5,*uoe*rd Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator.

1 Given that 1793 x 185:331705

write down the value of

(a) 1.193 x 185

(b) 331705 + i.85

33\:+o5

2 Mr Mason asks 240 Year 11 students what they want to do next year.

15%o of the students want to go to college.a

: of the students want to stay at school.4The rest of the students do not know.

Work out the number of students who do not know.

ldl.=zth -L =59 +)

s1.i \2 +3t --tEO

t133C)0(Total for Question I is 2 marks)

:. 216 ttno"'rr ; L+ do nlr (,t-na'l (+)

Sixteen babies are born in a hospital.

Here are the weights of the babies in kilograms'--.'.,-a:

2.4 2.7 ' 3.5'; 4.4 4.5 4.1

=- '\#1

4 t (* :,* 42 ,1,i, : o

Show this information in an ordered stem and leaf diagram.

4.4 2.8

,.i\:3.7 i',3.3 J\--*-/

Key:

3\s rrltenrs, 3'5

4 (a) Expand 3(2 + t)

6+3r{ l}

(b) Expand 3x(2x + 5)

6x..tr l5x-

(c) Expand and simplifli (m + 3)(m + 10)

rn2+t3''

o 335+8t r 2+4s

szs/\7s z\

/ \ l\5s3+

Jx52xt--*ggkl,U*Q"uq-qgul*,llmr*l)

Ed has 4 cards.There is a number on each card.

The mean of the 4 numbers on Ed's cards is 10

Work out the number on the 4th card.

12+5+\s+? vtO+

\2+ L+l:{ s 4o

+

(a) Translate shape P by the *"* [-;)

v-*5

lO

4

J

2

1

i^--t-- - rI

IIIa

(b) Describe fully the single transformation that maps shape A onto shape B.

(otr+tron r \8O" abo.^*, ( D/ I )

i-,--""-l

I

I

i1

lIt

!

*----llelellg.{-Q!*r-1i-q-+7r!l-Bgrtss)

8 Margaret has some goats.

The goats produce an average total of 21.7 litres of milk per day for 280 days.I

Margaret sells the milk in : litre bottles.

Work out an esti- imate fo, ,; total number of bottles that Margaret will be able to fiIl withthe milk.

You must show clearly how you got your estimate.

+L;XL tt2-ootu (s)

5 \apS . (r)

20 x2BO = s60C)

(Total for Question 8 is 3 marks)

9 Matt and Dan cycle around a cycle track,

Each lap Matt cycles takes hirn 50 seconds'

Each lap Dan cycles takes him 80 seconds.

Dan and Matt start cycling at the same time at the start 1ine.

Work out how many laps they w-i1l each have cycled when they are next at tire siar-t line

together.

Ic"n( sor8o) = 4oO

tv\^it= 8\aPs ) Da.n '=

l0 The diagram shows a garden in the shape of a rectangle.

4+3x

Diagram NOTaccurately drawn

x+6

All measurements are in metres.The perimeter of the garden is 32 metres.

Work out the value of x

? = 2(q+3x-) +l-z(x+6) , 8X-+ 20 = iL

Yx-=\ZDL= \'5 ('r)

11 Debbie drove from Junction 12 to Junction 13 on a motorway,

The travel graph shows Debbie's joumey.

Distance fromJunction 12

(kilometres)

Time (minutes)

Ian also drove from Junction 12 to Junction 13 on the same motorway'

He drove at an avetage speed of 66 km/hour'

Who had the faster average speed, Debbie or Ian?

You must explain Your answer.

AS lrcn rn 20 nntA

+S Lrnn tt'\' tXr(x r)

Da.u\rrq ='

a aJ t^^^ft .

12 On the grid, draw the graph of y: ! * * S for values of x from 1to 4"2

(Total for Question 12 is 3 marks)

*13 Here is a maP.

The position of a ship, S, is marked on the map'

Point C is on the coast.

Ships must not sail closer than 500 m to point C'

The ship sails on a bearing of 037'

Wiil the ship sail closer than 500 m to point C?

You must explain Your answer.

Scale 1 cm rePresents 100 m

$"r, hts Poth got\ts tnst)e tl"e- crrg{g '

14 -2<n {3(a) Represent this inequality on the number 1ine.

-54-3-2-10123

(b) Solve the inequality 8x - 3 ) 6x + 4

2x->.7

f,-z 3;S

(tr1e1*&r_Qssstjg"!_t*l-,1__1:1",.prh0"

*15 One sheet of paper is 9 x 10-3 cm thick.

Mark wants to put 500 sheets of paper into the paper tray of his printer.The paper tray is 4 cm deep.

Is the paper tray deep enough for 500 sheets ofpaper?You must explain your answer.

5Oo x n x\o-3

No ztuo1

5x q xtoz-x\o-3

cf S I [o-tq-s K lO rto-tLF.5 crn

rs ndv aeeP ernoq,\,.* ' (l)

Lrelel-&r-Q,!li[1ip-.1 15 is 3 marks)

16 The normal price of a television is reduced by 30% in a sale.

The sale price of the television is f'350

Work out the notmal price of the television'

n.,re*rc'A x c>'? = LZsor-./+ ,'orn\6r{ = $sA3so i€ = 3so*+

= 3J6Q+

16fl. =,!3SO+) to'r- = f,soro) toD'/' = Ewo

o.tb

G6 'S@

Cre*1sl{er-9J*s*is+*t-f isl-ryr$)---

17 Sumeet has a pond in the shape of a prism.

1.3 m

Diagram NOTaccurately drawn

The pond is completely full of water.

