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This page contains a selection of past paper questions and solutions to help you target your revision in the approach to the final exams. 1. Decimals, Fractions & Percentages (Solutions) 2. Algebra – including algebraic fractions, surds and indices (Solutions) 3. Data Handling – including diagrams and standard deviation (Solutions) 4. …

This page contains resources to help you revise for your prelim exams; Previous National 5 prelims National 5 Prelim 2015-16 (Marking Scheme) National 5 Prelim 2014-15 (All 3 units) National 5 Prelim 2013-14 Practice prelims (Int 2 level) Intermediate 2(123) 2008 Paper1 (Marking Scheme) Intermediate 2(123) 2008 Paper2 (Marking Scheme) Intermediate 2 (123) 2009 Paper 1 (Marking …

Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.

Alfred North Whitehead

*Further Ken Robinson Creativity*

This is another outstanding TED talk where Ken Robinson explains how we can improve education in the world. Ken highlights some key points about how education is failing learners and how we can change this. This video is a must watch as it leaves you inspired and motivated to change your practice.

“Children are not suffering from psychology disorders, they are suffering from childhood”

Sir Ken Robinson outlines 3 principles crucial for the human mind to flourish — and how current education culture works against them. In a funny, stirring talk he tells us how to get out of the educational “death valley” we now face, and how to nurture our youngest generations with a climate of possibility.”

Take a look at some of the Ken Robinson books that are available and worth a read if you are in need of some inspiration. You can also take a look at Ken Robinson’s TED video on changing education paradigms for another thought provoking talk.

Comments are FREE, please leave one below!

*Ken Robinson – How to escape education’s death valley*

So you want to know how to cheat on your Mathletics Maths homework and avoid a possible Maths detention! This is an interesting eye opener for teachers and Learners about online Maths homework set on Mathletics. This hack gets all the answers for your maths homework and lets you get extra points and marks. Take a look at the 3 methods below, the third is the most recent method updated.

I do have several pieces of advice that I have summarised below but beware that it might not be what you had hoped, but take a look anyway. So you have been searching the web for the ability to hack the system to get all the answers to your maths Mathletics task.

Independently try and teach yourself the maths behind the task and you easily get full marks and get that all aspiring “free stuff”. In the long term it is in your best interest to learn the material and apply the knowledge as the hack below will not be able to help you in a Maths exam or later on in life. It is also very likely that the Mathletics team have already read this post and fixed the bug. I know because I have already submitted the links to them!!

The video is self explanatory but unfortunately pupils I have sent the bug to Mathletics to deal with, so by the time you read this it might have been fixed and you will not be able to easily do your maths homework. Why not ask your Maths teacher for help or get yourself a Maths tutor.

The second method can be found on the *next* page.

If you are looking for dirty Math jokes then this is not the place, these are the the best funny Maths Jokes ever and are guaranteed to make you smile and laugh! The Math jokes below are a collection based on number of retweets on twitter and likes on face book. I think the jokes show that us Mathematicians can be funny if we want to be. ). If you still do not believe we can be funny then check out this funny Math calculator that is certain to make any Math class laugh.

Do not worry English teachers you can check out the Top 10 Funny English Puns. if you are feeling a little left out.

If you have any funny Math jokes that you want to added to the list then tweet @magicalmaths and we will try and get it added. Alternatively, remember that comments are FREE, so let us know what you think below.

Before you take a look at the Top 10 funny maths jokes watch the video below which explains some funny maths jokes.

*Top 10 Funny Math Jokes*

1) A Roman walks into a bar, holds up two fingers, and says: ”Five beers, please.”

2) Why is 2 x 10 the same as 2 x 11? Because 2 x 10 = 20 and 2 x 11 equals twenty two

3) Two men walk into a bar. One orders H20, the other says I’ll have H20 too. The second man dies.

4) An infinite number of mathematicians walk into a bar, the 1st orders a beer, the 2nd order 1/2 a beer, the 3rd orders 1/4 a beer. The bartender gets frustrated and says “You are all idiots and pours 2 beers”

5) Why are powers like fish? Because they’re all indices!

