E Maths Pratice Booklet + Ans

8/9/2019 E Maths Pratice Booklet + Ans.

http://slidepdf.com/reader/full/e-maths-pratice-booklet-ans 1/15

1. The price of a box of soap powder increased fiom $2.50 to $2.65. Calculate thepercentage inqease in price.

[Ans: 6%]

2. The rate ofexchange between Swedish krcna (K) and British pounds (!) was12.90K = t1. Calculate(a) the number ofkrcna received in exchange for f50,(b) the number ofpouds received in exchange for 12 900K.

[Ans: (a) 645K, (b) tl000]

3. ln 2000, Esther went to a tennis toumament. Her ticket cost $35. At the tournament,she bought a Fogramme costing S3 and an ice cream costing $2.(a) This inforrnation is to be shown on a pie chaxt. Calculate the angle ofthe

sector which represents the amount she spett on ice cream.(b) In 2001, the cost ofa tick€t was $36.75. Calculate the percentage increase in

the cost ofa ticket.

fAns: (a) 18', (b) 59lol

4. (a) A survey ofa TV channel showed that there were 50 minutes ofadvedisements dwing a 5 hour period. Calculate, in the form I : n, the ratio ofthe time spent on advertisements to the total time.

(b) A film started at 23 40 and finished 1f hours later. At what time did the film4

finish?(c) Sam wa.nts a television. He can either buy or rent it.

(i) The cost ofbuying is $960. Sam would pay a deposit of3070 followedby 12 equal monthly palments,(a) Calculate the deposit.(b) Calculate each monthly palment.

(ii) The cost ofrenting the television is $310 for the first year and then $20for each month after the first year.

(a) Calculate the total cost ofrenting it for 3 yeais.

(b) When will it become morc expensive to rent the television than to

buy it for $960?(iii) In a sale, a television is reduced Aom $960 to $900. Calculate the

percentage discount.



lAns: (a) 1 :6, (b) 01 2s, (cxixa) $288, (c)(DO) $56, (cxiD(a) $790,(c)(iiXb) 3 rr 9 mth, (c)(iit) 6.2s%l

5. (a) .), is directly prcportional to .{2.

It is known that.l, = 10 for a particular value ofx. Find the value of7 when this

value ofrc is halved.

(b) Seven men can paint a bridge in 15 days.

(i) Ho\r long would it take 3 men?

(ii) The bridge was painted irl I days. Write down an expression, in tems ofd, for the number ofmen needed to paint the bridge.

tAns: (a) 2.5. (bxi) 35 days. 1U1ii,1l0l1t'

r' Ernres\ as a sinsle fiacdon 4 32x I Sxtb

l4x + 27lAns:

-

I' (2r - l.X5,r + 6)-

7. Express as a fraction in its simplest form -l'+ 1 .

.t+3 r1r +A

[Ans: '']' r(.r+J)-

8. Factorisecompletely(a) 4x2 -16y1 ,

(b) 3ab 6ac 2bd + 4cd .

[Ans: (a) 4(;r-2y)(.t+ 2y),@ (b-zc\3a-2d)]

9. (i) Factorise completely 2p1 1op .

(ii) Factorise a7 +5a -6.(111) Factonse )4' - 2U.

tAns: (i) 2rG-s),(iD (.l+6Xa-1),(iii) s(a z\a + z)1

Io. Given that"=2d*1

.

3d -l'(a) calculate the value of c when d = l,4'(b) express d in terms ofc.

lAns:{a)-0.rb) I - | !."'?1'''- lc 2 ll



11.

t2.

Given that s =jL

-3V _1'

(a) ca.lculate the value of S when rR = 100 and Z= -13,(b) express /in terms ofR and s.

tAns:.{al 32.5. (b) Y= S 1

35-R -

lAns: (a) $52. (b) 5l?, ro rU OO. tar r; r,f,i t

9, Th€ total cost of the electricity supplied to a house is

found by adding two charges. These are a fixed standing

charge and a charge for each utrit of electricity used.

