math revision.pptx

8/20/2019 Math Revision.pptx

1/117

Algebra Number

Data Shape


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Algebra

Home

Brackets Two BracketsSolving

EquationsCollectinglike terms

Simplifing

! si"e"equations

Simultaneousequations

Solvingsimultaneous

equationsgraphicall

#actorisingCurve"$raphs

Sequences The Nth term%ua"raticSequences

Substituting #ormulae

%ua"raticEquation

#actorising%ua"ratics

Algebraic#ractions

Trial an"&mprovement

&nequalities

'aws of&n"ices

(arallel an"(erpen"icula

r lines

#in"ing the$ra"ient

)ritingE*pressions

+m * , c


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ShapeArea ofCircles

Circumference

Area oftriangles

Circle

theoryDoubleangle

Circletheorytriangles

Construction

Sin and CosSin, cos and

tanSin, cos and

tan 2

Sine rule Cosine ruleSine and

cosine rules

Trig-missingangles

Pythagoras

Angles on astraight lineand around

a point

Angles onparallel

lines

Angles in atriangle

Plans and

Elevations

Perimeter

ordedPythagoras

!e"ection # !e"ection 2 Translation !otation$D

Pythagoras

Circle

theoryanglesconnectedby a chord

Circletheorycyclic%uads

Circletheory

tangents

Angles inPolygons

&nterior andE'teriorangles

Polygons-(ndingsides

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Data

Home

-ean -e"ian an"range

-ean fromtables

-ean fromgroup tables

TreeDiagrams

Sampling-utuallE*clusive

Events

'isting.utcomes

Histograms

Cumulativefrequenc

/ea"ing (ieCharts

Drawing (ieCharts 0

Drawing (ieCharts !

Drawing BarCharts

Scatter$raphs

Bo* an")hisker plots

SampleSpace

Diagrams

The(robabilit

Scale

(robabilit as#ractions

Stem an"'eaf

Diagrams

/elative#requenc

/ea"ing BarCharts

/ea"ing (ieCharts !

-ean1 -o"e1-e"ian an"/ange

http://var/www/apps/conversion/tmp/scratch_7/%23action%3Fjump=firstslidehttp://var/www/apps/conversion/tmp/scratch_7/%23action%3Fjump=firstslide


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Number

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A""ing1subtracting"ecimals

B&D-AS A""ing an"subtractingfractions

Direct(roportion

#actors

#actor Trees

Directe"Numbers

Directe"Numbers !

Equivalent#ractions

#D(

#in"ing 2 /atioHC# an"

'C-&n"irect

(roportion'imits

-ultiplingan" "ivi"ing

"ecimals

-ultiplingan" Divi"ing

#ractions-ultiples

.r"eringDecimals

.r"ering#ractions

(ercentage&ncrease

/everse(ercentage

/oun"ing"p

/oun"ingsig 3g

Stan"ar"form


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A""ing an" Subtracting Decimals

Home

ANSWERSa) 0.5b) 1.2c) 0.8d) 1.3

e) 1.5

f) 1.47g) 1.28h) 1.66i) 0.97 j) 1.68

• a) 31.44b) 70.81c) 39.46d) 34.15e) 50.8

• a) 0.45

b) 0.54c) 0.49d) 0.71e) 0.7

• a) 2.94b) 39.02c) 67.25

d) 77.03e) 54.11

) 7/8


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A""ing an" Subtracting #ractions

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a) 7/8b) 8/12c) 7/9d) 7/10e) 2/3

f) 11/12g) 7/10h) 8/15i) 16/12 o 1 )

j) 11/24

!) 1 7/12

") 1 5/56#) 29/30$) 29/52o) 1 1/10

%) 5/8&) 5/12

) 1/3') 2/5() 1/2

) 7/20*) 8/21+) 23/36,) 9/22-) 71/126


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A""ing an" Subtracting Decimals

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A$'+e'1.

a)0.5b)1.2c)0.8d)1.3

e) 1.52.a)1.47b)1.28c)1.66d) 0.97e)1.68

3.

a)31.44b)70.81c) 39.46d)34.15e)50.8

4.a)0.45

b)0.54c) 0.49d)0.71e)0.7

5.a)2.94b)39.02c) 67.25

d)77.03e)54.11


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Direct (roportion

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#* &f A is directly proportional to +, rite an e%uation in the form A.+lin.ing the to variables if hen A / + 0*

2* All of the variables belo are directly proportional, rite an e%uation lin.ingthem1#* #2 hen 3 0

2* T 4 hen S#$* 5 $0 hen '20* 60/ hen 304* P 4 hen 7#8

$* + is directly proportional to C, hen + is #/ C is 29*

#* rite an e%uation lin.ing + and C2* :ind + hen C ;;$* :ind C hen + $8

0* < is directly proportional to 5, hen < 44, 54#* rite an e%uation lin.ing < and 5 2* :ind 5 hen < 99$* :ind < hen 58*#

4* 7 is directly proportional to =, hen 7#*/ = 8*;#* rite an e%uation lin.ing 7 and =2* :ind = hen 7 $*2$* :ind 7 hen =8*4

A$'+e'1.A22.1.42.5S3.17

4.125.N23.

1.1.52.443.45

4. 1.1.12.11-3.-7

5.1.N3

2.1.23.N1.5


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Bi"mas

Home

A4

05 67 , 7 4 * 8!5 8 * ! 9 :75 6: , ;4 < =85 : * 7 , ::5 6> 9 8 4 , :=5 0 , 0 9 0

;5 ! * 60: 9 !4?5 6: * 8 4 , !>5 6? , ! 4 < 0@0@5 6!0 * 0 4 9 !

B)

0560 , 084 9 6: *

7 4!560@ , = 4 < 68 *!47560 , ! 4 * 6= 9 74856! * = 4 9 608 <!4

:56; * !4 < 6 !@ 9=4=567 * 0@4 9 6! * !4;56> * :4 9 6 ! *0@4

C405 67 * 7 9 8 4 * 6! ,

!4!5 ! * 607 9 84 9 6!7

< !7475 7 * 60 , 84 9 6: *

!485 8 * 67 , !4 9 6 !8 9

:4:5 ; * 6 8 < ! 4 < 6 7

* : 0 4

A.1) 242) 33) 24) 20

5) 106) 17) 268) 229) 110)19

. 1) 02) 23) 94) 55) 16) 26

7) 25.

1) 202) 173) 54) 1

5) 16) 2


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#actors an" HC#

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1) Find all the factors of the following numbers:1) 20

2) 243) 274) 325) 406) 507) 568) 120) 200

2) 2 onl! has 2 factors "1 and 2)# how man! numbers can !ou find between 1 and 30 which ha$e e%actl! 2factors& "these are called 'rime numbers)

3) Find the highest common factors of the following 'airs of numbers:1) 18 and 542) 25 and 453) 12 and 184) 27 and 108

5) 30 and 754) Find the (F of these 'airs of numbers:1) 0 and 4502) 6 and 4803) 3 and 15


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ANSWERS1.

1.1:2:4:5:10:20

2.1:2:3:4:6:8:12:243.1:3:9:27

4.1:2:4:8:16:32

5.1:2:4:5:8:10:20:40

6.1:2:5:10:25:50

7.1:2:4:6:7:8:14:28:56

8.1:2:3:4:5:6:10:12:20:24:30:40:60:1209.1:2:4:5:10:20:40:50:100:200

2. 2:3:5:7:11:13:17:19:23:29 ;10 of (he#)

3.

1.18

2.5

3.64.27

5.15

4.

