5 EXAM

Transcript

AS Statistics Scheme 07-08

A2 Decision Planner 14-15

Date

Things

Topic

set

11/9

Thur/Fri only

Single lesson all blocks

“A level compared to AS”

15/9

C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy.

22/9

TT1CWC test

C3 Integration as the invers of differentiation

Functions – Domain, Range, Composite

29/09

C3 Functions – Modulus, Inverse, Transformations

6/10

C3 Natural logs including derivatives of e^x and lnx

13/10

TT2 (C3 + integration)

C3 Rcos(x+a),

20/10

C3 Inverse trig functions including graphs. Numerical Methods

October Half Term / End Term 1

3/11

C4 Partial fractions. *Forming Differential Equations.

10/11

Lessons on Monday

Reading Week – Open Eve, Dept Day, SRs Thurs/Fri

17/11

D1 Algorithms – Bubble sort, Quick sort, Bin packing, Binary search

24/11

TT3 (C3)**

C4 Integration using Trig, Partial Fractions

Integrals of form f1(x)/f(x) (substitution optional here)

1/12

D1 Algorithms on graphs (Dijkstra, Kruskal and Prims)

8/12

C4 Implicit Differentiation

15/12

No P4 Thursday

No P5,6 Friday

D1 Route inspection

Christmas / End Term 2

5/1

C4 Review of integration so far, trapezium rule and % error

12/1

TT4 pure/ applied

C4 Vectors* equation line, intersection, etc

19/1

D1 Linear programming, ruler and vertex methods

26/1

C4 Integration by Substitution/Parts

2/2

C4 Differential Equations & Connected Rates of Change

9/2

D1 Critical Path Analysis, Precedence tables, activity networks

February Half term / End Term 3

23/2

TT5

C4 Parametrics

2/3

D1 Gantt charts, scheduling

9/3

C4 Binomial Expansion, Vol of Revolution

16/3

D1 Matchings

23/3

C4 Mock

D1 Revision

Easter / End Term 4

13/4

D1 Mock

EXAM PRACTICE & REMOCK

20/4

C3 Mock

EXAM PRACTICE & REMOCK

27/4

EXAM PRACTICE & REMOCK

4/5

No monday

EXAM PRACTICE

11/5

EXAM PRACTICE

18/5

A2 Study Leave

F-J

A2 Statistics Planner 14-15

Date

Things

Topic

set

11/9

Thur/Fri only

Single lesson all blocks

“A level compared to AS”

15/9

C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy.

22/9

TT1CWC test

C3 Integration as the invers of differentiation

Functions – Domain, Range, Composite

29/09

C3 Functions – Modulus, Inverse, Transformations

6/10

C3 Natural logs including derivatives of e^x and lnx

13/10

TT2 (C3 + integration)

C3 Rcos(x+a),

20/10

C3 Inverse trig functions including graphs. Numerical Methods

October Half Term / End Term 1

3/11

C4 Partial fractions. *Forming Differential Equations.

10/11

Lessons on Monday

Reading Week – Open Eve, Dept Day, SRs Thurs/Fri

17/11

S2 Binomial Distribution

24/11

TT3 (C3)**

C4 Integration using Trig, Partial Fractions

Integrals of form f1(x)/f(x) (substitution optional here)

