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Number
Difficulty: Medium
Question Paper 1
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Medium
Booklet
Question Paper 1
Time allowed:
75 minutes
Score:
/64
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Question 1
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= {21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
A = { x : x is a multiple of 3}
B = { x : x is prime}
C = { x : x G 25}
(a) Complete the Venn diagram.
B
A
C
[4]
(b) Use set notation to complete the statements.
(i)
26 ..................... B
(ii)
A
[1]
B = .....................
(c) List the elements of B
(C
A).
[1]
[2]
(d) Find
(e)
(i)
n(C),
(ii)
n (B ‘
A
[1]
(B
C))
C is a subset of A
[1]
C.
Complete this statement using set notation.
2
[1]
Question 2
(a)
(i)
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Divide $105 in the ratio 4 : 3.
(ii) Increase $105 by 12%.
[2]
[2]
(iii) In a sale the original price of a jacket is reduced by 16% to $105.
Calculate the original price of the jacket.
[3]
(b) Jakob invests $500 at a rate of 2% per year compound interest.
Claudia invests $500 at a rate of 2.5% per year simple interest.
Calculate the difference between these two investments after 30 years.
Give your answer in dollars correct to the nearest cent.
3
[6]
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(c) Michel invests $P at a rate of 3.8% per year compound interest.
After 30 years the value of this investment is $1469.
Calculate the value of P.
[3]
(d) The population of a city increases exponentially at a rate of x% every 5 years.
In 1960 the population was 60 100.
In 2015 the population was 120 150.
Calculate the value of x.
4
[3]
Question 3
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The scale drawing shows the positions of three towns A, B and C on a map.
The scale of the map is 1 centimetre represents 10 kilometres.
C
North
A
North
Scale: 1 cm to 10 km
B
(a) Find the actual distance AB.
[1]
(b) Measure the bearing of A from B.
[1]
(c) Write the scale 1 cm to 10 km in the form 1 : n.
[1]
(d) On the scale drawing, a lake inside the national park has area 0.4 cm2.
Calculate the actual area of the lake.
5
[2]
Question 4
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(a) Kolyan buys water for $2.60 .
He also buys biscuits.
(i) The ratio
cost of biscuits: cost of water = 3 : 2.
Find the cost of the biscuits.
[2]
(ii) Kolyan has $9 to spend.
Work out the total amount Kolyan spends on water and biscuits as a fraction of the $9.
Give your answer in its lowest terms.
(iii)
[2]
The $9 is 62.5% less than the amount Kolyan had to spend last week.
Calculate the amount Kolyan had to spend last week.
[3]
(b) Priya buys a bicycle for $250.
Each year the value of the bicycle decreases by 8% of its value at the beginning of that year.
Calculate the value of Priya’s bicycle after 10 years.
Give your answer correct to the nearest dollar.
6
[3]
Question 5
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The diagram is a scale drawing of three straight roads, AB, BC and CD.
The scale is 1 : 5000.
C
D
A
B
Scale 1 : 5000
Find the actual length of the road BC.
Give your answer in metres.
7
[2]
Question 6
(a)
(i)
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Eduardo invests $640 at a rate of 2% per year compound interest.
Show that, at the end of 6 years, Eduardo has $721, correct to the nearest dollar.
[2]
(ii) Manuela also invests $640.
At the end of 4 years, Manuela has $721.
Find the yearly compound interest rate.
[4]
(b) Carlos buys a motor scooter for $1200.
Each year the value of the scooter decreases by 10% of its value at the beginning of that year.
Find the value of the scooter after 3 years.
8
[2]
Question 7
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(a) x is an integer.
A = {x: x is a factor of 12}
B = {x: x is an odd number}
C = {x: x is a prime number}
(i) Complete the Venn diagram to show this information.
A
B
C
[3]
(ii) Use set notation to complete each statement.
[3]
(iii) Find n(B).
[1]
(b)
X
Y
q
p
r
s
t
u
w
v
Z
(i) Use set notation to complete the statement.
{u, v} ...................... Z
(ii) Shade X
9
(Z
Y)'.
[1]
[1]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
N u m b er
Diffi c ult y: M e di u m
Q u esti o n P a p er 2
L e v el
I G CSE
S u bj e ct
M at hs ( 0 5 8 0/ 0 9 8 0)
E x a m B o ar d
CI E
T o pi c
N u m b er
P a p er
P a p er 4
Diffi c ult y
M e di u m
B o o kl et
Q u esti o n P a p er 2
Ti m e all o w e d:
9 3 mi n ut es
S c or e:
/81
P er c e nt a g e:
/100
Gr a d e B o u n d ari es:
CI E I G C S E M at hs ( 0 5 8 0)
A*
>83 %
A
67 %
B
51 %
C
41 %
D
31 %
CI E I G C S E M at hs ( 0 9 8 0)
9
>95 %
8
87 %
7
80 %
6
69 %
5
58 %
4
46 %
Q u esti o n 1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
T
B
11
9
x
6 – x
4
P
I n t h e V e n n di a gr a m,
= { c hil dr e n i n a n urs er y }
B = { c hil dr e n w h o r e c ei v e d a b o o k f or t h eir birt h d a y }
T = { c hil dr e n w h o r e c ei v e d a t o y f or t h eir birt h d a y }
P = { c hil dr e n w h o r e c ei v e d a p u z zl e f or t h eir birt h d a y }
x c hil dr e n r e c ei v e d a b o o k a n d a t o y a n d a p u z zl e.
6 c hil dr e n r e c ei v e d a t o y a n d a p u z zl e.
( a) 4 c hil dr e n r e c eiv e d a b o o k a n d a t o y.
5 c hil dr e n r e c ei v e d a b o o k a n d a p u z zl e.
7 c hil dr e n r e c ei v e d a p u z zl e b ut n ot a b o o k a n d n ot a t o y.
C o m pl et e t h e V e n n di a gr a m a b o v e.
[ 3]
( b) T h er e ar e 4 0 c hil dr e n i n t h e n urs er y.
Usi n g t h e V e n n di a gr a m, writ e d o w n a n d s ol v e a n e q u ati o n i n x .
2
[3 ]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( c)
W or k o ut
(i) t h e pr o b a bilit y t h at a c hil d, c h os e n at r a n d o m, r e c ei v e d a b o o k b ut n ot a t o y a n d n ot a p u z zl e,
[ 1]
(ii) t h e n u m b er of c hil dr e n w h o r e c eiv e d a b o o k a n d a p u z zl e b ut n ot a t o y,
[ 1]
(iii)
n(B ),
[ 1]
(i v)
n(B  P ),
[ 1]
[ 1]
( v) n(B  T  P )'.
( d)
T
B
P
S h a d e t h e r e gi o n B  (T  P )'.
3
[ 1]
Q u esti o n 2
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
S
N ort h
S c al e: 2 c m t o 3 k m
P
L
I n t h e s c al e dr a wi n g, P is a p ort, L is a li g ht h o us e a n d S is a s hi p.
T h e s c al e is 2 c e nti m etr es r e pr es e nts 3 kil o m etr es.
( a) M e as ur e t h e b e ari n g of S fr o m P .
[ 1]
( b) Fi n d t h e a ct u al dist a n c e of S fr o m L .
[ 2]
( c) T h e b e ari n g of L fr o m S is 1 6 0 °.
C al c ul at e t h e b e ari n g of S fr o m L .
4
[ 1]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( d) W or k o ut t h e s c al e of t h e m a p i n t h e f or m 1 : n .
( e)
T h e li g ht h o us e st a n ds o n a n isl a n d of ar e a 1. 5 c m 2 o n t h e s c al e dr a wi n g.
W or k o ut t h e a ct u al ar e a of t h e isl a n d.
5
[ 2]
[ 2]
Q u esti o n 3
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
J a n e a n d K at e s h ar e $ 2 4 0 i n t h e r ati o 5 : 7 .
( a)
S h o w t h at K at e r e c eiv es $ 1 4 0.
[ 2]
( b) J a n e a n d K at e e a c h s p e n d $ 2 0.
Fi n d t h e n e w r ati o J a n e’s r e m ai ni n g m o n e y : K at e’s r e m ai ni n g m o n e y.
Gi v e y o ur a ns w er i n its si m pl est f or m.
