**Year 12 Further Maths homework for 21/3/18**

Complete the new linear programming workbook we started today

https://mathsmartinthomas.files.wordpress.com/2014/08/180311linearprogramming.pdf

(not the old linear programming workbook: you’ll still have some questions not yet done from that, which we will use for practice later).

Please mark your own work using the answers in the back of the workbook, and please check you have an up-to-date Target Sheet in your folder.

**Year 13 Further Maths homework for 21/3/18**

Further maths homework is to go through the FP3 paper you did for the

mocks, correcting mistakes you made, filling in bits you blanked on.

The paper is here:

and so are the mark scheme and worked answers to help you.

If you’re puzzled even after reading the mark scheme and worked

answers, email me.

**Year 13 Further Maths homework for 14/3/18**

Between now and Wed 14 March you should all do at least one FP2 past paper, at least one S2 past paper, and at least one FP3 past paper.

I suggest do FP2 first, then S2, then FP3, because that’s the order of the mock exams.

For FP2: June 2012

For S2: summer 2011

For FP3 I suggest the official Edexcel FP3 Mock Paper. You should be able to attempt all questions except question 8 (which is about chapter 2, which you won’t cover until after the mocks).

Do each paper in as near to exam conditions as you can manage

then mark it against the mark scheme

scan your work and email me the scan for feedback

try to fix the bits where you made slips or blanked

if you still can’t see how to fix it after reading the mark scheme and puzzling over it, email me

Each of you will probably do well also to work on collections of past-paper questions on topics which you, individually, find more difficult. For example, here is a collection of past-paper questions on Mobius transformations:

https://mathsmartinthomas.files.wordpress.com/2016/02/fp2-loci-q1.pdf

For every topic in FP2, S2, or FP3, there is a collection of past-paper questions on that topic at

https://mathsmartinthomas.wordpress.com/2017/12/12/s2-statistics-materials/

https://mathsmartinthomas.wordpress.com/2016/02/19/fp2-past-papers/

or

https://mathsmartinthomas.wordpress.com/2016/02/19/fp2-past-papers/

For FP3, ignore for now the past-paper questions on conics, and on vectors try only the shorter question sheet I circulated in class.

Email me scans of this work, too?

I will send feedback on scanned work as fast as I can.

**Year 12 Further Maths homework for 14/3/18**

Homework for Wed 14th:

at least four more problems from the linear programming workbook

so everyone who was in school on Friday 2nd should get up to Q.8 at least (and that includes finding whole-number solutions when they’re asked for)

and everyone who missed school on Friday 2nd should get up to Q.4 at least (and that includes finding whole-number solutions when they’re asked for).

Use the vertex-checking method https://www.youtube.com/watch?v=iZ739tt1A2g

if you like, instead of drawing the parallel objective lines. Whichever you prefer.

I’ll do a marking marathon on your linear programming workbooks between Wednesday and Friday.

Make sure also you’ve done the Part A homework for Wednesday 7th (below).

**Year 12 Further Maths homework for Wednesday 7/3/18**

Abass: Redo Q.7(d) and Q.9(b) from the test (we discussed them). Try creating a new equation with roots 2α+1, 2β+1, 2γ+1 from the equation x^{3} – x = 0. Insert K into Gantt chart in Q.2(c) of Critical Path Analysis workbook. Do Q.8 of Critical Path Analysis workbook.

Aniqa: bring me your Critical Path Analysis and Dijkstra booklets next Wednesday, with Dijkstra questions done up to Q.5 inclusive, and CPA up to Q.8 plus also Q.14, 17, 18. Skip Q.5(e), 6(f), 7(d) in Critical Path Analysis workbook.

Callum: none

David: Try Q.3 from test paper (create new equation from x^{3}+3x^{2}+5x-1=0 with roots 2α+1, 2β+1, 2γ+1) by method of writing y=2x+1, deducing x=(y-1)/2, plugging (y-1)/2 in place of x in the original equation, and expanding, collecting terms, and simplifying to get an equation in y. Do more examples from your Critical Path Analysis workbook and give it to me next Wednesday.

Enoch: Dijkstra – try Q.6. Critical Path Analysis – expand your answer to Q.3(a) [why dummies?]. Do Q.4(e) [which activities on days 16 and 31]. Do Q. 6(c), 6(d), 7, 8. Try Q.3 from test paper (create new equation from x^{3}+3x^{2}+5x-1=0 with roots 2α+1, 2β+1, 2γ+1) by method of writing y=2x+1, deducing x=(y-1)/2, plugging (y-1)/2 in place of x in the original equation, and expanding, collecting terms, and simplifying to get an equation in y.

