Level 7 Answers.doc

7/23/2019 Level 7 Answers.doc

1/20

KS3 MATHEMATICS

10 4 10

Level 7 Mental Arithmetic QuestionsAnswers

Day 1

Mental Arithmetic Questions

1. What number is five cubed?

5 x 5 x 5 = 125

2. A circle has radius r.What is the formula for the area of the circle?

Area = pi x radius x radius

= r

3. Jenny and ar! share some money in the ratio t"o to three.Jenny#s share is one hundred and ten pounds.$o" much is ar!#s share?

x 55 2 % 3 x 55

11&

165

'. (he net of a trian)ular prism is made from trian)les andrectan)les. $o" many of each shape are needed?

3 rectan)les2 trian)les

5. ultiply minus six by minus t"o.

*+ x ,2 =12


2/20

Percentage Change

(a) -ne calculation belo" )ives the ans"er to the uestionWhat is ! increase" #y $%(ic! /0 the correct one.

hoose one of the other calculations.Write a uestion about percenta)es that this calculation

represents.alculation chosen..uestion it represents

4o" do the same for the remainin) t"o calculations.alculation chosenuestion it represents

/b0 ill in the missin) decimal number.

(o decrease by 1'67 multiply by

1&& , 1' = 8+ 8+6

&.8+

Co&&ee

A cup of coffee costs 91.:5

(he dia)ram sho"s ho" much money different people )et "hen youbuy a cup of coffee.

/a0 omplete the table to sho" "hat percenta)e of the cost of acup of coffee )oes to the retailers7 )ro"ers and others.

;ho" your "or!in)

91.:5 = 1:5p


3/20

KS3 MATHEMATICS

10 4 10

Level 7 Mental Arithmetic Questions

Answers

Day 2


1. What is one third of three*uarters of one hundred?

1 x 3 x1&& 1 of :5 = 253 ' 3

2. #m thin!in) of a number. call it n. suare my number and then add '.Write an expression to sho" the result.

n2 @ '

3. ("enty*one out of thirty*six pupils said they "atched (op of theops.What an)le on a pie chart "ould sho" this?

1 pupil = 3+&= 1&21 pupils = 21 x 1& = 21& 3+

'. (here are seven red and three blue balls in a ba). am )oin) tota!e a ball out of the ba) at random. What is the probability thatthe ball "ill be blue?

4o of Blue = 3(otal 1&

5. Write a multiple of three that is bi))er than one hundred.

1&27 1&57 1&87 .. or other


4/20

Powers

/a0 Write the values of ! and m.

6) = *2= )+= 2m

8 x 8= ' x 2 x ' x 2 == ' x ' x ' x ' = '3

! = ...3..m = ..+

/b0 omplete the follo"in)%

215= ,2 6*215 = 21) - 21 so ,2 6* 2

21) = .((16,*)..(

2 marks

' x ' x '

2 x 2 x 2 x 2 x 2 x 2

/0uares

;ome numbers are smaller than their suares.

or example% : C :2

Which numbers are eual to their suares?

*1 x ,1 = 1& x & = &1 x 1 = 1

;o only ! 1

2 marks


5/20

1 mark

KS3 MATHEMATICS

10 4 10


Day ,


1. am thin!in) of a number. call it n. double my number then subtract three.Write an expression to sho" the result.

n double it = 2n;ubtract 3 2n , 3

2. What percenta)e of fifty pounds is thirty*five pounds?

35 x 1&& = :&65&

3. -n avera)e7 the driest place on earth )ets only nou)ht point

five millimetres of rain every year.n total7 ho" much rain "ould it expect to )et in t"entyyears?

&.5 x 2& = 1&mm

'. (o the nearest "hole number7 "hat is the suare root ofei)hty*three point nine?

83.> = 81 D81 = >

5. t ta!es me one and a half minutes to s"im one len)th of thepool.$o" many len)ths can s"im in fifteen minutes?

15E1.5

1.5 x 1& = 15 1& len)ths


6/20

Pentagonal Pyrami"

(he dia)ram sho"s the net for a ri)ht*pyramid "ith a re)ularpenta)on as its base.

(he net is constructed usin) five strai)ht lines.

/a0 Without measurin)7 explain "hy an)le a must be 1&8F

/b0 alculate the siGe of an)le b.

Hou must sho" your "or!in)

sosceles..3+F

ab

s a re)ular penta)onnterior an)les = 3 trian)les = 3 x 18& = 5'&F

Ach an)le = 5'& = 1&8F 5

1 mark

1&8F

B

18& , 1&8 = :2

:2 I 2 = 3+

/c0 -n these nets7 the point mar!ed lies on theperpendicular bisector of a side of the penta)on.