1.90

2.96

3.39


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#actor Trees

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#* Dra factor trees for the folloing numbers1a> 28b>20c> 0/d>?8

e> /#f> 48g>94h> #28i> 288

@> #/882* sing your factor trees from %uestion #, rite thenumbers as products of their prime factors *


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A$'+e'

1.2.a)22,5b)3 , 23

c)3 , 24

d)2 , 32 , 5e)34

f)2 , 52

g)3 , 52

h)23 , 3 , 5i)23 , 52

j)23 , 32 , 52


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Directe" Numbers

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•ANSWERS1)


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Directe" Numbers !

Home

1) = a# B250 i$(o #- o*edaf( ;) b( (he$ = ge( %aid B535: ho+ #ch

+i"" = ha*e i$ #- ba$! acco$(>

2) he (e#%ea(e a( (he No(h o"e i'

3) = ha*e B32 a$d each #o$(h fo 4 #o$(h' = ha*e (o %a- B15 (o #-

#obi"e %ho$e: if = do$( %( a$- #o$e- i$(o #- acco$(: ho+ fa +i"" =

be i$(o #- o*edaf(>

4) = j#% o( of a %"a$e 125# abo*e (he ocea$: = (a*e""ed 191# befoe =

'(o%: ho+ fa a# = fo# (he 'face of (he +a(e>

5) = a# %"a-i$g ai hoc!e- +i(h #- fie$d: beca'e = a# a#ai$g = agee'(a( o$


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1. 2852. 233.


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Equivalent #ractions

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2


20/117

2*a)4b)15c)12d)20e)60f)8g)26

h)32i)120 j)15!)64

")154#)125$)400o)615%)9720


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/atio

Home

#* There are #8 girls and #4 boys in a class, hat is the ratio of girlsto boys in its simplest form

2* There are #0 cats and #; dogs in an animal shelter, hat is theratio of cats to dogs in its simplest form

$* There 22 caramels and 44 fudges in a bag of seets, hat is theratio of caramels to fudges in its simplest form0* Simplify these ratio to their simplest forms1

a> 0/1;8b> 04194c> ;$1#8/d> 241081/8e> 2014;1?;

f> #281#/81;88g> $2810881008

4* Archie and Charlie share their Thomas the tan. engine toys in theratio #10, ho many do they each get if they have1a* #8 toys b*$8 toys c*04 toys

;* Tom and erry share seets in the ratio 21$, ho many do theyeach get if they share1a* 28 seets b*$8 seets c*44 seets

9* Sue and =inda share some money in the ratio $19, ho many dothey each get if they share1a* B$8 b*B;8 c*B?8

/* 3i.e, Dave and 6enry share some little bits of blue tac. in theratio #121$, ho many do they each get if they share1a* ;8 pieces b*92 pieces c*$88 pieces

ANSWERS

1. 232. 783. 254.

a) 45b) 35c) 712d) 5816e) 3712

5.a) 2 a$d 8b) 6 a$d 24c) 9 a$d 36

6.a) 8 a$d 12b) 12 a$d 18c) 22 a$d 33

7.a) 9 a$d 21b) 18 a$d 42c) 27 a$d 63

8. a) 10 a$d 20 a$d 30b) 12 a$d 24 a$d 36c) 50 a$d 100 a$d

150


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#in"ing (ercentages

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#> Some percentages & can (nd easily by doing a single sum,hat single sums can & do to (nd1a* #8F b* 48F c*24F

2> &f & .no #8F ho can & (nd1a* 4Fb* #F c* 28 F d* ?8F$> &f & .no 48F ho can & (nd1

a* 4F b* 24F0> :ind1

a* $8F of 248 b* 08F of 488 c* #4F of 228 d* 94Fof /0

4> :ind1a* $4F of 008 b* ;4F of 048 c* #;F of 228 d* /2F

of ?;;> :ind1

a* ?0F of ;08 b* /F of 428 c* 29F of 228 d* 4$Fof ?;

9> Compare you methods for the %uestions above ith apartner, here they the same

ANSWERS

1.

a) di*ide b- 10

b) di*ide b- 2c) di*ide b- 42.

a) ha"f (he a$'+eb) di*ide b- 10c) dob"ed) #"(i%"- b- 9 o 'b(ac(

10B fo# oigi$a"&a$(i(-

3.a) di*ide b- 10b) ha"f 50B

4.a) 75b) 200c) 33d) 63

5.

a) 154b) 292.5c) 35.2d) 78.72

6.a) 601.6b) 41.6c) 59.4d) 50.88

E i l t # ti


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Equivalent #ractions

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A$'+e'

2. a)4b)15c)12d)20e)60

f)8g)26h)32i)120

j)15!)64

")154#)125$)400o)615%)9720


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HC# an" 'C-

Home

:ind the 6ighestCommon :actor of thesenumbers1•#/ and $8•

#4 and 28•#; and 20•#2 and $;•28 and $8•2/ and 98•$? and ;4•$/ and 49

:ind the =oestCommon 3ultiple ofthese numbers•; and 9•

0 and ;•4 and /•#8 and 0•#; and 4•#0 and 2#•2*2 and 4•8*0 and 9

1.422.123.404.20

5.806.427.558.14

1.62.53.84.125.10

6.147.138.19


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&n"irect (roportion

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#* &f A is indirectly proportional to + and henA 4 + ; 1

#*:ind . 2*rite an e%uation lin.ing A and +$*:ind A hen1

#* +$2*+#4

0*:ind + hen1#* A#2*A-$

2* &f A is indirectly proportional to + and henA 9 + #2 1

#*:ind . 2*rite an e%uation lin.ing A and +

$*:ind A hen1#* +02*+;

0*:ind + hen1#* A#82*A2

$* &f A is indirectly proportional to + and henA -0 + #8 1

#*:ind . 2*rite an e%uation lin.ing A and +$*:ind A hen1

#* +-/2*+#8

0*:ind + hen1#* A-#2*A-8*4

0* &f A is indirectly proportional to + and hen A 20 +#*:ind . 2*rite an e%uation lin.ing A and +

$*:ind A hen1a*+;b*+ -$

0*:ind + hen1a*A -2b*A #88

1.1.!302.A , 303.

1. A202.A2

4. 1. 302.


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#ractions1 Decimals an" (ercentages

Home

#*a> 94Fb> #8Fc> 28Fd> $4F

e> 02F2*

a> 8*9b> 8*24c> 8*$d> 8*#4e> 8*84

$*a> ;8Fb> 98Fc> /Fd> 29Fe> /8F

0*a> )b> $$H#88c> 4#H#88d> 0H4e> #H4

4*a> 8*0b> 8*?c> 8*90d> 8*8$e> 8*84

;*a> 9H#8b> $H4c> ##H48

d> 9H28e> 2#H48

lengths have been rounded to the nearest


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'imits

Home

#>These numbers have beenrounded to the nearest #8,rite don the largestand smallest values theycould be1

#>482>/8$>##8

2>These numbers have beenrounded to the nearesthole number, rite donthe upper and loerlimits1

#>$2>#9$>2$0>#884>-$

$>These lengths have beenrounded to the nearest

#8th

of a cm, rite theupper and loer limits1#>#2*4cm2>2#*9cm$>$4*/cm0>42*#cm4>/8*0cm

lengths have been rounded to the nearest

metre*

a> :ind the perimeter and area of the (eld

if these measurements are accurate

b> :ind the largest and smallest possible

perimeter

c> :ind the largest and smallest possible

area*

4> A rectangle has its area rounded to the

nearest hole number, it becomes 08cm2* Ine

side of the rectangle is e'actly #8cmJ (nd the

ma'imum and minimum lengths the other

length could have*

;> To lengths of ood are stuc. together and

their combined length is rounded to the nearest

mm and it is #0*?cm, one length is rounded to

the nearest mm and is 9*#cm* :ind the

minimum and ma'imum length of the other

length*

A$'+e'1.