[embedTweet align=”left” url=”526093493178220544″]

6) Sneeze! Sneeze! Sneeze!Sneeze! Sneeze!Sneeze!Sneeze! Sneeze!Sneeze!Sneeze!Sneeze!Sneeze! Fibonacchoo (@kathrynmc7712m)

7) Why was the maths teacher late for school? Because he got on the rhombus! (@lauren_lsm)

I am regularly asked about advice on the best Maths revisions guides or books to buy. The answer really depends on the type of student and type of Maths course they are studying. It is very important that pupil revision is active, which means the student should be doing Maths rather then just reading over a topic. To revise a topic effectively learners should be applying a skill by answering questions. Many of the Maths Revision books below have some very good problems solving activities and well defined questions with scaffolding in the correct places.

*Top 5 revision books or guides for Maths revision*

“This book is full of clear revision notes and diagrams for students studying KS3 Maths. It covers the current KS3 programme of study and is aimed at students working at levels 5-8. The whole thing’s designed to make revision straightforward – each section is split into a topic per page, with lots of handy questions to check what you’ve learnt as you go along. It’s all explained simply and thoroughly and there’s the odd joke thrown in to help break up the revision.”

“This book is full of clear revision notes, detailed diagrams and practice questions for KS3 Maths. It covers the current KS3 programme of study and it’s packed with useful tips for doing well in your exams. There are also lots of exam-style questions and a complete set of practice papers (answers are at the back). It’s easy to read and revise from – everything’s explained simply, in CGP’s chatty, straightforward style.”

“This book is full of test-style practice questions for students studying KS3 Maths. It covers all the topics from the National Curriculum and is aimed at levels 5-8. The questions are written in a clear, straightforward style to test what you know and how well you can apply your knowledge. The answers are in the back of the book so you can easily check your work and find out where you’re going wrong. Matching study notes and explanations are also available in the CGP Revision Guide (9781841460307).”

*4) GCSE Maths: Higher: Revision Guide + Exam Practice Workbook – Collins Revision (Paperback)* – Can be purchased here at the cheapest price Collins Revision – GCSE Maths: Higher: Revision Guide + Exam Practice Workbook

“Collins Revision GCSE Maths is an all-in-one revision guide and exam practice workbook for Key Stage 4. Written by experienced test markers, it shows how each student can follow their level, test their knowledge, check their answers and improve. This all-in-one revision guide and workbook for GCSE Maths revision offers: / Complete coverage for the GCSE Maths Edexcel A, AQA A and AQA B Higher exams. / Accessible graded content with lots of tried and trusted Maths questions, useful graphs and illustrations. / Detachable workbook answers for flexible practice. Follow your grade, test your knowledge and improve your results at Key Stage 4.”

“This updated and refreshed version of CGP’s bestselling Revision Guide is the ideal companion to Higher Level GCSE Maths – it even includes a free online edition that can be used wherever you have internet access. Every topic is explained in a concise, friendly style, with a sprinkling of CGP humour to keep things interesting. Grade information is included to show the difficulty level of each topic, and there are summary questions at the bottom of each page to test you on the important skills. And finally, a unique code is printed in the book that gives you access to the free online digital version (which also includes fully worked answers to all the test questions in the book).”

Comments are FREE, so please leave one below. If there are any Mathematics revision books or guides that you wish to add to this list please let us know.

This is an amazing video showing a new fluid simulation technique, using Position Based Dynamics approach. The water looks so real, so it is hard to believe that this is just a digital simulation of water.

This would make a great starter to a ICT lesson on animation or a science lesson on water.

We are 2 musical teachers who have developed a free Primary and SEN maths music resource (www.adamup.co.uk ). Songs are centred around an alien called Adam Up who uses a magic calculator to solve various mathematical problems. Bearded ‘Number Crunchers’ pop out of the calculator and sing tricks and concepts using memorable, thematic, simple and catchy songs. We are still in the editing process but have lots of songs available in video/audio form. To be honest, we are looking for global domination and therefore trying to build up as many users/followers as we can before the final product comes out.

Please take a look and befriend us at:

Website- www.adamup.co.uk Twitter – #adamup_maths

Youtube – search for ‘Samuel Kordan’

Please spread the word and get in touch to discuss ‘what went well’ and ‘even better ifs’. N.B- Please visit the PC version of the website as opposed to the mobile version. The mobile version is very basic and does not have all the songs and graphics that the PC version has.

