of quadraticfunctions2.2 solving quadratic equations byfactorisation2.3 competing the square2.4 solving quadratic equations bycompeting the square2.5 solving quadratic equations by

using the formula2.6 sketching graphs of quadraticfunctions

Examples:

Know and learn the quadratic formula:

Solve by completing the square: x2+ 8x+ 15 = 0; 2x212x+ 7 = 0

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

Show that the liney = x4is a tangent to the circle with equationx2+y2= 8

Extension:

Reproduce the proof of the Quadratic formula

Solomon worksheets

Standards Unit C1Linkingthe properties & forms ofQuadratic Functions

September Core 1: p2740Ch3. EQUATIONS &INEQUALITIES

3.1 Simultaneous equations by

Examples:

Solvex 4y 7 andx+ 2y= 16 by elimination and substitution

What about: 3x+y= 10 andx2+ 2xy+ 2y2= 17

Solomon worksheets


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elimination3.2 Simultaneous equations bysubstitution3.3 Simultaneous equations with 1linear & 1 quadratic3.4 solving linear inequalities3.5 solving quadratic i nequalities

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

Solve and sketch x2+ 8x+ 15 0; x2- 10x+ 21 0

September Core 1: p4168Ch4. SKETCHING CURVES

4.1 sketching graphs of cubic

functions4.2 interpreting graphs of cubicfunctions

4.3 sketching the reciprocal function4.4 using intersections points ofgraphs to solve equations4.5 The effect off(x+a), f(x-a) and f(x) +a4.6 The effect of af(x), -f(x)andf(-x)4.7performing transformations on thesketches of curves

Examples:

Know the graphs of: y = x; y = x2; y = x3; y = y = 2x;

Understand and sketch transformations of any given graph, inc. f(x+a), f(x-a), f(ax), af(x),

-f(x)andf(-x)say, for f(x) = x2

Extension Questions:

Solomon worksheets

October Core 1: p7390Ch5. COORDINATE GEOMETRYIN THE (x, y) PLANE

5.1 The equation of a straight line5.2 The gradient of the straight line5.3y y1= m(x x1)5.4 the formula for finding theequation of a straight line

5.5 Parallel and perpendicular lines

To know that:The equation of a straight line can be written asy = mx + c, where m is the gradient andc is the intercept with the vertical axis.Lines areparallelif they have the same gradient.

Two lines areperpendicularif the product of their gradients is -1.

If the gradient of a line is m, then the gradient of aperpendicularline is 1

m

The gradientof a l ine passing through the points

2 11 1 2 22 1

, and , isy y

x y x yx x

.

The equation of the straight line with gradientmthat passes through the point 1 1,x y is

1 1( )y y m x x .

The distancebetween the points with coordinates

2 2

1 1 2 2 2 1 2 1, and , isx y x y x x y y .

The midpointof the line joining the points

1 2 1 21 1 2 2, and , is ,2 2

x x y yx y x y

.

Example: Find the equation of the perpendicular bisector of the line joining the points

Solomon worksheets

Condensed 1 page notes

available with questions for

coordinate Geometry


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(3, 2) and (5, -6).

Example: Find the point of intersection of the lines:

2x+y = 3

and y= 3x1.

Extension Question:

October Core 1: p91111Ch6. ARITHMETIC SEQUNECES

6.1 Introduction to Sequences6.2 the nth term6.3 recurrence relationships6.4 Arithmetic sequences6.5 Arithmetic series6.6. the sum to n of an arithmeticseries

6.7 The sigma notation

Students usu. strugglewith the notion of Unbetter to start withsimple sequences andexplain how to find thenth term (like at KS3)

Formula for the nthterm and the sum of aseries will be given

If numbers ascend in 3s, thats the3 x table = 3n.

Then find the number before the 1stterm (=5), so, nth term is 3n+5nth term in sequence 8, 11, 14, 17, ..., ..., ...

Solomon worksheets

Standards Unit N13Analysing sequences

October Core 1: p112132Ch7. DIFFERENTIATION

7.1 derivative of f(x)

7.2 gradient of 7.3 gradients of simple functions7.4 gradients of functions with power

7.5. re-writing expressions to makethem easier to differentiate

7.6

7.7 Rate of change of a function at a

point7.8 Equations of Tangents andNormals

Find:

y= 4 22 5x x ; y= 27 12 5x x ; y= 6 415 9

2x x ; y=

1

22 2x x

NB: A turning point occurs where the gradient is zero, i.e. where 0.