1.45 a$d 54.9999999..

2.75 a$d 84.999....3.105 a$d 114.9999...

2.1.2.5 a$d 3.4999...2.16.5 a$d 17.4999...3.22.5 a$d 23.49999...4.99.5 a$d 100.4999..

5.


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-ultiples

Home

st the (rst 4 multiples of1

hat is the1 multiple of / multiple of ;th multiple of #2th multiple of #8th multiple of 4

h multiple of #$

C* =ist $ numbers hich are in1#* $ and 0 times tables

2* $ and 4 times tables$* #8 and 0 times tables0* ? and 2 times tables4* #2 and #8 times tables

D* hat is the loest common multiple of1

#* 4 and ;2* 9 and /$* 0 and /0* ? and ;4* #8 and ;

E* hat is the loest common multiple of1;* #$ and 49* #4 and #2/* #; and #8?* #0 and 2##8*2# and 98

a) 5:10:15:20:25b) 7.14.21.28.35c) 12:24: 36: 48: 60

d) 14:28:42:56:70e) 19:38:57:76:95

f) 72g) 42h) 144i) 110

j) 65!) 65

") 12:24:36#) 15:30:45$) 20:40:60o) 18:36:54%) 60:120:180

&) 30) 56') 8() 18) 30

*) 65+) 60,) 80-) 42

) 210


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-ultipling an" "ivi"ing fractions

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A$'+e'1.

a)3/32b) 5/48c)1/9d)4/25e)7/16

2.a)65/18b)11c) 8

d)1e)1/23.

a) 4/24 o 1/6b)20/12 o 5/3c)1d)1e)24/42 o 4/7

4.a)39/30 o 13/10b)22/18 o 11/9c) 32/36 o 8/9d)63/28e)50/16 o 25/8

A$'+e'


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-ultipling an" "ivi"ing "ecimals

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1 a) 0.8 , 7

b) 0.5 , 7

c) 0.1 , 6

d) 0.6 , 4

e) 0.3 , 3

2 a) 0.2 , 0.5

b) 0.4 , 0.7

c) 0.8 , 0.1

d) 0.9 , 0.9

e) 0.6 , 0.1

3 a) 1.9 , 0.3

b) 1.6 , 0.5

c) 1.6 , 0.5

d) 1.7 , 0.2

e) 1.3 , 0.7

3ultiplying Dividing#

a) 3.2 C 4b) 4.8 C 8c) 7.2 C 9d) 2.4 C 6e) 1.8 C 3

2f)5.6 C 0.7g)6.3 C 0.7

h)2.7 C 0.3i)4.9 C 0.7 j)2.8 C 0.7

3!) 1.65 C 0.15") 24 C 0.12#) 27.3 C 1.3

$) 0.03 C 0.005o) 0.99 C 0.0009

1.a) 5.6b) 3.5c) 0.6d) 2.4e) 0.9

2.a) 0.1b) 0.28

c) 0.08d) 0.81e) 0.06

3.a) 0.57

b)0.8c) 0.75d)0.34e)0.91

4.

a)0.594b)5.044c) 6.059d)0.506e)6.15

1.f)0.8g) 0.6h)0.8i)0.4 j)0.6

2.!)8")9#)9$)7o)4

3.%) 11&)200)21

')6()1100


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.r"ering #ractions

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ANSWERS1. 1/4 3/8 D a$d 4/8 3/42. 2/5 D 3/5 a$d 6/10 2/29

3. 1/3 5/12 1/1 4/6 3/44. 1/4 1/2 2/3 5/6 7/85. 1/4 2/5 1/2 6/10 3/46. 1/3 4/9 1/2 2/3 5/67. 2/6 1/4 5/12 2/3 7/98. 2/7 2/4 5/8 11/14 3/2

a)


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.r"ering Decimals

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#* :or each pair of numberssay hich is bigger byadding K or L*

a> 8*2 8*9b>8*$ 8*#c>8*9 8*?d>8*$ 8*0e>8*; 8*$f>8*20 8*2g>8*$ 8*$?

h>8*0 8*$4i>8*? 8*/4

@>8*22 8*$2* Try these1

a> 8*80 8*84b>8*82 8*8?

c>8*#2 8*82d>8*80 8*2$e>8*0 8*80

$* These are tric.ier1a> 2*$0 8*8?

b> 0*0? 0*888$c> 4*8# 4*#d> ;*$2 ;*$24e> 9*0$; 9*0$

f> /*$4 /*$04

0* Put these decimals in ascending orderMsmallest to biggest>1a* 8*2 8*$ 8*#4b* 8*9 8*;0 8*892c* 8*/4 8*? 8*024

d* 8*9$0 8*9$04 8*9$$4e* ;*2$0 ;*88? ;*0

a) b) Fc) d) e) Ff) Fg) h) Fi) F j)

• a) b) c) F

d) e) Ff)

• a) Fb) Fc) d) e) Ff) F

• a) 0.15 0.2 0.3b) 0.072 0.64 0.7c) 0.425 0.85 0.9d) 0.7335 0.734

0.7345e) 6.009 6.234 6.4

ANSWERS


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(ercentage &ncreaseDecrease

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#* E'plain ho you ould use acalculator to increase an amount by agiven percent*

2* &ncrease the folloing amounts by

02Fa>B224b> B$8;c>B#24d>B00/e>B4#2

$* A T costs B#28, ho much ill it costif its price is increased by1a> #2Fb>$#Fc>44Fd>;2*4Fe>??*?F

0* Simon puts B98 in a ban., each yearthe money in his ban. increase by4*4F, ho much does he have in1a> # yearb>2 yearsc>4 years

4* E'plain ho you ould use acalculator to decrease anamount by a given percent*

;* Decrease the folloing amountsby 2/F

a> B224b> B$8;c> B#24d> B00/e> B4#2

9* A T costs B#28, ho much

ill it cost if its price isdecreased by1f> #?Fg> $2Fh> 9?Fi> 9$*4F

@> 02F

/* A car bought for B;, 488depreciates in value by #2*4Feach year, ho much ill it beorth after1.> # yearl> 2 yearsm>4 years

1.2.

a) 319.5b)434.52c)177.5d) 636.16e)727.04

3. a)134.40b)157.20c)186d)195e)239.88

4.a)73.50b) 77.91

c)91.495.6.

a)162b)220.32c)90d) 322.56e)368.64

7.

a)97.20b) 81.60c)25.20d)31.80e)69.60

8.a)5687.50b) 4976.56c)333.91

/ "i Si i3 #i


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/oun"ing to Signi3cant #igures

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ai$1. Whe$ -o ae o$di$g (o deci#a"

%"ace' -o '(a( co$(i$g af(e (hedeci#a" %oi$(: b( +i(h 'ig$ifica$(fige' -o '(a( co$(i$g a( (he

fi'( $o$ eo $#be2.i. 1000 1500 1460ii. 200 160 157iii. 40 37 37.1i*. 6 6.1 6.09*. 0.006 0.0064 0.00640

3.a) 4.7b) 0.058c) 0.19d) 540

/ "i t D i l (l


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/oun"ing to Decimal (laces

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a) 1*463884266

b) 1*57266002

c) 3*783345228

d) 6*331313

e) 0*64036888f) 0*3261142

g) 4*2450435

h) 4*44623i) 1*447852851 +) 0*06143754

,or- out the following on a calculator and

gi$e the answer to 2 decimal 'laces.

