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GCSE MathematicsPractice Tests: Set 6

Paper lH (Non-calculator)Time: t hour 30 minutesYou should have: Ruler graduated in centimetres and millimetres,

protractor, pair of compasses, P€0, HB pencil, eraser, calculator.

Tracing paper may be used.

lnstructions

. Use black ink or ball-point pen.r Fill in the boxes at the top of this page with your name,

centre number and candidate number.. Answer all questions.

Answer the questions in the spaces provided

- ttlere may be more space than you need.Calculators may be used.Diagrams are NOT accurately drawn, unless otherwise indicated.You must show all your working out.

lnformation

. The total mark for this paper is 80

. The marks for each question are shown in brackets- use fhrs as a guide as to how much time to spend an each question.

Advice

o Read each question carefully before you start to answer it.. Keep an eye on the time-. Try to answer every question.. Check yorrr answers if you have time at the end.

ta

a

Practice Tests: Set 6 Regular (1I! - Version 1.0This publiation oay only be repoduced in amrdme with Pwn Edwtion Limited oplrigbl policy'02016 Pffion Education Limit€d.

1.

Answer ALL questions.Write your answers in the spaces provided.

You must write down all the stages in your working.

Use ruler and compasses to construct the bisector of angle ABC.You must show all your construction lines.

':- d:'

(Total2 marks)

,,Peter, Tarish and Ben share f54.

Tarish gets three times as much money as Peter.Ben gets twice as much money as Tarish.

How much money does Ben get?

{a*si1 : 3 x ?*+er9ot, : 2xTa-^.=h

R..n b Bzn :

D,u,d:r * S.r4oV) p4n*s

sh I P*te;-6 '.3 ;{f-:_-=z S-::/

va *3rvtla ra-h'o b,,? I ts (r+3 + t = rO

Ta*

Vatua of eocla p".f - FS+: uO = 3..2..,..*Q..:......(Total3 marks)&en gels 6 x fts: tt-o = f. sz.L{-o

E5 *?

On the grid draw the graph ofx +y : 4 for values ofx from -2 to 5

)c=

13

L

u , * -L.d:

tobb of valvu>

+ 5= + \ -,.l'

z- -'| lo I z 3 .+ s6 5 + 3 z t o -l

(Iotal3.marks)

Practbet€stpec fHGEtO: Versim 1.0

PORS is a square.

5 .rq

All measurements are in centimetres.

Show that the of the square is l0 cna.---\/"Al

,/rrrb/ 3r--2 t 3x-Z+:Lrt +(+t = tO

V tx-2 =ro \d, *''i :';) '*

8rL. \Z

-efrrudZ

Oe- * asVro:f a3r'2 = Lt I2l- / =tl7r -=3

L = l'5.-==-:.

)-x&*=

J;,

1ab 'h3r- r

nl5o th *de5

=

3 x [-S-2+"5 -22.5*--F

W o SarhaLF x 2.S

lengl-h so= t O errz^\

6-b tr'I;1+t = t"Stl

= ," q,1_ )

,nusl ba a SLuotz

(Total4 marks)

Practice test papff lH (Set 6): Version 1.0

5. The diagram shows the plan of a floor.

The area of the floor is 138 m2.

Work out the value ofx.

%d atoq =

Diagram NOT

$_3 accucrtcly drawn= Styr-

l2O +

l(cS

l1

L-l

+s -

-3r

\x

3( == t3g

=O

:3*

!39

).rrz) trr

[, iq :x

Nreo- = lS rS= [ 2.o rn'

lvtg \= 3 (tS- r)=+5-3*

t5-zc

Pracfice test p4er lH (Set 6): Version 1.0

(Iotal4 marks)

There are 40 litres of water in a barrel.

The water flows out of the barrel at arate of 125 millilitres per second.

1 litre : 1000 millilitres.

Work out the time it takes for the barrel to empty completely.

+O x IOOO E +o OoO mQ: .

il-v.vl^o

rro [urr.9

-4r*fQ

l+o pe,q,r2s

32c- -= 3{or2.s Io, oo o3t s

75()3.eC......... seconds

(fotal3 marks)

I.tO [t[ves

7. (a) S/ork out t21-+-54

2x-5

: = "fr z ?,F*[4

I6E1o

51-o

tr.LO

a)(b) v/ork out 3i

e29-x8

tonve-rt lo .tb

IE{ ll-

(3)

(Total5 marks)

Practice test pryer lH (Sef 6): Version L0

Lillian, Max and Nazia share a sum of money in the ratio 2 :3 : 5

(a) What fraction of the money does Max receive?

ft'\aX feCetvsS 3s4O

Naziareceives f,60

(b) Work out how much mooey Lillian receives.

ho l'eLl

T"fa ponfs :2+3+S =tO

1,,*,

3voto

"lta)

[6laj

)*:-to

Z=to

t ..........2.s.................(3)

(Iotal5 marks)

* Naacr {eco;,tos % of n^oytel *L6O

moneX = l'6c

iltortc , =f,no

vL

+ l-rlttara rc€rvos ""

oe mone-5

frtzo : to

frzxL== ftZLz+

Hicetestpeer lH(SetQ: Version 1.0

9. (a) S9lve ll -4y:6y-3

tl-$3=61-3

ll = tO)-3

It = ,oJl_Ll 'J

(b) Solve i -lx- 40 : 0

6 ""r, ntio- g2

(x.-a)(x+

*€ a -+o

+E = -3s) - p

)*n,L*3[: to v:

Q)

q,-) Y:..................) * .8.