[ 2]
( c) K at e i n v ests $ 1 2 0 f or 5 y e ars at 4 % p er y e ar si m pl e i nt er est.
C al c ul at e t h e t ot al a m o u nt K at e h as aft er 5 y e ars.
[ 3]
( d) J a n e i n v ests $ 8 0 f or 3 y e ars at 4 % p er y e ar c o m p o u n d i nt er est.
C al c ul at e t h e t ot al a m o u nt J a n e h as aft er 3 y e ars.
Gi v e y o ur a ns w er c orr e ct t o t h e n e ar est c e nt.
[ 3]
( e) A n i n v est m e nt of $ 2 0 0 f or 2 y e ars at 4 % p er y e ar c o m p o u n d i nt er est is t h e s a m e as a n i n v est m e nt of
$ 2 0 0 f or 2 y e ars at r % p er y e ar si m pl e i nt er est.
Fi n d t h e v al u e of r.
6
[ 3]
Q u esti o n 4
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
I n J ul y, a s u p er m ar k et s ol d 4 5 9 8 1 b ottl es of fr uitj ui c e.
( a)
T h e c ost of a b ottl e of fr uit j ui c e w as $ 1. 3 5 .
C al c ul at e t h e a m o u nt r e c ei v e d fr o m t h e s al e of t h e 4 5 9 8 1 b o ttl es.
Gi v e y o ur a ns w er c orr e ct t o t h e n e ar est h u n dr e d d oll ars.
[ 2]
( b) T h e n u m b er of b ottl es s ol d i n J ul y w as 1 7 % m or e t h a n t h e n u m b er s ol d i n J a n u ar y.
[ 3]
C al c ul at e t h e n u m b er of b ottl es s ol d i n J a n u ar y.
( c)
T h er e w er e 3 diff er e nt fl a v o urs of fr uit j ui c e.
T h e n u m b er of b ottl es s ol d i n e a c h fl a v o ur w as i n t h e r ati o
T h e t ot al n u m b er of b ottl es s ol d w as 4 5 9 8 1.
a p pl e: or a n g e : c h err y = 3 : 4 : 2.
C al c ul at e t h e n u m b er of b ottl es of or a n g e j ui c e s ol d.
[ 2]
( d) O n e b ottl e c o nt ai ns 1. 5 litr es of fr uit j ui c e.
C al c ul at e t h e n u m b er of 3 3 0 ml gl ass es t h at c a n b e fill e d c o m pl et el y fr o m o n e b ottl e.
( e)
5
9
of t h e 4 5 9 8 1 b o ttl es ar e r e c y cl e d.
C al c ul at e t h e n u m b er of b ottl es t h at ar e r e c y cl e d.
7
[ 3]
[ 2]
Q u esti o n 5
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
D a vi d s ells fr uit at t h e m ar k et.
( a) I n o n e w e e k, D a vi d s ells 1 2 0 k g of t o m at o es a n d 8 0 k g of gr a p es.
(i) Writ e 8 0 k g as a fr a cti o n of t h e t ot al m ass of t o m at o es a n d gr a p es.
Gi v e y o ur a ns w er i n its l o w est t er ms.
(ii)
Writ e d o w n t h e r ati o
m ass of t o m at o es: m ass of gr a p es.
Gi v e y o ur a ns w er i n its si m pl est f or m.
[ 1]
[ 1]
( b) (i) O n e d a y h e s ells 2 8 k g of or a n g es at $ 1. 5 6 p er kil o gr a m.
H e als o s ells 3 5 k g of a p pl es.
T h e t ot al h e r e c ei v es fr o m s elli n g t h e or a n g es a n d t h e a p pl es is $ 8 6. 3 8 .
C al c ul at e t h e pri c e of 1 kil o gr a m of a p pl es.
(ii)
[ 2]
T h e pri c e of 1 kil o gr a m of or a n g es is $ 1. 5 6 .
T his is 2 0 % m or e t h a n t h e pri c e t w o w e e ks a g o.
C al c ul at e t h e pri c e t w o w e e ks a g o.
[ 3]
( c) O n a n ot h er d a y, D a vi d r e c ei v e d a t ot al of $ 6 6 7 fr o m all t h e fr uit h e s ol d.
T h e c ost of t h e fr uit w as $ 3 1 4. 2 0 .
D a vi d w or k e d f or 1 0 12 h o urs o n t his d a y.
C al c ul at e D a vi d’s r at e of pr ofit i n d oll ars p er h o ur.
8
[ 2]
Q u esti o n 6
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) O n e d a y, M ari a t o o k 2 7 mi n ut es t o w al k 1. 8 k m t o s c h o ol.
S h e l eft h o m e at 0 7 4 8.
(i) Writ e d o w n t h e ti m e M ari a arri v e d at s c h o ol.
(ii) S h o w t h at M ari a’s a v er a g e w al ki n g s p e e d w as 4 k m/ h.
[ 1]
[ 2]
( b) A n ot h er d a y, M ari a c y cl e d t h e 1. 8 k m t o s c h o ol at a n a v er a g e s p e e d of 1 5 k m/ h.
(i) C al c ul at e t h e p er c e nt a g e i n c r e as e t h at 1 5 k m/ h is o n M ari a’s w al ki n g s p e e d of 4 k m/ h.
[ 3]
(ii) C al c ul at e t h e p er c e nt a g e d e c r e as e t h at M ari a’s c y cli n g ti m e is o n h er w al ki n g ti m e of 2 7
mi n ut es.
[ 3]
(iii) Aft er s c h o ol, M ari a c y cl e d t o h er fri e n d’s h o m e.
T his t o o k 9 mi n ut es, w hi c h w as 3 6 % of t h e ti m e M ari a t a k es t o w al k t o h er fri e n d’s h o m e.
C al c ul at e t h e ti m e M ari a t a k es t o w al k t o h er fri e n d’s h o m e.
9
[ 2]
Q u esti o n 7
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
A t e n nis cl u b h as 5 6 0 m e m b ers.
( a)
T h e r ati o
(i)
m e n : w o m e n : c hil dr e n
=
5 : 6 : 3.
S h o w t h at t h e cl u b h as 2 4 0 w o m e n m e m b ers.
(ii) H o w m a n y m e m b ers ar e c hil dr e n ?
[ 2]
[ 1]
( b) 5 of t h e 2 4 0 w o m e n m e m b ers pl a y i n a t o ur n a m e nt.
8
H o w m a n y w o m e n m e m b ers d o n ot pl a y i n t h e t o ur n a m e nt ?
[ 2]
( c) T h e a n n u al m e m b ers hi p f e e i n 2 0 1 3 is $ 1 9 8 f or e a c h a d ult a n d $ 7 5 f or e a c h c hil d.
(i) C al c ul at e t h e t ot al a m o u nt t h e 5 6 0 m e m b ers p a y i n 2 0 1 3.
[ 2]
(ii) T h e a d ult f e e of $ 1 9 8 i n 2 0 1 3 is 5. 6 % m or e t h a n t h e f e e i n 2 0 1 2.
C al c ul at e t h e a d ult f e e i n 2 0 1 2.
10
[ 3]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( d) T h e cl u b b u y s 3 6 t e n nis b alls f or $ 9. 5 0 a n d s ells t h e m t o m e m b ers f or $ 0. 7 5 e a c h.
C al c ul at e t h e p er c e nt a g e pr ofit t h e cl u b m a k es.
[ 3]
( e) A t e n nis c o urt is a r e ct a n gl e wit h l e n gt h 2 3. 7 m a n d wi dt h 1 0. 9 m, e a c h c orr e ct t o 1 d e ci m al pl a c e.
C al c ul at e t h e u p p er a n d l o w er b o u n ds of t h e p eri m et er of t h e c o urt.
11
[ 3]
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Number
Difficulty: Medium
Question Paper 3
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Medium
Booklet
Question Paper 3
Time allowed:
102 minutes
Score:
/89
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Q u esti o n 1
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) Ali a n d B e n r e c ei v e a s u m of m o n e y.
T h e y s h ar e it i n t h e r ati o 5 : 1.
Ali r e c ei v es $ 2 3 4 5.
C al c ul at e t h e t ot al a m o u nt.
[ 2]
( b) Ali us es 1 1 % of his $ 2 3 4 5 t o b u y a t el e visi o n.
