Maths GCSE Revision Cards
Target Grade C and Above
Work towards a Grade C or consolidate work for higher target grade candidates
For All UK
Exam Boards
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Collecting Like terms.
Simplify the following expressions
1) a + a + a + a
2) 4a + 3b—2a
3) 4xy + 2y—3xy + y
4) 3a2 + 2b + 3a2—4b
5) x2 + 2xy + 4xy + 3x2
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nth Term
3, 5, 7, 9, 11
Write the next 3 terms
Write the nth term
Find the 50th term of the sequence
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Collecting Like terms.
This is really write what you see. However the letters must be the same.
Do not add a to b or ab to bc.
If a letter is on its own, it has an imaginary 1 in front of it, we can think of y as 1y
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nth Term
Add 2 so the next terms are 13,15,17
If it is add 2 then it is the 2 times tables, so we call it 2n
The 2 times tables are 2,4,6,8,10. If we take the first number (2) and look at + or—to make the first number of the
pattern (3) we can see it is +1. The nth term is 2n+1
To find the 50th number we replace n with 50. Our sum becomes 2x50+1 = 101
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3 5 7 9 11
+2 +2 +2 +2
1) a + a + a + a = 4a
2) 4a + 3b—2a = 2a +3b
3) 4xy + 2y—3xy + y = xy + 3y
4) 3a2 + 2b + 3a2—4b = 6a2 –2b (note:2—4 = -2 so 2b—4b = -4b)
5) x2 + 2xy + 4xy + 3x2 = 4x2 + 6xy
Ratio
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Estimating Answers
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Estimate
Simplify the ratio
21: 35
If £35 is shared between Emilie, David and Kahrn in a ratio of 2:3:5, how
much more does Kahrn get compared to Emilie?
Ratio
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Estimating Answers
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If you see the word ESTIMATE you must do this.
Round each value to one significant figure. (see the significant figure card or revision guide if
you are unsure how to do this)
To calculate the final part there are 2 main methods
1) 0.2 goes into 1 5 times, so multiply the top by 5.
2) Multiply top and bottom by a power of 10 so you can complete a division using whole
numbers
= 135000 (270 000 ÷ 2)
21: 35
3:5
÷7 ÷7 Divide both sides by the highest
common factor (just like simplifying
or cancelling fractions)
1) Add all the parts of the ratio 2+3+5 = 10
2) Divide the quantity by the sum of the parts of the ratio 30 ÷ 10 = 3
3) Multiply each part of the ratio by the answer to step 2.
This should allow you to answer the question Kahrn has £15, Emilie has £6
15 - 6 = 9. Kahrn has £9 more than Emilie
2:3:5 x3
6:9:15
E:D:K
Fraction of a Quantity
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Mixed Numbers and Improper Fractions
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Improper Fraction, Top Heavy Fraction and Vulgar Fraction all mean the same thing.
Fraction of a Quantity
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Mixed Numbers and Improper Fractions
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1) The rule is
Multiply the whole number by the denominator and add the numerator
Leave the fraction over the original denominator
2)
Divide the numerator (top) by the denominator (bottom) and write the remainder.
20 ÷ 5 = 4
4 x 3 = 12
Divide the number by the denominator (bottom of the fraction)
Multiply the answer by the numerator (top of the fraction
Two Way Table from a Worded Question
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Two Way Tables
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Physics Chemistry Biology Total
Boys 20 40
Girls 30
Total 40 30 100
The table shows how many students study Physics, Chemistry and Biology
Complete the table
In a survey of how 80 students travel to school;
30 students were boys
30 students cycled to school of whom 20 were boys
40 students walked to school
5 boys took the bus
How many girls walked to school?
Two Way Table from a Worded Question
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Two Way Tables
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Physics Chemistry Biology Total
Boys 10 10 20 40
Girls 30 20 10 60
Total 40 30 30 100
HINTS
Where the are 4 columns look for a column that has 3 entries. It is then pos-
sible to work out the missing entry
Where there are 3 rows look for a row that has 2 entries. It is then possible
to work out the missing entry.
The easiest way to approach this question is to draw a 2
way table and complete the missing entries.
Cycle Walk Bus Total
Boys 20 5 5 30
Girls 10 35 5 50
Total 30 40 10 80
35 girls walked to school
Enlargement
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Translation
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Translate by Describe the transformation from A to B
Enlarge the shape, scale factor 2
with a centre of enlargement (0,0)
Describe the transformation from shape A to B
Enlargement
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Translation
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Across 3. + is right, - is left
Down 1. + is up, - is down
Translation
The shape moves 4 left and 3 up
The vector is
Draw ‘rays’ from the centre of enlargement through each corner
For scale factor 2 double each distance from the centre of en-
largement to each corner
This can be done by counting squares. 1 across, 1 up becomes 2
across, 2 up.