1/12

S2 Poisson Distribution (mean/var), Poisson as approximation to Binomial

8/12

C4 Implicit Differentiation

15/12

No P4 Thursday

No P5,6 Friday

S2 Binomial to normal approximation

Poisson to normal approximation

Christmas / End Term 2

5/1

C4 Review of integration so far, trapezium rule and % error

12/1

TT4 pure/ applied

C4 Vectors* equation line, intersection, etc

19/1

S2 CRVs pdf & cdf

26/1

C4 Integration by Substitution/Parts

2/2

C4 Differential Equations & Connected Rates of Change

9/2

S2 CRVs E(X),Var(X), median, mode, IQR,

February Half term / End Term 3

23/2

TT5

C4 Parametrics

2/3

S2 CRVs Uniform Distribution Sampling, Statistics, Distributions

9/3

C4 Binomial Expansion, Vol of Revolution

16/3

S2 Hypothesis Testing

23/3

C4 Mock

S2 Hypothesis Testing

Easter / End Term 4

13/4

S2 Mock

EXAM PRACTICE & REMOCK

20/4

C3 Mock

EXAM PRACTICE & REMOCK

27/4

EXAM PRACTICE & REMOCK

4/5

No Monday

EXAM PRACTICE

11/5

EXAM PRACTICE

18/5

A2 Study Leave

F-J

A2 Mechanics Planner14-15

Date

Things

Topic

set

11/9

Thur/Fri only

Single lesson all blocks

“A level compared to AS”

15/9

C3 Derivatives of tan, sec, cosec, cot.

dy/dx as 1 over dx/dy.

22/9

TT1CWC test

C3 Integration as the inverse of diffn Functions – Domain, Range, Composite

29/09

C3 Functions – Modulus, Inverse, Transformations

6/10

C3 Natural logs including derivatives of e^x and lnx

13/10

TT2 (C3 + integration)

C3 Rcos(x+a),

20/10

C3 Inverse trig functions including graphs. Numerical Methods

October Half Term / End Term 1

3/11

C4 Partial fractions. *Forming Differential Equations.

10/11

Lessons on Monday

Reading Week – Open Eve, Dept Day, SRs Thurs/Fri

17/11

M2 Projectiles

24/11

TT3 (C3)**

Integration using Trig & Partial Fractions

1/12

Motion in a straight line & on plane/vectors

8/12

Implicit Differentiation

15/12

No P4 Thursday

No P5,6 Friday

Centres of mass (discrete masses, frameworks, laminas,)

Christmas / End Term 2

5/1

TT4 pure/app

C4 Review of integration so far, trapezium rule and % error

12/1

C4 Vectors* equation line, intersection, etc

19/1

M2 Work, Energy& Power

26/1

C4 Integration by Substitution/Parts

2/2

C4 Differential Equations & Connected Rates of Change

9/2

M2 Centre of mass suspension, tilting

February Half term / End Term 3

23/2

TT5

C4 Parametrics

2/3

M2 Collisions

9/3

C4 Binomial Expansion, Vol of Revol’n

16/3

M2 Statics

23/3

C4 Mock

M2 Statics

Easter / End Term 4

13/4

M2 Mock

EXAM PRACTICE & REMOCK

20/4

C3 Mock

EXAM PRACTICE & REMOCK

27/4

EXAM PRACTICE& REMOCK

4/5

No Monday

EXAM PRACTICE

11/5

EXAM PRACTICE

18/5

A2 Study Leave

F-J

C3 Derivatives of tan, sec, cosec, cot. dy/dx as 1 over dx/dy.

Application of the chain rule, product rule and quotient rule

C3 Integration as the inverse of differentiation

Emphasis on correct notation for integration.

Make sure they understand the importance of dx in the integration

Good to do some definite integrations and insist on correct notation

C3 Functions – Domain, Range, Composite

They find domain and range difficult.

Emphasise two methods –

graph sketching: domain is x axis, range is y axis – good use of graphical calculators

look at domain and use algebra to work out domain

However, beware of this

y=9-x2 domain -3

whereas the correct answer is 0

Emphasise correct notation – e.g. domain -3

Emphaise care with < and ≤

http://www.educreations.com/lesson/view/range-and-domain/12776588/?ref=link

C3 Functions – Modulus, Inverse, Transformations

Modulus graphs can be easily drawn with graphical calculators – sometimes this is abs (absolute)

Inverse functions can be found by swapping x and y which is the same as reflecting the graph in the line y=x

http://www.educreations.com/lesson/view/c3-january-2006-q1/15341497/

C3 Natural logs including derivatives of e^x and lnx

Draw the graphs of y=2 x, y=3 x, y=2.5 x, y=2.7x and use Autograph to plot the gradient function. Show that y=ex is the same as its gradient function.

http://www.educreations.com/lesson/view/c3-january-2006-q3/15341593/

C3 Rcos(x+a),

Beware of using tan because they often invert to mistakenly get cot.

