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GCSE Mathematics Practice Tests: Set 4

Paper 3H (Calculator) Time: 1 hour 30 minutes

You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Instructions

• Use black ink or ball-point pen. • 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

- there 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.

Information

• The total mark for this paper is 80 • The marks for each question are shown in brackets

-use this as a guide as to how much time to spend on each question.

Advice

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

ALWAYS LEARNING PEARSON

Practice Tests: Set 4 Regular (3H) - Version 1.0 l11is pubhcutiun 11106)' only~ n:rrt>duccd in occ:urJ:ml!~ W1lh F1tt01t'IOII t::d~k'lli\)n Lul\ltctl ~Ollrritllll polky f"'2tll b Pcttrson Educuunn Lunitc~t.

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1. Here is a list of ingredients needed to make 20 cookies.

Cookies

Ingredients to make 20 cookies.

Sam is going to make some cookies.

She has these ingredients.

625 g butter

250 g butter 120 g caster sugar 300 g flour

360 g caster sugar 1000 g flour

Work out the greatest number of cookies that Sam can make with her ingredients. You must show your working.

&tkka$ \.1)~ hUtU

~~ US•'Y\j S~CXf

~4flou.r

eeo~·e.~ \.A,.$1~ butfiY

~e~ us,Yj s~W'

~\Ueb vs~t-lov~

I

625-:- '2.. so -=- '2.::i: ~ s "1€:0--7 \20 -:::. ~ 'oaJ.c.INl.~

tOOCi:- ~0 = ~ ~ ~:kW2 .. ~

'2. .;_ )< '2. 0 -:::a. ~0

~ )C '2.D -::::: <=>o

~~ ">< 2G ~ b6

............................ ... §'0 ...... . (Total 3 marks)

Procticc tc~c popcr JH (Set 4): Version 1.0 2

2. Celina and Zoe both sing in a band.

One evening the band plays for 80 minutes. Celina sings for 65% of the 80 minutes.

Zoe sings for~ of the 80 minutes. 8

Celina sings for more minutes than Zoe sings.

Work out for how many more minutes. You must show all your working.

C~a.. · bS'" "/o of tO ::: 0 ·6$" X: <l6

- SO~·~s

5~-.so

2. . ................................. ........ ..... nunutes

(Total 4 marks)

l'rnc ticc t~st pupcr 3H (Set 4): Version 1.0 3

3.

ABC is a straight line. DEFG is a straight line. A C is parallel to DG. EF=BF. Angle BEF = 50°.

Work out the size of the angle marked x. Give reasons for your answer.

A. 0 '

BFE -= :x:-= ~0

l'ruclicc lcsl p~pcdH (Scl4): Version 1.0 4

Ding:r:un ~OT nccurntely drnwn

.................. ................. ~O .. o

(Total 4 marks)

------

_,. I - - - J - -- . - -.- •- - ..:J

4. (a) Simplify (2 J..S)4

=~"-~<'")" == c c.'"~) ( c1 t) (c~e) (C'I.ic!)

:: C.B'(:..t.P S tO Ck

(1)

(b) Expand and simplify (3x + 5)(4x- I)

(sx:'rs)( 4-x..-•)

I 2.x... '1:-.3. -:t... + ?.D-x-- ~

r1.::x: . .'· +-rt- x.. - c; '2..

\ '2. -x.. ·H ~ - S" .......................................... (2)

(c) Solvex2 -3x-10=0 Sa\v,~ ~"C.S

~-s~ (x.-s)(.:~ .. :t2.) ::a

S.o\v-<L

~ ...

Pruc1icc 1cs1 pnpcr 3H (Sc14): Version 1.0 5

x= $ or -'2... .... ............................................................. (3)

(Total 6 marks)

.- -P0~~as ~ v~ 4 P"·~~

5. Here is a sandwich packet.

1.:! em

II Sandwiches

16 em

The packet is in the shape of a triangular prism. The triangular faces are right-angled triangles.

'\ Find the volume o[the sandwich packet.

~\'1-~.. "-'ttP ll'\t BPISE ·.

~ F"dftAo.Jonxs ·.

(-14l4-)

-JA;jS

e&A- == \2 x 'C> · SV& . . .

2..

Scm

~ '2. ~ ~ c..+-l.o = (, 12 ""\. +-b '""2...;: l b 't

l44fb"'t..-::. 2S6

b'2...= I 11.

b -= "l\'2- =- (C') . s !3 . . .

-- 6'3 .L.+A ~C>. . • -=-~ s

SO& 3 ..................... ......................... ctn

(Total S marks)

Procticc test pnpcr 3H (Set 4): Version 1.0 6

6. Make p the subject of the formu la y = 3p1 - 4.

(r-u.)