Draw the new shape
Draw rays through the corresponding corners
Where they cross is the centre of enlargement (-2,-1)
Divide the side lengths of the image (shape B) by the
side length of the object (shape A) This is the scale
factor. For this question 2 ÷ 1 = 2
Linear Graphs
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Trial and Improvement
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2x2 + x = 60
X lies between 5 and 6
By trial and improvement find x
Complete the table and draw the graph
For y = 2x + 2
x -2 -1 0 1 2
y
Draw the graph of y=2x—2
Linear Graphs
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Trial and Improvement
Start between the numbers given.
Use a table as below to show how you get your answer
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x 2x2 + x
5.5 2 x 5.52 + 5.5 = 66 Too big
5.2 2 x 5.22 + 5.2 = 59.28 Too small
5.3 2 x 5.32 + 5.3 = 61.48 Too big
5.25 2 x 5.252 + 5.25 = 60.375 Too big
When you have narrowed the answer
to 0.1 either side (in this example 5.2
and 5.3)
go half way between these numbers
If the final answer is too big go down
If the final answer is too small go up.
In this example 5.25 is too big so we go down to 5.2
The answer to 1 dp is 5.2
For y = 2x + 2
Use the x values in the table
2 x –2 + 2 = -2
2 x –1 + 2 = 0
Plot the points and draw a line through them
Draw the graph of y=2x—2
This is really the same question except you have not
been given a table, so draw a table and complete it!
2 x –2 –2 = -6
2 x –1 –2 = -4
Plot the points and draw though them
x -2 -1 0 1 2
y -2 0 2 4 6
(-2, -2) (-1,0) (0,2) (1,4) (2,6)
x -2 -1 0 1 2
y -6 -4 -2 0 2
(-2, -6) (-1,-4) (0,-2) (1,0) (2,2)
Area 2
Find the area of the following shapes
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Area 1
Find the areas of the following shapes
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10cm
5cm
10cm
5cm
8cm
6 cm
5cm
10 cm
4 cm
Area 2
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Area 1
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8cm
6 cm
5cm
10 cm
4 cm
10cm
5cm
10cm
Area = x base x height
= x 5 x 10 = 25cm2
Area = base x height
Area = 10 x 5 = 50cm2
5 cm
Area = x a x b where a and b are the diagonal lengths
Area = x 8 x 6 = 24cm2
Area =
=
Area = (a+b)h where a and b are the parallel sides
and h is the perpendicular height
Area = (10+4) x 5 = 35cm2
Highest Common Factor
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Product of Prime Numbers
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Express 150 as a product of its prime factors
Find the Highest Common Factor of 150 and 120
Highest Common Factor
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Product of Prime Numbers
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Draw a factor tree. Stop when you get to a prime number on a branch.
Do NOT use 1 as a factor
2
5
3
5
150
50
25
Note: 2 x 25 = 50
Note: 3 x 50 = 150
Note: 5 x 5 = 25
Learn your prime numbers. The first prime numbers are
2, 3, 5, 7, 11, 13, 17, 19, 23 ……………….
150 = 2 x 3 x 5 x 5 = 2 x 3 x 52
Method 1
List all the factors of 120 and 150
120
1, 2, 3, 4, 5, 6, 10, 12, 20, 24, 30, 40, 60, 120
150
1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
30 is the largest number in each list.
30 is the highest common factor
Method 2
2
5
3
5
150
50
25
3
2 5
10
2
2
120
60
30
2 x 3 x 52
23 x 3 x 5
For the highest common factor use the lowest power of
each number from the products of prime factors. If a
number is NOT in both sets, do not USE it.
2 x 3 x 5 = 30 Highest Common Factor is 30
Inequalities
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Stem and Leaf Chart
Complete the stem and leaf chart with the following values
15 25 36 12 17 36 28 36 45 18 23 12 45 30 23
Find the mode
Find the Median
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Key
Write the integer values represented by the inequality
Show the inequality on a number line.
-3 ˂ x ≤ 2
Inequalities
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Stem and Leaf Chart
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There is usually some space used before the stem and leaf chart. This allows you to complete an
unordered chart first. It is always a good idea, as it reduces the chance of missing numbers out.
Key
3 ǀ 6 means 36
Mode = 36 from the chart. The Median is the middle (found by counting in from both ends) = 25
-3 ˂ x ≤ 2
The answer is -2 -1 0 1 2
Integer means whole numbers
˂ > does not have the equals sign so does NOT include that number ≤ ≥ have equals, so include those numbers.
Note the less than and greater
than signs have an open circle
Note the less than or equal to
and greater than or equal to
signs have a filled circle
The key is important. You will get a
mark for completing a correct key.
Long Multiplication with Decimals
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Long Multiplication
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586 x 26 =
5.86 x 2.6 =
Long Multiplication with Decimals
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Long Multiplication
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Make sure you have a good long multiplication method you can use well.
The three most popular methods are shown below.
The first method is what most people try to use, but often get it wrong.
The second method is usually the most successful.
Just read the answer from the outside
586 x 26 = 15236
Note the carries in red.
Try not to add all the numbers together in
one go. Instead add the rows and then add
the 2 answers
5.86 x 2.6 =
Do not try and multiply the decimals
Instead work out 586 x 26
Note : see the long multiplication card if you are unsure how to do this
As there are 3 decimal places in the question
There must be 3 decimal places in the answer