a) 3*104 % 5*38

b) 2* % 8*82

c) 7*1537/ 3*111

d) 14*772

•Ro$d (he fo""o+i$g $#be' (o a) 1 deci#a" %"ace b) 2 deci#a"' %"ace' c) 3 deci#a" %"ace

ANSWERSa) 1.5 1.46 1.464b)1.6 1.57 1.573c) 3.8 3.78 3.783d) 6.4 6.39 6.393e) 0.6 0.64 0.640f) 0.3 0.33 0.326g) 4.2 4.25 4.250h) 4.4 4.45 4.447i) 1.4 1.45 1.448

j) 0.1 0.07 0.069•

a) 18.43b)26.37c) 2.30d)219.15e)3.67

/ ( t# hat ould you multiply anan amount by to decrease it


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/everse (ercentages

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#* hat ould you multiply anamount by to increase it by1a> #4Fb>24Fc>0F

d>8*4Fe>#$*4F

2* :ind the original prices of theseprices that have been increasedby the given percentage1a> Cost B0?*4 after #8F

increaseb>Cost B90*94 after #4Fincreasec>Cost B;# after 22F increased>Cost B#80 after $8F increasee>Cost B#28 after 48F increase

$* & have B242 in my ban. accountJthis is due to me earning 4Finterest on hat & originally hadput in* 6o much money did &have originally in my ban.account

yby1

a> #4Fb>24Fc>0Fd>8*4Fe>#$*4F

4* :ind the original prices ofthese items that have beendecreased by the givenpercentage1

a> Cost B92 after #8Fdecreaseb> Cost B?$*4 after #4F

decreasec> Cost B$? after $4F

decrease

d> Cost B0 ?fter 08Fdecrease

e> Cost B;9*48 after 44Fdecrease

;* A Cars value has droppedby ##*4F it is no orth

B$84$*24, hat as it orthhen it as ne

A$'+e'1.

a) 1.15b) 1.25c) 1.04

d) 1.005e) 1.1352.

a) 45b) 65c) 50d) 80e) 80

3. 2404.

a) 0.85b) 0.75c) 0.96d) 0.995e) 0.865

5. a) 80b) 110c) 60d) 15e) 150

6. 3450

St " " #


37/117

Stan"ar" #orm

Home

A$'+e'1. a:e:f:g

2.1. 474000000

2.190

3.86200004.640005.350006.663000007.9090000008.60009.8710000000

3.1.0.000000000136

2.0.000000000953.0.000006384.0.00000007965.0.00000566.0.000000005437.0.0000000006328.0.000489.0.000161

4.1.8.3 , 103

2.4.4 , 105

3.1.35 , 107

4.9.87 , 107

5.3.4 , 10


38/117

Two Brackets

Home

A$'+e'1.

1.,2G12,G352.,2G10, G 213.,2 G 5, G 64.,2 G 6, G 85.,2 G 9, G 8

2.1.,2 N 492.,2 G , N 123.,2 G 8,


39/117

#*:ind 'a>2' O 0 $' O #b>#8' O / 0' O $/

c>9' N $ $' O24d>##' O 4 ?' O 2#e>0 O ##' ' O ?

2*Solve these e%uationsa>2M$'O0> 2M0'-#>

b>2M$'-0> 0M' O $>c>0M$' O 2> /M2' -#>d>2M0'O2> 0M$'-#>e>0M$'O2>#8M'O0>

$*Solve these e%uations bymultiplying out brac.ets andsimplifying1a>$M' O2> O 4M'-#> 24

b>2M2' O #> O ;M' O $> 98

Ansers

#*

a>'$b>'4c>'9d>'/e>'8*

42*a>'4b>'#

8c>'$d>'2e>'#

#$*Home

Al b i # ti


40/117

Algebraic #ractions

Home

Ansers

#*a>'9b>'0

2

c>'2d>'#2

2*a>'#

8b>'$c>'2

/

d>'0

Ansers

$*a>'#

2b>'4c>'#

#0*a> '#

8

b> '4c> '2d> '9e> ';

f> '0

+ . t


41/117

+rac.ets

Home

ove the brac.ets from these e'pression by multiplying them out12M' O4>;M2' O9>

/M0' -2>4M$' -?>2M0 -2'>/M$ N 0'>'M' O $>'M2' O?>'M0' -9>

2'M? -4'>iply out the brac.ets1 'M$'2 O 4>2'M4'2 O ;>4'M$'$ - 9>iply out the brac.ets and simplify1

$M' O 0> O 0M'-;>9M' O 9> O 4M2'-/>$M0' O #> O 2M;'-?>4M4' - 0> - 0M$'-;>2M#$ -0'> - ?M'O ;>

ANSWERS1.

a) 2 G 10

b)12 G 42c) 32 N 16d)15 N 45e)8 N 4f) 24 N 32g) 2 G 3

h)22

G 9i) 42 N 7 j) 18


42/117

Collecting like terms

Home

#*Simplifya>#8a O 0ab>2b O 9b

c>$a O a O 0ad>##b N 0be>#0b N 4b O 0bf>$a N ;a O a

2*Simplifya>#8a O 0b Na O4b

b>/a O 4a O4b N $bc>#2b N 9a O $b Oad>2b N /b Na O ?ae>-#$b O 0a -4b -0af>##a O /b O 2c O ;a O $b -2cg>;b O 0b Na O;c O 4a N 0ch>9c O 0b- $b O a O #8c N 4ai> #8a O 0b O 9a O #8b N #9a N #0b

@> 4b O 0c O #/c N 22a O

A$'+e'1.a)14ab)9bc) 8ad)7be)13b

f)


43/117

Curve" $raphs

Home

? 4 4 ? #9

#$ ; # -2 -$

-0 -/ -; 2 #;

-2,? -#,4 8,4 #,? 2,#9

-2,#$ -#,; 8,# #,-2 2,-$

-2,-0 -#,-/ 8,-; #,2 2,#;

#actorising


44/117

#actorising

Home

A> :actorise the

folloingcompletely1

#*#8A O #42*20A O $;

$*#;A - ;00*#4+2 O 28+4*#0+2 O 0?+;*?+2 O 92+9*$$+2 - 00+

/*2C$ O /C?*4C0 O 08C#8*#8C$ O /C

+> :actorise thefolloingcompletely1

#* ?A+ O ;A2* #;A+ N 0+$* $8A2+ O 20A+0* #8A+2 N #4+2

4* #2A+C O 28 A+;* 2/A2+C O#0A+C

9* 0A+ N /A O#;+

/* #4A N #/+ N2#A+

?* ?+$ O #/+C O$8A+

#8*A+C-#8A+

ANSWERSA.

1. 5;2A G 3)2. 12 ;2A G 3)3. 16;A


45/117

#in"ing the gra"ient

Home

d the gradient beteen the points1M$,4> and M0,9>

M4,?> and M9,#9>M0,;> and M4,9>M#,0> and M0,#?>M8,##> and M0,2$>d the gradient beteen these points1M2,4> and M$,-$>M2,/> and M$,2>M0,/> and M/,0>M/,#4> and M;,$$>M9,#2> and M0,02>M0,/> and M$,#0> the gradient beteen these points1M$,4> and M0,4*4>

M4,?> and M9,/>M0,;> and M4,;*94>M#,0> and M0,0*94M8,##> and M0,##*0>

A$'+e'1.

a)2b)4c)1

d)5e)3

2.a)


46/117

> &saac 7etons second la of motion states :ma Mforce mass ' acceleration>#*:ind : if1

a*3#8 and a4b*3#2 and a#2c*38*4 and a##

2*:ind a if1a*:#88 and 328

$*:ind m if1a*:$; and a#2

+> Density e%ual volume divided by mass0*rite a formula for density

a*:ind D if

i*3#8 and v 08ii*3#2 and v92iii*34 and v?8

b*:ind 3 if1i*D0 and v42

c*:ind v if1i*D/ and m##

C> Electrical poer Mp> is e%ual to voltage M> s%uared divided by resistance Mr>4*rite a formula for poer;*:ind p if1

a* 0 and r/b*? and r$

9*:ind r if1a*P#; and v/

/*:ind v if1

a*P28 and r4

#ormulae

Home

A$'+e'A.