Helen: Look at my comment on Q.18(b) of Critical Path Analysis to check if you understand. Look at my comment on Q.2(b) in Dijkstra booklet to check if you understand.

Howard: to follow

Iris: Critical Path Analysis – complete Q.4(c) [floats]. Try again on Q.4(d) [which activities on day 31]. Complete 5(c) [floats], and 6(c) [can project still be completed on time]. Complete Q.14.

Jeffrey: Redo Q.8 of the test paper. Try Q.4(e) of the Critical Path Analysis workbook again, looking carefully at the floats on all the activities.

Lara: Do the Gantt chart bits of all the questions you’ve done in the Critical Path Analysis booklet.

Mya: to follow

Obi: Dijkstra workbook – redo your answer to Q.1(b) after looking at the answer given to the (similar) Q.7c in the back of the workbook. Critical Path Analysis workbook: do Q.1(e), 3(d). Redo Q.3(e) Gantt chart showing the floats on A and on F. Complete the Gantt chart in Q.4(d). Complete Q.5 (b), (c), (d), and Q.8.

Reece: Critical Path Analysis – try again on Q.16(a). Try again on Q.4(e) and Q.6(e), looking carefully at the floats. Do Q.14.

Part B, for those who were in class on 2/3/18

From linear programming workbook

https://mathsmartinthomas.files.wordpress.com/2018/03/linearp_q1.pdf

Complete Q.1 to 3. Where the answer has to be whole numbers, and your calculation gives you not-whole numbers, leave it with the not-whole number answers. That’s ok: we’ll find out next week how to get the best whole-number answers.

If you’re stuck, use the answers in the back of the workbook.

Part C: none for those who were in class on 2/3/18, but those who weren’t in class on 2/3/18 should do up to Q.9 inclusive in the Dijkstra workbook https://mathsmartinthomas.files.wordpress.com/2014/12/dijkstra.pdf

**Year 13 Further Maths homework between now and after mocks (14/3/18)**

Between now and Wed 14 March you should all do at least one FP2 past paper, at least one S2 past paper, and at least one FP3 past paper.

I suggest do FP2 first, then S2, then FP3, because that’s the order of the mock exams.

For FP2: June 2012

For S2: summer 2011

For FP3 I suggest the official Edexcel FP3 Mock Paper. You should be able to attempt all questions except question 8 (which is about chapter 2, which you won’t cover until after the mocks).

Do each paper in as near to exam conditions as you can manage

then mark it against the mark scheme

scan your work and email me the scan for feedback

try to fix the bits where you made slips or blanked

if you still can’t see how to fix it after reading the mark scheme and puzzling over it, email me

Each of you will probably do well also to work on collections of past-paper questions on topics which you, individually, find more difficult. For example, here is a collection of past-paper questions on Mobius transformations:

https://mathsmartinthomas.files.wordpress.com/2016/02/fp2-loci-q1.pdf

For every topic in FP2, S2, or FP3, there is a collection of past-paper questions on that topic at

https://mathsmartinthomas.wordpress.com/2017/12/12/s2-statistics-materials/

https://mathsmartinthomas.wordpress.com/2016/02/19/fp2-past-papers/

or

https://mathsmartinthomas.wordpress.com/2016/02/19/fp2-past-papers/

For FP3, ignore for now the past-paper questions on conics, and on vectors try only the shorter question sheet I circulated in class.

Email me scans of this work, too?

I will send feedback on scanned work as fast as I can.

**Year 12 Further Maths homework for 28/2/18**

Please hand in, next Wednesday 28th:

- Your critical path analysis workbook, with questions 1-8, 13, 14, 17, 18 done. I’ve selected 13, 14, 17, 18 because they include drawing graphs from precedence tables, which is the trickiest part. Skip the

bits about “scheduling” – Q.5e, 6f, 7d, 9d,f,g, and 10e,f. (Those bits were in the old syllabus, but now are in Year 13). - Your Dijkstra workbook. (I’m not asking you to do any more from that this week. I just want to double-check where you’re all up to on that).
- Your test paper from 9 February, with your corrections and fixing,
*unless*I’ve seen it this week and written feedback which indicates you’ve fixed it near enough completely.

**Year 13 Further Maths homework for 21/2/18**

First calculate a mark for yourself on the paper you did last Thursday, and let me know.

Second, do a past paper in 90 minutes. Open book or closed book, that’s up to you, but in a single session of 90 minutes without distractions.