Sumeet wants to empty the pond so he can clean it.Sumeet uses a pump to empty the pond.

The volume of water in the pond decreases at a constant rate.

The level of the water in the pond goes down by 20 cm in the first 30 minutes.

Work out how much more time Sumeet has to wait for the pump to empty the pond

completely.

Sv-€r\ ?+" er?eLLor'\ 3 (r'3*"'s)xe =l-g

2-

Vo\r;ue- --\ . K x \ = l' 8 .*3

Vo\.lF/\o- 1 u^.rafer tlA frrst 3Opt'""

a

,.rR =g'srn3 l. .t n." l€-N\^\nrn3

3'5 CxSo) z IOS 3rtr6

IOS rv'|N\

*Lr*rJUJg_f-9",1'"9!9e.,!-17*_iS_f-*1.1l.S)

18 Solve the simultaneous equations4x+7y -1 GS)3x + 101,: 15 (y (t)

tLx-"1}3-:1o\2a +z\5 = 3

\qb=5t

(2c+ 2l = \ =) (4 L=

L9 Write these numbers in order of size.

Start with the smallest number.

51 0.5

*=o''

) - 5r o;27 o.s, I

-5 50

t

[','

-', o'5, 5 o

(rotal for Qrysfle!_l?A ?;g3fSI __

20

Diagram NOTaccurately drawn

ABCD is a square with a side length of 4xM is the midpoint of DC.N is the point on AD where ND : x

BMN is a right-angled triangle.

Find an expression, in terms of x, for the area of triangle BWt.Give your expression in its simplest form.

N ,I*t, 7-

N L.D

\ l*sL,t\* =f,-'

4y* c--

ftrs^ A gr*tv ?5

l6f -6*-*5E

- LhLL(*)

21 The table below shows information about the heights of 60 students.

Height (x cm) Number of students

140<x(150 4

150<x(160 5

160<x(i70 t6

170<x(180 27

180<x(190 5

190< x(200 -)

Lt

n

a5

sL

5+

6o

(a) On the grid opposite, draw a cumulative frequency graph

for the infotmation in the table.

Cumulativefrequency

naHeight (cm)

180

(b) Find an estimate

(i) for the median,

l+r ...cm

(ii) for the interquartile range.

t\6 - t6S

\t

gglsl3r.-Q-uslt-q*-1-u-f--ry-,-r"rl.0--

22 P and Q are two triangular prisms that are mathematically similar.

Diagram NOTaccurately draw

12 cm

Prism P Prism Q

Prism P has triangle ABC as its cross section.Prism Q has triangle DEF as its cross section. &

AC: 6 cmDF: 12 cm

The area of the cross section of prism P is 10 cm2.

The length of prism P is 15 cm.

Work out the volume of prism Q.

s$"= & =) S€u = t=8

Vo\ p z lOcfnt * ISG'nA -- tSo.,63

.'- Vo\oy= tSOXg = lzCDcr'^3 (.r)

(Total for Question22 is 4 marks)

Simplifi,4(x + 5)

G)= l-+

)c*x2 +2x-15

24 Blll works for a computer service centre.

The table shows some information about the length of time, I minutes, of the phone callsBill had.

Time (l minutes) 0<l< 10 10</< 15 15<r(20 20<r<30 30<r(45

Number of calls t2 15 13 18 J

cr, \o S S to lS

$.oL vL 3 2,b l-3 o.e

On the grid, draw a histogram to show this information.

ti

rll'l:,lt:

::

0s1015202530354045Time (t minutes)

3

Frequencydensity L

(Total for Question24 is 3 marks)

25 The expression x2 - 8x * 2l can be written in the form (x - a)' + b for all values of x.

(a) Find the value of a and the value of b.

(x-\)"-t6+z\Cr-q)''r 5

The equation of a curve it.y : f(x) where f(x) : x2 - 8x + 2l

The diagram shows part of a sketch of the graph of y : f(x)

The minimum point of the curve is M.

(b) Write down the coordinates of M.

+u - ...............

6: 5

{.1 }

(Total for Question 25 is 4 marks)

26 Fiza has 10 coins in abag.There are three f,l coins and seven 50 pence coins.

Fiza takes at random, 3 coins from the bag.

Work out the probability that she takes exactly fl2.50

tl*r5og

soP

br

+l

b\50P

br

I 3x Ax ?"7)

-_t?3?2r>

{*16

)1

Diagram NOTaccurately drawn

PQRS is a parallelogram.1/ is the point on SQ such that Sl/ : NQ:3 : 2-->PQ: a

PS:b(a) Write down, in terms of a and b, an expression for

-->SQ

_->SQ : q-k)

_>(b) Express NR in terms of a and b.

-)= esa. =5._)

zNS+g12-

la-Z-L= Z* -IU rb

-)N(a

-)NA

q-r

= Io,*+b (,+)

28 The diagram shows a sketch of the graph of y : cos .tro

(a) Write down the coordinates of the point A.

(b) On the same diagram, draw a sketch of the graph of y :2 cos xo

,Qoor\" " """'){3}

{{}

(Total for Question 28 is 2 marks)

TOTAL FOR PAPER IS 1OO MARIG