Paper 1
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
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.
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
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
If you are doing the HIGHER level exam, the
key additional topics for you to learn are:
1. Trigonometry
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.
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-and-
leaf 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?
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?
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…
Increase/decrease ratio
Denominator frequency
outcome relative frequency
inequality nth term rule
bearing external/internal angle
tessellate substitute
perimeter radius/diameter
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
Calculating with Fractions
Finding the mean from a table
The table shows the height of 100 five-year-old boys.
Calculate an estimate of the mean height of these boys.
8
3
5
2
3
2
4
3
8
31
58
3
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
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!
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
Drawing Straight line Graphs
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)
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
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.
Finding and Explaining angles in parallel lines
Find a and b and give reasons for your answers
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.
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
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
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
Calculate the surface area
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
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
Work out the area of each of the faces
separately, then add all of these together.
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!
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:
___________________________________________
___________________________________________
___________________________________________
- 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]