C al c ul at e t h e c ost of t h e t el e visi o n.
( c)
[ 2]
A diff er e nt t el e visi o n c osts $ 3 3 0.
(i)
B e n b u ys o n e i n a s al e w h e n t his c ost is r e d u c e d b y 1 5 %.
H o w m u c h d o es B e n p a y ?
[ 2]
(ii) $ 3 3 0 is 1 2 % l ess t h a n t h e c ost l ast y e ar.
C al c ul at e t h e c ost l ast y e ar.
[ 3]
2
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( d) Ali i n v ests $ 1 5 0 0 of his s h ar e i n a b a n k a c c o u nt.
T h e a c c o u nt p a y s c o m p o u n d i nt er est at a r at e of 2. 3 % p er y e ar.
C al c ul at e t h e t ot al a m o u nt i n t h e a c c o u nt at t h e e n d of 3 y e ars.
[ 3]
( e) Ali als o b u ys a c o m p ut er f or $ 3 2 5. H e
l at er s ells t his c o m p ut er f or $ 2 5 0.
C al c ul at e Ali’s p er c e nt a g e l oss.
[ 3]
3
Q u esti o n 2
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
A n n a, B o b b y a n d C arl r e c ei v e a s u m of m o n e y.
T h e y s h ar e it i n t h e r ati o 1 2 : 7 : 8 .
A n n a r e c ei v es $ 5 0 4.
( a)
C al c ul at e t h e t ot al a m o u nt.
( b) (i) A n n a us es 7 % of h er $ 5 0 4 t o p a y a bill.
C al c ul at e h o w m u c h s h e h as l eft.
(ii) S h e b u y s a c o at i n a s al e f or $ 6 4. 6 8.
T his w as 2 3 % l ess t h a n t h e ori gi n al pri c e.
C al c ul at e t h e ori gi n al pri c e of t h e c o at.
[ 3]
[ 3]
[ 3]
( c) B o b b y us es $ 2 5 0 of his s h ar e t o o p e n a b a n k a c c o u nt.
T his a c c o u nt p a ys c o m p o u n d i nt er est at a r at e of 1. 6 % p er y e ar.
C al c ul at e t h e a m o u nt i n t h e b a n k a c c o u nt aft er 3 y e ars.
Gi v e y o ur a ns w er c orr e ct t o 2 d e ci m al pl a c es.
[ 3]
( d) C arl b u y s a c o m p ut er f or $ 2 8 8 a n d s ells it f or $ 3 2 4.
C al c ul at e his p er c e nt a g e pr ofit.
[ 3]
4
Q u esti o n 3
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
= { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
E = { x : x is a n e v e n n u m b er }
F = { 2, 5, 7 }
2
G = { x :x - 13x + 36 = 0}
( a) List t h e el e m e nts of s et E .
[ 1]
( b) Writ e d o w n n( F ).
[ 1]
2
( c) (i) F a ct oris e
[ 2]
x - 1 3 x + 3 6.
2
(ii) Usi n g y o ur a ns w er t o p a rt ( c)(i), s ol v e
( d) Writ e all t h e el e m e nts of
x - 1 3 x + 3 6 = 0 t o fi n d t h e t w o el e m e nts of G . [ 1]
i n t h eir c orr e ct pl a c e i n t h e V e n n di a gr a m.
E
F
G
[ 2]
( e) Us e s et n ot ati o n t o c o m pl et e t h e f oll o wi n g st at e m e nts.
(i) F ∩ G =
(ii) 7
(iii) n( E
[ 1]
E
[ 1]
F) = 6
[ 1]
5
Q u esti o n 4
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) I n a s al e, J e n b u y s a l a pt o p f or $ 3 5 1. 5 5.
T his pri c e is 2 1 % l ess t h a n t h e pri c e b ef or e t h e s al e.
C al c ul at e t h e pri c e b ef or e t h e s al e.
[ 3]
( b) Al e x i n v ests $ 4 0 0 0 at a r at e of 8 % p er y e ar si m pl e i nt er est f or 2 y e ars.
B o b i n v ests $ 4 0 0 0 at a r at e of 7. 5 % p er y e ar c o m p o u n d i nt er est f or 2 y e ars.
W h o r e c ei v es m or e i nt er est a n d b y h o w m u c h ?
[ 6]
6
Q u esti o n 5
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
C hil dr e n g o t o c a m p o n h oli d a y.
( a)
F ati m a b u y s b a n a n as a n d a p pl es f or t h e c a m p.
(i)
B a n a n as c ost $ 0. 8 5 p er kil o gr a m.
F ati m a b u y s 2 0 k g of b a n a n as a n d r e c ei v es a dis c o u nt of 1 4 %.
H o w m u c h d o es s h e s p e n d o n b a n a n as ?
[ 3]
(ii) F ati m a s p e n ds $ 1 6. 4 0 o n a p pl es aft er a dis c o u nt of 1 8 %.
C al c ul at e t h e ori gi n al pri c e of t h e a p pl es.
(iii) T h e r ati o
[ 3]
n u m b er of b a n a n as: n u m b er of a p pl es = 4 : 5.
T h er e ar e 1 0 8 b a n a n as.
C al c ul at e t h e n u m b er of a p pl es.
[ 2]
7
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( b) T h e c ost t o hir e a t e nt c o nsists of t w o p arts.
T h e t ot al c ost f or 4 d a ys is $ 2 7. 1 0 a n d f or 7 d a ys is $ 3 4. 3 0.
Writ e d o w n t w o e q u ati o ns i n c a n d d a n d s ol v e t h e m.
[ 4]
( c) T h e c hil dr e n tr a v el 2 7 0 k m t o t h e c a m p, l e a vi n g at 0 7 4 3 a n d arri vi n g at 1 5 1 3.
C al c ul at e t h eir a v er a g e s p e e d i n k m/ h.
[ 3]
( d) T w o y e ars a g o $ 5 4 0 w as p ut i n a s a vi n gs a c c o u nt t o p a y f or t h e h oli d a y.
T h e a c c o u nt p ai d c o m p o u n d i nt er est at a r at e of 6 % p er y e ar.
H o w m u c h is i n t h e a c c o u nt n o w ?
[ 2]
8
Q u esti o n 6
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) W or k o ut t h e f oll o wi n g.
(i)
1
[ 1]
0. 2 2
[ 1]
5. 1 2 + 4 × 7. 3 2
(ii)
(iii) 2 5
1
2
× 1000
−
2
[ 2]
3
( b) Mi a i n v ests $ 7 5 0 0 at 3. 5 % p er y e ar si m pl e i nt er est.
C al c ul at e t h e t ot al a m o u nt s h e h as aft er 5 y e ars.
[ 3]
4
( c)
Writt e n as t h e pr o d u ct of pri m e f a ct ors 4 8 = 2 × 3.
(i)
Writ e 6 0 as t h e pr o d u ct of pri m e f a ct ors.
[ 2]
(ii) W or k o ut t h e hi g h est c o m m o n f a ct or ( H C F) of 4 8 a n d 6 0.
[ 2]
(iii) W or k o ut t h e l o w est c o m m o n m ulti pl e ( L C M) of 4 8 a n d 6 0.
[ 2]
9
Q u esti o n 7
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
L u c y w or ks i n a cl ot h es s h o p.
( a) I n o n e w e e k s h e e ar n e d $ 2 7 7. 2 0.
1
(i) S h e s p e nt
of t his o n f o o d.
8
C al c ul at e h o w m u c h s h e s p e nt o n f o o d.
( b)
[ 1]
(ii) S h e p ai d 1 5 % of t h e $ 2 7 7. 2 0 i n t a x es.
C al c ul at e h o w m u c h s h e p ai d i n t a x es.
[ 2]
(iii) T h e $ 2 7 7. 2 0 w as 5 % m or e t h a n L u c y e ar n e d i n t h e pr e vi o us w e e k.
C al c ul at e h o w m u c h L u c y e ar n e d i n t h e pr e vi o us w e e k.
[ 3]
T h e s h o p s ells cl ot h es f or m e n, w o m e n a n d c hil dr e n.
(i) I n o n e d a y L u c y s ol d cl ot h es wit h a t ot al v al u e of $ 2 2 0 0 i n t h e r ati o
m e n : w o m e n : c hil dr e n = 2 : 5 : 4.