-n side of the re)ular penta)on belo"7 use compassesand a strai)ht ed)e to construct the perpendicular

bisector.

Hou must leave in your construction lines.

P P

C

D


7/20

1 mark 2 marksKS3 MATHEMATICS

10 4 10


Day )


1. (ari "on one hundred pounds in a maths competition. $e )avet"o*fifths of his priGe money to charity. $o" much of his priGemoney7 in pounds7 did he have left?

1 2

35=,

35,

35 o& 1!!135= 2!

,35= , - 2! = 6!

2( What is three 'oint nine "i4i"e" #y two,($ 2 , 2 = 1(5

!($ 2 = !()5 1($5

,( 7he instructions &or a &ruit "rin+ say to mi- one 'art#lac+currant 8uice with &our9'art water( : want to ma+eone litre o& this &ruit "rin+( ;ow much #lac+currant 8uiceshoul" : use


8/20

unning Machine

Mali uses a runnin) machine to !eep fit.

(he simplified distance*time )raph sho"s ho" she used the machinedurin) one run.

Lse the )raph to ans"er these uestions.

4

3

2

1

D i s t a n c e( k m )

0 9 3 0 0 9 4 0 0 9 5 0 1 0 0 0

T i m e

/a0 Bet"een &>3& and &>'&7 "hat "as her speed in !ilometresper hour?

>m % Mins1 1& x +

+&

+!mEh

/b0 (hrou)hout the run7 for ho" many minutes did she travelat this speed?

>.3& , >.'& and >.5& , 1&.&&1&mins @ 1&mins

2!mins

/c0 At &>'&7 she increased her speed.By ho" many !ilometres per hour did she increase herspeed?

&>.'& .>.5& travelled 2K !m

Mins % >m1& &.5+& >

> is 3!mEh more than +

3!mEh

/d0 -n another day7 Mali started runnin) at &>35. ;he ranfor2' minutes at a constant speed of 1& !ilometres perhour.1&!m % +&mins2.5 15mins

2.5!m in 15mins

;ho" this information on the )raph

1 mark

x x

5 *

1 mark

2 marks

1 mark


9/20

KS3 MATHEMATICS

10 4 10


Day 5


1 What is three*fifths of forty pounds?1E5of 9'& = 98 so

3E5 is 3 x 8 = 92'

2 (he lon)est bone in the human body is in the le). (he

avera)e len)th of this bone in a man is fifty centimetres. na "oman it is ten percent less.What is the avera)e len)th of this bone in a "oman?

5&cm 1&6 less than 5&cm10% of 0 6 0 6 *cm

or -oman is 100% 8 10% 6 90% 90% of 0 6 *cm

3. Lsin) three as an approximation for pi7 "hat is the area of a

circle "ith radius five centimetres?a = N x r2 = 3 x 52 = 3 x 25 = 5cm2

'. am thin!in) of a t"o*di)it number that is a multiple of ei)ht.(he di)its add up to six.What number am thin!in) of?

ultiples of 8. 1+7 2'7 32 2 = ' = + = 2)

5. am thin!in) of a number. call it n. add five to my number.Write an expression to sho" the result.

4 @ 5


10/20

?oci

(he dia)ram belo" sho"s t"o points A and B that are +cm apart.

Around each point are six circles of radius 1cm7 2cm7 3cm7 'cm7 5cm and+cm. Oach circle has either A or B as its centre.

/a0 -n the dia)ram7 mar! "ith a cross any points that are 'cm a"ay

from A and 'cm a"ay from B.

(his is "here '!m circles cross

/b0 4o" dra" the locus of all points that are the same distance fromA as they are from B

Join the 2 pointsa!e sure they extend beyond the circles

6 c m

6 c m

5 c m

5 c m

4 c m

4 c m

3 c m

3 c m

2 c m

2 c m

1 c m

1 c m

A

B

1 mark

1 mark

earrange

(he subPect of the euation belo" is p

= 2 /e @ f0


11/20

KS3 MATHEMATICS

10 4 10


Day 6


1. ive percent of a number is 8. What is the number?

56 = 85&6 = 8&

1&&6 = 1+&

2. A fair spinner has ei)ht eual sections "ith a number on eachsection. ive of them are even numbers. (hree are odd numbers.What is the probability that spin an even number?

5 * no of even8 (otal no.

3. can ma!e a three*di)it number from the di)its t"o7 three andfour in six different "ays.$o" many of these three*di)it numbers are even?

27 37 '

'. What is the volume of a cuboid measurin) five centimetres by six

centimetres by seven centimetres?Q x W x $ = 5 x + x :

3& x : = 21!