When I was in the classroom, I used to tell students that if two students had exactly the same answers to a GCSE paper, some right, some wrong, then the one who showed their working out would get the better marks.

I used to ban correction fluid, not because they would sniff it, but because the working out and mistakes were important to me as a teacher trying to help them understand some aspect of mathematics.

So I have always been wary of online offerings that rely on multiple choice, on simple correct/incorrect analyses and on inputting the correct answer only. Offerings that completely miss the working out, the different ways students reach an answer, the reasoning as to WHY they reached an answer.

Providing good learning analytics is hard work. So generally, we only do easy learning analytics. “Student x took 10 minutes and scored 65% on subject test y”. “Student y moved to level 3 after 10 questions”

*“Getting learning analytics wrong on the learning dimension is a recipe for disaster, (it) must be done carefully and with understanding. Without a semantic ability to understand what is happening, we won’t even know if we’re doing harm to our students by using algorithms to optimise for things we don’t understand”.*

But how can we do things differently and what should, could, we do to get this understanding?

And to avoid doing harm to our students?

Michael Feldstein in his ‘Taxonomy of Adaptive Analytics Strategies’ draws on the work of Kurt Vanlehn’s best practices in learning design of describing outer loop and inner loop learning.

- Outer loop learning is that indicated above. Did the learner get the correct answer?
- Inner loop learning examines the steps a learner is taking to solve a problem and at appropriate moments, intervenes to provide feedback directly relevant to some mistake the learner is making.

So to create an online offering where inner loop learning takes place, and in which all that learning is fed back to the teacher… that sounds good to me.

Students get hints when they need help, and be able to progress. They have to show their working out, and indicate their reasoning when solving a problem.

Teachers will be able to see all that feedback and all the working out for every student in the class.

They will be able to analyse by student – where did a student need help, even if the question was eventually right. Or analyse by question – which questions did more of the class have a problem with? What *part* of what question did they have a problem with?

All with the aim of aiding teachers to help students, and to help students understand more.

Now as noted above, this has not been possible in the past, but a company in Australia, Mathspace, is about to launch in the UK. In our opinion, it does Inner Loop learning and provides help to the students and details to the teacher, in real time, that have never before been possible.

Take a look at www.mathspace.com.au for a sample,

download the free ipad app (android and Windows 8 coming soon) to use the incredible ‘myscript’ handwriting capability,

get in contact with by email – tstirrup at mathspace.com.au – if you would like a classroom trial

and keep in touch by following us on twitter.com/mathspaceuk.

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10 Direct Proportion 1.If A is directly proportional to B, write an equation in the form A=kB linking the two variables if when A= 8 B= 4. 2.All of the variables below are directly proportional, write an equation linking them: 1.V= 12 when M =4 2.T= 5 when S=1 3.Y= 34 when x=2 4.H=48 when M=4 5.P= 5 when N=10 3.B is directly proportional to C, when B is 18 C is Write an equation linking B and C 2.Find B when C= 66 3.Find C when B = 30 4.Z is directly proportional to Y, when Z =55, Y=5 1.Write an equation linking Z and Y 2.Find Y when Z = 77 3.Find Z when Y=0.1 5.N is directly proportional to L, when N=1.8 L =0.6 1.Write an equation linking N and L 2.Find L when N= Find N when L=0.5

11 Bidmas A) 1.(3 + 3 ) x x 2 – 5 3.(5 + 7) ÷ x (9 – 4 ) – x (15 – 2) 8.(5 x 4 ) (8 + 2 ) ÷ (21 x 1 ) – 2 B) 1.(1 + 14) – (5 x 3 ) 2.( ) ÷ (4 x 2) 3.(1 + 2 ) x (6 – 3) 4.(2 x 6 ) – (14 ÷ 2) 5.(7 x 2) ÷ ( 20 – 6) 6.(3 x 10) – (2 x 2) 7.(9 x 5) – ( 2 x 10) C) 1.(3 x 3 – 4 ) x (2 + 2) 2.2 x (13 – 4) – (23 ÷ 23) 3.3 x (1 + 4) – (5 x 2) 4.4 x (3 + 2) – ( 24 – 5) 5.7 x ( 4 ÷ 2 ) ÷ ( 3 x 5 -1 ) 6.((9 + 7 x 3 ) ÷ 10) – 1

