Maths GSE Revision ards - Monmouth Comprehensive...

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

www.gcse-maths-revision-resources.co.uk

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can be compared side by side.

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

Maths Revision Cards Target Grade C © www.gcse-maths-revision-resources.co.uk

nth Term

3, 5, 7, 9, 11

Write the next 3 terms

Write the nth term

Find the 50th term of the sequence


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


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


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


Estimating Answers


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


Estimating Answers


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


Mixed Numbers and Improper Fractions


Improper Fraction, Top Heavy Fraction and Vulgar Fraction all mean the same thing.

Fraction of a Quantity


Mixed Numbers and Improper Fractions


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


Two Way Tables


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


Two Way Tables


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


Translation


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


Translation


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


Trial and Improvement


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


Trial and Improvement

Start between the numbers given.

Use a table as below to show how you get your answer


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


Area 1

Find the areas of the following shapes


10cm

5cm

10cm

5cm

8cm

6 cm

5cm

10 cm

4 cm

Area 2

Maths Revision Cards Target Grade C ©

Area 1


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


Product of Prime Numbers


Express 150 as a product of its prime factors

Find the Highest Common Factor of 150 and 120

Highest Common Factor


Product of Prime Numbers


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


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


Key

Write the integer values represented by the inequality

Show the inequality on a number line.

-3 ˂ x ≤ 2

Inequalities


Stem and Leaf Chart


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


Long Multiplication


586 x 26 =

5.86 x 2.6 =

Long Multiplication with Decimals


Long Multiplication


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

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