I Work out the value of

2 A group ofstudents take a test.

The group consists of 12 boys and 8 girls.The mean mark for the boys is 18

The mean mark for the girls is 16.5

Calculate the mean mark for the whole group.

Answer ALL TWENTY TWO questions.

\Mrite your answers in the spaces provided.

You must write down all the stages in your working.

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= (z,a rt37) ; zo

[1,4J--v-::b)*

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Bhavik left his home at 12 00 to cycle to Sam's house.

On the way Bhavik stopped for a rest, and then continued his journey.The distance-time graph shows his loumey.

45

40

35

30

25

20

15

l0

5

01200 1300 1400 l5 00

Time

1600 t700 t800

(a) (i) For how many minutes did Bhavik stop for a rest?

3:4. . minutes

(ii) After his rest, how many more kilometres did Bhavik cycle to Sam's house?

39 - lY

2l km

(b) Bhavik stayed at Sam's house for 2 hours.He then cycled back to his home.He arrived home at 17 15.

Show all this information on the graph.

(c) Write down the times at which Bhavik was 24 kilometres from his home.

l?,7116 78

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Distancefrom home(km)

4

P40661A0420

(d) Work out the average speed, in kilometres per hour, of Bhavik's journey from Sam'shouse back to his home.

Give your answer correct to I decimal place.

31 :

= 39;

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1

i"-"^*"'?-""*""*t

?.

_."----,"i.....-.-"^"

(a) Describe fully the single transformation that maps shape P onto shape Q.

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,(rytl\Igr Qr"eqligq l- js e mry[9)

i ,'.',

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kmih

Re€lectron in the, line *=l(b) On the grid, rotate shape P 90o clookwise about the point (2, 0).

Label the new shape R.

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2I.-"It

I

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5 (a) Show that 1* 7 =155 15 7

(b) show that 5i -r1=r*

4t5

60 tz

IL1

35 1

tL tL -t5_t-1 1-ll

L-4

_atLL+3

tL tL

+3LLtL

Calculate the lenglh of MN.Give your answer correct to 3 siguificant figures.

?r-r MN--

-sintt - Sin-.lZ

-#)34 x sinl"b

= l)U,G l+ 1,,.5in l8

t,1')

"...."....""---lT-:JA-!v:.9v::!::".F*:tE:"-::3y)

Diagram NOTaccurately drawn

z\oN-- lg

(rottr_!y-p*u_9;j92_9_ry"3_^y_ljr9-_

cm

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Ij

D-3q -6b=-15

-!--r 3qrz6--|- l+b=-\

r- - -14o=---+$ =3,5

-1a = .....................L......

o: 3,5F"plA"9:9yp:!ip.t*7is3-ryvj:)-."

E Express 300 as a product of its prime factors.

23

55 ^2 _Lo(:7 x3 x5

', ""----Iv,

%aw

7

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9 The table shows infonnation about the snowfall in Ottawa in January one year.

.. 9"gyl:tr (1cmf-

: 0(s<2I:-.1'' "f

dryj

19

2 f ::"44(s<66(s<g 0

8(s<10 I

Work out an estimate fbr the total snowfall in January.

9

3

(t ^rq)

r- (axr) t (s 13) + (- ,o) {q ^

r)

: lq I 24t- t5tOtl

10 (a) Expand and simpliff

(i) 5(2x + l) -- 3(3x - l)

lOy,-r5 - lacr3

= cats

(ii) 0'* S;1y 7)

Zt-J'-li r55 -35Z= y. -Zj -35

(b) Make r the subject of the formula V = rrzh where r is positive.

V =Tr.'

6_1 cm

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itt The mass of the Space Shuttle is 7.8 x l0akilograms.

(a) Write 7.8 x 104 as an ordinary nunrber.

-l ,g x (tox(oxloxro)

-78 ooo

The Space Shuttle docks with the International Space Station.Tlre mass of the International Space Station is 4.62 x l0s kilograms.

(b) Calculate the total mass of the Space Shuttle and the International Space Station.Give your answer in standard form.

1,nxlo* t [+. 6zrtos:1,a1 rc4+q(r,ZxlO+: 5q xlgtt

= 5,q Y tCs5,t t

trx l0-

(Totat for Question ll is 3 marks)

A, B and C are three sets.

AaB:A and CcA

kg

t2

(a) Complete the Venn diagram to show the sets B and C

(b) On the Venn diagram, shade the region that represents A a Ct

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_(Total for Qgegtiol l2 is 3 marks)

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P40661A0920 Turn over

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10

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13 (a) Complete the table of values fory: x1 - 3x --

(b) On the grid, draw the graph of-y : I - 3x - 1 for _-2 ( x ( 3

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i./

-t-.-'- i.. -':.

.1".i-J:ii- i ..t.-i..r. i

l*t.l-i..:::ti,i:ff'J +'i. "t" "-'?r,

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(c) By drawing a suitable straight line on the grid, find an estimate for the solution oftheequationf -3x 6:0Give your answer correct to I decimal place.

3=5

(d) For the curve with equation y = xt -3x -l(i) nrd I

dx 3='-t - 3z

= 5x- -5

(ii) find the gradient of the curye at the point where x : 4

A =3a.'--3d.x, - s

= ]x4, _3

=3x16 _3

= Li5

=f=lo:_l

|, i ,:,

(Total for Question l3 is 10 marks)

ltr(ro!1! !9r Q_".e9_ti-o.! .I a !.-a_ p3rks).