12 Factors and HCF 1)Find all the factors of the following numbers: 1)20 2)24 3)27 4)32 5)40 6)50 7)56 8)120 9)200 2)2 only has 2 factors (1 and 2), how many numbers can you find between 1 and 30 which have exactly 2 factors? (these are called prime numbers) 3)Find the highest common factors of the following pairs of numbers: 1)18 and 54 2)25 and 45 3)12 and 18 4)27 and 108 5)30 and 75 4)Find the HCF of these pairs of numbers: 1)90 and 450 2)96 and 480 3)39 and 195

13 Factor Trees 1.Draw factor trees for the following numbers: a)20 b)24 c)48 d)90 e)81 f)50 g)75 h)120 i)200 j) Using your factor trees from question 1, write the numbers as products of their prime factors.

15 Directed Numbers 2 1)I am £ 250 into my overdraft ( ) but then I get paid £ 535, how much will I have in my bank account? 2)The temperature at the North Pole is -17°C; luckily the temperature in my living room is 40°C warmer than that, what is the temperature in my living room? 3)I have £ 32 and each month for 4 months I have to pay £ 15 to my mobile phone, if I don ’ t put any money into my account, how far will I be into my overdraft? 4)I jump out of a plane 125m above the ocean, I travelled 191m before I stop, how far am I from the surface of the water? 5)I am playing air hockey with my friend, because I am amazing I agree start on -9 points, we play first to 14, how many points do I need to score?

17 Ratio 1.There are 10 girls and 15 boys in a class, what is the ratio of girls to boys in its simplest form? 2.There are 14 cats and 16 dogs in an animal shelter, what is the ratio of cats to dogs in its simplest form? 3.There 22 caramels and 55 fudges in a bag of sweets, what is the ratio of caramels to fudges in its simplest form? 4.Simplify these ratio to their simplest forms: a)48:60 b)45:75 c)63:108 d)25:40:80 e)24:56:96 f)120:180:600 g)320:400:440 5.Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do they each get if they have: a.10 toysb.30 toysc.45 toys 6.Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share: a.20 sweetsb.30 sweetsc.55 sweets 7.Sue and Linda share some money in the ratio 3:7, how many do they each get if they share: a.£30b.£60c.£90 8.Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do they each get if they share: a.60 piecesb.72 piecesc.300 pieces

18 Finding Percentages 1)Some percentages I can find easily by doing a single sum, what single sums can I do to find: a.10%b. 50% c.25% 2)If I know 10% how can I find: a.5%b. 1% c. 20 %d. 90% 3)If I know 50% how can I find: a.5% b. 25% 4)Find: a.30% of 250b. 40% of 500 c. 15% of 220 d. 75% of 84 5)Find: a.35% of 440b. 65% of 450 c. 16% of 220 d. 82% of 96 6)Find: a.94% of 640b. 8% of 520 c. 27% of 220 d. 53% of 96 7)Compare you methods for the questions above with a partner, where they the same.

20 HCF and LCM Find the Highest Common Factor of these numbers: 18 and and and and and and and and 57 Find the Lowest Common Multiple of these numbers 6 and 7 4 and 6 5 and 8 10 and 4 16 and 5 14 and and and 7

21 Indirect Proportion 1.If A is indirectly proportional to B and when A= 5 B= 6. 1.Find k 2.Write an equation linking A and B 3.Find A when: 1.B=3 2.B=15 4.Find B when: 1.A=1 2.A=-3 2.If A is indirectly proportional to B and when A= 7 B= 12. 1.Find k 2.Write an equation linking A and B 3.Find A when: 1.B=4 2.B=6 4.Find B when: 1.A=10 2.A=2 3.If A is indirectly proportional to B and when A= -4 B= 10. 1.Find k 2.Write an equation linking A and B 3.Find A when: 1.B=-8 2.B=10 4.Find B when: 1.A=-1 2.A= If A is indirectly proportional to B and when A= 24 B= 0.5. 1.Find k 2.Write an equation linking A and B 3.Find A when: a.B=6 b.B= -3 4.Find B when: a.A= -2 b.A= 100