(3)

(Total5 marks)

10. There are 11 pens in a box.

6 of the pens are black.3 of the pens are red.2 of the pens are green.

Henry takes at random two pens from the box.

Work out the probability that he takes one blackpen and one greenpen.

9-to

st2 =ft"4 t?- \= - \

r Io ) f"* lrobob,l$| =,3, r tzI rto rrott

tL_ \: Zt=, ilo'/ l,lo

".......*.,...(fotal4 marks)

t

11. The size of the obtuse angle in an isosceles triangle is x".

Write an expression, in tenns ofx, for the size, in degrees, of one of the other two angles.

2 anqlas the Sarne becattP tsosr.elz-s .L.t + Ll = lgo' )Lt/rr,x

;',rluX- Jr'J -;:I

12. (a) Write downthe value of 9i

I

(b) Write down &e value of 8 l

2k :16

(c) Write down the value offr.

2o = ['6

(fotal2 marks)

=?

2Jai

I

2

tl)

lf=Lf

=L'ff .)-Z

K+L :2{1)

(d) Solve g5 - 22m+3

85 = 2"^nu

'(t')'= 2'^"

2't = l^*t

r5 ,L2 3

o

furn+31t-

2r!'1t l:z711b

n...:..b-

-

(3)

(Totat 6 marks)

&43pp::-q1tL. ,h otn,tlkadcl. [-o I g,n " -.

to S@me

Prac*b test pryer lH (Set O: Version 1.0

13. Tom recorded the times, in seconds, some boys took to complete an obstacle course.

He drew this box plot for his results.

110 120Tirue (seconds)

14090

Tom also recorded the times some girls took to complete the obstacle course.

Herearethetimes,inseconds,forthegirls. ol-ot*lQoorh[e n'\ n/rtddte o{ tot*r klf

Kse tol lo3 106 @ loe llo lro lr1 @113 114 115 lls e, na 124 t2s 132 -t

N Uoos Quoth\e rvtedtar'a,h ,ni,&ate of uPo€r h4lf . u^ rntddta '

Compare the distribution of the times for the boys with the distribution of the times forthe girls.

C tr, boys v'^edrau/I = [rS s Cu ct fvredta.r.l = ttl s

5o 6n avLIqAe the

rntr-luonfite taLfle = [2o - tO3 t-'l s1srr,rJer-?t.o.rhh. *Tu = [t 1 -tO8

5o +l^e @- scores wJe @lass spreod ouf ) "

O f,, bo5sfo, 3,lts

t

Strts

@ Ar:r*te dor^tn c"rt'eaf

0') N rtYL do'nt n ukqt

shn buh&s ahE5S*!te ynecttans alL- *h*t CaIOR oro .W\u1 Cornp&rp

(Total for4 marks)

Practice test papsr lH (Set 6): Version L0

,n@t4. (a) write 8.2 * loshP#ffi

tr.Q066ffrJecirnal Po,nf 5 ,Jrn^Ps rrght'g 2ooo o.

(b) write offdd?1ain standard form.

cLciwrql

(c) Workoutthevalueof(2.3 " 1012) -(4-6" 103)Give your answer in standard form.

tL,'' 2 '3\,x tO'-t'

bi * tc 3

E'5 X [o

,''{) '5 \f

,\-t

5xtEr.'

-l r-{5x tCg

5xrO

cttlc '<

)xtDq (2){Total4 marks)

5xg

tc

*fu. ,.,"rt| ,,r,r stand o . dfurr-n lsulauU d^?,Nbebr. de crvrcal P;,^fvrtus I be l:r1 .

II

pomt jr*Ps +

Pra.tice test paper lH {Set 6): Versist 1.0

15.

Diagram I{OTaccrrrately dras'tr

LLt

\BoD

In the diagram,

OB:b

od:"l-oC:!oAaJ1-

BD: , BA4

Find CD in terms of b and c.

Give your answer in its simplest form.You must show all your working.

.-St

e D zShrl u* Cfirrrth af D

ts,4gfa'r* at b

firuerr al O

t b,- b): i'- +b: '(+b *?c-ib i(sb-. )

*7c. & . Bb

-c rb t- 8144)

= *08 + ff, +CA

"- -$ +c + 2c: 3c - b.

