Edexcel Maths GCSE Revision Support Booklet

GCSE Maths Exam Dates 2015 Paper 1 Thursday 4th June am Paper 2 (calculator) Monday 8th June am

Dear Parents, Guardians and GCSE students

Often, students just don’t know how and what to revise – and they never get properly started. We hope this booklet will help you to help your child make sense of the revision process, and to achieve their C grade in Maths GCSE this summer. From years of experience we have found that students who regularly talk about their work at home are more likely to succeed when it comes to exams. This booklet aims to give you some starting points for revision in the summer. Questions you could discuss over dinner or in the car, a list of the most challenging topics (they may not ‘crack’ all of them but should know the majority), and a list of keywords. By talking through these pages, confidence will grow and grades will improve. It does not matter if the parent/guardian is confident with the maths or not, your student will teach you! Success in maths will change your child’s life. Their future plans, and the future that they haven’t yet planned for, could depend upon it. We would like to work together with you to help support you in providing you with the best possible future opportunities. Please stay in touch with your Maths teacher and keep talking Maths at home!

The Stonehenge Maths Team

Working together… 20 Key C Grade areas. Please discuss these areas, rate them then use revision materials to help revise them. Rate again at the end- which can you REALLY do? 1.

Sharing out an amount in a given ratio

2.

Rounding numbers to one or two decimal places, or to one significant figure.

3.

Add/subtract and multiply/divide fractions

4.

Estimate the mean from a grouped frequency table

5.

Compare two sets of data – using an average and the range

6.

Expectation in probability/Relative frequency

7.

Converting between fractions, decimals and percentages.

8.

Prime factorisation

9.

Factorising a single bracket

10.

Substituting numbers (especially negatives) into an algebraic expression

11.

Solving an equation, especially with the unknown on both sides

12.

Sequences, and the nth term

13.

Drawing and recognising straight line graphs

14.

Working out one number as a percentage of another

15.

Finding the area and circumference of a circle

16.

Finding and explaining missing angles on parallel lines

17.

Gaining full marks on a ‘trial and improvement’ question

18.

Describing a rotation, reflection or translation

19.

Using Pythagoras’ Theorem

20.

Finding the surface area of prisms

If you are doing the HIGHER level exam, the key additional topics for you to learn are: 1. Trigonometry 2. Probability tree diagrams 3. Quadratic Equations 4. Simultaneous Equations 5. Cumulative Frequency 6. Reverse Percentages 7. Circle Theorems 8. Compound Interest

If you can really do all of the above; not just recognise the words, but actually do questions on them, then you will get a C grade.

Good luck!

Working together… Questions to ask your child, if they cannot answer then this is something they need to revise: Number Questions Can you explain to me how to add two fractions with different denominators? Can you tell me the decimal equivalent of 1/4? 1/5? 3/20? What is 4.28 to one decimal place? How would you share £65 in the ratio 3:2? Can you round 57,346 to one significant figure? Can you explain to me the difference between a factor and a multiple? What is negative 4 add negative 7? What are the rules about multiplying and dividing with powers? How do you split a number up into it’s prime factors? What is an improper fraction? What is 16 as a percentage of 20? How do you increase £40 by 15%, without a calculator? How do you add 3.5 and 4.06? Estimate the product of 4.79 and 13.22 What is the answer to 0.3 x 0.2? Data Questions What does frequency mean?

The mode of some numbers is 5. What does this mean? Explain how to find the median of this list of numbers; 8, 8, 2, 4, 5, 3 What is the difference between continuous and discrete data? What is a data collection sheet? How do you start to draw a pie chart? What do you always need to remember when you draw a stem-andleaf diagram? What is the probability of rolling a 5 on an ordinary dice? If the probability that it rains today is 0.4, what is the probability that it doesn’t rain? Algebra Questions How would you expand 5(y – 2)? What is the value of 3f + 2t, if f = 4 and t = -5? What is factorising? Solve 6k – 4 = 26

Solve 4x + 3 = 2

How do you solve an equation when the unknown is on both sides? What is the 7th term of the sequence 5n + 2? What is the nth term rule for the sequence 7, 13, 19...? What can you tell me about the line y = 3x -4? It’s gradient? Trial and Improvement questions always ask for the answer to 1 decimal place. What does this mean? How do you get full marks? What does the graph of x = 2 look like? What about y = -4? y = x?

What shape will the graph of x2 + 3x – 2 be? Shape Questions What does ‘order of rotational symmetry’ mean? Which formula do you need for the circumference of a circle? Area? Explain Pythagoras’ Theorem, what are the two types of question? How many miles is equivalent to 15km? How do you work out the bearing of town A from town B? What equipment do you need for constructions and loci questions? Why do you need a pair of compasses? What is the difference between perimeter and area? An answer for a volume question is “32cm2”. How do you know this is wrong? What’s so special about a ‘regular’ polygon? Explain how to find the area of a triangle. What are Alternate angles? Corresponding? Allied? Draw a rough sketch to show these types of angles. The diameter of a circle is 5cm. How do you find it’s area? How do you find the area of a semi-circle? What does a question mean when it asks for the midpoint on a line? What does ‘translate’ mean? Is there a special way of writing it?

How did you do? Can you answer these questions? What do you need to revise NOW??

Working together… Some technical words to learn and understand: Increase/decrease

ratio

Denominator

frequency

correlation

grouped frequency table

compare

criticise

mean; median; mode; range

event

outcome

relative frequency

sample space diagram

integer

expand

factorise

sum

product

multiple

factor

one significant figure

congruent

highest common factor

least common multiple

inequality

nth term rule

gradient

parallel

quadrilateral – all of them

regular

bearing

external/internal angle

circumference and π

prism

order of rotational symmetry

hypotenuse

tessellate

substitute

perimeter

radius/diameter

trial and improvement

simplify

midpoint

Working together…

Some Key C Grade GCSE Questions- with answers and learning points  Sharing in a Ratio An alloy is made from tin and copper. The ratio of the weight of tin to the weight of copper is 1 : 4 Sally made 35 grams of the alloy.