1.a) 50b) 144c) 6.5

2.a) 5

3.a) 3

.1. H/2.

a) 4b) 6c) 18

3.a) 13

4.a) 88

.

1. I2/R2.

a) 2b) 27

3.a) 4

4.

a) 10


47/117

&nequalities

Home

ANSWERS1.1),F62),F93),J114),J2

5),126) ,K207),K208),20

2.1)6 , K 10

2)9 , 163)11 K , 154) 2 K , K 8

'aws of in"icesANSWERS1.


48/117

'aws of in"ices

Home

1. Simplify:a) A2 x Ab) A4 x A2

c) A8 x A2d) 3A9 x A3

e) 4A2 x 5A1

2. Simplify:a) A10 ÷ Ab) A21 ÷ A7

c) A20 ÷ A4d) 9A12÷ 3A6

e) 12A6 ÷ 4A4

3. Simplify:a) (A2)4

b) (A3)3

c) (A2)6

d) (2A9)2

e) (3A4)3

4. Simplifya) A0

b) B0

c) 990d) 520

e) 0.0610

5. Simplify:f) A4

!) A6

") A2

i) 2A4

#) 9A3

6. Simplify f$lly:%) 25A4 ÷ 5A7

l) 3A9 x 2A3

m)(A2)6 x (2A2)2

&) (2A3)8 ÷ (2A4)6

') (A2)6

.a)A3

b)A6

c)A10

d) 3A12

e)20A3

2.

a)A9

b)A14

c)A16

d) 3A6

e)3A2

3.a) 1b)1c)1

d)1e)14.

a)A8

b) A9

c)A12

d)4A18

e)27A12

5.

a) 1/A4b) 1/A6c) 1/A2d) 2/A4e) 9/A3

6*a) 53

b) 66

c) 416

d) 4e) 112

•

(arallel an" (erpen"icular lines


49/117

(arallel an" (erpen"icular lines

Home

ANSWERS1.2.

a)-3,


50/117

#in" the Nth term of these sequences

04 =1 0;1 781 :;1 ?=

!4 71 0?1 801 ;!1 000

74 ;1081!71 781 8;84 ?1 0>1 781 :71 ;=

:4 !1 0!1 7@1 :=1 >@

Answers04 7n!,!n

,0!4 8n!,7n8

74 n! , 8n ,!

84 !n! ,:nHome

The qua"ratic equation


51/117

The qua"ratic equation

Home

1. Lo each of (he'e e&a(io$': +ha( i' a: b a$d c> ;(he fi'( o$e ha' bee$do$e fo -o)a) 2,2G4,


52/117

#actorising %ua"ratics

Home

1. Lac(oi'e a$d 'o"*ea) 2 8 12 0b) 2 7 10 0c) 2 13 12 0d) 2 17 700e) 2 200f) 2 4 120

g) 2 12 2002. Reaa$ge: fac(oi'e a$d 'o"*e

a) 2 21 3212b) 2 8 5 15c) 2 6 23 5 3

3. So"*ea) 32 21 5115b) 22 18 106c) 42 8 4 36 4%

ANSWERS1. a)


53/117

q

Home

05 Cop "own the following sequences an" a"" the ne*t three termsa) 3 6 12 15b) 2 7 12 17 22c) 4 10 16 22 28d) 13 24 35 46 57

e) 50 48 46 44 42!5 #or each of the questions in question what is rule to 3n" the ne*tterm in the sequence5 6This is calle" the term to term rule4

75 Cop the following sequences1 write the term to term rule an" 3n"the ne*t 7 terms5

a) 0*3 0*7 1*1 1*5 1*b) 1*4 1*7 2 2*3 2*6c) 40 3*5 3 38*5 38

d) 5* 5*3 4*7 4*1 3*5e) 11*4 12*5 13*6 14*7 15*8

85 Cop the following sequences1 write the term to term rule an" 3n"the ne*t 7 terms5

a) 5 0 5 10 15b) 3 1 5 13c) 20 16 12 8 4

d) 30 27*525 22*520:5 Cop the following sequences1 write the term to term rule an" 3n"the ne*t 7 terms5

a) 1 2 4 8 16b) 1 3 6 10 15c) 1 3 7 13 21

A$'+e'1.

a) 18:21:24b)27:32:37c)32:36:40d)68:79:90e)40:38:36

2.a)add 3b)add 5c)add 4d) add 11e)(a!e a+a- 2

3. a)2.3:2.7:3.1 ;add 0.4)b) 12.9:3.2:3.5 ;add 0.3)c)37.5:37:36.5 ;(a!e a+a- 0.5)d)2.9:2.3:1.7 ;(a!e a+a- 0.6)e)16.9:18:19.1 ;add 1.1)

4.a)


54/117

The Nth term

Home

•1) Find the nth term of the following seuences:a) 4 7 10 13 16

b) 2 7 12 17 22c) 4 10 16 22 28d) 13 24 35 46 57e) 1 17 25 33

•2) a-e the following nth terms and find the first 5 termsa) 3n 1b) 4n 2c) 5n 5d) 4n 9 1e) 6n 3f) 10n 3

•3) 9f the nth term is 7n 4 what isa* he 4th term b* he 12th term c* he 100th term

•4) 9f the nth term is 8n 2 what isa* he 4th term b* he 12th term c* he 100th term

•

5) 9f the nth term is 11n 3 what isa* he 4th term b* he 12th term c* he 100th term

•6) 9f the nth term is n what isa* he 4th term b* he 12th term c* he 100th term

1.a)3$G1b)5$


55/117

p g p

Home

A$'+e'1.

a)20a4

b)18a7

c)63a8

d)20a2b4e)18a2b7

f)63a2b8

g)8a2b2c5

h)60a2b2c14

i) 36a8b8c j) 12a5b4c4

2.a)4ab)3a4

c)7a2

d)6a3

b3

e)9a4/b5

3.a)10a2

b)10ab2

c)ab6/10

d)ab2

e)119a3b8

Simultaneous Equations


56/117

Simultaneous Equations

Home

1* Find a and b for each 'air of simultaneous euations:a) 5a 2b 14 6a 2b 16b) 7a 3b 27 6a 3b 24c) 10a 2b 30 3a 2b 2d) a 6b 42 6a 6b 18

2* Find a and b for each 'air of simultaneous euations:a) 4a 7b 27 4a 7b 13

b) 3a 2b 35 2a 2b 10c) 11a 8b 4 a 8b 44d) 5a 3b 6 7a 3b 75

3* Find a and b for each 'air of simultaneous euations:a) 5a 6b 28 6a 2b 18

b) 4a 4b 36 6a 2b 22c) 2a 8b 16 3a 2b 2d) a 6b 84 3a 3b 25*5

A$'+e'1.a) a2 b2b)a3 b2c) a4 b5d)a8 b5

2.a) a5 b1b)a9 b4c) a4 b5d)a12 b3

3.

