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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
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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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic Questions
Answers
Day 2
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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
7/23/2019 Level 7 Answers.doc
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1 mark
KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day ,
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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
7/23/2019 Level 7 Answers.doc
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1 mark 2 marksKS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day )
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day 5
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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?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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day 6
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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@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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day *
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic QuestionsAnswers
Day $
Mental Arithmetic Questions
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
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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
7/23/2019 Level 7 Answers.doc
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KS3 MATHEMATICS
10 4 10
Level 7 Mental Arithmetic Questions
Answers
Day 1!
Mental Arithmetic Questions
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
7/23/2019 Level 7 Answers.doc
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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.
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