Work out the weight of copper she used

Add up the parts in the ratio (1+4 = 5). Then divide the total by this amount- this gives you the value for one ‘part’ (35 ÷5 = 7). Sally has used 4 parts of copper, so 4x7 = 28g copper

 Calculating with Fractions (a) Work out

2

2 3  5 8

3

(b) Work out 5 3 – 2 4

For adding and subtracting, start by changing the fractions so they have a common denominator (for a this is 40, for b this is 12). Work out the new numerators, then add/subtract these. For mixed numbers, turn them into improper fractions first. The answers are a) 31/40

b) 2 11/12

If the question was a multiply, just times the fractions across. For a divide; Keep, Change, Flip!

 Finding the mean from a table The table shows the height of 100 five-year-old boys. Height, h (cm) Frequency

Calculate an estimate of the mean height of these boys.

8 31 58 3

Find the mid-point of each grouped category (85, 95, 105, 115) and multiply by the frequency for each. Take the total of these values (10,060) and divide it by the total frequency (100). The answer to this question is 100.6cm

 Factorising

Look for what goes into both parts of the expression and place this on the outside of the brackets. To work out what goes inside, see what you have to multiply this by for each part. Answer to a is 5(m + 2) and b is x(x – 5)

 Solving Equations

Start by removing the smaller amount of the letter (2x) by subtracting this from both sides. This leaves 2x + 1 = 12. Next remove the ‘+1’ by subtracting this from both sides, giving 2x = 11. Finally divide by 2 so x = 5.5

 Drawing Straight line Graphs Draw out a table of values X 0 1 2 3 Work out what the y values will y be by taking each number and substituting it into the equation (take each value, times it by 2 then subtract 1). This gives you the coordinates to plot on your graph. Join these up and extend the line the whole size of the graph. The coordinates for this graph are (0, -1), (1,1), (2,3), (3, 5)

Finding Area and Circumference of a Circle The top of a table is a circle. The radius of the top of the table is 50 cm. (a)

Work out the area of the top of the table.

The base of the table is a circle. The diameter of the base of the table is 40 cm. (b)

Work out the circumference of the base of the table.

Students MUST learn the two formulae for circles (they may use ‘the circle song’ on youtube to help them!) Area = πr² and Circumference = πd. Using these, the area for this table is π x 50² = 7854cm² and the circumference is π x 40 = 126cm

 Finding and Explaining angles in parallel lines Find a and b and give reasons for your answers Students need to know what CORRESPONDING (F), ALTERNATE (Z) and ALLIED (C) angles are, as these will be their reasons. For this question a = 73 as it is corresponding (it makes an F shape) and b is 107 as angles on a straight line add up to 180

 Trial and Improvement The equation

x3 – x = 30 has a solution between 3 and 4

Use a trial and improvement method to find this solution. Give your answer correct to 1. decimal place. You must show all your working. This question is always worth 4 marks. Student should set up a table with three columns headed guess, answer, comment. They then need to try values between 3 and 4 (eg3.5, 3.3 etc). They substitute this value in, work out the answer and comment whether it is too big or too small for what they want (ie in this case is the answer bigger or smaller than 30)- this gains them one mark. Once they find to values next to each other, one which is too big and one which is too small they get their second mark. At this point, they much go half way for their third mark. If this is too big, they take the smaller value and vise versa if too small.

 Pythagoras Theorem Diagram NOT accurately drawn

The diagram shows three cities. Norwich is 168 km due East of Leicester. York is 157 km due North of Leicester. Calculate the distance between Norwich and York. Give your answer correct to the nearest km Instead of worrying about a, b and c, students need to simply learn to Square, Add/Subtract, Root. If they want the Biggest side, they add if they want the Smaller side, they subtract So for this question, 157² = 24649 168² = 28224. Add these = 52873. Then square root = 230km Note they will lose a mark if they have not rounded correctly

 Fractions, Decimals and Percentages

 Surface Area of Prisms Students need to remember a flow chart for converting so they know how to turn fraction decimal percent. For this question a) 8/100 = 2/25 b) 7/20 = 35/100 = 35%, c) 128/1000 = 16/125 d) 5 ÷ 8 = 0.625

 Surface Area Work out the area of each of the faces separately, then add all of these together.

Calculate the surface area

So the two triangles have areas 54m², and the three rectangles are 300m², 240m² and 180m². add these up (including two triangles) to get total SA= 828m²

Working together…

SO- What NOW??? - You should be revising for Maths about 3 times a week (at least) You have 17 weeks (from today)- this could make a MASSIVE difference! - Use this guide, your revision guides, mymaths.co.uk, mathswatch.co.uk, your exercise books, exam papers etc all to help you - You need to be doing as many practice questions as you can. My key topics for revision are:

___________________________________________ ___________________________________________ ___________________________________________ Places to go for help… -

Every Tuesday and Thursday lunchtime: KS4 Maths clinic Room 44 Thursday after school Maths revision Maths tutor group/extra Maths lessons ANY Maths Teacher ANY time! Extra revision opportunities later in the year Half term revision sessions (May)

Good Luck with your Maths revision!  Please Stay in touch with your teacher- let us know how you are getting on and ask for help if you need it! Parents/guardians, feel free to email or phone us any time. Your teachers address can be found below.

Mr Cornelius [email protected] Mr Selwood [email protected] Mrs Edmunds [email protected] Mrs Levey

[email protected]

Mr Faulkner

[email protected]

Mrs Richardson [email protected]