And you can also use the 2ndderivative to decide whether a turning point is a maximum

or a minimum:

If2

2

2

2

0 then it is a minimum

d y 0 thenit isa maximum.dx

d y

dx

;

Equation of a tangenttells you the gradient of a curve.

The gradient mof a tangent line at the point 1 1,x y can be found from.

The equation of the tangent is then )( 11 xxmyy .

Perpendicular lines

Solomon worksheets

Standards Unit C2exploring functions involving

fractional and negativepowers of x

Standards Unit C3matching functions &derivatives

Standards Unit C4

differentiating & Integratingfractional and negative

powers of x

Standards Unit C5Findingstationary points of cubicfunctions


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Suppose 2 lines have gradients1 2&m m

. These lines are perpendicular if1 2 1m m ,

i.e.2

1

1m

m .

Equation of a normal

To find the equation of a normal at the point 1 1,x y :

Find the gradient fromthen find the gradient mof the normal using 1m

dydx

and the equation of the normal is1 1( )y y m x x

Example:

Find the equation of the normal to the graphy = x(x+ 1) (x2) at x= -1.

October OCTOBER HALF TERM

October Core 1: p133142Ch8. INTEGRATION

8.1 Integrating 8.2 Integrating simple expressions

8.3 using the 8.4 Simplifying before integrating8.5 Finding c

Rule: Increase thepower by 1 and divideby the new power.Integration is thereverse ofdifferentiation.

Example:

Find y if 2 6 2dy

x xdx

andy= 4 when x= 3 (answer: 3

23 2 16

3

xy x x

)

Questions:

1. 2(3 4 2)v x x dx .If v= 3 when x= 0, find vas a function of x. Hence calculate the value of vwhen x= 1.

Solomon worksheets

Standards Unit C4differentiating & Integrating

fractional and negativepowers of x

November/December

START CORE 2

3rdNovember

Core 2: p117Ch1. ALGEBRA & FUNCTIONS

1.1 Simplifying algebraic fractions1.2 Dividing a polynomial1.3 factorising a polynomial1.4 Using the remainder theorem

6 hour teacher on theirown teaching C24hour teacher start theApplied module

Factor Theorem: (xa) is a factor of a polynomialf(x) iff(a) = 0.

Remainder Theorem: The remainder when a polynomialf(x) is divided by (xa) isf(a).

Extended version of the factor theorem:

(ax + b) is a factor of a polynomialf(x) if0

bf

a

1. g(x) = 3 23 13 15x x x .(a) Show thatg(-5) = 0 andg(3) = 0.(b) Hence factoriseg(x).(c)

Sketch the graph ofy=g(x).(d) Write down the full set of values of xfor whichg(x) > 0.

Extenstion Question:

Heinemann C2 Live Text on

CD to use in lessons to

support explanations.

Solomon worksheets

available

Tarsias available



factor theorem

Standards Unit A11

factorising cubics


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December Core 2: p1837Ch2: THE SINE & COSINE RULE

2.1 Sine rule for missing sides2.2 Sine rule for unknown angles2.3 Solutions for a missing angles2.4 Cosine rule to find unknown sides2.5 Cosine rule to find missing angles2.6 Sine, Cosine & Pythagoras2.7 Area of a triangle

Know the 3 trig ratios using: SOH CAH TOA

Only the cosine rule formula will be provided in the formula book.

Know the Area of a triangle is A = 1 sin2

ab C

Know sintan

cos

xx

x and

2 2sin cos 1x x

Solomon worksheets

available

Core 2: p3850Ch3: EXPONENTIALS &LOGARITHMS

3.1 The functiony = ax3.2 writing expressions as a logarithm3.3 calculating using log to base 103.4 Laws of Logs3.5 solving ax= b3.6 changing the base

Extension questions: Solomon worksheetsavailable

Standards Unit A13

simplifying Log

expressions


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December CHRISTMAS HOLIDAYS Revise for the C1MOCK Exam inJanuary

Look into 1-Day revision sessions at UCL/Imperial College

January 2015

C1 MOCK Exam (internal) C1 Solomon Paper ?? Solomon PaperTBC at dept. meeting closer to the timeThis will take place during lesson time. Y12 will have a Mock week later in the year.