The total cost of 100 units is $22 and other costs are

given in rhe table below.

Number of unils used 100 200 500 I 000

Total cost($) 22 27 42 6',7

(a) Find the totat cost of 700 units. I11

(b) Find the fixed standinC char8e. tll(c) Fidd the number of units used when the total cost

is $80. 121

(d) The bral cost when n udts are used is C dollars.

Write down th€ formula for C in terms of n. t2l

. JOO IYD



ri. [Ans: (a) [?99.]n,", I 'oo,')0, ("xt .,* om *;,,,' '(.x J '' \x+51

(rl) x = 47 .62, -2-62, (iii) 252 minl'lVp. The dis'aDce beMeen t\!o houses, p and O. is 200 km.

Joe ravelled by car fiom ,P to O a! an average speed of

(e) Wrire do\rn an expression, in tenns ofr. for theDurnber ofhours !e took to travel ftom p ro O.(b) He .etumed fron O to p ar an avemge 6peed of(r + 5) tar^.Write dowr an erp!€ssion, in derms ofx, for the

number of hours he took to havel from O lo p.(c) The toral rine he took to go fmn _p to O snd roretum llom O to p was 8 hours.(i) Wdre down sn equation in r and show thst it

simplifies in

x, -4Sx_ rZS _0. l4l(it) Solve rhe cquarionr:_45i_ 125=O, givingeach ans\,rer coEect to 2 decinal place!. [4](iii) Calculate, conect to the near€st rninute, thetime he took to rravet ftom p to O. el'd\

/ JO}U4D

200 200

t .ir+5



64

--fc)

12114. [Ans: (ixa) 1 or- 1- - {ii) haDeziuml

51 57

Itr the diagram, A,

=8cm,AC=3cmand At is parallel

to CD. c(i) Find the Yaiue of

(al-.D

tll

t1l-. Area of triangle ABE

Area of Fi angle A CD

- - Alea ol trianale .4dr('r

A,;;aq,"d"l"*,l8cDE(ii) What is the speciat name given to the quadrilateral

t1lJ99 IYD

8

-.(b)

11

/.

Lzl

BCDE2

15. [Ans; (a)(i) 107", (il) 34", (b) ZAEC = 146" = twice of ZEBC. This satisfies the

property of angle at cente: twice angle at circurnferenoe. Thus centre of circle Ilies on circle III

Ps 124, q 9

In the diagram, the points,4, A, C and D tie on circle L

The points.4, E, C and I lie on circle U.

AtB and ADF sre shaight litres.

EBC = 73" aad AEC = 146" .

(a) Catculate

(i:) ADC,(ii) cE{.

(b) Explain why the centre ofcircle I lies on circte It.

t21

lMw

tUIU



16. [Ans: (a) (i) 35', (ii) s5', (iii) 125", (iv) 20", O) 67 5 cm?]

A circle lvith ccntre

C, D and 6.

ol tl,c circle,

/lB is liaftltel to OC.

(r) Fhd

O oAc.

(iii) Aic.(iv) .168.

til

tllt2l

L^o.

t2l

J9ltlltD

(b) X is th€ point (]n AD such ihat AX =

Giver that thc arcr of (.iangle t4D is

calculalc the arca olLrirngte EXD.

I

nl

1'7. lAns: (a) 14.9 cm, (b) 20.7 crlt, (c) 181 cm'z, (d) 17'5 cml

The diagram shows a straight line,4aC and a poin!r'

AB =22 cm. BD = 19 cm, ABD = 60" and ACD = 34'.

Calculaie

(a) the length of AC, t4l

(b) the lensth ofAD, t4l(c) the area oftriansleAAD, l2l

(d) the shortes! distdce from a to AD. I2lIO2IJJD

10.



[Ans: (a) 7?.1 l<rn, (b) 114', (c) 65.2 km, (d) 57.5 kr]

21.The diagran'shows rhe position of a harbour, H, and

three islandsA, B aDd C.

C is due Northof H.The bearing ofl from fl is 062" and /l?aB = 128..

