sequences and formulae 1.look at the pattern below copy and complete the table below 4 710 131631...

Sequences and Formulae

1. Look at the pattern below

Pattern No 1 2 3 4 5 10 100 n

No of Matches

Copy and complete the table below

4 7 10 13 16 31 301 3n+1

2. Look at the table arrangements below

No of Tables 1 2 3 4 5 10 100 n

No of Chairs 5 8 11 14 17 32 302 3n+2

3. Copy and complete the table below

431 2 5 10 nHouses

Cards 5 9 13 17 21 41 4n + 1

4. Copy and complete the following table

Term 1 2 3 4 5 10 n

No 12 20 30 42

Factors

56

3x4 4x5 5x6 6x7 7x8 12x13

156

(n+2)(n+3)

n2+5n+6


Term 1 2 3 4 5 10 n

No 10 18 28 40

Factors

54

2x5 3x6 4x7 5x8 6x9 11x14

154

(n+1)(n+4)

n2+5n+4


Term 1 2 3 4 5 10 n

No 15 28 45 66

Factors

91

3x5 4x7 5x9 6x11 7x13 12x23

276

(n+2)(2n+3)

2n2+7n+6


Term 1 2 3 4 5 10 n

No 4 12 24 40

Factors

60

1x4 2x6 3x8 4x10 5x12 10x22

220

n(2n+2)

2n2+2n


Term 1 2 3 4 5 10 n

No 3 15 35 63

Factors

99

1x3 3x5 5x7 7x9 9x11 19x21

399

(2n-1)(2n+1)

4n2- 1

E.G Making x the subject of formula

eg 1 eg 23

3

4xV cmxy

ycmx

cymx

m

cyx

Vx 3

3

4

4

33 Vx

3

4

3

V

x

E.G Making x the subject of formula

eg 3 eg 4 yx

x

1cx

y3

3cx

y

xcy 3

3c

yx

1 xyx

yyxx

yxyx

yxy 1

y

yx

1

1y

yx

Ex Make x the subject of formula

ex 1 ex 2 43 yxyx 5

5yx yx 43

3

4 yx


ex 3 ex 4 hxV 2

3

1bxa 3

abx 3

bax 3

3

bax

Vhx 2

3

1

h

Vx

32

h

Vx

3


ex 5 ex 62b

a

xy baxa

baxa 2

baax 2

a

bax

2

a

xby 2

2byax


ex 7 ex 8 yx

x

2cx

y2

cx

y2

xcy 2

c

yx

2

xyx 2

xyyx 2

yxyx 2

yxy 21

y

yx

1

2

Statistics and Probability

Calculate the semi-interquartile range from the Stem and leaf diagram2 5 2 7 1 0 23 1 6 0 24 2 1 9 3 4 3 1 85 1 2 9 2 8 2 0 2 26 3 1 0 4 7 3 1 1

2 0 1 2 2 5 73 0 1 2 64 1 1 2 3 3 4 8 95 0 1 2 2 2 2 2 8 96 0 1 1 1 3 3 4 7

Q2 = (35+1) 2 = 18th entry

Q1 = (17+1) 2 = 9th entry

Q3 = (17+1) 2 = 27th entry

Q2 = 49%

Q1 = 32%

Q3 = 59%

SIQR = (59 – 32) 2 = 13.5

Pupil A scored the following grades in her S1 tests

89%, 61%, 75%, 84%, 99%, 67%, 91%, 62%, 79%, 90%, 64%

Draw a box plot to illustrate her grades

61%, 62%, 64%, 67%, 75%, 79%, 84%, 89%, 90%, 91%, 99%

Q2 = (11+1) 2 = 6th entry

Q1 = (5+1) 2 = 3rd entry

Q3 = (5+1) 2 = 9th entry

Q2 = 79%

Q1 = 64%

Q3 = 90%

30 40 50 60 70 80 90 100

Pupil B scored the following grades in his S1 tests

59%, 61%, 60%, 51%, 58%, 68%, 49%, 57%, 63%, 56%

Draw a box plot to illustrate his grades

49%, 51%, 56%, 57%, 58%, 59%, 60%, 61%, 63%, 68%

Q2 = (10+1) 2 = 5th/6th entry

Q1 = (5+1) 2 = 3rd entry

Q3 = (5+1) 2 = 8th entry

Q2 = 58.5%

Q1 = 56%

Q3 = 61%

30 40 50 60 70 80 90 100

64 79 90

56 58.5 61

Pupil A

Pupil B

Observations ?

