int 1 unit 2 nab revision integer coordinates integer addition dst pythagoras stem and leafpie chart...

Int 1 Unit 2 NAB Revision

Integer Coordinates Integer Addition

DST

Pythagoras

Stem and Leaf Pie Chart

Frequency Table Scatter Diagram

Mode Range

Median

Mean Probability

Integer Coordinates

2 31 4 65-3-4-5-6 -2 -1

3

6

4

5

2

1

-1

-2

-3

-4

-5

-6

x

y

What are the coordinates of the point

A( , )

Start at the centre and decide whether to go left - or right +

-2

Is the point above + or below -

4

AB

B


5 - 4

C

C

Point is below centre so x coord is 0


0 - 3

Where is the Point

2 31 4 65-3-4-5-6 -2 -1

3

6

4

5

2

1

-1

-2

-3

-4

-5

-6

x

y Where is the point

( , )P - 2- 5

P

( , )Q -30

As x is 0 the point will be either above or below the centre

Q

( , )R -53

R

Click Coordinates

Start

-2 -1 1 2 3 4

4 5

4 -1

-4 3

-4 -1

0 3

-5 0

-5 -2

0 -5

4 0

-1 -3

1

2

3

4

5

-5

-4

-3

-2

-1-3-4-5

A( ),

B( ),

C( ),

D( ),

E( ),

F( ),

G( ),

H( ),

I( ),

J( ),“Touch” the correct point

Adding Integers

Jill Fred Kevin

Round 1 -4 5 -3

Round 2 -3 -1 2

Round 3 5 -2 -4

Total -2

Scores are for a quiz. 1 pt for correct answer. 1 pt deducted if answer is incorrect. Totals are added

Jill scores ( - 4 ) + ( -3 ) + 5

Add negatives together then positives ( -4 ) + ( - 3 ) = ( - 7 )

= ( - 7 ) + 5 =-2

Fred’s Score

Jill Fred Kevin

Round 1 -4 5 -3

Round 2 -3 -1 2

Round 3 5 -2 -4

Total -2 2


Fred scores 5 + ( -1 ) + ( -2 )

There are two negatives ( - 1 ) is 1 down; ( - 2) is 2 down so ( -1 ) + ( -2 ) =

- 3

= 5 + ( - 3 ) =

5 + ( - 3 ) is 5 up then 3 down

= 2

Kevin’s Score

Jill Fred Kevin

Round 1 -4 5 -3

Round 2 -3 -1 2

Round 3 5 -2 -4

Total -2 1 -5


Kevin scores ( - 3 ) + 2 + ( - 4 )

- 7

= ( - 7 ) + 2 =

- 5

Cover up the 2 … work out ( - 3 ) + ( - 4 )

Integer Practice

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

6 ( -2 ) ( -3 )+ + =

( -3 ) 10 ( -6 )+ + =

( -2 ) 11 ( -5 )+ + =

5 ( -7 ) ( -3 )+ + =

( -4 ) ( -3 ) 2+ + =

(a)

(b)

(c)

(d)

(e)

Next

Slope indicates speed

D

ista

nce

Time

Fast

StoppedSlower

Interpreting a graph

Distanc Time GraphDistance – Time Graph

Dis

tan

ce (

km

)

Time (hours)

Leigh

40

80

120

160

200

Barnstow

Sandford

Crawley

0700 0800 0900 1000 1100

B

A

C D

Leaves Leigh at 07 00B … At 0800 arrive at Barnstow 80 km from LeighHorizontal. Stopped at Barnstow for 1 hourC Leave Barnstow as 0900Slope is not as steep as AB so travelling slower

Finding Distance

1215

D

S X T

Time = sec

D = S x T

X

Speed= m/s

180 miles

15 12

=

Can find distance

D= 15 x 12

What is the Speed

x

T

D

S

5

375

T=

S=

km/hr

hr

x

S = D ÷ T

S = 375 ÷ 5

S= 75

D= 375 km

÷÷

minT= 5 h

r

hr

min

How long is the journey

x

T

D

S

44

88

T=

S=

44 km/hr

hr

x

T = D ÷ S

T = 88 ÷ 44

T= 2

D= 88 km

÷÷

minT= h

r

hr

min

Pythagoras

3 22.4

c

3

c² = a² + b²Use

When you have both sides of the right angle you ADD the squares

c²= a² + b²

c=

Opposite of ² is √

c²=

Start Next

=

=

a= b

=

0

1 2 3

4 5 6

7 8 9

C

.