5. What is the remainder "hen you divide three hundred by t"enty*nine?

2>x 1& = 2>& 1! is remain"er 1!

x 10 10

x

4*4* *4

*4 4* *4

* even


12/20

@4ens or ""s

Ba m is an o"" num#er(

Which of the numbers belo" must be even7 and "hich must be odd?

Write Rodd# or Reven# under each one.

If unsure by some o numbers in eac! one"

/b0 m is an odd number.

s the number m @ 1 odd7 or even7 or is it not possible to tell? 2

(ic! /#0 the correct box.

Oxplain your ans"er.

f m is odd m @ 1 is evenor m @ 1 to be even7 m @ 1 must be a multiple of '.

2

2m

Oven

m2

-dd

3m * 1

Oven

/m , 10 /m @ 10

Oven

-dd Oven 4ot possible to tell

2 marks

1 mark

actors Again

/a0 y

@ 2y @ 18

H2 @ 18

H2@ 11y @ 18

4eed factors of@12 "hich add to @

8

actors

1 12*1 *122 +

*2 *+' 3*' *3

/y @ 20 /y @ 10

/y @ 30 /y @ '0 /y @ :0 /y @ 10

/y @ 10 /y @ 120 /y @ 30 /y @ 50

1 mark

! 9

!

@ >y 2y

2 marks


13/20

KS3 MATHEMATICS

10 4 10


Day


1. ("enty*five percent of a number is seven. What is the number?

256 is :

5&6 is 1'1&&6 is

2. (here are fourteen )irls and thirteen boys in a class. What is theprobability that a pupil chosen at random "ill be a )irl?

(otal = 1' @ 13 = 2:

irls = 1'(otal 2:

3. (he first even number is t"o. What is the hundredth evennumber?

2 x 1&& = 2&&

'. (he mean of t"o numbers is 8. -ne of the numbers is t"o. Whatis the other number?

(otal must be 8 x 2 = 1+

? @ 2 = 1+ ? = 1'

5. $o" many ed)es are there on a suare based pyramid?

' on base' on sides

= 8

x

x

x

x 28


14/20

Angles

(his pattern has rotation symmetry of order +

/a0 What is the siGe of an)le "?

;ho" your "or!in).

.3'F

/b0 Oach uadrilateral in the pattern is made from t"o con)ruentisosceles trian)les.

What is the siGe of the an)le y? ;ho" your "or!in)

An)les at point = 3+&F

7ele4ision

A headteacher "ants to choose a pupil from year :7 8 or > to appearon television.

(he headteacher )ives each pupil one tic!et

(hen she "ill select the "innin) tic!et at random

(he table sho"s information about the tic!et used

/a0 What is the probability that the "innin) tic!et "ill be blue?

4umber of blue = :5(otal numbers 2'5

;implify /I50 = 15 '>

/b0 What is the probability that the "innin) tic!et "ill sho"number 3>?

(here "ill be red 3>7 blue 3>7 yello" 3>so 3 tic!ets "ith 3>. 3

2'5/c0 (he headteacher selects the "innin) tic!et at random. ;he

says% R(he "innin) tic!et number s 3>.# What is the probabilitythat this "innin) tic!et is blue?

4umber is 3> 3 tic!ets "ith 3> blue is 1 of 31E3

$ o t r a % na c c u r a t e & y

w

y

2 6 '

(here are + an)les2+Fso + x 2+ = 15+F

An)les at a point = 3+&F;o 3+& * 15+F = 2&'F2&'F to share bet"een +

an)les

2&' I + = 3'F

2 marks

$ o t r a % na c c u r a t e & y

y

1 3 '

14:

14:

1;0 14 14 6 1*:

#$

A


15/20

KS3 MATHEMATICS

10 4 10


Day *


1. ultiply 8.: by 2

8 x 2 = 1+&.: x 2 = 1.'

2. A bat flies at an avera)e speed of 32 !ilometres an hour. Atthis speed7 ho" far "ill it fly in 15 minutes?

32!m % +&mins1+!m % 3&mins8!m % 15mins

3. ultiply the brac!ets /2x @ 10 /x , 10

'. #m thin!in) of a number. call it t. half it andsubtract five. Write an expression to sho" the result.

t * 5:

5. (he first odd number is 1. What is the hundredth oddnumber?

1$$

1:.'

x x

8 18x

x

8 1

x 1

x x x 1

x x 1


16/20

wls

-"ls eat small mammals.(hey re)ur)itate the bones and fur in balls called pellets.

(a) (he table sho"s the contents of +2 pellets from lon)*eared o"ls.

