edexcel gcse mathematics practice tests: set 4 4...2. there are 50 counters in a bag. the counters...
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edexcel
GCSE Mathematics Practice Tests: Set 4
Paper lH {Non-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 (lH)- Version 1.0 nuto JIUblu,:;atiiiR " ">' only b.: ICIUOO~~ tn :u."CUIIi.n-.:c Wllh rtanou l\IU..Olll\ln I lmHnt ropyn•'" puh,y. ' 2111 b 1\:wr• -n hlucull\)n linutcJ
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1. Write these numbers in order of size. Start with the smallest number.
16
You must show clearly how you got your answer.
s 2. -:::... '2.-'<:.L >C L X' 2 X" '- -::. '1.'2. ~ I .1.
~ a~~ b~-= -!?it ~
lf~ 4. '( 4- 'I( 4- 6LJ- ® I J.
~ 0 -# -=-~ f~ 2 0. (J)
\b l6
() 0 0 t;4-0 =-\ -
1 I 3 - 'i. S'"
... (4:~. /... .~ .. ~ (. .. ~~. L .. \ .. ~ . !.. ... ~..r. ... ~ ............................................................................ .. (Total 3 marks)
l'ructicc test paper I H (Sct4): Version 1.0 2
2. There are 50 counters in a bag.
The counters are blue or yellow or black or white. A counter is taken at random from the bag.
The table shows each of the probabilities that the counter will be blue or black or white.
Colour blue yellow black white
Probability 0.4 0 - \4 0.3 0.16
Work out the number of yellow counters in the bag.
S.U....~oJA~(\~·~==-1 p(~ov-3)-=- \-0-4: - 6 .5-0 ·tb 0 . 3 - ~ · lb
0 . \ 4 '>(_s-o -:::::: \· Lk )(: 5 "::::+-
=
l -4- 'f. s + .0 'Z.
(Total 4 marks)
l'nlClicc test rarer Ill (Set 4): Vcrsiou 1.0 3
3. Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes.
A bus to Acton and a bus to Batton both leave the bus station at 9 00 a.m.
When will a bus to Acton and a bus to Barton next leave the bus station at the same time?
qE;
LCJVI..-:::. l ~ La..o..ve.A+ f\....Q_ ~~ n\11.--Q. I 'l..C> """"~ c.-f{er q ! 00 a. IN\
ct ·. 00 +- 'L.~C> u.rS -= ,, .. OOo...M
l' ·- oc4U'\
(Total3 marks)
Pruc1icc lcsl paper I H (Sci 4): Vcn~ion 1.0 4
4. Here is a trapezium.
5
2Y 13
All the measurements are in em. The area of the trapezium is 18 cm2
•
Calculate the numerical value of the perimeter of the trapezium.
Pr-= '-t"( '2.. -x...-'3a +- 2..?C..:t-~ -""L
18 -=-- 4- ( l..x.. -3.1-'l..:c.-t-3.) "2....
I & .... _ 4-(4~) "2.
( ~ -= 'L ( lt.::L)
l ~ =~:X...
!..K- :X:. &
p -:. '5 + S+ £.::( ... + :!> +- £..:~--3
p - \o+-4X.
p 'o+ 4- (JfJ ~ ,o ~ z-2-
g
-=- t o r 't -=\l1 -==-
............................................................. . cn1
(Total 6 marks)
Prncticc tcsr p~rcr Ill (Sct4): Version 1.0 5
~k_ \)e_r~ -e_ ~
5. The normal price of a television is reduced by 30% in a sale.
The sale price of the television is £350
Work out the normal price of the television.
I GO~/ b - 'Soe( o !::. 1--0 °/0
isso :::- t-otl/0
'SCD £ ........... ... ............ ................... .
(Total 3 marks)
Praclice 1es1 paper I H (Sci 4): Version 1.0 6
6. Work out an estimate for the value of
G; , ~ "=: f-1 Ci I 0== Q..OO
0 .oSI ~-0-0S"
Practice test paper I H (Set 4): Version 1.0
6.8 x 191
0.05 1
b - ~X \~I
o -oSI
7
2 <iS c.:t::J:.)._. ............ ..... ................ .
(Total 3 marks)
7. ~em
7 em /Sc.tv , <.: -
@ 2cm
, oJ. 7 em
~~~he diagram shows the cross-section of a solid prism . .; The length of the prism is 2 m.-: ~ CW'\
~ '/ (/ ~ The P'i'm i> made from metal. (/. The density of the metal is 8 grams per cm3.
Work out the mass of the prism.