C al c ul at e t h e v al u e of t h e w o m e n’s cl ot h es s h e s ol d.
(ii) T h e $ 2 2 0 0 w as
[ 2]
44
of t h e t ot al v al u e of t h e cl ot h es s ol d i n t h e s h o p o n t his d a y.
73
C al c ul at e t h e t ot al v al u e of t h e cl ot h es s ol d i n t h e s h o p o n t his d a y.
[ 2]
10
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Number
Difficulty: Medium
Question Paper 4
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Medium
Booklet
Question Paper 4
Time allowed:
86 minutes
Score:
/75
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Q u esti o n 1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) I n 2 0 0 8 t h e t ot al n u m b er of ti c k ets s ol d f or a n at hl eti cs m e eti n g w as 3 1 3 6.
T h e r ati o c hil d ti c k ets s ol d : a d ult ti c k ets s ol d = 1 7 : 3 2.
(i)
H o w m a n y c hil d ti c k ets w er e s ol d ?
[ 2]
(ii) C hil d ti c k ets c ost $ 2 e a c h a n d a d ult ti c k e ts c ost $ 4. 5 0 e a c h.
S h o w t h at t h e t ot al a m o u nt r e c ei v e d fr o m t h e s al e of t h e ti c k ets i n 2 0 0 8 w as $ 1 1 3 9 2.
[ 2]
( b) I n 2 0 0 9 t h e a mo u nt r e c ei v e d fr o m t h e s al e of ti c k ets f or t h e at hl eti cs m e eti n g w as $ 1 2 7 4 8.
C al c ul at e t h e p er c e nt a g e i n cr e as e i n t h e a m o u nt re c ei v e d fr o m 2 0 0 8 t o 2 0 0 9.
[ 3]
( c) I n 2 0 0 8 t h e a m o u nt of $ 1 1 3 9 2 w as 2 8 % m or e t h a n t h e a mo u nt r e c ei v e d i n 2 0 0 7.
C al c ul at e h o w m u c h
2
w as r e c eiv e d i n 2 0 0 7.
[ 3]
Q u esti o n 2
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) H a nsi a n d M e g a n g o o n h oli d a y.
T h e c osts of t h eir h oli d a y s ar e i n t h e r ati o
H a nsi’s h oli d a y c osts $ 7 5 6.
Fi n d t h e c ost of M e g a n’s h oli d a y.
H a nsi : M e g a n = 7 : 4.
[ 2]
( b) I n 2 0 0 8, H a nsi e ar n e d $ 7 8 0 0.
(i)
H e e ar n e d 1 5 % m or e i n 2 0 0 9.
C al c ul at e h o w m u c h h e e ar n e d i n 2 0 0 9.
[ 2]
(ii) I n 2 0 1 0, h e e ar ns 1 0 % m or e t h a n i n 2 0 0 9.
C al c ul at e t h e p er c e nt a g e i n cr e as e i n his e ar ni n gs fr o m 2 0 0 8 t o 2 0 1 0.
[ 3]
( c) M e g a n e ar n e d $ 9 7 2 0 i n 2 0 0 9. T his w as 2 0 % m or e t h a n s h e e ar n e d i n 2 0 0 8.
H o w m u c h di d s h e e ar n i n 2 0 0 8 ?
[ 3]
( d) H a nsi i n v est e d $ 5 0 0 at a r at e of 4 % p er y e ar c o m p o u n d i nt er est.
C al c ul at e t h e fi n al a m o u nt h e h a d aft er t hr e e y e ars.
[ 3]
3
Q u esti o n 3
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
T h o m as, Urs ul a a n d V a n ess a s h ar e $ 2 0 0 i n t h e r ati o
T h o m as : Urs ul a : V a n ess a = 3 : 2 : 5.
( a)
S h o w t h at T h o m as r e c ei v es $ 6 0 a n d Urs ul a r e c ei v es $ 4 0.
[ 2]
( b) T h o m as b u y s a b o o k f or $ 2 1.
W h at p er c e nt a g e of his $ 6 0 d o es T h o m as h a v e l eft ?
[ 2]
( c) Urs ul a b u y s a c o m p ut er g a m e f or $ 3 6. 8 0 i n a s al e.
T h e s al e pri c e is 2 0 % l ess t h a n t h e ori gi n al pri c e.
C al c ul at e t h e ori gi n al pri c e of t h e c o m p ut er g a m e.
[ 3]
( d) V a n ess a b u y s s o m e b o o ks a n d s o m e p e n cils.
E a c h b o o k c osts $ 1 2 m o r e t h a n e a c h p e n cil.
T h e t ot al c ost of 5 b o o ks a n d 2 p e n cils is $ 6 4. 2 0.
Fi n d t h e c ost of o n e p e n cil.
[ 3]
4
Q u esti o n 4
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
Al b ert o a n d M ari a s h ar e $ 2 4 0 i n t h e r ati o 3 : 5.
( a)
S h o w t h at Al b ert o r e c eiv es $ 9 0 a n d M ari a r e c ei v es $ 1 5 0.
( b) (i)
Al b ert o i n v ests his $ 9 0 f or 2 y e ars at r % p er y e ar si m pl e i nt er est.
At t h e e n d of 2 y e ars t h e a m o u nt of m o n e y h e h as is $ 9 9.
C al c ul at e t h e v al u e of r.
(ii) T h e $ 9 9 is 6 0 % of t h e c ost of a h oli d a y.
C al c ul at e t h e c ost of t h e h oli d a y.
( c) M ari a i n v ests h er $ 1 5 0 f or 2 y e ars at 4 % p er y e ar c o m p o u n d i nt er est.
C al c ul at e t h e e x a ct a m o u nt M ari a h as at t h e e n d of 2 y e ars.
( d)
[ 1]
[ 2]
[ 2]
[ 2]
M ari a c o nti n u es t o i n v est h er m o n e y at 4 % p er y e ar c o m p o u n d i nt er est.
Aft er 2 0 y e ars s h e h as $ 3 2 8. 6 7.
(i)
C al c ul at e e x a ctl y h o w m u c h m or e t his is t h a n $ 1 5 0 i n v est e d f or 2 0 y e ars at 4 % p er y e ar
si m pl e i nt er est.
[ 3]
(ii) C al c ul at e $ 3 2 8. 6 7 as a p er c e nt a g e of $ 1 5 0.
5
[ 2]
Q u esti o n 5
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
D a ni ell a is 8 y e ars ol d a n d E d w ar d is 1 2 y e ars ol d.
( a)
T h eir p ar e nts gi v e t h e m s o m e m o n e y i n t h e r ati o of t h eir a g es.
(i)
Writ e t h e r ati o
D a ni ell a’s a g e : E d w ar d’s a g e
i n its si m pl est f or m.
[ 1]
:
(ii) D a ni ell a r e c ei v es $ 3 0.
S h o w t h at E d w ar d r e c ei v es $ 4 5.
[ 1]
(iii) W h at p er c e nt a g e of t h e t ot al a m o u nt of m o n e y gi v e n b y t h eir p ar e nts d o es E d w ar d r e c ei v e ?
[ 2]
( b) D a ni ell a i n v ests h er $ 3 0 at 3 % p er y e ar, c o m p o u n d i nt er est.
C al c ul at e t h e a m o u nt D a ni ell a h as aft er 2 y e ars.
Gi v e y o ur a ns w er c orr e ct t o 2 d e ci m al pl a c es.
[ 3]
( c) E d w ar d als o i n v ests $ 3 0.
H e i n v ests t his m o n e y at a r at e of r % p er y e ar, si m pl e i nt er est.
Aft er 5 y e ars h e h a s a t ot al a m o u nt of $ 3 2. 2 5.
C al c ul at e t h e v al u e of r.
[ 2]
6
Q u esti o n 6
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
M ar c us r e c ei v es $ 8 0 0 fr o m hi s gr a n d m ot h er.
( a)
H e d e ci d es t o s p e n d $ 1 5 0 a n d t o di vi d e t h e r e m ai ni n g $ 6 5 0 i n t h e r ati o
s a vi n gs : h oli d a y = 9 : 4.
[ 2]
C al c ul at e t h e a m o u nt of his s a vi n gs.