÷

x

0

+

On

²

-

Ans

=

√

(-)

22.4

Stem and Leaf

50 54 79 0 4 0 7 2

7 2 8 7 1

9 3 8

4 7 6

2 6 4 2

67

92 62 6850

67 57 9652

61 84 9473

92 78 8687

5

6

7

8

9

92 represented by leaf 2 in level 9

Key 5 0 is 50

Each row is called a level

Level 7 contains 79, 73 and 78

A key must be included so that the data can be interpreted

Pie Chart

BBC1

STV

SKY

other

A Pie chart is used to compare categories which can be chosen from

This pie chart compares the channels 80 pupils watched at 8pm one evening

Which was the most popular

SKY

The small square indicates that the angle for BBC is

90°

¼ of the pupils were watching BBC 1

¼ of 80 = 80 ÷ 4 = 20

Frequency Table

Diameter Tally Frequency

56

57

58

59

60

61

62

7

3

9

9

5

8

7

58

60

58

56

59

59

57

60

61

59

59

57

60

60

56

59

58

58

59

56

61

60

57

58

58

62

59

58

6061596257

5960596159

6258615960

5960586062

lIll

lIII lI

lIl

lIII

lIII lIll

lIII lI

lIII

lIII lI

The last diameter to be entered is 60The tally marks are then counted

ScatterGraph

Temperature °C

Sale

s of

Hot

Soup

Draw a line of BEST FIT

A scattergraph shows the connection between two quantities24 bowl of soup were sold on March 1st when the temperature was 5°

0

4

8

12

16

20

24

28

32

0 5 10 15 20 25 30 35

On the 2nd March the temperature was 8° and 20 cups were sold

Temperature °C

On the 3nd March the temperature was 5° and 28 cups were sold

Line of Best Fit

0

4

8

12

16

20

24

28

32

0 5 10 15 20 25 30 35Temperature °C

Sale

s of

Hot

Soup

The Scattergraph shows a connection between the temperature outside and the cups of Hot Soup sold


The line shows roughly where the point are. Some above. Some below.

Using a Best Fit LineSale

s of

Hot

Soup

0

4

8

12

16

20

24

28

32

0 5 10 15 20 25 30 35Temperature °C

Once the line is drawn you do not need the points. The line shows the connection ( correlation ) between temperature and sales.Estimate how many bowls of soup would be sold when the temperature is 20°C.

9 bowls sold

How many bowls when temperature is 5°C

For a temperature of 5° about 25 bowls would be sold

Line of Best Fit

0

4

8

12

16

20

24

28

32

0 5 10 15 20 25 30 35Temperature °C

Sale

s of

Hot

Soup


0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

Temperature

Bowls of Soup16

StartNext Temperature

Statistics … Mode

7 11 11 2 12 12 17 16 14 4 2 202

New Data

To find the median the data needs to be in order.

It is easier to find the Mode and the Range if the data is in order

Mode is the number which there is MOre of

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

Mode =

1

Sort

Finding the Range

The range is the difference between the highest number and the lowest number.

Next

10 20 10 25 30 8

High Low

-

-=

=

Range

=

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

Median

The MEDIAN of data is the middle value when put in order.

5, 7, 7, 10, 14, 16, 16, 18

There are 8 values. Split into two equal groups

8 ÷ 2 = 4of four

5 , 7 , 7 , 10 , 14 , 16 , 16 , 18

No number in the middle so find the number halfway between 10 and 14

Median =10 + 14

2

24

2= = 24 ÷ 2 =

12

What is the Median

3 9 19 9 175

5 9 9 17 193

New Data

Sort

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

Can have two groups of

Median = 9 ( 9 + 9 ) ÷ 2Working

3

Find the Median

New Data

Sort

Split into two groups of

3

Median = Working

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

Mean of 4 numbers

29 17 16 10

Mean

=29+17+16+10

4 How Many

Total

= 72 ÷ 4

= 18

Mean

=

Total

How Many

Mean of 6 numbers

26 11 19 22 26 22

Mean

=26+11+19+22+26+22

6 How Many

Total

= 126 ÷ 6

= 21

Mean

=

Total

How Many

Probability

14

Win

15

16

123

4

5

6

7

89 10

11

12

13

Probability=

Favourable

Possible

16 different numbers are possible with this spinner

Probability of a 9

P(9) = Favourable

Possible16

Only one position will win when the spinner stops at 9

1

Probability

What is the Probability of getting a four on the throw of a dice

P(4) =

Favourable

Possible

Possible

6

Favourable 1 Favourable outcome

1

Possible outcomes

0

1 2 3

4 5 6

7 8 9

C

.

÷

x

0

+

On

²

-

Ans

=

√

(-)

0 1 2 3 4

5 6 7 8 9

C

.

÷x

0+ On

²

-

Ans

=

√(-)

int 1 unit 2 nab revision integer coordinates integer addition dst pythagoras stem and leafpie chart...

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