Diagram ~ OT accurately drav .. ·n
fY\ -::.. 0 X \/'
V''::-CSA-x~th
CSA . -. CS.A- ::: ~ co +-AN-o. (b) -=- (-:=tc:M ><'LCN~) + ( Scn.JoC ~)
v
fVI-;;. Dxv
Practice test paper I H (Set 4): Version 1.0
=- l 4-C#Y\ 'l. +- \0 C/Y\ "-
'L =- ~C;v\ -= '2.4c..tvJ7....X 2.00CM
-=. '+ g a::) ov?
= Lt~~")( ~~Jd
~ '3,~400 J
8
.. 3..~.4.0~·········· (Total 5 marks)
8. The diagram shows a straight line, L1 , drawn on a grid.
A straight line, L2, is parallel to the straight line L1 and passes through the point (0, -5).
Find an equation of the straight line L2.
L2. ,·s ~o.JA.Jll t-o Lt '.. L.'- '-'.~ Sa...vWL ~o-Q ,· -vJ o-P Lt
m-= j~"3l Z .-z..-..:<.t
( c:> ,3.) CV\ol ( 4' s-)
(o ,-r-)
Practice test paper I H (Set 4): Version 1.0
' --'-
9
(Total3 marks)
9. The Venn diagram shows the numbers 1 to II
(a) Work out P (A u B) O(l.
-r ( Nl.t.M~ ~ Pr or B J
(b) WorkoutP(B ' )
l\:>c.-r6
Practice test paper I H (Set 4): Version 1.0 10
4
7
-- l '
--
-l '
(2)
I I
(2)
(Total4 marks)
10.
J'
7
6
5
4
3
~
- 1 () 2 3 4 5 6 7 X I) 10 X
- I
(a) Describe fully th~ single transformation that maps triangle Ponto triangle Q .
.. ~ ... !':0 .. ~ .. ~ ... ?., .. :::; .. $':' ...................... .. .. .......... ........ ................ .
(2)
7
5
- 4
3
2
- 1 () 2 3 4 5 6 7 X 9 10 X
- I
(b) Enlarge rectangle R, with scale factor 3 and centre (4, 0).
~ ve~: (~') SfX3 (2)
Practice test paper I H (Set 4): Version 1.0 l l
- 8
5
- 8 - 7 - 6 - 5 -4 - 3 - 2 - 1 () 7 X X
- I
ShapeS can be transfonne~ to shape T by the translation ( _ ~) followed by a rotation.
:s ct~\.V'\ (c) Describe the rotation .
... i)~ .... c.to.~~~-f .... ~ ... J~/ .. ~) ....................................................... .
Practice test paper I H (Sct 4): Version 1.0 12
(3)
(Total 7 marks)
11. The lines y = x - 2 and x + y = I 0 are drawn on the grid.
I'
10
9
7
6
5
4
' .>
0
x :::.3>
2 4 5 6 7
y-x - 2
9 10 I I 12 X
On the grid, mark with a cross (x) each of the points with integer coordinates that are in the region defined by
(o , o) WCY"L.t.S.
( o , o") "'-~CI"~
y >x - 2 'SI\~d
x+y < lO%~ ·
x > 3 1\l~s ~w-~
c C) - wc:l.l~ <!:14\J IH"E- L::!J-JC.i ~0 ~ Cev'\,1'"
~ ·
Practice test paper I H (Set 4): Version 1.0 13
(Total 3 marks)
12. Harry travels from Appleton to Brockley at an average speed of 50 mph. He then travels from Brockley to Cantham at an average speed of 70 mph.
Han y takes a total time of 5 hours to travel from Appleton to Cantham. The distance from Brockley to Cantham is 2 10 miles.
Calculate Harry's average speed for the total distance travelled from Appleton to Cantham.
~~\ ~-:;,B)
s-::.. so~"' o= looM ,·~@ '\ -::.. "2.. hO\f ~ @
s = J2. - ~\0 '"""'La..r I S"-.o~
Practice tes t paper I H (Set 4): Version 1.0
-:J~7.
(B~<..)
s ~~~~ D-::. 2lOM.ilc2.J
l :. 3~C()(S ([)
b~ .......... .......... ........ ..... ............. tnph
(Total 4 marks)
14
13. A
B D
Diagram NOT accumtcly drawn
A, B, C and D are points on the circumference of a circle with centre 0 . AngleABC = 116°.
Find the size of the angle marked x. Give reasons for your answer.