( b) (i) H e us es 8 0 % of t h e $ 1 5 0 t o b u y s o m e cl ot h es.
[ 2]
C al c ul at e t h e c ost of t h e cl ot h es.
(ii) T h e m o n e y r e m ai ni n g fr o m t h e $ 1 5 0 is 3 7
1
2
% of t h e c ost of a d a y tri p t o C air o.
C al c ul at e t h e c ost of t h e tri p.
( c) (i)
[ 2]
M ar c us i n v ests $ 4 0 0 of his s a vi n gs f or 2 y e ars at 5 % p er y e ar c o m p o u n d i nt er est.
C al c ul at e t h e a m o u nt h e h as at t h e e n d of t h e 2 y e ars.
[ 2]
(ii) M ar c us’s sist er als o i n v ests $ 4 0 0, at r % p er y e ar si m pl e i nt er est.
At t h e e n d of 2 y e ars s h e h as e x a ctl y t h e s a m e a m o u nt as M ar c us.
C al c ul at e t h e v al u e of r.
7
[3 ]
Q u esti o n 7
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
B e atri c e h as a n i n c o m e of $ 4 0 0 0 0 i n o n e y e ar.
( a)
S h e p a y s:
n o t a x o n t h e first $ 1 0 0 0 0 of h er i n c o m e;
1 0 % t a x o n t h e n e xt $ 1 0 0 0 0 of h er i n c o m e;
2 5 % t a x o n t h e r est of h er i n c o m e.
C al c ul at e
(i) t h e t ot al a m o u nt of t a x B e atri c e p a ys,
[ 2]
(ii) t h e t ot al a m o u nt of t a x as a p er c e nt a g e of t h e $ 4 0 0 0 0.
[ 2]
( b) B e atri c e p a ys a y e arl y r e nt of $ 1 0 8 0 0.
Aft er s h e h as p ai d h er t a x, r e nt a n d bills, s h e h as $ 1 2 0 0 0.
C al c ul at e h o w m u c h B e atri c e s p e n ds o n bills.
[ 1]
( c) B e atri c e di vi d es t h e $ 1 2 0 0 0 b et w e e n s h o p pi n g a n d s a vi n g i n t h e r ati o
s h o p pi n g : s a vi n g = 5 : 3.
(i) C al c ul at e h o w m u c h B e atri c e s p e n ds o n s h o p pi n g i n o n e y e ar.
[ 2]
(ii) W h at fr a cti o n of t h e ori gi n al $ 4 0 0 0 0 d o es B e atri c e s a v e ?
Gi v e y o ur a ns w er i n its l o w est t er ms.
[ 1]
( d) T h e r e nt of $ 1 0 8 0 0 is a n i n cr e as e of 2 5 % o n h er pr e vi o us r e nt.
C al c ul at e h er pr e vi o us r e nt.
8
[ 2]
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Number
Difficulty: Medium
Question Paper 5
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Medium
Booklet
Question Paper 5
Time allowed:
77 minutes
Score:
/67
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Question 1
1
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Each year a school organises a concert.
(a) (i) In 2004 the cost of organising the concert was $ 385.
In 2005 the cost was 10% less than in 2004.
Calculate the cost in 2005.
[2]
(ii) The cost of $ 385 in 2004 was 10% more than the cost in 2003.
Calculate the cost in 2003.
[2]
(b) (i) In 2006 the number of tickets sold was210.
The ratio
Number of adult tickets : Number of student tickets was
How many adult tickets were sold?
23 : 19.
[2]
(ii) Adult tickets were $ 2.50 each and student tickets were $ 1.50 each.
Calculate the total amount received from selling the tickets.
[2]
(iii) In 2006 the cost of organising the concert was $ 410.
Calculate the percentage profit in 2006.
[2]
(c) In 2007, the number of tickets sold was again 210.
Adult tickets were $ 2.60 each and student tickets were $ 1.40 each.
The total amount received from selling the 210 tickets was $ 480.
How many student tickets were sold?
2
[4]
Question 2
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Maria, Carolina and Pedro receive $800 from their grandmother in the ratio
Maria: Carolina: Pedro = 7:5:4.
(a) Calculate how much money each receives.
(b) Maria spends
2
7 of
[3]
her money and then invests the rest for two years
at 5% per year simple interest.
How much money does Maria have at the end of the two years?
[3]
(c) Carolina spends all of her money on a hi-fi set and two years later sells it at a loss of 20%.
How much money does Carolina have at the end of the two years?
[2]
(d) Pedro spends some of his money and at the end of the two years he has $100.
Write down and simplify the ratio of the amounts of money Maria, Carolina and Pedro have at
the end of the two years.
[2]
(e) Pedro invests his $100 for two years at a rate of 5% per year compound interest.
Calculate how much money he has at the end of these two years.
[2]
3
Question 3
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A Spanish family went to Scotland for a holiday.
(a) The family bought 800 pounds (£) at a rate of £1 = 1.52 euros (€).
How much did this cost in euros?
[1]
(b) The family returned home with £118 and changed this back into euros.
They received €173.46.
Calculate how many euros they received for each pound.
[1]
(c) A toy which costs €11.50 in Spain costs only €9.75 in Scotland.
Calculate, as a percentage of the cost in Spain, how much less it costs in Scotland.
[2]
(d) The total cost of the holiday was €4347.00.
In the family there were 2 adults and 3 children.
The cost for one adult was double the cost for one child.
Calculate the cost for one child.
[2]
(e) The original cost of the holiday was reduced by 10% to €4347.00.
Calculate the original cost.
[2]
(f) The plane took 3 hours 15 minutes to return to Spain.
The length of this journey was 2350 km.
Calculate the average speed of the plane in
(i) kilometres per hour,
[2]
(ii) metres per second.
[1]
4
Question 4
1
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The population of Newtown is 45 000.
The population of Villeneuve is 39 000.
(a) Calculate the ratio of these populations in its simplest form.
[1]
(b) In Newtown, 28% of the population are below the age of twenty.
Calculate how many people in Newtown are below the age of twenty.
[2]
(c) In Villeneuve, 16 000 people are below the age of twenty.
Calculate the percentage of people in Villeneuve below the age of twenty.
[2]
(d) The population of Newtown is 125% greater than it was fifty years ago.
Calculate the population of Newtown fifty years ago.
[2]
(e) The two towns are combined and made into one city called Monocity.
In Monocity the ratio of
men : women :children
is
12 : 13 : 5.
Calculate the number of children in Monocity.
[2]
5
Question 5
8
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(a) The technical data of a car includes the following information.
Type of road
Petrol used per 100 km
Main roads
9.2 litres
Other roads
8.0 litres
(i) How much petrol is used on a journey of 350 km on a main road?
[1]
(ii) On other roads, how far can the car travel on 44 litres of petrol?
[1]
(iii) A journey consists of 200 km on a main road and 160 km on other roads.
(a) How much petrol is used?
[2]
(b) Work out the amount of petrol used per 100 km of this journey.
[1]
(b) A model of a car has a scale of 1 : 25.
(i) The length of the car is 3.95 m.
Calculate the length of the model.
Give your answer in centimetres.
[3]
2
(ii) The painted surface area of the model is 128 cm.
Calculate the painted surface area of the car, giving your answer in square centimetres.
(iii) The size of the luggage space of the car is 250 litres.
Calculate the size of the luggage space of the model, giving your answer in millilitres.
6
[2]
[3]
Question 6
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(a) At an athletics meeting, Ben’s time for the 10 000 metres race was 33 minutes exactly and he finished
at 15 17.
(i)
At what time did the race start?
[1]
(ii)
What was Ben’s average speed for the race? Give your answer in kilometres per hour.
[2]
(iii)
The winner finished 51.2 seconds ahead of Ben.
How long did the winner take to run the 10 000 metres?
[1]
(b) The winning distance in the javelin competition was 80 metres.
Otto’s throw was 95% of the winning distance.
Calculate the distance of Otto’s throw.
[2]
(c) Pamela won the long jump competition with a jump of 6.16 metres.
This was 10% further than Mona’s jump.
How far did Mona jump?
[2]
7
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Number
Difficulty: Hard
Question Paper 1
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Hard
Booklet
Question Paper 1
Time allowed:
114 minutes
Score:
/99
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Question 1
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(a) A library has a total of 10 494 fiction and non-fiction books.