AA = 54 km and48 = 3l kn.(a) Calculate rhe disraflce flB. I4l(b) Find the bearing ofB ftonA. tl](c) The bea.inc of.4 frorn Cis 133".

Calculate fte distance,{C I4l(d) A lighiship, t, is posirioned due No(h of,FJ ald

equidisrant from A and E.

Calculare the distance flL. t3l

JO3 TIJD

19. fAns: (a) Use sine rule to find the value of AC' @) 347 m,(c)(i) 42 5 m' (ll) 29'6"1

9. Three buoys, A, B and C, are positioned in a lake to

provide a course for a yacht race AB = 800 m ABC =

32.. BAC = 22" and. N is the point on,4B whicb is

200 m from A.

(a) Show that the distance AC is 524 m, correci to the

lzl

H

(b) Calcutate the distanceNc t4l

(c) A heticopter, E, is hovering at a point verticallv

(i) The angle of elevation of the helicopter fron

A is 12".

Calculate the height of lhe helicoprer tzl(ii) P is the point onAC which is nearest to the

helicopter.

Calcllate the angle of elevation of the

helicopter from P. t4l

J98 II,D



20. [Ans: (a)(i)

5.

02s', (ii) 5.55 km, (iii) s1.5", (bxi) 1.2 cm, (ii) 75 krn'?l

In t\e diagram, which is nor drawn ro scale.,,t, B, C,

and D represent four tow$. aC= 5 km, C, = 6 km.

l6c = qs", Cqo = 7Oo, D is due east of d and

AeB = 90. .

(a) Calculate

(i) the beains of a from A, l2l(ii) the distance AC, lzl(iii) the angle BrC. t3l

(b) A map of this area is drawn to a scale of I cm

to 5 km.

(i) Calculate the distance, in centimerres,

between the points rep.esenting C and D on

(ii) A forest is represented by an area of3 cm:

on the map.

Calculate the actnal area,io square

kilometres, of rhe foresr. l2lT9'I IW

4.

21. [Ars: (a) 2h 30 min, (b) 3 h 12 min, (c) 14 12]

Thecumulative frequency curve shows the disrriburion

ofthe times of300 competirors in a women's mearbon

234Time (hous)

U,e the cur\ r ro anqwer lne follov rng quesl,onc(a) The race was wonby Tesla.

Find her time, Siving your answer in hours andminutes. tll

(b) Find the median d;e in houls and minures. Ll I

(c) The qoalifying tine for the Olympic Games was

achieved by te! percenr ofthe runners The'ace

began at 11.30. At what time did the last qualifving

alhlete finish the race?

Express your answer using rhe 24 hou!clock [2]

J02W

5 2oo

E

.E

E



22. [Ans: (axi) 154 cm, (ii) 12 cm, (iii) 6, (b)(i) lsl cm, (ii) 12 cml

E

O

A long ruter was fartened to a wall and used ro m€asure

the heishrs of 120 children. The diagram shows thecumulative flequency $aph of these heights.

(a) Use the graph ro esrimate

(i) the median.

(li) the interquartile range,

(iii) the numer of chitdren whose height is greacrihan 170 cm nl

(b) Several days later, ir was noticed that the rule!had been *rongly posirioned. and thar alt heightsshould b€ 3 cm tess.

State what adjusrment, if any, shoutd be made toyour resuhs for parrs (a)(i) and (a)(ii) in o.der rogive the correct vatue of(i) lhe median,

(ii) the interquaniie range.

t1l

l2l

tU

lrlJ96 II|D



23. [Ans: (axi)(a) 60, @) 22, (c) 32, (ii) t2', (l'Xi) 0,

,,/,. -Z {a) one hundied md sixty srndenE tool., d exMinadon.

/ Therable sho$s rhe maJks needed ior ea.h grade.

The cumulative frequency curve shows the

distribution of thei' marks-

Use the grlph !o estimate

(a) the median, tll

(i0I .... I

. lrrr I -....1-(rvt

tRl

9""g

:30

,

(D

(ii) A pie chan was &awn to illirstrate the Srades

aw&ded to the srudents.