I prefer to find R using Pythagoras and then equate

e.g. express 3 cos x + 4 sin x in the form Rcos(x-a)

R= 5 (Pythagoras)

R cos (x-a) = 5(cos x cos a + sin x sin a)

3 cos x + 4 sin x = 5(cos x 3/5 + sin x 4/5)

Then equate to get cos a = 3/5 or sin a = 4/5

http://www.educreations.com/lesson/view/c3-january-2006-q6/15341838/

C3 Inverse trig functions including graphs. Numerical Methods

Make sure they put in the correct words for Numerical solutions.

“Because there is a change of sign and the graph is continuous, there is a solution between x = 1.65 and x = 1.66” or “Because there is a change of sign and the graph is continuous, x = 2.71 to 2 decimal places” – in the last example they should have shown that x = 2.705 and 2.715 produce a different sign

http://www.educreations.com/lesson/view/c3-june-2010-q4/20993529/?ref=link

C4 Partial fractions. *Forming Differential Equations.

Three types to consider

1) 2) 3)

http://www.mmacve.mistral.co.uk/BHASVIC/PartialFractions.htm

D1 Algorithms – Bubble sort, Quick sort, Bin packing, Binary search

At some point, students will need to memorise the definitions that are listed in the syllabus on page 100. Don’t be tempted into getting them to memorise all definitions in the textbook as there are lots of extra ones in the textbook.

Bubble Sort:

http://www.educreations.com/lesson/view/d1-bubble-sort/13419797/

Bin Packing:

http://www.educreations.com/lesson/view/d1-bin-packing/13357407/

http://www.educreations.com/lesson/view/tt4-q5/15605051/

Quick Sort:

http://www.educreations.com/lesson/view/d1-quick-sort/13419106/

Binary Search

http://www.educreations.com/lesson/view/d1-binary-search/13421243/

This includes flow charts and algorithms

Some teachers don’t normally bother teaching flow charts, just set one in homework although others feel that students find it hard to blindly follow the rules of a flow chart and do exactly what they are told to! Well, they are teenagers.

Common Mistakes; Not packing all the items in the original list

Finding ‘H’ and thinking it’s Hugo when actually it’s Hannah and Hugo isn’t in the list

Not copying the whole list down

They find bubble sort harder than quick sort. They find alphabets and decimals harder than integers

Common mistakes with sorting: Not writing ‘sort complete’ at the end

Numbers changing from one line to the next

S2 Binomial Distribution

M2 Projectiles

C4 Integration using Trig, Partial Fractions

Integrals of form f1(x)/f(x) (substitution optional here)

They need constant reminders of all this stuff. Regular testing of easy work is recommended, e.g. a weekly five minute test asking them to integrate

1) sin x

2) cos x

3) tan x

4) cot x

5) sin2x

6) sin2x

7) cos2x

8) cos2x

9) sec2x

10) cosec2x

11) cosec x cot x

12) sec x tan x

13)

14)

http://www.educreations.com/lesson/view/integration-tan-and-cot/14317813/?s=YSIQbF&ref=link

D1 Algorithms on graphs (Dijkstra, Kruskal and Prims)

Dijkstra:

http://www.educreations.com/lesson/view/dijkstra/14115699/

http://www.educreations.com/lesson/view/d1-june-2012-q5/20624802/

Kruskal:

http://www.educreations.com/lesson/view/kruskal/14113569/

Prim:

http://www.educreations.com/lesson/view/prim-s-algorithm-on-a-network/14114338/

http://www.educreations.com/lesson/view/prim-s-algorithm-on-a-matrix/14114795/

http://www.educreations.com/lesson/view/d1-june-2010-q2/21102377/

Scribbling along the arcs as you update helps accuracy

Must show method for route

TROLL pneumonic (top label, remove row, O round the smallest, LIST! LIST! – ie list the order the arcs were chosen in)

Common mistakes: Adding wrong

Missing an arc to update

Doubling up on the ‘order’ so having two 6th vertices

Units missing

S2 Poisson Distribution (mean/var), Poisson as approximation to Binomial

M2 Motion in a straight line and on plane/vectors

C4 Implicit Differentiation

I always make them write differentiate b.s.w.r.t.x (both sides with respect to)

e.g.