(-:-3)

~.: ~p"t. -4 jtU. -=- 3p (_

';j+"4--=- p '1. 3

!. r;;;;- = 'P -:.J~

Prncticc test pupcr 31 I tSct4): Version I .0 7

-;; ±.J ~; ...... f. ........ ........... ................ . (Total 3 marks)

7. There are 10 boys and 20 girls in Mrs Brook's class. "3 0 ~·~ Mrs Brook gave all the class a test.

The mean mark for all the class is 60. The mean mark for the girls is 56.

Work out the mean mark for the boys.

'2.o x S.b -= 11'2..0

6'80.7:- lO - '=>~

Prnc ti~c lest paper 311 (Scl4): Vers ion 1.0

(Tota13 marks)

8. The diagram shows a ramp next to a step.

Di:Jgram MH

Step R"mp ~~"m!ely """'~

(i) Work out the size of the angle marked x.

26*~'~ 1~0° ~ ~ +v-\0\g\a.

(ii) Give a reason for your answer.

x= ~0 o ............. .................................

J 0 . ······· .~O. ..... I.P.\ ... (}..,., .... t.·r.f.~\.~ ................................ .... ... ....... ............................ . .

(Total3 marks)

J>mcticc lCSl paper 3H (Scl4): Version 1.0 9

9. The decision tree diagram gives information about the probability of snow for the first 50 days in winter and the probability of whether buses will run or not run.

(a) Complete the decision tree diagram.

\oVcalhcr Buses

Buses will run

Buses will not nm

Buses will nm

Buses will not run

(b) Work out the probability that it will snow and tbe buses will not run.

'P(~,~ ~)-:::. o . 2. '-t(' 0 ·3

0 ·06

0 ·06

(2)

(2)

(Total 4 marks)

Practice tcsr purer 31 I (Set 4): Version 1.0 10

10. A baker makes jam rolls.

The baker uses flour, butter and jam in the ratio 8 : 4 : 5 to make jam rolls.

The table shows the cost per kilogram of some of these ingredients.

Cus l p t' l' 1\ilugr :tm

F lour 40p 13uller £2.50 Jam £1.00

The total weight of the flour, butter and jam for each jam roll is 425 g.

Work out the cost of these ingredients for 200 jam rolls.

J2c..tH o "F : t6 : -:J ~ ·. 4- '·"S'""

( 7 I:J.)

'6 +-4- +-~ =. I 7 foA-S

l~.s - 4'25"3

\ \-:>art- - "2S ,5

<t ·. u. ·. -s--'2.00 : (00 '. n ... .s- pe..,t j~ rou... c~~YCA.M..s)

'2oo IO"U.S ( X::'-06)

(~\(:>(:X:')

~ '. '2.Q:::OO : 'l.SOOO (IL_5)J~cl ~~~ .. )

40 ·. 20 : 'LS"'" (\~)

4Dx 40p. -- I coop -=- ~(6

-i::Z-~0 x 2.0 -=- i:: ~ 0

£ 9t .............................................. (Total 6 marks)

l'ruclicc ICSI paper 3H (Sci 4 ): Version 1.0 I I

11. A student did a survey of teachers' ages.

The cumulative frequency curves show infom1ation about the ages of the male teachers and the ages of the female teachers.

100

90

. r r:::r= - - - . - J -. - 1-

--- .• . -. '·

-t 1 - --1-. . .... -. xo

70

60 Cumulative

., ~r ~I I ' ~ i I

1- ~: ~ ' !- I male tcachc rs f.J I

Frequency 50

40

30

t 'I ..j. ~- . l y I . P: -

I f.r::t . --. • l- + - . !:' . - f< -- ij~ ~ It

7 •·· -fc n lc teac hers

20

to

~ ~~1 .. .

J

• l~ -

"" v.--- 'll ~ - .

I U.l: ±I· - - -~ f-1+ - 1-i..L

T ;- H-:.,..o' ()

20 40 "" t .. 50 60 •. ,-:.If,. \JQ-:. n ..

70

Age in years

(a) Find an estimate for the number of the male teachers older than 50 years of age.

~ ~ ~ Q...ll4- \J..f ~ \ ~ 0..8 oQ. ap ~C) too ~ UJ\ -fclaJ

I00-6 <z:S--::.. '3"2_ --

Prncticc tc~r pnpcr 311 (Sct4): Version 1.0 12

(2)

The youngest male teacher was 21 years of age. The oldest male teacher was 65 years of age.

(b) On the grid, draw a box plot to show the distribution of the ages of the male teachers.

20 30 40 50 GO 70

Age in years

(4)

The box plot below shows information about the ages of the female teachers .

female teachers ~ ·I- I I II Ill II II I

•• -H-h I++H >-1- = : .. H+H

:-I - ·--+ - - tr· , - ~ dtt. t ,·lrt ~ -~ 20 30 40 50 GO 70

Age in years

(c) Make two comparisons between the distributions of the ages of male teachers and female teachers.