Calculale tbe angle of the sector which

tepresenled the number ofsludents who were

t2)

(b) the inrerqu,rtile mnge, 12)

(c) the number of students who wereawarded a crade C. l2l

An ordinary unbiased die has faces numbered r,

2, 3, 4, 5 end 6.

Sdah and Terry each threw this die once.

Expressingeach answe. as a fraction

i.its lowest

terms, find the probability that

(i) Sarah rhrew a 7,

(ii) $ey both tkew a 6,

Illflt

(iii) neilher tkew an even number, tll(iy) Saran thrcw exactly four more than Terry'

trlJO3 II/'D

G.ade A 70 < mark

Grade C 40<mark<55Grade D 20<m&k<40

Grade U mark< 20

(b)



*1. The four faces of a red terrahedrat die are marked I, Z,

2 and 3.

The four faces of a biue ietrahedEr die are narked t, 2,

When such adi€ is thrown, rhe score is rhe nurnberon

the face on which it lands

The two dice are thro!+r together dd lheir scores added.

The possibility diagram in the answer space shows some

of the totals.

(a) (i) Complete the possibiliry diasram. (lI

Red

Expressing your answer in terms of',

find the

probability thar a red ball \{as chosen each time.

t1l(ci The process was carried our nine times. Pind rhe

probability thar

(i) a rcd bau was chosen every tine, ttl(ii) at least oDe biue ball was choseL tll

N95 I,D

A box ofchocolates contained 6 chocolates with hard

certres and 4 chocolates with sofr centresAnn took s chocolate. selected ar random. from rhe box

Bnce then tookachocolaie, selected at random, from

Expressing each answer as a fraction in irs simpt€st

form, find the probabili.y thar

(a) Ann took a chocolar€ with a hard cenrre. lrl(b) Ana took a chocolate wifi a hard cenlre and Bruce

took a chocolate with a soft cenrre, ttl(c) bo.h Ann and Bruce took a

chocolare with a softt1l

(d) Bruce took a chocolate with a sofi centre. IllJ96 W

In a game two dice are used.

Die A has 2 red faces and 4 whire faces.

Die B has 4 red faces and 2 blue faces.

The two dice are thrown toserher.

(a) By usrng the Iree diagram betow. or orhers ise,

fiod tne probabiliry that

(i) borh dice show a red face oo rop, Itl(ii) just one die shows a red face on rop. Izl

3.

Blue

(ii) Find the probabiliry that the roral score is 7.

tll(b) The faces of a Cre€D rerrahedial die are marked

10, 20, 30 and 40-

All tbree dice are thrown together and rhe scores

added.

Find the probability rhat rhe rotal is more rhan j0

but less than 35. l2lJ95 llD

A bag contains a rumber of balls each one coloured

A ball is chosen ar random and then pur back inro rhe

bag.

This process is repeated several rimes.

(a) The probability of choosing a red ball is'.

Write down, in terms of r, rhe probability ofchoosing a blue batl.

2 ,. 3

2 l5 1

6 9

4.

2-

ttlDie B

Red

Blu€

Red

Blue

(b) The tree diagran below represens rhe situalion

when the process has been caried out rv/ic€.

2J

i---\3

23

-i----a

If both dice show red, rhe player wins a prize.Ifjust one die shows red, the player thlows both

dice again.

(f)

(b)



He wins a prize if both show red this time.

Calculate rhe probability thal lhe player wins a

prize on eitherthe first throw or rhe second rtuow

Lzl

N96 YD

When a particular die is thrown, the probability of a

score of .rx rJI. lbe Drobabrblre\ ol score\ ol lwol

three- four and five are each !6

(a) Find the plobability of scoring one. tll(b) Explain the significance ofthe answerto part (a).

t1l(c) The die is thrown lwice and ihe sum ofthe lwo

(i) Wdte down the possible scores on the twotlt

(ii) Calculale the probability thal the suD ofthe

t:21

J99 VD

(a) Find the p'obabilily that John

(i) fails ihe first examination snd passes th{

Irl(ii) passes the exaDination in eitherlhe firsto

tll(iii) fails lhe firs! thr€e examinations, tll(iv) passes rbe examiDation in one of ihe ifs! fou

children living in lhem,

5.