The ratio fiction books : non-fiction books = 13 : 5.
Find the number of non-fiction books the library has.
[2]
(b) The library has DVDs on crime, adventure and science fiction.
The ratio crime : adventure : science fiction = 11 : 6 : 10.
The library has 384 more science fiction DVDs than adventure DVDs.
Calculate the number of crime DVDs the library has.
[2]
(c) Every Monday, Sima travels by car to the library.
The distance is 20km and the journey takes 23 minutes.
(i)
Calculate the average speed for the journey in kilometres per hour.
(ii)
One Monday, she is delayed and her average speed is reduced to 32km/h.
Calculate the percentage increase in the journey time.
[2]
[5]
(d) In Spain, the price of a book is 11.99 euros.
In the USA, the price of the same book is $12.99 .
The exchange rate is $1 = 0.9276 euros.
Calculate the difference between these prices.
Give your answer in dollars, correct to the nearest cent.
[3]
(e) 7605 books were borrowed from the library in 2016.
This was 22% less than in 2015.
Calculate the number of books borrowed in 2015.
2
[3]
Question 2
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(a) Alex has $20 and Bobbie has $25.
(i)
Write down the ratio
(ii)
Alex and Bobbie each spend 1 of their money.
5
Find the ratio
(iii)
Alex’s money : Bobbie’s money
in its simplest form.
Alex’s remaining money : Bobbie’s remaining money
in its simplest form.
[1]
[1]
Alex and Bobbie then each spend $4.
Find the new ratio
Alex’s remaining money : Bobbie’s remaining money
in its simplestform.
[2]
(b) (i)
The population of a town in the year 1990 was 15 600.
The population is now 11420.
Calculate the percentage decrease in the population.
(ii)
[3]
The population of 15600 was 2.5% less than the population in the year 1980.
Calculate the population in the year 1980.
3
[3]
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(c) Chris invests $200 at a rate of x% per year simple interest.
At the end of 15 years the total interest received is $48.
Find the value of x.
[2]
(d) Dani invests $200 at a rate of y% per year compound interest.
At the end of 10 years the value of her investment is $256.
Calculate the value of y, correct to 1 decimal place.
4
[3]
Question 3
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An energy company charged these prices in 2013.
(a)
(i)
Electricity price
Gas price
23.15 cents per day
plus
13.5 cents for each unit used
24.5 cents per day
plus
5.5 cents for each unit used
In 90 days, the Siddique family used 1885 units of electricity.
Calculate the total cost, in dollars, of the electricity they used.
(ii)
[2]
In 90 days, the gas used by the Khan family cost $198.16 .
Calculate the number of units of gas used.
[3]
(b) In 2013, the price for each unit of electricity was 13.5 cents.
Over the next 3 years, this price increased exponentially at a rate of 8% per year.
Calculate the price for each unit of electricity after 3 years.
[2]
(c) Over these 3 years, the price for each unit of gas increased from 5.5 cents to 7.7 cents.
(i)
Calculate the percentage increase from 5.5 cents to 7.7 cents.
5
[3]
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(ii)
Over the 3 years, the 5.5 cents increased exponentially by the same percentage each year to
7.7 cents.
Calculate the percentage increase each year.
[3]
(d) In 2015, the energy company divided its profits in the ratio
shareholders : bonuses : development
= 5 : 2 : 6.
In 2015, its profits were $390 million.
Calculate the amount the company gave to shareholders.
[2]
(e) The share price of the company in June 2015 was $258.25 .
This was an increase of 3.3% on the share price in May 2015.
Calculate the share price in May 2015.
6
[3]
Question 4
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(a) Annie and Dermot share $600 in the ratio 11 :9.
(i)
Show that Annie receives $330.
[1]
(ii)
Find the amount that Dermot receives.
[1]
(b) (i)
Annie invests $330 at a rate of 1.5% per year compound interest.
Calculate the amount that Annie has after 8 years.
Give your answer correct to the nearest dollar.
(ii)
[3]
Find the amount of interest that Annie has, after the 8 years, as a percentage of the $330.
[2]
7
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(c) Dermot has $70 to spend.
He spends $24.75 on a shirt.
(i)
Find $24.75 as a fraction of $70.
Give your answer in its lowest terms.
[1]
(
ii)
The $24.75 is the sale price after reducing the original price by 10%.
Calculate the original price.
[3]
(d) After one year, the value of Annie’s car had reduced by 20%.
[2]
At the end of the second year, the value of Annie’s car had reduced by a further 15% of its value at the
end of the first year.
(i)
Calculate the overall percentage reduction after the two years.
(ii)
After three years the overall percentage reduction in the value of Annie’s car is 40.84%.
Calculate the percentage reduction in the third year.
8
[2]
Question 5
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(a) In 2016, a company sold 9600 cars, correct to the nearest hundred.
(i)
Write down the lower bound for the number of cars sold.
(ii)
The average profit on each car sold was $2430, correct to the nearest $10.
[1]
Calculate the lower bound for the total profit.
Write down the exact answer.
[2]
(iii)
Write your answer to part (a)(ii) correct to 4 significant figures.
[1]
(iv)
Write your answer to part (a)(iii) in standard form.
[1]
(b) In April, the number of cars sold was 546.
This was an increase of 5% on the number of cars sold in March.
Calculate the number of cars sold in March.
[3]
(c) The price of a new car grows exponentially by 3% per year.
A new car has a price of $3000 in 2013.
Find the price of a new car 4 years later.
9
[2]
Question 6
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The Smith family paid $5635 for a holiday in India.
The total cost was divided in the ratio travel : accommodation : entertainment = 10 : 17 :8.
(a) Calculate the percentage of the total cost spent on entertainment.
[2]
(b) Show that the amount spent on accommodation was $2737.
[2]
(c) The $5635 was the total amount Mr Smith received from an investment he made 5 years ago.
Compound interest at a rate of 2.42% per year was paid on this investment.
Calculate the amount he invested 5 years ago.
[3]
(d) Mr Smith, his wife and their three children visit a theme park.
The tickets cost 2500 Rupees for an adult and 1650 Rupees for a child.
Calculate the total cost of the tickets.
[2]
(e) One day the youngest child spent 130 Rupees on sweets.
On this day the exchange rate was 1 Rupee = $0.0152 .
Calculate the value of the sweets in dollars, correct to the nearest cent.
10
[2]
Question 7
(a)
(i)
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Each year the value of a car decreases by 15% of its value at the beginning of that year.
Alberto buys a car for $18 000.
Calculate the value of Alberto’s car after 3 years.
(ii)
[2]
Belinda bought a car one year ago.
The value of this car has decreased by 15% to $14025.
Calculate how much Belinda paid for the car.
[3]
(b) Chris invested some money at a rate of 5% per year compound interest.
After 2 years the value of this investment is $286.65 .
Calculate how much Chris invested.
11
[2]
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(c) Dani invested $200 and after 2 years the value of this investment is $224.72 .
Calculate the rate of interest per year when the interest is
(i)
simple,
[3]
(ii)
compound.
[3]
12
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Number
Difficulty: Hard
Question Paper 2
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Hard
Booklet
Question Paper 2
Time allowed:
104 minutes
Score:
/90
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Question 1
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(a) $1= 3.67 dirhams
Calculate the value, in dollars, of 200 dirhams.
Give your answer correct to 2 decimal places.
(b) (i)
[2]
Write as a single fraction, in its simplest form.
1000 - 1000
x
x+1
[3]
(ii) One day in 2014, 1 euro was worth x rand.
One year later, 1 euro was worth (x + 1) rand.
Winston changed 1000 rand into euros in both years.
In 2014 he received 4.50 euros more than in 2015.
Write an equation in terms of x and show that it simplifies to
9x2 + 9x - 2000 = 0.
2
[3]
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(iii)
Use the quadratic formula to solve the equation 9x2 + 9x - 2000 = 0.
Show all your working and give your answers correct to 2 decimal places.
[4]
(iv)
Calculate the number of euros Winston received in 2014.
Give your answer correct to 2 decimal places.
[2]
3
Question 2
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(a) A jigsaw puzzle has edge pieces and inside pieces.
The ratio edge pieces : inside pieces = 3 : 22.
(i)
There are 924 inside pieces.
Calculate the total number of pieces in the puzzle.
