Notesale: Turn your study into money

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by raihana

•

maths notes:

•

f i n d t h e nth t e r m -

key words:

-

nth term
The nth term rule tells us what
to multiply each position by to
get its matching term value
...


#
4 , 8 , 12 , 16 , 20 , 24
+ 4

Therefore the nth term rule is 4n
2) The nth term sequence is -1 , 3 , 7 , 11 , 15
to work out the nth term you need to find the common difference
between all numbers
...

What fraction of students walk to school as a fraction
...

1) add the percentages together e
...
g 100 - 85 = 15
3) convert your answer to a fraction
e
...
g 15/100 = 3/20

f i l l i n t h e b l a n k s:

I
#I
I
-

percentage

-

10%

-

fraction

-

35%

-

10/100

-

decimal

60/100

-

0
...


40/100

-

0
...
7

short and long multiplication
l o n g m u l t i p l i c a t i o n e x a m p l e s:

R

2 7 x
1
...
Each student must pay
£35 to go on the trip
...
What is the
total cost of the trip?

↑*
3
2

5x
9

total cost
= 81015

315 +
7 O

1015

2) Taylor is making cakes for the school cake sale
...
Each cake needs 3 eggs
...
89
how much will it cost to buy all the eggs to make the cakes
...


67

calculations with measurements
example

a thousand
kilometre
-

&

5
...
3 seconds

- a hundred
centimetre

5
...
30

a thousandth
millimetre
-

>
-

345 seconds

- a unit

unitmetre
=

10

-

+ 100

1000

Y

I

I

milli
- cent - unit - kilo
N
↑

↑

X 10

X

100

X

1000

questions
1) 1
...
0 0 6 km x 1 0 0 0 =
3) 6 0 g

÷ 100=

4) 4 6 cl ÷ 1 0 0 =
5) 7 2 6 ml ÷ 1 0 0 0 =

Answers are upside down

Ishoch

place

$4901

19278(2
4091

horal

holder

reflect = mirror or flip the shape over

reflecting shapes
examples
6

6

6

5

5

5


...


1

2

3

4

reflect

in

1
0

[

5

6

III

2

-

line


...


I

1

7

2

3

4

reflect

the

line

shown

5

in

6

7

the

shown

practices
6

!
5

4

3

2

1
0

1

2

3

6

4

5

6

7

6

6

5

5

!
4

&

3

-

3

2

2

1

-

0

1
0

1

2

3

6

l

4

#
/

J

4

5

6

7

1

2

3

4

5

6

7

6

IIII/

L #L
-

-

-

-

-

5

S /
/

4

-

-

5
4

3

3

2

2

1

1

0

1

I

I

I

2

3

4

-

-

-

6

7

4
3
2

·
1

-

0

5

5

1

I

I

I

2

3

4

0

5

6

7

1

I

I

I

2

3

4

5

6

7

s i g n i f i c a n t f i g u r e s:
examples

non zero

digits

-

0
...
All non zero digits are significant
1,2,3,4,5,6,7,8,9

...
All zeros to the right of a number as a decimal are significant
3
...
0 8 0 0

6) 2 8 0 4

2) 0
...
8 4

3) 9 1 6 0 0

8) 0
...
0 0 3 0 0 5

9) 1 0

5) 2 5 0

10) 7 5 0

p e r ce n t a g e i n c r e a s e s & d e c r e a s e s
60 starting number
90 final number

method

8 O starting
60

numbers

final numbers

calculating percentage increase calculating percentage decrease
1) find the difference between
the starting and final number
...
g 90 - 60 = 30

1) find the difference between
the starting and final number
...
g 80 - 60 = 20

2) divide your answer by the
starting number

2) divide your answer by the
starting number

e
...
50

e
...
25

3) multiply your number by 100
e
...
50 x 100 = 50% increase

3) multiply your number by 100
e
...
25 x 100 =25% decrease
·

practice questions
1) decrease 60 by 20%

5) increase 20 by 60%

2) decrease 40 by 30%

6) increase 30 by 49%

3) decrease 52 by 31
...
She sells that
house for £213,590
...

213590 - 201500 = 12090
12090
——— x 100
201500
12090 ÷201500 =
0
...
06 x 100 = 6
Therefore the
percentage change is
6%
•

Jo paid £245 for her car
insurance
...
Work
out the percentage change
...
638 ÷ 245 = 2
...
408163%

questions
1) Tom buys a painting for £1350
...

Work out his percentage loss
...
He want to resell for £1435
...


expanding brackets
model

number

4(x+3)
↑

↓

If its

varible

LXC

24
=

X 3

12 +

=

=

4
12

4xC

oustide the

bracket , you

multiply

have to

the varibles

inside the bracket

examples
1
...
4 ( m - 3 ) 4xm = 4m 4x3 = 124m-12
3
...

2
...

4
...


4(d+2)
5(b+5)
6(j - 4)
2(5+f)
10 ( 1 - n )

1
...
5 ( x - y)
3
...
2 ( a + b )
5
...
5- f)

multiplying fractions
model

important info

2
3
— x—
3
5

when multiplying fraction
you do not need to make
the denominators the same

>
-

numerator

·

↓
denominators

word problem
Safari has raised £2400 for some
charities
...
cancelling ratio until the given item
is 1

...
g ratio of girls to boys in the form
n:1

model
unit of


...


-

example

~

girls
600
5

...


...
1m = 100m
E2m = ……
...


2
...


questions


...
:
divide 12
I

30
&

...


divide

model
map : real
G1cm : 120m
15cm : 1800m

-

X 15

X 15

: 50
:
...
3 cm

L

2

3
...


3

adding&subtracting fractions
examples

key info

xi3
...

6

when adding or
subtracting fractions
you need to make the
denominators the
same

+

&

↑

X

↓

4 x 3+ 3

when adding your
fractions together
you can change
your improper
fractions to a mixed
number
...

14
—
+
-—— = 5
...

24
&

-

&

I

don't

add the

denominators

1) 1
...
# + 2 —
4
...
A
2
2) 5 —
...
r
3

1 + 5

3) 7
...
a - —
3
12
4) 5
...
& —
4

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