. .

t+5

There are 3l students in a class.The only languages available for the class to study are French and Spanish.

l7 students study French.15 students study Spanish.6 students study neither French nor Spanish.

Using a Venn diagram, or otherwise, work out how many students study only one

langrrage. ^. t t , i \-'.o-'-o-. 3l-6 :25 (d (eqst \ languTelZ5-t1

25-tst5- x

tofS = ltr

1l

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l5 Diagrarn NOTaccurately drawn

A, B, C and D are four points on a circle, centre O.AD is a diameter of the circle.Angle BAD: 58" o

(a) Calculate the size of angle ADB. ABD = 90

:. lBo-(90+58)

(b) (i) Calculate the size of angle BCD.

r80 -q58=122

3Lo

l7L o

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(Total.f_o_r Q-u,e.gtion t5_iq 1 mar[g)

12

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16

A, B, C and D are four points on a circle.ABX and DCX are straight lines.AB : 7 cm, BX:5 cm and CX: 6 cm.Angle BXC:28"

(a) Calculate the length of AC.Give your answer correct to 3 significant figures.

*c' - tf+ c'- (zrextzxLos2y)ht __ 5L,85ss)c63

^c=ffi4C= 1,2101tr,.,

(b) Calculate the length of DC.

(cx , xo)=(BX ,. /x)(ee ,. xD). $x tZ

XD=IC.'o bC= yD-cx

Dc= to -6qcm

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Diagram NOTaccurately drawn

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t7 The histogram shows infbrmation about the times, I minutes, patients spent at a doctors'surgery on one day.No patient spent more than 40 minutes at the surgery.

Frequencydensity

20 30

Time (t rninutes)

5010

!-r:: .i lti: i..ii i i-: :;;i,."i-i.r. l: -?-:!'-,,

(a) Calculate the percentage of the patients who spent between 25 and 40 minutes at the

sursery. ?5fo qOHt"= 90 srnoll btocks

g5P X /CO = lg

(b) 16 patients spent between l0 and 15 minutes at the surgery.

Calculate the total number of patients at the surgery that day.

F lo +o t5 = \Q sn^o\l blochs

4o; 16 = 2,5

Scn :2,5 = Z@

Zoc

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P40661A01420

Bill and Jo play some games of table tennis.The probability that Bill wins the first game is 0.7

When Bill wins a game, the probability that he wins the next game is 0.8

When Jo wins a game, the probability that she wins the next game is 0.5

The first person to win two games wins the match.

(a) Complete the probability tree diagram.

First game Second game

Billwlns

.Io

wll1s

Billwlns

Jo

wlns

(b) Calculate the probability that Bill wins the match.

Third gan-re

Billwlns

Jo

wlns

Billwlns

Jo

wins

(o.:, x o. g') + ( o, '1

xo, >

: 0"15

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t3or15 / tr

l8 is 6 marks)(Total for Question

15

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19 f(x) = 3x-2

e@)=:i

(a) Express the inverse function f t in the form f '(r) : ...

J=32--Zj* 2 --3x

(z.rZ)?f ' (x) :.........................J

(b) Find gf(x)Simplify your answer.

y =T.3

Je*-z) = r'l)r,

-r9srk): 3*-i "i" ,i

{!--.o}A-l-o:.9t"::.!:v-}2s-1.y-?:\})..--""-."""-"

Do NOT write in this space

,.

i-

16

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20 Show that (6 -.6')' = 44 -24J,Show each stage of your working clearly.

(a -JT) (a-tE)

zq2 =.t[nsz

5g

i (x+2) (x-2):

S}row clear algebraic working.

;,(6 JT)t=q\-\z59

- 5z-lot9rtl8 =L"c'-+

ll-re.+6 =Z*-g2*-7-8 t\x-=cZ*z - )!x -16 = O

t x'L -1--Y) = O

r-=8 o( Cc: -l

(Total for Question 20 is 3 marks) i

T=8 or -l(Total for Question 21 is 5 marks)

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17

-Turn over t

l-

22r c:m

T'w'o solid spheres, each of radius r cm, fit exactly inside a hollow cylinder.The radius of the cylindel is r cm.The lreight of the cylinder is equal to 4i.cm.

The volume of the space insicle the cylinder, not occupiecl by the spheres, i. 9rr cmr6

Calculate the value of r.

Show your working clearly.

Diagram NOTaccurately drawn

f=2,5

),5(Total I'or Quegtion 22 ys 5 marks)

.:::1..:;:',)t:):.::t::t:: 1:..t::..t::::1t:.... .,:,:::tt:,::.:::.. .:..t:.ra::r.: .:_:i:,:1.)r): r.:. :.: ..t:)i..:)

TOTAL FOR PAPER TS TOO NIARKS

V xcal in&r -!x sprtfes = V x rnpy 5poce

W Vxcyclinde,-= 1Tr'h:1Tr'\ .= 4T[r3

Ixv xsP

: 5rr.=

ffi.3- 3rr,. = En Tf

4 rL5-l-

?

v3 tzql- _a

(= i25:,6

l8

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