January Core 2: p5172

Ch4. COORDINATE GEOMETRYIN THE (x, y) PLANE

4.1 The mid-point of a line4.2 Distance between two points4.3 The equations of a circle

The equation of a circlecentre (a, b) with radius ris 2 2 2( ) ( )x a y b r .

Example: Find the centre and the radius of the circle with equation2 22 6 6 0x x y x

Extension Question:

Solomon worksheets

available

January Core 2: p7686

Ch5. THE BINOMIALEXPANSION

5.1 Pascals Triangle5.2 Combinations and FactorialNotation

5.3 Using in the binomialexpansion

5.4 Expanding

(

)

Note that in C2 n e.g. 1: Find the expansion of

43x y .

e.g. 2: Find the first 4 terms in the expansion 10

2 3a b .

e.g. 3: Find the coefficient of 4 4x y in the expansion of8

13

2x y

E.g. Find the non-zero value of bif the coefficient of2x in the expansion of

62b x

is equal to the coefficient of5x in the expansion of

82 bx .



Binomial theorem

Solomon worksheets

available

January/

February

Core 2: p87101

Ch6: RADIAN MEASURE

6.1 Using radians to measure angles6.2 The length of an arc6.3 The area of a sector6.4 The area of a segment

Know that 360o= 2radians

Why are there 360oin a circle?

What is 1 radian?

Convert rads into degrees

Convert 150ointo radiansProve the length of an arc is l = r

Show that the area of a sector is A =

Show that the area of a segment in a circle is A =

Solomon worksheets

available


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March Core 2: p154170

Ch10. TRIGONOMETRICALIDENTTIS AND SIMPLEEQUATIONS

10.1 Simple Trigonometric identities10.2 Solving simple Trig equations

Know and use ; Sketch the graphs of: and show coordinates of intersection with the axes

Solomon worksheets

available

March Year 12 MOCK week C1 MOCK exam(Hall)

We will assess C2 during April along with mocks for the Applied modules (D1, M1 and

S1) which will take place during lesson time.

March/April EASTER HOLIDAYS Students to continue with their revision into the Easter Holidays

April Core 2: p154170 continued

Ch10. TRIGONOMETRICALIDENTITIES AND SIMPLEEQUATIONS

10.3 Solving Equations of the form:Sin (n + a), Cos(n + a) & Tan(n +

a)10.4 Solving quadraticTrigonometrical equations

Example:(a) Solve the equation sin x= in the interval 0 x 540(b) The height of the water above mean tide level in a harbour thours after midnight is hmetres, given by the equation 1.8sin(30 90)h t .

Use your answers to part (i) to find three times on the same day when the water is 0.6m

above mean tide level.



available with questions

Solomon worksheets

available

April Core 2: p171192

Ch11. INTEGRATION 2

11.1 Simple Definite integration11.2 Area under a curve

11.3 Area under a curve that givesnegative values11.4 Area between a line & a curve11.5 The trapezium rule

Definite Integration Example:

Find: 41

(2 1)( 2)dx x x .

Evaluate: ,

02

2

1

1 dx x

,

7

3

11 ( 2)( 5)x x x dx

.

Finding areas

Integration can be used to find the area underneath a curve.

Example 1: Find the area beneath the curve 23 5y x between the lines x= 2 and x=

4.

Tarsias available:

Solomon worksheets

available 3

1 )1( dxx


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x-1 1 2 3 4 5

y

10

20

30

40

50

NB: Areas beneath the x-axis are negative. You need to calculate areas above and below the axes

separately.

Example 2:The diagram shows the curvey= x(x3). Find the shaded area (answer:5 1 16 2 3

1 4 6 )

x-1 1 2 3 4 5

y

-2

2

4

6

8

10

To find the area between 2 curves you can use the formula:

Area= (top curve - bottom curve)dx



10/17

C1 & C2DeadlineWeek

Core 1 & Core 2

REVISION & CATCH-UP WEEK

Teachers to aim to complete all teaching by this week to allow time for past paper

practice, revision & last minute intervention.

Comprehensive notes are available for C2 from the 1-day revision day at UCL

C2 & M1 Notes from May

2013 Lectures at UCL on

Fronter

April C1 & C2 MOCK EXAMS Teachers to conduct these during lesson time or do a HOME-Mock to save lessontime. Papers to use will be discussed nearer the time. The papers will be printed for

you.