-+Cb

Practice tst pqer lH (Set O: Version l-0 t2

(Total4 marks)

16. Two events,l and B, are mufually exclusive.

P(A):0.3

P(A):0.5

(a) Work out P(l) .

P(C):4.4P(D):A.2P(Cnr):0.06

(c) Are C andD independent events?Explain your answer.

0,o*ab,tfu oF _A not LwpPn,n{ "Jt-P(k)=0.7

(b) Work o&P(Aw B)

t+ muruoilq cxclusrrre P(OUB) -- P(A\ t P0B)J

0.1(1)

(1)

.1t....C..A$t.D..,dopn de$t...a;r':rts....ttre*...ms...gI.oheh,rldrtr..0.f...*fi.e,m

(2)

(Total4 marks)

Plactbetmtpryer lH(Se*6): Version 1.0 13

11.

+

I

SimpliS tully2x2 +9x-56x2 -5r+1

x

+5

2*+ q1

=(1"-r)(x

\

I

/

I

Foilox* hp and bottorn slf @ raleLS I 6"+r,, A1-Eem .- 5 usi3 rt-ve1e 3n "l*5)

-l . +9{

+ 6r"-s* + [= (\'-2t< - 3x + I

= 2x(gr-,)- (y-l)

=(2*-r)(lr-n).

( ,, Tt,lh, 0-L x-3 a

1:1+ -5. 3

; [;[F\6rl= 6.:5.

Lxz+%:_5

6*"-s:Lt I= bryl') ("+ s)(y-r)(tr-r)

zr

18.

/

/ _,,-tv/ -t"i

Diagnrnr -\() l'aucuratrrl!' drarvn

!Ii

,4Ii

t

AB is a diameter of a circle.C is apoint on the circle.D is the point inside the circle such that BD : BC and BD is parallel to CA.

Find the size of angle CDB.

You must give reasons for your answer.

.lfj /I

J

,a/

Acg =

CBD=

qi b..qrr-So (LrnXte- {ta a Sovylt-qrcje

qO bcorr*o co -rn-feNor arXbs rl.r[rvr,es cdd t'o ltrO"'

= gc)' '

poratte-l

CCB : t 8o_ 10 = +S o irr, a-.jr b ote a,-5le s o+ ltaLt S o scetp s l},,r.o n5te are auu\ .

tt'S o

Practice test paper lH (S:et 6): Version 1,0

(Total4 marks)

19.

bs buclr-eLt1irll,t!lir

JI

Srno t.Jaul-

Each equation in the table represents one of the graphs A to F.Write &e letter of each Saph ia the correct place in &e table.

Equation Graph

l: 4 sinx" Ly: 4 cos xo

ts

Y:t - 4x+ 5 ?!:4b C

Y:f+4 o4y:-x A

Prartic€ test pryer lH (Set 6): Vemion L0

(fotal3 marks)

Expand (1 + {2X3 -.lZ'l

Give yorn answ€r in the form a + O'l}where a rrrrdb are integers.

+J2

3 \*3.J"2-{" -')

r,= 3 r3{i.-{, * 2: 3 tLl-L-Z

A:t b"2

-fi

...4...:. !.. r...h.. :..2........

(Iotal2 marls)

Practb test paper lH (Stt 6): Versim 1.0

op-

Diagrarus l{0"fac*urately r*arun

. -2-(att)

(3)

21. Umar thinks (a +l)z : a' + 1 for all values of a.

(a) Show that Umar is wrong.

=l (l+t\-,L"zu rl :

Here are two right-angled triangles.All the measurements are'tlllr

{c+ 1}

: *+2s+ |f at+t

"IL,iq@

22

Uqtu(9

O) Show thatZa+2b + l:2c

r & rr"-= c"t**r/. O

Ca+r)zr(b*r\'=@+t)zcf rl;:*l + bzt2btt = LLrZc+ t

@" 2.ct rr.b +2 = LLtzc+ t.tCL fr2a+2lo tL.{rZL+l1

i -ce2a+,.b+Z=7e+l \ I)- l

lat{b+[ = 2c Ya, b andc cannot all be integers.

(c) Exptain why. 2a+ab\.-.t----/

+l=2c\'tJ

\a[**s qrereueca-iisz-R'x hbbalwags wan

5o r^rlrerr add Ino.ryl ba ODO 5g c.,,t+ be rrrrna,]E.Ss (,^ltrote ntrnl,ws) (1)

olA.yal15a Odd =aIUt . (Total6 marks)

Z

tr-$t ruqhftu d hr!.^d6rdD 8

th.c,Jr

at'I, + l)

2-

Practice test pryer lH (Set 6): Version 1.0

TOTAL TORPAPERIS 80 MARKS