23 Limits 1)These numbers have been rounded to the nearest 10, write down the largest and smallest values they could be: 1)50 2)80 3)110 2)These numbers have been rounded to the nearest whole number, write down the upper and lower limits: 1)3 2)17 3)23 4)100 5)-3 3)These lengths have been rounded to the nearest 10 th of a cm, write the upper and lower limits: 1)12.5cm 2)21.7cm 3)35.8cm 4)52.1cm 5)80.4cm 4) A field is 100m wide and 120m long, both lengths have been rounded to the nearest metre. a) Find the perimeter and area of the field if these measurements are accurate b) Find the largest and smallest possible perimeter c) Find the largest and smallest possible area. 5) A rectangle has it’s area rounded to the nearest whole number, it becomes 40cm 2. One side of the rectangle is exactly 10cm; find the maximum and minimum lengths the other length could have. 6) Two lengths of wood are stuck together and their combined length is rounded to the nearest mm and it is 14.9cm, one length is rounded to the nearest mm and is 7.1cm. Find the minimum and maximum length of the other length.

24 Multiples A. List the first 5 multiples of: B. What is the: 1.9 th multiple of th multiple of th multiple of th multiple of th multiple of th multiple of 13 C. List 3 numbers which are in: 1.3 and 4 times tables 2.3 and 5 times tables 3.10 and 4 times tables 4.9 and 2 times tables 5.12 and 10 times tables D. What is the lowest common multiple of: 1.5 and and and and and 6 E. What is the lowest common multiple of: 1.13 and and and and and 70

26 Multiplying and dividing decimals 1a)0.8x7= b)0.5x7= c)0.1x6= d)0.6x4= e)0.3x3= 2a)0.2x0.5= b)0.4x0.7= c)0.8x0.1= d)0.9x = e)0.6x0.1= 3a)1.9x0.3= b)1.6x0.5= c)1.6x0.5= d)1.7x0.2= e)1.3x0.7= 4a)5.4x0.11= b)5.2x0.97= c)8.3x0.73= d)4.6x0.11= e)8.2x0.75= Multiplying Dividing 1 a)3.2 ÷ 4 b)4.8 ÷ 8 c)7.2 ÷ 9 d)2.4 ÷ 6 e)1.8 ÷ 3 2 a)5.6 ÷ 0.7 b)6.3 ÷ 0.7 c)2.7 ÷ 0.3 d)4.9 ÷ 0.7 e)2.8 ÷ 0.7 f)1.65 ÷ 0.15 g) ÷ 0.12 h)27.3 ÷ 1.3 i)0.03 ÷ j)0.99 ÷

28 Ordering Decimals 1.For each pair of numbers say which is bigger by adding > or or

29 Percentage Increase 1.Explain how you would use a calculator to increase an amount by a given percent. 2.Increase the following amounts by 42% a)£225 b)£306 c)£125 d)£448 e)£512 3.A TV costs £120, how much will it cost if its price is increased by: a)12% b)31% c)55% d)62.5% e)99.9% 4.Simon puts £70 in a bank, each year the money in his bank increase by 5.5%, how much does he have in: a)1 year b)2 years c)5 years? a)Explain how you would use a calculator to decrease an amount by a given percent. b)Decrease the following amounts by 28% a)£225 b)£306 c)£125 d)£448 e)£512 c)A TV costs £120, how much will it cost if its price is decreased by: a)19% b)32% c)79% d)73.5% e)42% d)A car bought for £6, 500 depreciates in value by 12.5% each year, how much will it be worth after: a)1 year b)2 years c)5 years?

31 Rounding to Decimal Places a) b) c) d) e) f) g) h) i) j) Work out the following on a calculator and give the answer to 2 decimal places; a)3.104 x b)2.99 x 8.82 c)7.1537÷ d) Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places

32 Reverse Percentages 1.What would you multiply an amount by to increase it by: a)15% b)25% c)4% d)0.5% e)13.5% 2.Find the original prices of these prices that have been increased by the given percentage: a)Cost= £49.5 after 10% increase b)Cost= £74.75 after 15% increase c)Cost= £61 after 22% increase d)Cost= £104 after 30% increase e)Cost= £120 after 50% increase 3.I have £252 in my bank account; this is due to me earning 5% interest on what I originally had put in. How much money did I have originally in my bank account? 4. What would you multiply an amount by to decrease it by: a)15% b)25% c)4% d)0.5% e)13.5% 5. Find the original prices of these items that have been decreased by the given percentage: a)Cost= £72 after 10% decrease b)Cost= £93.5 after 15% decrease c)Cost= £42.5 after 35% decrease d)Cost= £4 after 40% decrease e)Cost= £67.50 after 55% decrease 6. A Cars value has dropped by 11.5% it is now worth £. what was it worth when it was new?