~ ~llL 0::2xll6 :: 2~2.0
Practice test paper Il l (Set 4): Version 1.0 IS
(Tota14 marks)
14. The nth term of a quadratic sequence is n2 + 3n - 2
(a) Find the fourth term of this sequence.
v'\ "'t. +-3."' -2..
(4-)l- t-3(4) -2
l(:, +- \ '2... -L. - '1..6 -Here are the fi rst five tenns of a different quadratic sequence.
7 17 31
(b) Find, in tenns of 11, an expression for the nth term of this sequence.
CD ~0--=- 4 ~ ~C\.=-L-
@ ~o...+-\o -= b _..') 3 (2..) 1- b -:::... b -==--.> 'o -=- D
@ 0\..+-bt"C= I ~ "2-t-o;-c...-::::.. I ~..., c... -:::.-1
2 V\ 2 +o"" - 1
Practice test paper Il-l (Sci 4): Version 1.0 16
(2}
49
2 (\'l--I (3)
(Total 5 marks)
15. Fiza has 10 coins in a bag. There are three£ I coins and seven 50 pence coins.
Fiza takes at random, 3 coins from the bag.
Work out the probability that she takes exactly £2.50.
H.o\.JU fV\.~ ~.S 1o McA.Luz... j'). .S'Q?
Practice lest paper Ill (Sct4): Version 1.0 17
( i:J 1 fJ, SOp )or( iL scy, il) 0 r~GJ>J"it11J
-=: "3> "X p ( 1:\,--f:\, SOp)
P(-i:-1, 'i-1, ~oo"\ - ;!.. ~ 3::.... +-,)) - lb .... -1 "'T
- 4-"1--"1"2.0
(Total 4 marks)
16. M is directly proportional to L3.
When L = 2, M = 160
Find the value of M when L = 3
(-==- <6)
Practice lest paper 1 H (Scl4): Version 1.0
MoL L3
f'\ ~ \L.L3 ----~> -:>
l bO-=:. ~ ( 2..) l bO -=- g \<:..
-:l.O =- "-
18
1 M~'LCL
M -=- 2D (3)~
M -:::. '2..0 "~<" '2-1-
M -=- S4o --
S"40
(Total 4 marks)
17. Solve(x -1)2 -2(x- 1) - 3 = 0
~01\.SA (:x._ -,)(::t_.-.) - 2.( X...-•) -3 :::. 0
~ '-- -:x:_- :x_ +-I - t..(.?L-1) -'J> ::0
'2-?(.. -X..-?(:~- ( -L:X_.+-2. -5 =-0
~Ck 'l... :::0 'X- -4.:X:...
PP\..c.J-c.V i u. ')(... (x..-4) :::-0
Sc\ v'-e_ '):.....-= 0 oiL. X--=- 4 '-'""
(Tota14 marks)
Practice test paper I H (Set 4): Version 1.0 19
18. OACD is a trapezium made from three equilateral triangles.
OA =a
OB = b
M is the midpoint of CD.
(a) Write AB in ter~~f a a~.
~-::A0-'-06
(b) Show that OC is parallel to BM .
A
0 h
- 0... o\-lo - -
p a.ra.UQ..l '\ ~ s c a.letr
~p~ oF-~ dWlr
ot~oa+~
-"l. -? c.o =- p,.o.
~c.Wt SJ2..
::> -"'"> Oc = A~M
Practice test paper I H (Set 4): Version 1.0
__:::;:. oc..
- ~ +-~
-
I I \ . C\_--01..+--~ .,__ -z.. -
20
D
(1)
(4)
(Total 5 marks)
19. Prove algebraically that the sum of the squares of two consecutive integers is a lways an odd number.
\n~~==-A
Ccns.eCA..I.k\~ ~ V\~
Practice test paper l H (Set 4): Version 1.0
( 'L 1..
V\+1) + (n)
1... 2A + 'l.t>'\ ;- I
21
2_ ( r'\ ~ ~) ~ s: ./2>.J'(!..Y\.
'2 ((I L. ~ -M , .. s oot.cA · (]_
(Total3 marks)
. 8-~ 20. G1ven that J2 = a + b J2, where a and b are integers,
find the value of a and the value of b.
' ~ - '3>J"i , 0
..Ji
2o.n'cYOL~
~c~) - ~-~~ ..Jl. - v -
-J7.. ~
..J2_ X~L-:::.. '2_ ..s-L( g -:) ~)
£_
~~-b "'2
~-s ,.
a = ...... :-:-:-.3 ............... . b= ...... ~ ................. ..
(Total 3 marks)
TOTAL FOR PAPER IS 80 MARKS
Practice test paper I H (Sct4): Version 1.0 22