[2]
(ii)
Find the percentage of the total number of pieces that are edge pieces.
[1]
(iii)
Anjum and Betty spent a total of 9 hours completing the puzzle.
The ratio Anjum’s time : Betty’s time = 7 : 5.
Work out how much time Anjum spent on the puzzle.
[2]
(b) The price of the puzzle was $15.99 in a sale.
This was 35% less than the original price.
Calculate the original price of the puzzle.
4
[3]
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(c) Betty takes a photograph of the completed puzzle.
The photograph and the completed puzzle are mathematically similar.
The area of the photograph is 875 cm2 and the area of the puzzle is 2835 cm2.
The length of the photograph is 35 cm.
Work out the length of the puzzle.
(d) (i)
The area of another puzzle is 6610cm2.
Change 6610 cm2 into m2.
(ii)
[3]
[1]
The cost price of this puzzle is $12.50 .
The selling price is $18.50 .
Calculate the percentage profit.
5
[3]
Question 3
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(a) Kristian and Stephanie share some money in the ratio 3 : 2.
Kristian receives $72.
(i)
(ii)
Work out how much Stephanie receives.
Kristian spends 45% of his $72 on a computer game.
Calculate the price of the computer game.
(iii)
[2]
[1]
Kristian also buys a meal for $8.40 .
Calculate the fraction of the $72 Kristian has left after buying the computer game and the meal.
Give your answer in its lowest terms.
[2]
(iv)
Stephanie buys a book in a sale for $19.20 .
This sale price is after a reduction of 20%.
Calculate the original price of the book.
6
[3]
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(b) Boris invests $550 at a rate of 2% per year simple interest.
Calculate the amount Boris has after 10 years.
[3]
(c) Marlene invests $550 at a rate of 1.9% per year compound interest.
Calculate the amount Marlene has after 10 years.
[2]
(d) Hans invests $550 at a rate of x% per year compound interest.
At the end of 10 years he has a total amount of $638.30, correct to the nearest cent.
Find the value of x.
7
[3]
Question 4
1
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A football club sells tickets at different prices dependent on age group.
(a)
(i)
At one game, the club sold tickets in the ratio
under 18 : 18 to 60 : over 60 = 2 : 7 : 3.
There were 6100 tickets sold for people aged under 18.
(ii)
Calculate the total number of tickets sold for the game.
[3]
Calculate the percentage of tickets sold for people aged under 18.
[1]
(b) The table shows the football ticket prices for the different age groups.
Age
Price
Under 18
$15
18 to 60
$35
Over 60
$18
At a different game there were 42 600 tickets sold.
•
•
•
14% were sold to people aged under 18
2 of
3
the tickets were sold to people aged 18 to 60
The remainder were sold to people aged over 60
Calculate the total amount the football club receives from ticket sales for this game.
[5]
(c) In a sale, the football club shop reduced the price of the football shirts to $23.80 .
An error was made when working out this sale price.
The price was reduced by 30% instead of 20%.
Calculate the correct sale price for the football shirt.
8
[5]
Question 5
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Aasha, Biren and Cemal share $640 in the ratio 8 : 15 : 9.
(a) Show that Aasha receives $160.
[1]
(b) Calculate the amount that Biren and Cemal receive.
[2]
(c) Aasha uses her $160 to buy some books.
Each book costs $15.25 .
Find the greatest number of books that she can buy.
[2]
(d)
[3]
9
Question 6
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(a) Meena sells her car for $6000.
This is a loss of 4% on the price she paid.
Calculate the price Meena paid for the car.
[3]
(b) Eisha changes some euros (€) into dollars ($) when the exchange rate is €1 = $1.351 .
She receives $6000.
Calculate how many euros Eisha changes.
Give your answer correct to the nearest euro.
[3]
(c) Meena and Eisha both invest their $6000.
Meena invests her $6000 at a rate of 1.5% per year compound interest.
Eisha invests her $6000 in a bank that pays simple interest.
After 8 years, their investments are worth the same amount.
Calculate the rate of simple interest per year that Eisha received.
10
[5]
Question 7
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A film company uses 512 actors in a film.
The actors are in the ratio men : women : children = 7 : 11 : 14.
(a)
(i)
(ii)
Show that there are 224 children in the film.
[2]
Find the number of men in the film.
[1]
(b) Every working day, each child is given $1 to spend.
Each child works for 45 days.
Calculate the total amount that the film company gives the children to spend.
Give your answer correct to the nearest $100.
[2]
(c) The children have lessons every day in groups of no more than 12.
Calculate the smallest possible number of groups.
[2]
(d) The film costs four million and ninety three thousand dollars to make.
(i)
Write this number in figures.
[1]
(ii)
Write your answer to part (d)(i) in standard form.
[1]
(e) A DVD copy of the film costs $2.75 tomake.
The selling price is $8.20 .
Calculate the percentage profit.
11
[3]
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Number
Difficulty: Hard
Question Paper 3
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Hard
Booklet
Question Paper 3
Time allowed:
93 minutes
Score:
/81
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Question 1
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12000 vehicles drive through a road toll on one day.
The ratio cars : trucks : motorcycles = 13 : 8 : 3.
(a)
(ii)
(i)
Show that 6500 cars drive through the road toll on that day.
Calculate the number of trucks that drive through the road toll on that day.
[1]
[1]
(b) The toll charges in 2014 are shown in thetable.
Vehicle
Charge
Cars
$2
Trucks
$5
Motorcycles
$1
Show that the total amount paid in tolls on that day is $34500.
2
[2]
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(c) This total amount is a decrease of 8% on the total amount paid on the same day in 2013.
Calculate the total amount paid on that day in 2013.
[3]
(d) 2750 of the 6500 car drivers pay their toll using a credit card.
Write down, in its simplest terms, the fraction of car drivers who pay using a credit card.
[2]
(e) To the nearest thousand, 90000 cars drive through the road toll in one week.
Write down the lower bound for this number of cars.
3
[1]
Question 2
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(a) Last year a golf club charged $1650 for a family membership.
This year the cost increased by 12%.
Calculate the cost of a family membership this year.
[2]
(b) The golf club runs a competition.
The total prize money is shared in the ratio 1st prize : 2nd prize = 9 : 5.
The 1st prize is $500 more than the 2nd prize.
(i) Calculate the total prize money for the competition.
[2]
(ii) What percentage of the total prize money is given as the 1st prize?
[1]
(c) For the members of the golf club the ratio men: children = 11 : 2.
The ratio women : children = 10 : 3.
(i) Find the ratio men:women.
4
[2]
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(ii) The golf club has 24 members who are children.
Find the total number of members.
[3]
(d) The club shop sold a box of golf balls for $20.40 .
The shop made a profit of 20% on the cost price.
Calculate the cost price of the golf balls.
5
[3]
Question 3
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Jaideep builds a house and sells it for $450000.
(a) He pays a tax of 1.5% of the selling price of the house.
Show that he pays $6750 in tax.
[1]
(b) $6750 is 12.5% more than the tax Jaideep paid on the first house he built.
Calculate the tax Jaideep paid on the first house he built.
[3]
(c) The house is built on a rectangular plot of land, 21 m by 17 m, both correct to the nearest metre.
Calculate the upper bound for the area of the plot.
[2]
(d) On a plan of the house, the area of the kitchen is 5.6 cm2.
The scale of the plan is 1: 200.
Calculate the actual area of the kitchen in square metres.
6
[2]
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(e) The house was built using cuboid blocks each measuring 12 cm by 16 cm by 27 cm.
Calculate the volume of one block.
[2]
(f) Jaideep changes $12000 into euros (€) to buy land in another country.
The exchange rate is €1 = $1.33 .
Calculate the number of euros Jaideep receives.
Give your answer correct to the nearest euro.
7
[3]
Question 4
1
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(a) Alfonso has $75 to spend on the internet.
He spends some of the money on music, films and books.
(i) The money he spends on music, films and books is in the ratio
music : films: books = 5 : 3 : 7.
He spends $16.50 on music.
Calculate the total amount he spends on music, films and books.
(ii) Find this total amount as a percentage of the $75.
[3]
[1]
(b) The download times for the music, films and books are in the ratio
music : films: books = 2 : 9 : 1.
The total download time is 3 hours and 33 minutes.