K

8.

t2l

r00 !/T)

l1l

tilI2l

NOO I,'D

tll(b) (i) Fi.d lhe probabilily, in terms of n, that Johr

fails the first n examinations. tll(ii) Write dow. the probability that John passe

lhe examination in one of the first, months

tllNOi I,T

9. The dot diagramshows the number of

children living in lhe

houses on a certain

6. Tbe probabilily $at Catberine oversleeps is 0.4.

If she oversleeps. the probability that she cycles to

scbool is 0.7.Ifshe does not overcleep, the probability

flat she cycles to school js 0.1.

(a) Complete the lree diagtam, in ihe answer space, to

rcpreseDr ftis information. L2l

(b) Calculate the probability that Catherine cycles to

Fitrd

(a)

012345\Nlmber ofchil&eo

the percentage of houses that have at least 3

t1

(b) the probability rhat r\ro houses, chosen at rardon

would each l.ate mor€ thao 3 children liv:ngin

A bag contaiDs 3 black and 2 whire balls.

Two balls are taken from the bag at ralrdom, wilhou!

By drawing a tree diagram, o. othelwise, calculate the

probabilily that

(a) both balts are black,

(b) at least o'e ball is white.

(c) the two balls aie the sane colour.

Ar examination is set eve.y monlh. John lakes the

examinatioD each month untit he passes. Each time he

takes lhe examinalion, the probability tb3t he Passes

is 0.9.

that they

(i) show lhe same number

(ii) show ditrerent numbers.

(b) Tkee unbiased dice are lhrown. Find the

probability Ihal

(i) they all show different numbels.

The two circles shown have radii r

(a) A point is chosen, at random,

inside the ldser circle.

Find, ir its simplesl fractionai

form, ihe probability thar this

poinl is in the shaded area.

(0l)

(.....-.1

(.......)

(.....)-..-

10. (a) Two urbiased dice de tuown. FiDd the probabilit

(c) the mean number of chil&en.

Ir

I1

NO2I,

IIII

tl(ii) at least two show the same nulnbel tlNO2I,T

12

(b) Find, in its simplest form. the ratio circ'rnferencofthe large circle : sum of circumferences oftt

12

NOU IA

7.

11.



UnBt 9

PAPEB 2

*1. An unbiased Biue die is nunbered l, 9. 10, ll, 12 and

13.

An unbiased Red die is numbered 2, 3. 4, 14, 15 and

t6.

The possibility diaSram when the two dice are tluown

The ietter R indicates tha! the nurnber (14) thrown on

the Red die is greater than lhe number (9) thrown on

the Blue die-

Ii 5 or 6 is thrown, the bulton is moved one squde to

the nght.

(i) The button is placed on squde X. The die is thrown

once. what is the probability that the butlon

rs moved to rhe riShl? tll(ii) on another occasion, the buttoD is Placed on squde

L The die is thrown once and the button is moved.

The die is thrcwn a second time and ihe button is

movedagain.Findtheprobabilitythatthebutton

(a) at P,

(b) at O,

(c) at I,(d) atPorOorr.

Blue

9 t0 ll 12

Red

2

l4

14 ,R

l5

t5

(i) Copy the diagrarn. Put a letter R ifl each square

where the number thmwn on the Red die is greater

lh3n lhe number tlEown on lhe Blue die. 121(ii) Show that. when rhe two dice are each *trown once,

the probability drat the number thrown on ihe Red

dieis grealer than the number throwq o! the Blue

die is a. tll12

(iii, The rwo di-e are each thrown r$rce. By u\ing a

tree diagram, or otherwise, calculnte the p.obability

that the number thrown on the Red die is greater

than the numbe( tkown on lhe Blue die.