Pupil A interquartile range = 26

Pupil B interquartile range = 5

Pupil A stronger student

Pupil B more consistent

Copy and complete the table finding the mean and median

Donation FrequencyCumulative Frequency

Donation x Frequency

£5 2

£10 4

£15 5

£20 11

£25 4

2

6

11

22

26

10

40

75

220

100

Total = 445

Mean = 445 26 = £17.12

Median = (26+1) 2 = 13th/14th = £20

Copy and complete the table finding the mean and median

Darts Scores

Mid value

FrequencyCumulative Frequency

Mid score x Frequency

0 – 19 10 7

20 – 39 30 8

40 – 59 50 4

60 – 79 70 3

80 – 99 90 2

7

15

19

22

24

70

240

200

210

180

Total = 900

Mean = 900 24 = 37.5

Median = (24+1) 2 = 12th/13th = 20 – 39 30

The average range fall was recorded over one week

City A 16mm, 30mm, 2mm, 27mm, 26mm, 30mm, 30mm

City B 0mm, 2mm, 68mm, 75mm, 9mm, 0mm, 0mm

Calculate the mean and standard deviation for both Cities

Comment on your results

1

.

2

n

xxds

X

16

30

2

27

26

30

30

-7

7

-21

4

3

7

7

49

49

441


xx 2xx

16

9

49

49

n

xx

7

161x 23x

1

.

2

n

xxds

6

662. ds

...3.110. ds

5.10. ds

X

0

2

68

75

9

0

0

-22

-20

46

53

-13

-22

-22

484

400

2116

xx 2xx

2809

169

484

484

n

xx

7

154x 22x

1

.

2

n

xxds

6

6946. ds

...6.1157. ds

0.34. ds


Summary

23Ax

5.10. Ads

22Bx

0.34. Bds



OBSERVATIONS?

Although both Cities had a similar average rainfall for the week, the higher standard deviation for City B suggests that the rain fall was much more varied.

Probability

Quick reminder

Measured on a scale form 0 to 1

0 10.5

50/50

outcomes ofnumber Total

outcomes favourable ofNumber eventP

E.g.s

JackP heartP

1diceP dicetwowithpairP

08.052

4 25.0

4

1

83.06

5 17.0

36

6

unlikely likely

Combined Probabilities

)2( heartsorAceP

)( QueenorJackP

)( HeadandHeadP

)1( dieonandTailP

52

5

52

1

52

4

52

8

52

4

52

4

13

2

4

1

2

1

2

1

12

1

6

1

2

1

Combined Probabilities

)( TailandTailP

)6( dieonandHeadP

4

1

2

1

2

1

12

1

6

1

2

1

H

T

H

T

H

T

HH

HT

TH

TT

H

T

H6

Future Expectation

Chris plays the game 30 times, how many games should he expect to win?

LW

L

WL

300 people were born in August. How many would you expect to be born on the 1st?

trialsofNoWP )(

wins12305

2

peopleofNoP st )1(

7.930031

1 ??9wins

Relative Frequency

Result Frequency

1 80

2 64

3 46

4 53

5 107

6 50

Hannah makes a die, rolls it 400 times and records her results

a. Calculate the relative frequency of a 2

b. Calculate the relative frequency of a 5

c. What can you deduce about the die?

16.0400

642. fR

27.0400

1075. fR

17.06

15 P

Implies too many fives, perhaps her dice is biased

sequences and formulae 1.look at the pattern below copy and complete the table below 4 710 131631...

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