a) a2 b3b)a5 b4c) a10 b0.5d)a9 b0.5

Solving Equations


57/117

Solving Equations

Home

#* :ind ' if1a> 9' 02b> #2'$;c> 4' 08

d> #8' ##8e> 6o did you anser these %uestions

2* :ind ' if1a> Q O #8 #9b> Q O #4 29c> Q O 24 $8d> Q- ? #4

e> Q N #$ 08f> 6o did you anser these %uestions$* :ind ' if

a> $' O ; 2#b> 9' O ## ;9c> 4' O 0 20d> ?' N 2 24e> ##' N #0 $8

f> #8' - 9 4$g> #2' O ## #44h> #4' - #0 ;#i> #$' O 24 ?8

@> 6o did you anser these %uestions

A$'+e'1.

a) 8b) 6c) 3d)10

2.a) 7b)12

c) 5d)16e)27

3.a) 5b) 8

c) 4d) 3e) 4f) 6g) 12h) 5i) 5

Rraphical Simultaneous


58/117

Rraphical SimultaneousE%uations

Solve these simultaneous equationsgraphicall 6"raw * a*is to 0@ an" a*is to 0:4

05 +!* , 8 an" +7* 0

!5 +:* 7 an" +8* , 0

75 +* , ; an" +!* , 8

85 +!* , ! an" +=7*

:5 +0@ 9 !* an" +0!7*

05 6:1084

!5 6!1;475 6710@4

85 60174

:5 6!1=4

Home

SubstitutingANSWERS1.


59/117

Substituting

Home

#*&f A is 4 hat is1

a>4Ab>##Ac>;A N #8d>?A O #4e>#88-4A

2*&f + is 9 hat isa>2M+O/>b>$M+-4>c>+M+O4>d>?M#8-+>e>M$O+>QM+-4>

$*&f A ; and +9 hat is1a>AO+b>+-Ac>;AO2+d>A+e>AM+O#>

f>A2

+

a) 2b) 55c)20d)60e)75

2.

a)30b) 15c)84d)27e)20

3.a)13b)1c) 50

d)42e)48f)252

4.a)8b)


60/117

#* se trial and improvement to (nd the positivesolution to these %uadratic e%uations to # dp,you may li.e to use a table, the table for the

(rst %uestion has been dran for you Mallansers are beteen # and 4>*a>Q2 O $' -$88b>Q2 O 2' -288c>Q2 O 0' -#88d>Q2 -2' -48

2* se trial and improvement to (nd the positivesolution to these %uadratic e%uations to 2dpMall ansers are beteen # and 4>

a>$Q2 - 4' -#88b>2Q2 O 2' -248

Trial an" &mprovement

Home

' Q2 O$

'

-

$8

+ig or small

ANSWERS1.

a) ,4.2

b),3.6c),1.7d),3.4

2.a) ,2.84b) ,3.07

)riting E*pressions

# 3 i C it i f th f th b f

A$'+e'


61/117

)riting E*pressions

Home

#* 3y age is C, rite e'pressions for the ages of the members ofmy family if1

a>3y brother is $ years older than meb>3y sister is 2 years younger than mec> 3y mum is double my age

d>3y dad is 4 years older than my mume>3y Rran is 0 times my agef> 3y Rrand Dad is tice my Dads age

2* &f & have S seets, rite an e'pression for the number ofseets my friends have if &1

a> & give Tom all my seets and he has 4 of his onb>& give Alan half of my seetsc> & eat four seets then give Simon the rest

d>& give =ucy a %uarter of my seets, then an e'tra #$* 3y favourite song last 3 minutes, ho long do & spend listening

to music if1a> & listen to the song once and hour all day Mand including

hen &m asleep>b>& listen to half the song / timesc> & listen to the intro Ma %uarter of the song> 4 timesd>& listen to my song, then the ne't one hich is e'actly

tice as longe> & listen to my song, then the ne't one hich is e'actly

tice as long, and do this 4 times throughout the day0* &f a rectangle has lengths ' and y, rite an e'pression for1

a>The area of the rectangleb>The area covered by ; rectanglesc> The perimeter of the rectangle

A$'+e'1.

a) G 3b) N 2c)2d) 2G5e)4f)2;2G5) R 4 G10

2.a)SG5

b) S/2c)S


62/117

m* ,c

Home

#* Copy and complete1a> A line ith a positive gradient ill go from left to rightb> A line ith a negative gradient ill go from left to right

2* =oo. at the e%uations belo, rite don the gradient and the coordinates of theintercept of the line they represent*

a> 5$'O0b> 5 2'-4c> 5;'O?d> 5'- 9e> 5#8'f> 54O/'g> 59-##'

$* Dra an a'is from -#8 to #8, plot the folloing linesa> 5 2' O $

b> 5 $' N 2c> 5 -2' O 4d> 5 -$' O ?

85 #in" the gra"ient of the line between these pairs of coor"inates b "ivi"ing the change in b thechange in *5

a> M$,$> M4,4>b> M4,4> M;,9>c> M#,2> M$,/>d> M#8,?> M;,#>

e> M#4,28> M#8,4>4* sing the gradient or.ed out in the last %uestion and one of the coordinates, (nd the

value of c for the line beteen the pairs of points in %uestion 0*;* rite out the e%uation of the line beteen the pairs of points in %uestion 0 in the form

ym'Oc

A$'+e'1.

a) bo((o# / (o%b) (o% / bo((o#

2.

a) gadie$(< 3 i$(e'ec(io$< ;0:4)b) gadie$(< 2 i$(e'ec(io$< ;0:


63/117

ou can find the area of a circle b! using the formula

rea ; %


64/117

Area of Triangles

Home

05 #in" the area ofthe triangles on the

left

!5 #in" the missinglengths of the

triangles on theright

1. 6m2. 24m2

3. 3m2

4. 20m2

5. 12m2

6. 35m2

7. 44m2

8. 15m2

9. 31.5m2

10.72m2

A&e*:

1. 10m2. 14m3. 6m4. 10m5. 10m6. 3m7. 20m


65/117


66/117

Triangles insi"e circles


67/117

60>

,

0 ! 7

70 !

72>

,

, ,

, -

-

,

100>

,30>

22>

-

Ansers#> Q$82>'#/$>'04

0>Q08

y084>'$8 y#28;>'22y#$;

,

Home

Triangles insi"e circles

Angles connecte" b a chor"


68/117

25>

,

0!

7

=8:

-15>

-

,

-

,

,

-

-

,

25> 53>30>

-

,

80>

17>5>

35>

40>

125>

15>

40>

10>

100>

Ansers

#> '24 y#42>'#24 y08 #4$>'#8 y98#880>Q#84 y08$44>'4$ y $8

92;>'/4 y/8#9

Home

g es co ec e" b a c o "

Tangents to a circle

A&e*:


69/117

40> ,-

7

120>

,

8

140>

,

!

,35 >

0

-

Home

g1. x+552. x+403. x+50 y+50

,+404. x+60 y+60

,+30

Cclic %ua"rilaterals


70/117

,

-,

-

,

-

5> 110> 54>

75>

20>

80>

, 2a

4b

15> 70> a

b

0

25>

-

+

! 7

8 :

Ansers#> '98y/4

2>'#2;y#84$>'#88y#;8

0>#4 '98y;4 244>a;8b$;

Home

%

Construction


71/117

Home

Trigonometr Sin an" Cos

A&e*:

1.