/b0 alculate the mean number of mammals found in each pellet.;ho" your "or!in) and )ive your ans"er correct to 1 decimalplace.

T fx = 1:& = 2.:' 2.:.to 1 decimal placeTf +2

/c0 (here are about 1& &&& lon)*eared o"ls in Britain. -navera)e7 a lon) eared o"l re)ur)itates 1.' pellets per day.Alto)ether7 ho" many mammals do the 1& &&&lon)*eared o"lseat in one day? ;ho" your "or!in) and )ive your ans"er tothe nearest thousand.

ammals in pellet x pellets per day x no. of o"ls2.: x 1.' x 1& &&&= 3: 8&&

+$umber of mamma&s

foun in t!e ,e&&et 1 2 3 4 5 6

f -re.uency 9 1) 24 6 5 1 /f 62

f+ $o" of mamma&s

fre.uency

1 + 9

9

2 + 1)

34

3 + 24

)2

4 + 6

24

5 + 5

25

6 + 1

6

1)0

Bfx6 170

x

ectangle est

(he dia)ram sho"s a rectan)le that Pust touches an euilateraltrian)le.

/a0 ind the siGe of the an)le mar!ed x;ho" your "or!in).

/b0 4o" the rectan)le Pust touches the euilateral trian)le so thatAB is a strai)ht line


17/20

KS3 MATHEMATICS

10 4 10


Day $


1. Add four to minus five.

*5 @ ' = *1

2. What number should you add to minus three to )et the ans"erfive?

3. $o" many nou)ht point fives are there in ten?

&.5 x 2 = 1 1 x 1& = 1&

'. -n avera)e7 the driest place on earth )ets only nou)ht point fivemillimetres of rain every year. n total7 ho" much rain "ould itexpect to )et in t"enty years?

&

5. What is the sum of the an)les in a rhombus?

All '*sided shapes /uadrilaterals0 have inside an)les "hich sum to3+&F

(hin! of number line or thermometer

84 8 0 1 4 * 81

;

0


18/20

7rue or alse

upils started to solve the euation +x @ 8 = 'x @ 11 in different "ays.

or each statement belo"7 tic! /0 (rue or alse.

/b0 A different pupil used trial and improvement to solve the euation +x

@ 8 = 'x @ 11

Oxplain "hy trial and improvement is not a )ood method to use

t "ould ta!e a lot of trialsor (a!es a lon) timeor Hou can solve it uic!ly by doin) the same thin) toboth sides

6 7*04 711x x

14 015x x

6 7*04 711x x

6 04 3x x+

6 7*04 711x x

2 03x

6 * 4 11x x9 6 9

6 74 0117*x x

6 7*04 711x x

2 7*011x

6 7*04 711x x

83082x

so

so

so

so

so

so

UTrue

True

True

True

True

True

-a&se

-a&se

-a&se

-a&se

-a&se

-a&se

UU

Hou need to solve euation /*80 /*'x0

+x @ 8 = 'x @ 11+x = 'x @ 11 , 8+x , 'x = 11 , 82x = 3

+x @ 8 = 'x @ 11/*'x0 +x , 'x @ 8 = 112x @ 8 = 11

+x @ 8 = 'x @ 11/*80 +x = 'x @ 11 , 8+x @ 'x @ 32x @ 8 = 11

11 , 8 = 3

3 marks

1 mark


19/20

KS3 MATHEMATICS

10 4 10

Level 7 Mental Arithmetic Questions

Answers

Day 1!


1. t ta!es some*one one and half minutes to s"im the len)th of thepool. $o" many len)ths can s"im in 15 minutes?

2. ultiply minus ei)ht by minus three.

3. f 'x @ 3= 237 "hat is the value of x?23 , 3 = 'x2& = 'x2& ' = x

- = 6

)( : ha4e a &air eight si"e" "ice num#ere" 12 to 1$( What isthe 'ro#a#ility that : will throw a 'rime num#er

/prime number0 =3E8

5. What must multiply n suared by to )et n cubed?

n2= n x nn3= n x n x n

so n2x n = n3

1 1 D

6 1 1.

=10 lengths10 x 1. 6 1so 1 5 1. 6 10

*8 x *3 = 2) 8 x 3 = 2'*8 x 3 = * 2'8x , 3 = *2'*8 x ,3 = 2'

-r used matchedline


20/20

o"ents

(he scatter )raph sho"s the avera)e body len)th and avera)e footlen)th of different species of rodents.

/a0 What does the scatter )raph tell you about the type ofcorrelation bet"een the body len)th and foot len)th for theserodents?

ositive orrelation

/b0 ra" a line of best fit on the scatter )raph.

Documents

Level 7 Answers.doc