Harder a Star Questions

8/19/2019 Harder a Star Questions

1/17

Uxbridge High School

More Really Annoying Mixed Stuff

178 min146 marks

1.

Diagrams NOT accurately drawn

A rectangular tray has length 60 cm, width 0 cm and de!th " cm#

$t is %ull o% water#

&he water is !oured into an em!ty cylinder o% diameter 8 cm#

'alculate the de!th, in cm, o% water in the cylinder#

(i)e your answer correct to * signi%icant %igures#

################################ cm(Total 5 marks)

2. Sim!li%y "*

1""

"

++

++

x x

x x

####################################(Total marks)

. &oby in)ested +00 %or " years in a sa)ings account#Uxbridge High School 1


2/17

He was !aid - !er annum com!ound interest#

How much did &oby ha)e in his sa)ings account a%ter " years.

+ ############################

(Total marks)

!.

1 0 c m

c mD i a g r a ma c c u r a t e l y d r a w n

N O T

&he diagram shows a cylinder with a height o% 10 cm and a radius o% cm#

/a 'alculate the )olume o% the cylinder#


###########################cm*

(2)

&he length o% a !encil is 1* cm#&he !encil cannot be broen#

/b Show that this !encil cannot %it inside the cylinder#

()

(Total 5 marks)

5. &he table shows the number o% boys in each o% %our grou!s#

(rou! A 2 ' D &otal

3umber o% boys *" * *8 14 1*"

5amie taes a sam!le o% 0 boys strati%ied by grou!# 'alculate the number o% boys %rom grou! 2 that

should be in his sam!le#

(Total 2 marks)

".

Uxbridge High School 2


3/17

y

O

x

/ 1 , 7

/ * , 1 7

Diagram NOT accurately drawn

&he setch shows a cur)e with euation

y ka x

where k and a are constants, and a 0# &he cur)e !asses through the !oints /1, 7 and /*, 17#

'alculate the )alue o% k and the )alue o% a#

k ################################

a ################################(Total marks)

#. Here are the %irst %i)e terms o% an arithmetic seuence#

−1 * 7 11 1

/a 9ind, in terms o% n, an ex!ression %or the nth term o% this seuence#

::::#::::::::##(2)

$n another arithmetic seuence the nth term is 8n − 16# 5ohn says that there is a number that is in both

seuences#

/b ;x!lain why 5ohn is wrong#

::::::::::::::::::::#::::::::::##:#:##

::::::::::::::::::::::::::::::::#:#(2)

(Total ! marks)

$.



4/17

y

"

6

8

1 0

B / " , 8

A / 0 # , 1

" < " < O x

&he diagram shows a setch o% the gra!h y ab x

&he cur)e !asses through the !oints A /0#, 1 and B /", 8#

&he !oint C /or out the )alue o% x

x = ######################################(2)

(Total ! marks)

1&. @aty dro)e %or "*8 miles, correct to the nearest mile#



5/17

She used "7#* litres o% !etrol, to the nearest tenth o% a litre#

etrol consum!tion used !etrolo% litreso% 3umber

tra)elledmileso% 3umber

>or out the u!!er bound %or the !etrol consum!tion %or @atyBs Courney#

(i)e your answer correct to " decimal !laces#

###################################### miles !er litre(Total marks)

11. &he mass M grams o% a cube with edges o% length L cm and density D grams !er cm

*

isgi)en by the %ormula

M DL*

D 8 correct to 1 signi%icant %igure#

L = 6# correct to 1 decimal !lace#

'alculate the u!!er bound o% M.

(i)e your answer correct to " signi%icant %igures#

#####################################(Total marks)



6/17

1.

x °

P 1 " c m R

Q

# c m

Diagram NOT

accurately drawn

PQR is a right?angled triangle#

PR = 1" cm#

QR = # cm#

Angle PRQ = 40#

>or out the )alue o% x. (i)e your answer correct to one decimal !lace#

x = ####################################(Total marks)

1!. &he gra!h o% y % / x is shown on the grids#

/a En this grid, setch the gra!h o% y % / x < 1

(2)



7/17

/b En this grid, setch the gra!h o% y " % / x

(2)

(Total ! marks)

1". A school has 0 students#

;ach student studies one o% (ree or S!anish or (erman or 9rench#

&he table shows the number o% students who study each o% these languages#

'anguageNumer of

students

(ree 1

S!anish 1"1

(erman 148

9rench 186

An ins!ector wants to loo at the wor o% a strati%ied sam!le o% 70 o% these students#

9ind the number o% students studying each o% these languages that should be in the sam!le#

(ree ###########################

S!anish ########################

(erman ########################

9rench #########################(Total marks)



8/17

1#. Use your calculator to wor out the )alue o%4#10*#"

8#74,#8

×

+

/a >rite down all the %igures on your calculator dis!lay#

#####################################

(2)

/b >rite down your answer to !art /a correct to * signi%icant %igures#

#####################################(1)

(Total marks)

1%. A lighthouse, L, is *#" m due >est o% a !ort, P #

A shi!, S , is 1#4 m due 3orth o% the lighthouse, L#

/a 'alculate the siFe o% the angle mared x#


x ::::::## ()

/b 9ind the bearing o% the !ort, P , %rom the shi!, S #


:::::::### °

(1)

(Total ! marks)



9/17

2&. &he diagram shows a !yramid# &he a!ex o% the !yramid is V # ;ach o% the slo!ing edges is o% length 6

cm#

&he base o% the !yramid is a regular hexagon with sides o% length " cm# O is the centre o% the base#

/a 'alculate the height o% V abo)e the base o% the !yramid#

(i)e your answer correct to * signi%icant %igures

::::::##cm(2)

/b 'alculate the siFe o% angle DVA#


::::::##o

()

/c 'alculate the siFe o% angle AVC #


::::::##o

(!)