72/117

g

Home

1. d+"yp'-e&$e2. e+ad#ace&-3. f+ 'pp'i-e4. "+"yp'-e&$e5. !+ad#ace&-6. i+'pp'i-e

7. #+"yp'-e&$e8. %+ad#ace&-9. l+'pp'i-e10. m+"yp'-e&$e11. '+ad#ace&-12. &+'pp'i-e13. p+"yp'-e&$e14. +ad#ace&-15. *+'pp'i-e

A&e*:

2.a) 6.1b) 3.5e)7.1f) 7.1!)2.6i)3.1%) 2.1l) 14.9&) 11.3')3.8p)12.6*)18

Trigonometr 3n"ing angles


73/117

g g g

Home

20cm

$2cm

A&e*:1) 41.42) 76.23) 49.34) 51.4

5) 70.66) 53.1

2?cm

Cosine ruleA&e*:1 32


74/117

Cosine rule

Home

1. 32cm2. 3.5cm3. 45.4c/

4. 139.5 /5. 25.2 '*11.1cm

6. 16.7cm

22cm

4cm

The Sine rule


75/117

Home

A&e*:1) 10cm

2) 3.0cm3) 3.4 cm4) 25.7cm5) 50.2cm6) 26.7cm

The Sine rule

Trigonometr


76/117

Sin1 Cos an" Tan

Home

A&e*:

1. a)15.7b)46.7c)32.2d)30.6e)21.9f)63.5

2.a)6.1b) 11.9c) 69.3

d) 15.6e) 2.1f)7.7

#4*9cm

Sine an" Cosine /ule


77/117

Home

A&e*:1)25.6/2)6.5cm

3)20.4cm4)21.6 '* 15.6

cm5)9.73cm6)40 /

7)34 /8)5.3cm9)14.3/10)42cm11) 24.46cm12)27.6 '* 3.6

cm

/cm

#8cm

#0cm

#4cm

22cm

#?cm

Sin1 cos an" tan !


78/117

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A&e*:1) 3.1cm2) 6.1cm

3) 5.1cm4) 17.1cm5) 4.5cm6) 8.6cm7) 20.5cm

8) 31.1cm9) 117.6cm10)1.5cm11)4.1cm12)108.9cm

Translation


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/eection !


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/eection 0


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/eect these shapes in the mirror lines

7D (thagoras


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g

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#in" the length of the longest "iagonal of these cuboi"s

#> Ansers

2> ##*2cm$> #2*8cm0> #2*2cm4> ?*0cm;> #$*0cm

9> #4*2cm


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#in" the (erimeter of


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5cm

8cm

8cm

5cm

4cm

cm cm

4cm

12cm

10cm3cm

15cm

7cm

11cm

these shapes

8cm8cm

5cm

4cm

cm

4cm

8cm

3cm

5cm4cm 12cm

11cm

13cm

All of these shapes are regular

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Ansers#*2;cm2*2;cm$*$8cm0*24cm

4*$;cm

Ansers#*2#cm

2*#9cm

Ansers#*#;cm2*24cm$*92cm0*$?cm4*?;cm;*##8cm

9*02cm

)or"e" (thagoras


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)or"e" (thagoras

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#*A hunter (res an arro to .ill a bird, the bird falls 28m and the hunter

has to al. 08m to pic. it up, ho far did the arro travel to the bird

2*A boat travels 04 miles east then ;8 miles north, ho far is it from here

it started

$*A simming pool is 24m by #2m, if someone sam from one corner to the

other, ho far ould they have sum

0*A .ite is "ying on a string hich is #8m, the .ite is "ying ;m of the

ground, if the .ite plummets straight don ho far ill the .ite "yer have

to al. to pic. it up

4*A totem pole is tied to the ground ith ropes stuc. in the ground ith

pegs, if the rope is #0m long and the pole is ?m long, ho far ill the

pegs be from the base of the totem pole

;*A lighthouse shines a light on a ship, the light beam is /8m long, the ship

is ;8m aay from the base of the lighthouse, ho tall is the lighthouse

Ansers

#*00*9m2*90miles$*29*9m0*/m

4*#8*9m;*42*?m

a# b and c gi$ing reasons for each answer* Ansers#* a29

Mcorresponding>


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a

b110 >

Find a# b and c gi$ing reasons for each answer*

c a

bc

120 >a

bc

55 >

a

115 >

b

ca b

c25 >

a

b

c

10>

a

27?

120?

b

a

94?

45?b

110 ?c

95 ?c

Mcorresponding>2* b #28

Malternate>$* c /4 Minterior>

0* a #84 Minterior>4* b04 Malternate>;* c ##8

Malternate>

Ansers#* 98,98,##82* ;8,;8,;8$* 44,#24,44

0* ##4,;4,;44* #44,24,24;* #98,#98,#8

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i$d (he *a"e' of ,

Li$d (he *a"e' of ,

Ansers# #$4

Ansers#* #842 #28


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45 ?

130 ?

30 ?

,,

,,

45 ?

55?

25?

Li$d (he *a"e' of ,

,,

,,

95?15?

60?

35?

30?

120?

Li$d (he *a"e' of ,

,95?

35 ?,

110?70 ? 120?25 ?2,

,2,

3,?80 ?

4,2,

,

, ,5,

#* #$42* #48$* ?80* 48

2* #28$* #840* $8

Ansers#* #042* #04

Ansers#* 042* $;$* /8

0* $#

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(lans an" Elevations


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Draw the plan an" the

front an" si"eelevations for theseshapes


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A7SE!S&n terior and


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:ind the e'teriorand interiorangles of a

regular shapehich has1a>? sidesb>#8 sidesc>#2 sidesd>#4 sidese>24 sides

A7SE!S#*

a> &#08, E08b> &#00, E$;

c> &#48, E$8d> ,E20e> &#;4*;,

E#0*0

e ' terior

angles

A7SE!S!egular pol ygons N

mber of


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#* 6o many sides does aregular polygon have if itse'terior angles are1a> 04b> 08c> $8

d> 22*4e> 28f> $

A7SE!S#*

a> /b> ?

c> #2d> #;e> #/f> #28

(nding number o f

sides

2* 6o many sides does aregular polygon have if itsinterior angles are1

a> #48b> #4;c> #49*4d> #;2e> #;4f> #;/*94

A7SE!S2*

a> /b> ?c> #2

d> #;e> #/f> #28

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(thagoras


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ANSWERS

1.a)5#b)10#c)13#d)10.8#e)6.3#f)3.3#g)6.9#

h)8.7#2. 5.83. 1.9#

-ean

#*:ind the mean from these numbers1

1.a) 4


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a> 4,$,0b> #8, ##, #, 9c> #4, /, 9, #8d> #0, 2, 0, #, 0

e> 9, /, 4, #8, 0, 2f> 20, 2;, $2, #9, #g> 8*2, 8*#, 8* 4, 8*2h> 28, ?, $, /, /, 9,#i> #9, #/, #4, #8, /, 2, ?,#

@> 8,8,8,8,8,#/

2*6o ould you (nd the1a> 3ean age of players in a football teamb> 3ean height of a familyc> 3ean number of seets eaten by boys in a dayd> 3ean number of hours spent atching T for a

pupil each nighte> 3ean number of times someone says U=I=V a

day$*rite don $ possible lists of numbers if there are1

a> 0 numbers ith a mean of ;b> 4 numbers ith a mean of /c> 9 numbers ith a mean of ?