May REVISION & INTERVENTION PAST PAPERS

Year 12 study leavestarts May

Students should do about 15-20 past papers for every modules they will be sitting in

the summerthis could be a combination of actual and Solomon papers

26thMay30thMay

MAY HALF TERM

May/June EXTERNAL ASEXAMS Exams for C1, C2, S1 & M1

Jun 2015 START OF THE NEWTIMETABLE_ START C3 SOW

June Core 3: p111Ch1. ALGEBRAIC FRACTIONS

1.1 Simplify algebraic fractions by

NB: Both 4hr &6hrteachers to teach C3until October Half-term

Solomon worksheets

available


11/17

cancelling common factors

1.2 Multiply and divide algebraic

fractions.

1.3 Add and subtract algebraic

fractions

1.4 Dividing algebraic factions and

the remainder theorem.

Core 3: p1230Ch2. FUNCTIONS

1.1

Mapping diagrams andgraphs of operations.

1.2 Functions & Function

notation

1.3 Range, Mapping diagrams,

graphs & definitions of

functions

1.4 Using composite functions

1.5 Finding &using inverse

functions

Solomon worksheets

available

July Core 3: p3144

Ch3. THE EXPONENTIAL & LOG

FUNCTIONS

3.1 Introducing exponential

functions of the form y = ax

3.2 Graphs of exponential functions

and modelling using y = ax

3.3 Using exand the inverse of the

exponential function logex Sketch the functions ax, a > 0, ex, lnx and and their graphs.

IV has matching

activities/tarsias & extension

problems

Solomon worksheets

available

23rdJuly1stSept 2014 SUMMER HOLIDAYS

1stSept 2014 C3: Review Chapters 1-3 ( week)

Sept 2014 C3: p4557Ch4 NUMERICAL METHODS

4.1 finding approximate roots of f(x)= 0 graphically4.2 using iterative & algebraicmethods to find approximate roots off(x) = 0

Before you teach Ch5

familiarise yourself with

Autograph - speak with

BMM on how to use this

software

Solomon worksheets

available


12/17

September C3: p6382Ch5 TRANSFORMING GRAPHSOF FUNCTIONS

5.1 Sketching graphs of the modulus

function ||5.2 Sketching graphs of the function

||5.3 solving equations involving amodulus5.4 applying a combinations of

transformations to sketch curves5.5 sketching transformations &labelling the coordinates of a givenpoint

Autograph

Solomon worksheets

available

Standards Unit A12


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October 2014 C3: p83105Ch6 TRIGONOMETRY

6.1 The functions secant , cosecant and cotangent 6.2 The graphs of secant , cosecant and cotangent

6.3 simplifying expressions, provingidentities & solving equations usingsec , cosec and cot

6.4 using identities

6.5 using inverse trigonometricalfunctions and their graphs

Solomon worksheets

available

October 2014 C3: p106131Ch7 FURTHERTRIGONOMETRIC IDENTITIES& THEIR APPLICATIONS

7.1 using additional trigonometricalformulae7.2 using double angletrigonometrical formulae7.3 solving equations and provingidentities using double angleformulae

7.4 using the form in solving trigonometrical problems7.5 the factor formulae

Solomon worksheets

available

October 2014 OCTOBER HALF TERM

November2014

Core3: p132151Ch8 DIFFERENTIATION

8.1 Differentiating using the chainrule8.2 Differentiating using the productrule8.3 Differentiating using the quotientrule

8.4 Differentiating the exponentialfunction8.5 finding the differential of thelogarithmic function8.6 Differentiating sin x8.7 Differentiating cos x8.8 Differentiating tan x8.9 Differentiating furthertrigonometric functions8.10 Differentiating functions formedby combining trigonometrical,exponential, logarithmic &

C3 PAST PAPERBOOKLETS

DISTRIBUTED forstudents to revise fromover the Christmas break

papers including fullsolutionswe will useSolomon Papers A-L

Solomon worksheets

available


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polynomial functions

December2014

START TEACHING CORE 4 Must start C4 before Christmas to allow you time for revision & past papers of C3 & C4 in April& May