Do either FP2 **June** 2011 or S2 January 2011, as you prefer.

Send me a scan of your work. I will send feedback.

Mark your work yourself.

See if you can fix all the bits where you made slips, or blanked. If you can’t work it out even with help from the mark scheme, email me for help.

Do the following exercises to get used to dot-product and cross-product.

Ex.5A Q.1, 2, 3

Ex.5D Q.1, 3, 5

Ex.5E Q.1 to 4

Review Exercise 2 Q.5

and Example 18 from p.158 of the textbook

Since you have half-term, I’d suggest you also try the same process with an FP3 paper – attempt the paper in 90 minutes (open book or closed book, as you prefer), send me a scan, mark it yourself, try to fix where you’ve made slips or blanked, email me where you can’t fix it.

I suggest the official Edexcel FP3 Mock Paper

You should be able to attempt all questions except question 8 (which is about chapter 2, which you won’t cover until after the mocks).

**Year 12 Further Maths homework for 21/2/18**

First: I will send you a scan of your test paper from 09/02/18. Please work through to see if you can fix all the slips you made and any points where you blanked.

Then: two more questions from the Critical Path Analysis workbook.

Critical Path workbook: https://mathsmartinthomas.files.wordpress.com/2014/12/cpa_q.pdf

Read the notes about dummies, and be careful to get them right.

https://mathsmartinthomas.wordpress.com/2018/02/04/dummy-edges-in-critical-path-analysis-graphs/

And two more questions from the Dijkstra workbook, taking care not to miss any connections (even apparently “backwards” ones); to label all the little boxes; to put the order of labelling (not the order on the shortest path) in the middle little box; and to explain well how you find which vertices are on the shortest path.

This is how the mark schemes say you must explain finding those vertices:

“General explanation – trace back from J [end node]. Include arc XY if Y is already on path and if difference in trial labels equals length of arc”.

Dijkstra workbook: https://mathsmartinthomas.files.wordpress.com/2014/12/dijkstra.pdf

**Year 12 Further Maths homework for 7/2/18**

Review the Core Pure paper you did over Xmas:

https://mathsmartinthomas.files.wordpress.com/2017/12/y12-pure.pdf

To help you: Hints and part-solutions for that paper at https://mathsmartinthomas.files.wordpress.com/2018/01/core-pure-textbook1.pdf

Textbook answers here: https://mathsmartinthomas.files.wordpress.com/2017/12/y12-pure-answers.pdf

There’s a typo in Q.5. It should be +78z^{2}, not −78z^{2}

I’m not asking you to re-do the whole paper, but to check which questions you can see how to do easily, and which puzzle you or which you’ve forgotten how to do, and to work through what you’re not confident with.

Also: one more question from the Critical Path Analysis workbook.

Critical Path workbook: https://mathsmartinthomas.files.wordpress.com/2014/12/cpa_q.pdf

And one more question from the Dijkstra workbook, taking care not to miss any connections (even apparently “backwards” ones); to label all the little boxes; to put the order of labelling (not the order on the shortest path) in the middle little box; and to explain well how you find which vertices are on the shortest path.

This is how the mark schemes say you must explain finding those vertices:

“General explanation – trace back from J [end node]. Include arc XY if Y is already on path and if difference in trial labels equals length of arc”.

Dijkstra workbook: https://mathsmartinthomas.files.wordpress.com/2014/12/dijkstra.pdf

**Year 13 Further Maths homework for 7/2/18**

First mark your own work on the paper you did after class on Thursday. See if you can fix all your mistakes or the bits you blanked on. Email me if you get stuck.

On Saturday I will send you feedback on your paper, to help.

That’s – Umut and Bolaji, S2 January 2010; Mohaned and Tegan, F2 IAL June 2016; Onesimus and Michelle, FP2 June 2016

Then do exercise 6G up to at least Q.6 (Q.8 for Mohaned).

**Year 13 Further Maths homework for 31/1/18**

Transforming points, lines, and planes by 3×3 matrices: do at

least two more of these questions from the FP3 book in addition to

those you did in class.

Ex.6E Q.1

Ex.6D Q.2

Ex.6D Q.3

Ex.6D Q.5

Ex.6D Q.8

If you didn’t complete the FP2 June 2009 past paper after class today,

please complete it and send a scan (preferably) or photos from your

phone (failing that) to me by end of school on Friday 26/1/18. I’ll

email you feedback quickly.

**Year 13 Further Maths homework for 31/1/18**

Transforming points, lines, and planes by 3×3 matrices: do at

least two more of these questions from the FP3 book in addition to

those you did in class.