(a) both times, lll

(b) just once. 12)(iv) ADunbiased Green die is numbered 5,6,7,8, t?

and 18.

Showing your workrng cledly, find out whether

the Red or the Blue die is nore iikely to show

anumber greater than the number shown on the

t3l

t96 tw

There were 12 girls and 3 boys in a sroup of children.One child was chosen at random from the Sroup

Anofierctuld $as chosen al r dom ltom the temajning

childre!. Expressing each answer as a fraclion in its

snnphst form, calculate the probability that

(i) the first child chosen was a girl, tll(ii) the first child chosefl was a sirl and fte second

tll(iii) a child of each sex was chosen. tll

I99 TW

A packe! contains a large number of flower seeds which

look identical, but produce fiowers wnh one of the

three colours, white, yelow or red.

one halfofthe seeds produce white flowers and one

thi.d produce yellow flowers. The remainder ofthe

seeds produce red flowers.

(a) Explain why the Probability that a particular sed

tlltrlt2l

tllJ98 II,D

tllirr prcduce a red nower is :.(b) Find lhe probability that a particular seed will

produce a flower thal is not yellow. I1l(c) T!'o seeds are planted.

(i) Draw a tr€e diagram to show the Possible

outcornes and their probabilities. t2l

(ii) Find the probabitity that

(a) both will produce a yellow flowea tll(b) both will produce a blue flower, tI1

(c) one will produce a yellow flower and

the other a white flower I2l

(d) oeilher will produce a red fiower. t2l

N98 lvD

2. X o Y

The diasrm shows a gridofsquares. A button is placedon one ofthe squares. A fair die is thrown.If t,2.3 or

4 is thown. the button is moved one squ&e to the left



5. A bag cortains 15 identical discs. There are 8 red' 4

blue and 3 white discs. A disc js picked out al nndom

and not replaced. A second disc is then picked nut at

random and Dot replaced. The iree diagram belod shows

the possible outcomes and some of their Probabilities

25(a) (i) (rr) -99

(a) o(b) lt is not possible to score oDe

(c) (i) (2, 4), (3, 3), (4,2)

(a)

,,,, 1' 1)

(i) Catculate the values ofP, 4, r and r shown on

r2l

.t? sru.

(ii) BxpressinS each of your answers as a fraction in

its lowest terms. calculate fie probability thai

A'-o *"0r.ed -/ 14 p;-.

--b'-wr,'.

(a) both,.Iscs wiu be red, tll

t21N99II,D

@q),z

-l,--;;-...--o.-".9Fl9!C...

(b) 0.34

t. rat !l0

8. (a) (i) 0.09

(iii) 0.001

(b) (i) (0.r)'

9. (^) 25E

(c) 1.75

,1, 1l0

(ii) 0.99

(iv) 0.9999

(ii) r (0.1)"

(b) 0

2(c) -

(b) one disc will be rcd and ihe other blue t2l

(iii) A third disc is now picked out at random'

Calculate the probability that trone of rhe tbree

1. (a) (t)

3.

(b) I(ii) 1-/

,rrr 1t52(d) i

._. 3lltlr6

lbt :

(a) I /(c) (i) .'

,", l52(c)-

10. G) (i) ; (it) :(b) (i) ; (rt) I

1 rar 199

t2(iii)

?3

(c)

rtr I'l

,,r, ,u, I (b) o9

^6it - ( ii)-J5

r11(a) It-3=a

ff. ,r, ! (b)3:4

PAPER 2

zt11. (ii) - = -(shownr ,o 15

riii) rar -! n = ,4^(b) ::

(iv) Blue die is nore likelv io show a number greaier

rhan Lhe numbet shown on De Gteen dre

Answers u"lt s

1 2 2 3

1 z 3 l2 l 5

5 6,7

7 8

6 7 8 8 9

(b)



(c) (i) lsts€ed

_... _. I

9

_l

Red \R

RY

RR

(b) 0

ta.r 3s. (i) p=+,q= n.,=i.'-.1

(ti) G) * (b) # (tti);l

Documents

E Maths Pratice Booklet + Ans