Find if sin x + 6y2 = 2xy

Differentiate b.s.w.r.t.x

(sin x) + (6y2) = (2xy)

(sin x) + (6y2) = y (2x) + 2x (y)

cos x + 12y = 2y + 2x

(12y – 2x) = 2y – cos x

http://www.educreations.com/lesson/view/implicit-differentiation/14661757/

D1 Route inspection

http://www.educreations.com/lesson/view/d1-route-inspection/14976698/

http://www.educreations.com/lesson/view/d1-june-2013-q5/20646531/?ref=link

http://www.educreations.com/lesson/view/tt4-q6/15605113/

Common mistakes; Thinking AB direct is the best link of A and B

Writing ‘repeat AB’ when you mean ‘repeat AC, CB’

Units missing S2 Binomial to normal approximation

Poisson to normal approximation

M2 Centre of mass suspension, tilting

C4 Review of integration so far, trapezium rule and % error

Although they have done the trapezium rule in C2, don’t assume that they remember how to do it.

Beware complex methods and formulae for working out h

e.g.

6.4

6.6

6.8

7.2

7.4

Don’t use h = (b-a)/(n-1)

Do use h=0.2 because the x numbers are increasing by 0.2 each time

http://www.educreations.com/lesson/view/integration-trapezium-rule-and-parts/15604632

A large number of videos at http://www.mmacve.mistral.co.uk/BHASVIC/integration.htm

C4 Vectors* equation line, intersection, etc

Vectors are traditionally hard for students to understand.

A large number of videos at

http://www.mmacve.mistral.co.uk/BHASVIC/Vectors.htm

D1 Linear programming, ruler and vertex methods

http://www.educreations.com/lesson/view/linear-programming/16103186/?ref=link

http://www.educreations.com/lesson/view/d1-june-2012-q7/20626877/?ref=link

http://www.educreations.com/lesson/view/d1-january-2012-q6/20368333/

http://www.educreations.com/lesson/view/tt5-q6-january-2012-q6/18838295/

http://www.educreations.com/lesson/view/linear-programming/16103186/

http://www.educreations.com/lesson/view/d1-june-2011-q3/21778189/

Common mistakes: Mistakes using simultaneous equations

Twisting ruler en route and getting wrong vertex

Wrong integer solution

Shading y

Not labelling lines

At least twice as many x as y as an inequality

S2 CRVs pdf & cdf

M2 Work, Energy and Power

C4 Integration by Substitution/Parts

It’s very important to insist that students set their work out carefully and methodically in this topic. It’s always important for every topic, obviously, but it’s very easy for their work to become excessively muddled in these topics.

For substitution, I insist that they draw a vertical line with the main working on the left and the substitution and limit replacement on the right.

http://www.educreations.com/lesson/view/integration-by-substitution/16293496

http://www.educreations.com/lesson/view/c4-june-2013-q1/20646568

C4 Differential Equations & Connected Rates of Change

http://www.educreations.com/lesson/view/differential-equations-separating-the-variable/16293986

D1 Critical Path Analysis, Precedence tables, activity networks

http://www.educreations.com/lesson/view/critical-path-analysis/16766656/?ref=link

http://www.educreations.com/lesson/view/tt5-q7-d1-jan-2012-q7/18838855/

http://www.educreations.com/lesson/view/d1-june-2012-q6/20625635/

S2 CRVs E(X),Var(X), median, mode, IQR,

M2 Centre of Mass suspension, tiling

C4 Parametrics