Ex.6E Q.1

Ex.6D Q.2

Ex.6D Q.3

Ex.6D Q.5

Ex.6D Q.8

If you didn’t complete the FP2 June 2009 past paper after class today,

please complete it and send a scan (preferably) or photos from your

phone (failing that) to me by end of school on Friday 26/1/18. I’ll

email you feedback quickly.

**Year 12 Further Maths homework for 31/1/18**

Finish the Chinese postman (route inspection) exercises

https://mathsmartinthomas.files.wordpress.com/2014/08/chinesepostman-newbook1.pdf

Do the first two questions (only) of the big Dijkstra booklet, taking to fill in *all* the little boxes (Edexcel insists) and not to miss shorter connections which look like they involve going “backwards”.

https://mathsmartinthomas.files.wordpress.com/2014/12/dijkstra.pdf

**Year 12 Further Maths homework for 24/1/18**

Finish the Dijkstra exercises for which you have printed templates.

Dijkstra exercises with printed templates

You got copies of the first two in the lesson, and copies of the third exercise will be available at reception at the 6th Form Building.

Don’t do the Dijkstra exercises for which you don’t have printed templates:

New-syllabus Dijkstra examples

but read through them to notice the extra things you may be asked in the new syllabus, e.g. things about the order of the algorithm and calculation time.

**Year 13 Further Maths homework for 24/1/18**

Basic homework for everyone but Genie and Tegan: rework the questions from the S2 January 2013 paper which you got wrong or blanked on.

Mohaned and Bolaji, in particular, have very little work of that sort to do, because they got very little wrong. They would do well to do another FP2 paper – I recommend F2 IAL June 2016.

Genie and Tegan: do as much as you can of the FP2 paper you were working on in class.

We’re starting FP3 matrices next Wednesday, so everyone should take a moment to refresh their memory of FP1 matrices a bit.

**Year 13 Further Maths homework for 17/1/18**

All but Genie and Tegan: finish S2 June 2017 paper https://mathsmartinthomas.files.wordpress.com/2015/03/s2-pp-2010-2017.pdf *and mark your own work*.

Complete Ex.3E Q.1, 2, 3, 4, 10.

Genie: exercises (of Genie’s choosing) on polar coordinates and first order differential equations (up to and including integrating factor).

Tegan: do at least one of the two FP2 practice papers compiled from Review Exercise questions in the book. (I’m proposing these because answers can be found in the back of the textbook, and further help on Solution Bank). Bring to next Wednesday’s lesson a list of FP2 “issues”.

**Year 12 Further Maths homework for 17/1/18**

Rework the questions you got wrong or failed to complete in the two holiday worksheets:

This test paper on pure maths: https://mathsmartinthomas.files.wordpress.com/2017/12/y12-pure.pdf

and

this test paper on decision maths: https://mathsmartinthomas.files.wordpress.com/2017/12/y12-d1.pdf.

Hints and part-solutions to the core pure paper

Please mark your own work before handing it in. Answer sheets here:

Pure maths: https://mathsmartinthomas.files.wordpress.com/2017/12/y12-pure-answers.pdf

Decision maths: https://mathsmartinthomas.files.wordpress.com/2017/12/y12-d1-answers.pdf

Question 4 of the Decision Maths homework says: “Bubble sort is an algorithm of quadratic order”. It means it is of order n^2.

(Like a quadratic equation is one which has x^2 in it but not higher powers).

**Year 12 Further Maths homework for 10/1/18**

As above.

**Year 13 Further Maths homework for 10/1/18**

Sampling and hypothesis testing: Exercise 7D Q.1-10 and Exercise 6C Q.6, 7, 8.

Exercise 7D Q.1-10 and Exercise 6C Q.6, 7, 8

And the “Examination practice paper” at the end of the S2 book, p.131-132, questions 1 to 6.

You may find these two summary sheets useful:

“Do and don’t” for S2 statistics

and these notes:

How many marks does Edexcel take off for bad writing in S2?

Then please do these more demanding tasks: two FP2 practice papers compiled from Review Exercise questions in the book. (I’m proposing these because answers can be found in the back of the textbook, and further help on Solution Bank).

And the June 2016 FP2 paper (which was a harder-than-usual paper). You can find the paper, plus worked answers and a mark scheme, at: https://mathsmartinthomas.wordpress.com/2016/12/07/june-2016-fp2-notes/

Archive of older homework at:

https://mathsmartinthomas.wordpress.com/2017/12/21/homework-archive-2014-2017/