35 Two sided linear equations 1.Solve these equations: a)85-3x = 49 b)45 + 2x = 79 c)52 – 8x= 20 d)101 – 9x = 29 e)71 – 11x = 38 2.Find x a)2x + 4 = 3x + 1 b)10x + 8 = 4x + 38 c)7x – 3 = 3x +25 d)11x + 5= 9x + 21 e)4 + 11x = x Solve these equations by multiplying out brackets and simplifying: a)3(x +2) + 5(x-1)= 25 b)2(2x + 1) + 6(x + 3)= 70 c)4(3x + 3) – (x + 5)= Solve these equations a)2(3x+4)= 2(4x-1) b)2(3x-4)= 4(x + 3) c)4(3x + 2) = 8(2x -1)

37 Brackets 1.Remove the brackets from these expression by multiply them out: a)2(x +5) b)6(2x +7) c)8(4x -2) d)5(3x -9) e)2(4 -2x) f)8(3 – 4x) g)x(x + 3) h)x(2x +9) i)x(4x -7) j)2x(9 -5x) 2.Multiply out the brackets: a) x(3x 2 + 5) b)2x(5x 2 + 6) c)5x(3x 3 - 7) 3.Multiply out the brackets and simplify: a)3(x + 4) + 4(x-6) b)7(x + 7) + 5(2x-8) c)3(4x + 1) + 2(6x-9) d)5(5x - 4) - 4(3x-6) e)2(13 -x4) - 9(x+ 6)

38 Collecting like terms 1.Simplify a)10a + 4a b)2b + 7b c)3a + a + 4a d)11b – 4b e)14b – 5b + 4b f)3a – 6a + a 2.Simplify a)10a + 4b –a +5b b)8a + 5a +5b – 3b c)12b – 7a + 3b +a d)2b – 8b –a + 9a e)-13b + 4a -5b -4a f)11a + 8b + 2c + 6a + 3b -2c g)6b + 4b –a +6c + 5a – 4c h)7c + 4b- 3b + a + 10c – 5a i)10a + 4b + 7a + 10b – 17a – 14b j)5b + 4c + 18c – 22a + z

40 Factorising A) Factorise the following completely: 1.10A A A B B 5.14B B 6.9B B 7.33B B 8.2C 3 + 8C 9.5C C 10.10C 3 + 8C B) Factorise the following completely: 1.9AB + 6A 2.16AB – 4B 3.30A 2 B + 24AB 4.10AB 2 – 15B ABC + 20 AB 6.28A 2 BC + 14ABC 7.4AB – 8A + 16B 8.15A – 18B – 21AB 9.9B BC + 30AB 10.ABC-10AB +AB

41 Finding the gradient 1) Find the gradient between the points: a)(3,5) and (4,7) b)(5,9) and (7,17) c)(4,6) and (5,7) d)(1,4) and (4,19) e)(0,11) and (4,23) 2) Find the gradient between these points: a)(2,5) and (3,-3) b)(2,8) and (3,2) c)(4,8) and (4,8) d)(8,15) and (6,33) e)(7,12) and (4,42) f)(4,8) and (3,14) a)Find the gradient between these points: a)(3,5) and (4,5.5) b)(5,9) and (7,8) c)(4,6) and (5,6.75) d)(1,4) and (4,4.75 e)(0,11) and (4,11.4)