)b) 7c) 10d) 5e) 6

f) 20g) 0.25h) 8i) 10 j) 3

2.a) Add a"" %"a-e' age':

di*ide b- (he $#beof %"a-e'

b) Add a"" (he heigh('(oge(he di*ide b-$#be of %eo%"e

c) Add % $#be of'+ee(' ea(e$ b- bo-':di*ide b- $#be of

bo-'d) Add a"" (he ho'(oge(he di*ide b- (he$#be of %%i"'

e) Add (oge(he ho+#a$- 'o#eo$e 'a-' "o"each da- fo "o(' ofda-': di*ide b- (he$#be of da-'

-ean1 -o"e1 -e"ian an" /ange


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#*hich of these could you not (nd a median fora> 6eightb> :avourite colour

c> Score in a testd> :avourite football team

2*:ind the mean, mode, median and range for these sets of numbers1a> 4,9,2,/,/b> 2,#2,;,$,2c> #4,0,##,;,0d> 28,$8,$4,#4,#4

e> 0,9,8,#0,8,#?,4f> 2,?,#/,#2,9,2,;g> 2#,#$,#4,2,#4,$,#

$*rite $ diWerent lists of 4 numbers hich have a mean of 9*0*rite $ lists of numbers hich have a median of ##4*ould mode be a good thing to (nd if e ere loo.ing at pupils e'act

@ourney time to school E'plain your anser*;*Can any of mean, median, mode and range be negative E'plain youranser

ANSWERS

1. fa*oi(e co"o

a$d fa*oi(efoo(ba"" (ea#2.

a)6:8:7:6b)5:2:3:10c)8:4:6:11

d)23:15:20:20e)7:0:5:19f)8:2:7:16g)10:15:13:20

3.4.Ei(he (he #ea$ o

(he #edia$5.A"" ca$ be $ega(i*e

e,ce%( (he a$ge.

-e"ian an" /ange

AN WER


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ANSWERS

1.a)edia$


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-ean from tables


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ANSWERS

1.a)18b)24c)1.3

2.a)30b) 44c)1.5

3.a)47

b) 107c)2.3

Drawing (ie charts 0#


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#*a> /b> dog#H/,

cat#H0,(sh4H/

2*c> green#H#

8Pin.#H0+lue$H#8!ed 2H4

b> green2H28Pin.0H28+lue;H28

!ed /H28


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#a* $;

ii>#8b>08,98,#88,#48

2a* 92 ii>4b>$8,04,;8,04,#/8

$a* #/8

ii>2b>48,#00,;0,28,/#

0a* 928

ii>8*4b>#88,;8,48,04,48,;4

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/elative #requenc


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ANSWERS

1.a)75b)37.5c) 125

2.a) "e


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05 &f & ip a coin an" roll a "ice1 list all the possible outcomes & coul" get5!5 & spin two fair spinners number 0 to 75

a4 Cop an" complete the table to show all the possible outcomes5

75 )hen & have breakfast & have a "rink an" something to eat5 The "rinks &

choose from are tea1 coFee an" Guice an" & eat a bagel1 toast or cereal5)rite "own all the "iFerent combinations & coul" have for breakfast585 &f & toss 0 coin there are ! possible outcomes1 3n" the number of outcomes

fora5 ! coins b5 7 coins c5 8 coins "5 coins

:5 'uc1 Am an" $eorge are going to have their photo taken so the sit in a

linea4 How man "iFerent was coul" the or"er themselvesIb4 An" Goins them1 how man "iFerent was coul" the or"er

themselves nowI

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Spinner 0 Spinner ! Total

1.1:2:3:4:5:6:1: 2:3:4:5:6

2.1.1G12

2.1G233.1G344.2G135.2G246.2G357.3G148.3G259.3G36

3.b:(:c:b:(:c:b:(:c

4.a) 4

b) 8c) 64d) 2,

5.

a) 6b) 24

Drawing Bar Charts


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Tree Diagrams

A> & have a bag ith 28 balls in, there are #$ pin., 9 orange pull a ball out, put it bac. then pullanother*

# D t di h i ll ibl t

ANSWERS


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#*Dra a tree diagram shoing all possible outcomes2*se your tree diagram to (nd the probability of getting1

a*2 pin. b*2 orange,c*A pin. and an orange*

+> The probability & have toast for brea.fast is 8*;, the probability & ill miss my bus is completelyunrelated to my brea.fast choice and is 8*2

$*hat is the probability & ill 7IT1a*6ave toast for brea.fastb*3iss my bus

0*Dra a tree diagram shoing all possible outcomes4*se your tree diagram to (nd the probability of1

a*6aving toast and missing my busb*7ot having toast and missing my busc*7ot having toast and not missing my bus

C> & am tossing a coin and rolling a dice1;*Dra a tree diagram to sho all possible outcomes*9*se your tree diagram to (nd the probability of1

a*A head a $b*A tails and a number bigger than 0c*A tails ith a $ or a heads ith a #

D> & have some songs on my mp$ player, 0 are roc., 9 are Pop and ## are 6ip 6op* & put my mp$

player on shuZe and listen to 2 songs Mit is possible to listen to the same song tice in a ro>/*Dra a tree diagram to sho all the possible outcomes,a*:ind the probability that & ill listen to1

i*6ip 6op then Popii*!oc. ticeiii*A !oc. song and a pop song in any orderiv*2 songs hich are the same style Mroc. and roc. or pop and pop ect*>

A.2.

a) 169/400b) 49/400

c) 91/400.

1.a) 0.4b) 0.8

3.a)0.12

b)0.08c)0.32.

2.a) 1/12b) 1/6c) 1/6

H.

a)i. 7/44ii. 4/121iii. 14/121i*. 93/242

Stem an" 'eaf Diagrams


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ANSWERS

2.a) Ra$ge


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%uestions p 1 gor no correlation an" tr to give a

reason wh

Temperature

&ce Creamssold

0; =7

70 :7

0! ;;7: 70

7> !?

78 87

78 8=!! =8

7; !?

70 7:

Time ta.en

to al. to

school

Score in

spelling

test

29 2

#8 08

#0 4

29 #

08 ;

#0 02

#4 09

#9 22$4 0

$/ $#

#9 #$

#/ 2

29 #$

6ours

spent

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intern

et

Score on

&CT test#$ #0$$ $?29 $9$/ 04#$ #/

$? ;2#8 #?$8 40#? $;2? $0#; 2224 02

2/ $$Home

The (robabilit 'ine


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ANSWERS

2.

i. 0.1ii. 0.5iii. 0.2i*. 0.2*. 0*i. 1*ii. 0.4*iii.0.6

Bo* an" )hiskerplots


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-utuall E*clusive Events


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ANSWERS

1.a) 0.7

b) 0.6c) 0.48d) 0.79e) 75Bf) 2Bg) 3/5h) 4/10

i) 3/152.a) (a""-

e,c"'i*eb) No( #(a""-

e,c"'i*ec) No( #(a""-

e,c"'i*e

d) (a""-e,c"'i*e

3.a) 0.1b) 0.2c) 0.23

4. 0.24

Sample Space Diagrams

ANSWERS


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1.a)

i. 1/36ii.1/12iii.1/9

b) 7: i( a%%ea' (he#o'(

2. a)03.4.

1.2.

a)6/25b)19/25c) 9/25d)8/25

Sampling


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ANSWERS

1.• ea 7< 20• ea 8


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ANSWERS

1.i. i'(oga#' ha*e $e*e$

c"a'' i$(e*a"':ii. (he fe&e$c- i'

e%e'e$(ed b- (heaea of (he ba $o( (heheigh(:

iii.fe&e$c- de$'i(- i'di'%"a-ed o$ (he - a,i'

#8 8*44 #

#4 4

$8 2*4;8 00:

Drawing Cumulative #requenc $raphs


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?ie harts

nswers:1* 20 and 202 ll are 25


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?ie harts

40 'eo'le

100 'eo'le 40 'eo'le 36 'eo'le

48 'eo'le320 'eo'le 640 'eo'le 720 'eo'le

2* ll are 253* ll are 5

4* ellow and blueare red is 185* ellow and red are

12 others are 66*


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/ea"ing BarCharts

08

0!

0


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ANSWERS

1.a) 5b)3c) 5d)39

2.

a) $!b)R$c) 51d) $!: R$:

e(a"/Ra%:o%/Reggae

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Homer

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