-r.~.~--·~-~CW. ... f~ .. tj~ .... ~ .. ~ ... ~

.~ .... ~ ..... C .. ~~~----~·M.l~--~---~--~· ·· · · ····· ~~----9:8~~---~.3 ..... ~ ... ~ .. ~.~-- -~-~~ .. . . (:?.~ .... ~.~~ .. : .................................................................................................... .

(2)

(Total 8 marks)

Prncticc tes t pnpcr 311 (Sc14): Version 1.0 13

12. The diagram shows a sector of a circle of radius 6.8 em.

p

PQ is an arc of the sector. Angle PRQ = 100°.

Work out the perimeter of the sector.

R

Give your answer cotTect to 3 significant figures.

Q

G.~ t: m

- ~· g- \--6 . ~ T- ANS

- 2S . s ( ~s ·f) c'"""'

2S .S"" ......................................... ...... ............... ctn

(Total3 marks)

Pructicc lcstpupcr 311 (Sct4): Version 1.0 14

13. f is the function f(x) = 2x + 5.

(a) Find f(3).

(b) Express the inverse function r 1 in the form r-1(x) = 'j ~ 1.:::(. t-~

( -s) 'j-s = '2.~

" (1)

(~'2..) ~:. ..lL -z...

z r 1(x) = ................................ .............................. ..

~~'Cr'- ~ -= f -·l'<.) "2..

g is the function g(x) = x 2 - 25.

(c) Find g(-3). '-jC-3)= (-3) -25

-=- 9- 2..$"'"

-::: - l C:, _.-

(d) (i) Find gf(x). Give your answer as simply as possible.

2-~ -FC~e) -=- ( 2.::c;tS) - '2- s-

-=- (2:c.;S")("2.4+S)- Z..S

(2)

(1)

-:=. 4-'l:' +-<O'lC....+(O"- +l.S -"l.S'

(ii) Solve gf(x) = 0.

l'raclicc ICSI popcr 311 (Scl 4 ): Version 1.0

-=.... '+::L'L4 c..O~ - 4..X..{X..+S) - gf(x) = ... ~-~.(~-~-~) .................................. ..

15

(5)

(Total 9 marks)

14. Dan does an experiment to find the value of 1r.

He measures the circumference and the diameter of a circle.

He measures the circumference, C, as 170 mm to the nearest millimetre. He measures the diameter, d, as 54 mm to the nearest millimetre.

c Dan uses 1r = - to find the value of 1r.

d

Calculate the upper bound and the lower bound for Dan 's value of1r.

16C\ ... S ~. 1\ . .. ( 9 s - ~) upper\1uffd = ........ ~:Y\ ................... ........ .

lower bound = ..... ~ .. : .. ~ . ! ............................. . (Total4 marks)

Practice test paper 3H (Set 4): Version 1.0 16

15. Simplify x+I x+3 - + -

2 3

Ad~ A\_8~~ ~~~

c~~~)

~ ~-~ -sc.~ ... -tl) ·\- 2(!X:--r~)

~

s :X:...-\"\

............................... E? ........... . (Total 3 marks)

Pr:tcllcc test paper 3H (Sct4): Version 1.0 17

16. The diagram shows an isosceles triangle XYZ.

XZ = YZ

M is the midpoint of XZ. N is the midpoint of YZ.

Prove that triangle XMY is congruent to triangle YNX. Give reasons for each stage of your working.

'I..O:C='-1~

.' . ~')( ~ ':- 'i, :c. @) _· . 'i.M -:.. '1"-'

®

B~ s "'~ , 6 )(t"t\ '-t Cl'd

6'1 N '1C (I..JI(2... ~ •

I:]

Practice test paper 3H (Set 4): Version 1.0 18

(Total 4 marks)

17. A: 8 :C = x+l: 3 :x- l

A + 8 + C=60

8 =30

Work out the value ofx . c

?(.+I 3 x - 1

G i v-e...n ~ ::.. '2:0 I 0 ( :::(..+1)

( Qo..-T\o ~':> ~ 'K. \0)

lOx.. -t-l<:.:l ~-;:.o + t OX-- l 0 -=-- 6 0

20 ".)(. t-~0

(Total 5 marks)

Practice test paper JH (Set 4): Version 1.0 19

18. Prove that

(2n + 3)2- (2n - 3? is a multiple of 8

for all positive integer values of n.

~ \ S ~~ ~ ~ !..z..-4A ~ ~ 0.. ~'f~~ d'"

Q .

(Total3 marks)

TOTAL FOR PAPER IS 80 MARKS

Practice test paper 3H (Sct4): Version 1.0 20