42 Formulae A) Isaac Newton’s second law of motion states F=ma (force= mass x acceleration) 1.Find F if: a.M=10 and a=5 b.M=12 and a=12 c.M=0.5 and a=11 2.Find a if: a.F=100 and M=20 3.Find m if: a.F=36 and a=12 B) Density equal mass divided by volume 1.Write a formula for density a.Find D if i.M=10 and v= 40 ii.M=12 and v=72 iii.M=5 and v=90 b.Find M if: i.D=4 and v=52 c.Find v if: i.D=8 and m=11 C) Electrical power (p) is equal to voltage (V) squared divided by resistance (r) 1.Write a formula for power 2.Find p if: a.V= 4 and r=8 b.V=9 and r=3 3.Find r if: a.P=16 and v=8 4.Find v if: a.P=20 and r=5

44 Laws of indices 1.Simplify: a)A 2 x A b)A 4 x A 2 c)A 8 x A 2 d)3A 9 x A 3 e)4A 2 x 5A 1 2.Simplify: a)A 10 ÷ A b)A 21 ÷ A 7 c)A 20 ÷ A 4 d)9A 12 ÷ 3A 6 e)12A 6 ÷ 4A 4 3.Simplify: a)(A 2 ) 4 b)(A 3 ) 3 c)(A 2 ) 6 d)(2A 9 ) 2 e)(3A 4 ) 3 1.Simplify. a)A 0 b)B 0 c)99 0 d)52 0 e) Simplify: a)A -4 b)A -6 c)A -2 d)2A -4 e)9A -3 3.Simplify fully: a)25A 4 ÷ 5A 7 b)3A 9 x 2A -3 c)(A 2 ) 6 x (2A 2 ) 2 d)(2A 3 ) 8 ÷ (2A 4 ) 6 e)(A 2 ) -6

47 The quadratic equation 1.For each of these equations, what is a, b and c? (the first one has been done for you) a)2x 2 +4x -3 =0a=2b=4c=-3 b)6x 2 +x - 10=0 c)x 2 -4x -5=0 d)2x 2 -10x + 7=0 e)0.5x 2 +8x + 2=0 2.Use your answers from question one to find the possible values for x. 3.Rearrange these equations to the form ax 2 + bx + c =0, then solve with the quadratic equation: a)2x 2 + 9x -2 =10 b)4x + 5x =2 c)x 2 + 5x -3=x d)2x 2 -10x - 2= x 2 e)3x x =8 + 7x

48 Factorising Quadratics 1.Factorise and solve: a)X 2 + 8X + 12= 0 b)X 2 + 7X + 10= 0 c)X X + 12= 0 d)X X + 70=0 e)X 2 + X – 20=0 f)X 2 - 4X- 12=0 g)X X + 20=0 2.Rearrange, factorise and solve a)X X + 32=12 b)X 2 + 8X -5 = 20 c)X 2 + 6X + 23 = 5 – 3X 3.Solve a)3X X + 51=15 b)2X =-6 c)4X 2 -8X -4= x

49 Sequences 1.Copy down the following sequences and add the next three terms: a) b) c) d) e) For each of the questions in question what is rule to find the next term in the sequence. (This is called the term to term rule) 3.Copy the following sequences, write the term to term rule and find the next 3 terms. a) b) c) d) e) Copy the following sequences, write the term to term rule and find the next 3 terms. a) b) c) d) Copy the following sequences, write the term to term rule and find the next 3 terms. a) b) c)

50 The Nth term 1) Find the nth term of the following sequences: a) b) c) d) e) ) Take the following nth terms and find the first 5 terms a)3n + 1 b)4n +2 c)5n + 5 d)4n – 1 e)6n + 3 f)10n -3 3) If the nth term is 7n + 4 what is a.The 4 th termb. The 12 th termc. The 100 th term 4) If the nth term is 8n - 2 what is a.The 4 th termb. The 12 th termc. The 100 th term 5) If the nth term is 11n + 3 what is a.The 4 th termb. The 12 th termc. The 100 th term 6) If the nth term is n + 9 what is a.The 4 th termb. The 12 th termc. The 100 th term

52 Simultaneous Equations 1.Find a and b for each pair of simultaneous equations: a)5a + 2b= 14 6a + 2b= 16 b)7a + 3b= 27 6a + 3b= 24 c)10a - 2b= 30 3a - 2b= 2 d)9a - 6b= 42 6a - 6b= 18 2.Find a and b for each pair of simultaneous equations: a)4a + 7b= 27 4a - 7b= 13 b)3a + 2b= 35 2a - 2b= 10 c)11a - 8b= 4 a + 8b= 44 d)5a + 3b= 69 7a - 3b= 75 3.Find a and b for each pair of simultaneous equations: a)5a + 6b= 28 6a + 2b= 18 b)4a + 4b= 36 6a - 2b= 22 c)2a - 8b= 143a + 2b= 41 d)9a + 6b= 84 3a - 3b= 25.5