December2014

Core 4: p19Ch1. PARTIAL FRACTIONS

1.1 Adding & subtracting algebraicfractions

1.2 Partial fractions with two linearfactors in the denominator

1.3

Partial fractions with three ormore linear factors in thedenominator

1.4 Partial fractions with repeatedlinear factors in the denominator

1.5 Improper fractions into partialfractions

Solomon worksheets

available

December2014 CHRISTMAS HOLIDAYS

January 2015 Core 4: p1022Ch2. COORDINATE GEOMETRYIN THE (x, y) PLANE

1.6 Parametric equations usedto define the coordinates ofa point

1.7 Using parametric equationsin coordinate geometry

1.8 Converting parametricequations into Cartesianequations

1.9 Finding the area under acurve given by parametricequations

Solomon worksheets

available

Standards Unit A14

Exploring equations in

parametric form

Core 4: p2335

Ch3. THE BINOMIALEXPANSION

3.1 The binomial expansion for apositive integral index3.2 using the binomial expansion to

expand 23.3 using Partial fractions with thebinomial expansion

Solomon worksheets

available


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January 2015 Core 4: p3650Ch4. DIFFERENTIATION

4.1 Differentiating functions givenparametrically4.2 Differentiating relations which areimplicit

4.3 Differentiating the function 4.4 Differentiating rates of change4.5 Simple differential equations

Solomon worksheets

available

February2015

FEBRUARY HALF TERM

February Core 4: p5186Ch5. VECTORS

5.1 Vector Definitions and VectorDiagrams5.2 Vector arithmetic and the unitvector5.3 using vectors to describe points in2 or 3 dimensions5.4 Cartesian components of a vectorin 2D5.5 Cartesian components of a vectorin 3D5.6 Extending 2D vector results to 3D5.7 The scalar product5.8 The vector equation of a straightline5.9 Intersecting straight line vectorsequations5.10 The angle between two straightlines

Solomon worksheets

available

March/April Core 4: p87128

Ch6. INTEGRATION

6.1 Integrating standard functions6.2 Integrating using the reversechain rule6.3 using trigonometric identities inintegration6.4 using partial fractions to integrateexpressions6.5 using standard patterns tointegrate expressions6.6 Integration by substitution

C4 PAST PAPER BOOKLETS DISTRIBUTED for students to revise from over the half-term

breakpapers including full solutionsuse Edexcel

Solomon worksheets

available


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6.7 Integration by parts6.8 Numerical integration6.9 Integration to find areas andvolumes6.10 using integration to solvedifferential equations6.11 Differential equations in context

Mid April2015

Core 4: REVISION

EASTER HOLIDAYS

April 2015 C3, C4 + APPLIED MODULESREVISION

PAST PAPERS PAST PAPER BOOKLETS

April 2015 C3, C4 + APPLIED MODULESREVISION

PAST PAPERS PAST PAPER BOOKLETS

NOTES FOR THE TEACHER

DEADLINE

AS Teachers must aim to complete teaching by end of March 2015 to leave sufficient time for exam prep & past paper revision

A2 Teachers must aim to complete teaching by mid-April 2015 to leave sufficient time for exam prep & past paper revision

MAIN RESOURCE

Teachers will use the LiveText for all modules. Students will buy these themselves and bring to each lesson.

Additional resources are available from MEP, clickHERE

HOMEWORK
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htmhttp://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htmhttp://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htmhttp://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htm


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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 should also ask students to make

summary notes of each chapter as independent study. Fronter has been loaded with a wealth of homework practice which students should be directed to by you.

Students are expected to spend as much time outside lessons as in them i.e. about 5 hours on maths outside lessons each week. Most of this time will be spent on homework set by the teacher.

= I am confident with what I am doing (able)set Mixed exercise/Review exam style questions

= I am ok with thisbut could do with a little more practice (so-so)set questions from normal exercises focussing on end of exercise questions

= I am struggling with this topic/subject (weak)set usual exercises for extra practice (Ex 1A, 1B etc.)

FMSP REVISION COURSES

Payment to be collected before the publication of revision dates. Places to be allocated on a first come first served basis. Deposits to be collected by front office and must NOT be handled by

the Maths department.

G&T PROVISION

Pure Investigationsand Pure what if & whyproblems available for the most able from The Centre for Teaching Maths (Plymouth University) covering C1-C4

RULES FOR CLOSING THE GAP:

Know your students; Plan effectively; Enthuse & Inspire; Engage & Guide; Feedback appropriately & Evaluate together.

ASSESSMENT:

What about short tests in class?

Teachers should simply get students to do questions straight from the book to avoid printing costs maybe do a couple of carefully chosen questions each month to assess student retention of

prior learningor maybe flash a select few questions on the IWB

Alternatively, the Integral website from FMSP has lots of End of chapter assessments speak to Mr Mani about these

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