(Total % marks)



10/17

21.

ictures NOT

accurately drawn

A "0 ;uro note is a rectangle 1** mm long and 7" mm wide#

A 00 ;uro 3ote is a rectangle 160 mm long and 8" mm wide#

Show that the two rectangles are not mathematically similar#

(Total marks)

22.

D i a g r a ma c c u r a t e l y d r a w n

N O T

A

BC

D

E F

6 0 c m

* 0

&he diagram re!resents a !rism# AEFD is a rectangle# ABCD is a suare#

EB and FC are !er!endicular to !lane ABCD.

AB = 60 cm# AD = 60 cm#

Angle ABE = 40# Angle BAE = *0#

'alculate the siFe o% the angle that the line DE maes with the !lane ABCD. (i)e your answer correct

to 1 decimal !lace

##########################(Total ! marks)

2. A garage ee!s records o% the costs o% re!airs to its customersB cars#



11/17

&he table gi)es in%ormation about the costs o% all re!airs which were less than +"0 in one wee#

'ost, /+C 9reuency

0 G C ≤ 0

0 G C ≤ 100 8

100 G C ≤ 10 7

10 G C ≤ "00 10

"00 G C ≤ "0 11

/a 9ind the class inter)al in which the median lies# #############################

&here was only one %urther re!air that wee, not included in the table#

&hat re!air cost +1000#Da)e says &he class inter)al in which the median lies will change#B

/b $s Da)e correct. ;x!lain your answer#

##############################################################################################################################

&he garage also sells cars# $t o%%ers a discount o% "0- o%% the normal !rice %or cash# Da)e !ays +"00

cash %or a car#

/c 'alculate the normal !rice o% the car#

+############################ (Total " marks)

2!. &he shutter s!eed, S , o% a camera )aries in)ersely as the suare o% the a!erture setting, f #

>hen f 8, S 1"

/a 9ind a %ormula %or S in terms o% f #

##########################()

/b Hence, or otherwise, calculate the )alue o% S when f

S ####################(1)

(Total ! marks)

25.



12/17

x

x

A cuboid has a suare base o% side x cm#

&he height o% the cuboid is 1 cm more than the length x cm#

&he )olume o% the cuboid is "*0 cm*#

/a Show that x* I x

" "*0

(2)

&he euation x* I x

" "*0

has a solution between x and x 6#

/b Use a trial and im!ro)ement method to %ind this solution#

(i)e your answer correct to 1 decimal !lace#

Jou must show all your woring#

x ###########################(!)

(Total " marks)



13/17

2".


N O T

6 7

1 1 # 7 m

" 8 # * m

A

B C

AB 11#7 m#

BC "8#* m#

Angle ABC 67°#

/a 'alculate the area o% the triangle ABC #


::::::::::# m"

(2)

/b 'alculate the length o% AC #


::::::::::# m()

(Total 5 marks)

2#.

* # 8 c m

" # c m

D i a g r a m N O Ta c c u r a t e l y d r a w n

An ice hocey !uc is in the sha!e o% a cylinder with a radius o% *#8 cm, and a thicness o% "# cm#

$t is made out o% rubber with a density o% 1# grams !er cm*#

>or out the mass o% the ice hocey !uc#


############### grams(Total ! marks)



14/17

2$. y" ba

ab

+

a * K 108

b " K 107

9ind y#

(i)e your answer in standard %orm correct to " signi%icant %igures#

y ###################################(Total marks)

2%.


N O T

7 0

A

BC

X

8 c m

1 c m

$n triangle ABC ,

AC 8 cm,

CB 1 cm,

Angle ACB 70#

/a 'alculate the area o% triangle ABC #


############################### cm"

(2)

X is the !oint on AB such that angle CXB 40#

/b 'alculate the length o% CX #


################################ cm(!)

(Total " marks)



15/17

&.

L m

x

;lliot did an ex!eriment to %ind the )alue o% g mLs", the acceleration due to gra)ity#

He measured the time, T seconds, that a bloc too to slide L m down a smooth slo!e o% angle x#

He then used the %ormula g ° xT

L

sin

""

to calculate an estimate %or g #

T 1#* correct to 1 decimal !lace#

L #0 correct to " decimal !laces# x *0 correct to the nearest integer#

/a 'alculate the lower bound and the u!!er bound %or the )alue o% g #

(i)e your answers correct to * decimal !laces#

Mower bound #########################################

U!!er bound ##########################################(!)

/b Use your answers to !art /a to write down the )alue o% g to a suitable degree o% accuracy#

;x!lain your reasoning#

##############################################################################################################################

##############################################################################################################################

####################################(1)

(Total 5 marks)



16/17

2. Use your calculator to wor out the )alue o%

41#1"*#6

*"#08141#7/ *

+

×−


::::::::::(Total marks)

. Henry in)ests +00 at a com!ound interest rate o% - !er annum#

At the end o% n com!lete years the in)estment has grown to +64#78#

9ind the )alue o% n#

::::::::

(Total 2 marks)

!. &he diagram re!resents a )ertical %lag!ole, AB#

&he %lag!ole is su!!orted by two ro!es, BC and BD, %ixed to the horiFontal ground at C and at D#


N O T

1 " # 8 m

" A

B

C D6 # 8 m

AB 1"#8 m#

AC 6#8 m#

Angle BDA "°#

/a 'alculate the siFe o% angle BCA#


::::::::::°

()

/b 'alculate the length o% the ro!e BD#


:::::::::: m()



17/17

(Total " marks)


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