54 Solving Equations 1.Find x if: a)7x= 42 b)12x=36 c)5x = 40 d)10x = 110 e)How did you answer these questions? 2.Find x if: a)X + 10 = 17 b)X + 15 = 27 c)X + 25 = 30 d)X- 9 = 15 e)X – 13 = 40 f)How did you answer these questions? 3.Find x if a)3x + 6 =21 b)7x + 11 = 67 c)5x + 4 = 24 d)9x – 2 =25 e)11x – 14= 30 f)10x - 7= 53 g)12x + 11= 155 h)15x - 14= 61 i)13x + 25 = 90 j)How did you answer these questions?

55 Substituting 1.If A is 5 what is: a)5A b)11A c)6A – 10 d)9A + 15 e)100-5A 2.If B is 7 what is a)2(B+8) b)3(B-5) c)B(B+5) d)9(10-B) e)(3+B)X(B-5) 3.If A= 6 and B=7 what is: a)A+B b)B-A c)6A+2B d)AB e)A(B+1) f)A 2 B

56 1.Use trial and improvement to find the positive solution to these quadratic equations to 1 dp, you may like to use a table, the table for the first question has been drawn for you. a)X 2 + 3x -30=0 b)X 2 + 3x -30=0 c)X 2 + 2x -20=0 d)X 2 + 4x -10=0 e)X 2 -2x -5=0 2.Use trial and improvement to find the positive solution to these quadratic equations to 2dp a)3X 2 - 5x -10=0 b)2X 2 + 2x -25=0 3.Use trial and improvement to find the positive solution to these quadratic equations to 3dp a)X 2 + x -6=0 b)3X 2 - 2x -11=0 Trial and Improvement xX2X2 +3x-30Big or small?

57 Writing Expressions 1.My age is C, write expressions for the ages of the members of my family if: a)My brother is 3 years older than me b)My sister is 2 years younger than me c)My mum is double my age d)My dad is 5 years older than my mum e)My Gran is 4 times my age f)My Grand Dad is twice my Dads age 2.If I have S sweets, write an expression for the number of sweets my friends have if I: a)I give Tom all my sweets and he has 5 of his own b)I give Alan half of my sweets c)I eat four sweets then give Simon the rest d)I give Lucy a quarter of my sweets, then an extra 1 3.My favourite song last M minutes, how long do I spend listening to music if: a)I listen to the song once and hour all day (and including when I’m asleep) b)I listen to half the song 8 times c)I listen to the intro (a quarter of the song) 5 times d)I listen to my song, then the next one which is exactly twice as long e)I listen to my song, then the next one which is exactly twice as long, and do this 5 times throughout the day 4.If a rectangle has lengths x and y, write an expression for: a)The area of the rectangle b)The area covered by 6 rectangles c)The perimeter of the rectangle

58 Y=mx +c 1. Copy and complete: a)A line with a positive gradient will go from ________ left to ________right b)A line with a negative gradient will go from ________ left to ________right 2.Look at the equations below, write down the gradient and the coordinates of the line they represent. a)Y=3x+4 b)Y= 2x-5 c)Y=6x+9 d)Y=x- 7 e)Y=10x f)Y=5+8x g)Y=7-11x 3.Draw an axis from -10 to 10, plot the following lines a)Y = 2x + 3 b)Y = 3x – 2 c)Y = -2x + 5 d)Y = -3x Find the gradient of the line between these pairs of coordinates by dividing the change in y by the change in x. a)(3,3) (5,5) b)(5,5)(6,7) c)(1,2)(3,8) d)(10,9)(6,1) e)(15,20) (10,5) 5.Using the gradient worked out in the last question and one of the coordinates, find the value of c for the line between the pairs of points in question 4. 6.Write out the equation of the line between the pairs of points in question 4 in the form y=mx+c

60 Area of Triangles 1. Find the area of the triangles on the left 2. Find the missing lengths of the triangles on the right