Calculate the download time for the films.
Give your answer in hours, minutes and seconds.
[3]
(c) The cost of $16.50 for the music was a reduction of 12% on the original cost.
Calculate the original cost of the music.
8
[3]
Question 5
2
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There are three different areas, A, B and C, for seating in a theatre.
The numbers of seats in each area are in the ratio A: B : C = 11: 8 : 7 .
There are 920 seats in area B.
(a) (i) Show that there are 805 seats in area C.
[1]
(ii) Write the number of seats in area B as a percentage of the total number ofseats.
[2]
(b) The cost of a ticket for a seat in each area of the theatre is shown in the table.
Area A
$11.50
Area B
$15
Area C
$22.50
For a concert 80% of area B tickets were sold and 53 of area C tickets were sold.
The total amount of money taken from ticket sales was $35834.
Calculate the number of area A tickets that were sold.
[5]
(c) The total ticket sales of $35834 was 5% less than the ticket sales at the previous concert.
Calculate the ticket sales at the previous concert.
9
[3]
Question 6
1
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Last year Mukthar earned $18900 .
He did not pay tax on $5500 of his earnings.
He paid 24% tax on his remaining earnings.
(a) (i) Calculate how much tax Mukthar paid last year.
(ii) Calculate how much Mukthar earned each month after tax had been paid.
[2]
[2]
(b) This year Mukthar now earns $19750.50 .
Calculate the percentage increase from $18900.
[2]
(c) Mukthar has $1500 to invest in one of the following ways.
●
Account A paying simple interest at a rate of 4.1% per year
●
Account B paying compound interest at a rate of 3.3% per year
Which account will be worth more after 3 years and by how much?
10
[5]
Question 7
7
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Noma flies from Johannesburg to Hong Kong.
Her plane leaves Johannesburg at 18 45 and arrives in Hong Kong 13 hours and 25 minutes later.
The local time in Hong Kong is 6 hours ahead of the time in Johannesburg.
[2]
(a) At what time does Noma arrive in Hong Kong?
(b) Noma sleeps for part of the journey.
The time that she spends sleeping is given by the ratio
sleeping : awake = 3 : 4 .
Calculate how long Noma sleeps during the journey.
Give your answer in hours and minutes.
11
[2]
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(c) (i) The distance from Hong Kong to Johannesburg is 10 712 km.
The time taken for the journey is 13 hours and 25 minutes.
Calculate the average speed of the plane for this journey.
[2]
(ii) The plane uses fuel at the rate of 1 litre for every 59 metres travelled.
Calculate the number of litres of fuel used for the journey from Johannesburg to Hong Kong.
Give your answer in standard form.
[4]
(d) The cost of Noma’s journey is 10148 South African Rand (R). This
is an increase of 18% on the cost of the journey one year ago.
Calculate the cost of the same journey one year ago.
12
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Number
Difficulty: Hard
Question Paper 4
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Hard
Booklet
Question Paper 4
Time allowed:
93 minutes
Score:
/81
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Q u esti o n 1
1
( a) (i)
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
I n a c a m er a m a g a zi n e, 6 3 p a g es ar e us e d f or a d v erts.
T h e r ati o n u m b er of p a g es of a d v erts : n u m b er of p a g es of r e vi e ws = 7 : 5 .
C al c ul at e t h e n u m b er of p a g es us e d f or r e vi e ws.
[ 2]
(ii) I n a n ot h er c o p y of t h e m a g a zi n e, 5 6 p a g es ar e us e d f or r e vi e ws a n d f or p h ot o gr a p hs.
T h e r ati o n u m b er of p a g es of r e vi e ws : n u m b er of p a g es of p h ot o gr a p hs = 9 : 5 .
C al c ul at e t h e n u m b er of p a g es us e d f or p h ot o gr a p hs.
(iii)
[ 2]
O n e c o p y of t h e m a g a zi n e c osts $ 4. 9 0 .
A n a n n u al s u bs cri pti o n c osts $ 4 8. 8 0 f or 1 3 c o pi es.
C al c ul at e t h e p er c e nt a g e dis c o u nt b y h a vi n g a n a n n u al s u bs cri pti o n.
2
[ 3]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( b) I n a c ar m a g a zi n e,
2 5 % of t h e p a g es ar e us e d f or s elli n g s e c o n d- h a n d c ars,
6 2 21 % of t h e r e m ai ni n g p a g es ar e us e d f or f e at ur es,
a n d t h e ot h er 3 6 p a g es ar e us e d f or r e vi e ws.
W or k o ut t h e t ot al n u m b er of p a g es i n t h e m a g a zi n e.
3
[ 4]
Q u esti o n 2
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
A f a ct or y pr o d u c es bir d f o o d m a d e wit h s u nfl o w er s e e d, mill et a n d m ai z e.
( a)
T h e a m o u nts of s u nfl o w er s e e d, mill et a n d m ai z e ar e i n t h e
r ati o s u nfl o w er s e e d : mill et : m ai z e = 5 : 3 : 1 .
(i)
H o w m u c h mill et is t h er e i n 1 5 k g of bir d f o o d ?
[ 2]
(ii) I n a s m all b a g of bir d f o o d t h er e is 6 0 g of s u nfl o w er s e e d.
W h at is t h e m ass of bir d f o o d i n a s m all b a g ?
[ 2]
( b) S u nfl o w er s e e ds c ost $ 2 0 4. 5 0 f or 3 0 k g fr o m J o n’s f ar m or € 9 6. 4 0 f or 2 0 k g fr o m A n n’s f ar m.
T h e e x c h a n g e r at e is $ 1 = € 0. 7 1 8.
W hi c h f ar m h as t h e c h e a p est pri c e p er kil o gr a m ?
Y o u m u st s h o w cl e a rl y all y o u r w o r ki n g.
4
[ 4]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( c) B a gs ar e fill e d wit h bir d f o o d at a r at e of 4 2 0 gr a ms p er s e c o n d.
H o w m a n y 2 0 k g b a gs c a n b e c o m pl et el y fill e d i n 4 h o urs ?
[ 3]
( d) Bri a n b u y s b a gs of bir d f o o d fr o m t h e f a ct or y a n d s ells t h e m i n his s h o p f or $ 1 5. 3 0 e a c h.
H e m a k es 1 2. 5 % pr ofit o n e a c h b a g.
H o w m u c h d o es Bri a n p a y f or e a c h b a g of bir d f o o d ?
[ 3]
( e) Bri a n or d ers 6 0 0 b a gs of bir d f o o d.
1
.
50
H o w m a n y b a gs w o ul d Bri a n e x p e ct t o b e d a m a g e d ?
T h e pr o b a bilit y t h at a b a g is d a m a g e d is
5
[ 1]
Q u esti o n 3
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) T h e M arti n e z f a mil y tr a v els b y c ar t o S e at o w n.
T h e dist a n c e is 9 2 k m a n d t h e j o ur n e y t a k es 1 h o ur 2 5 mi n ut es.
(i)
T h e f a mil y l e a v es h o m e at 0 7 5 0.
Writ e d o w n t h e ti m e t h e y arri v e at S e at o w n.
[ 1]
(ii) C al c ul at e t h e a v er a g e s p e e d f or t h e j o ur n e y.
[ 2]
(iii)
D uri n g t h e j o ur n e y, t h e f a mil y st o ps f or 1 0 mi n ut es.
C al c ul at e 1 0 mi n ut es as a p er c e nt a g e of 1 h o ur 2 5 mi n ut es.
[ 1]
(i v) 9 2 k m is 1 5 % m or e t h a n t h e dist a n c e fr o m S e at o w n t o D e e cit y.
C al c ul at e t h e dist a n c e fr o m S e at o w n t o D e e cit y.
6
[ 3]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( b)
T h e M arti n e z f a mil y s p e n ds $ 1 5 0 i n t h e r ati o
f u el : m e als : gifts = 1 1 : 1 6 : 3 .
(i)
S h o w t h at $ 1 5 is s p e nt o n gifts.
A ns w er ( b) (i)
[ 2]
(ii) T h e f a mil y b u y s t w o gifts.
T h e first gift c osts $ 8. 2 5.
Fi n d t h e r ati o
c ost of first gift : c ost of s e c o n d gift.
Gi v e y o ur a ns w er i n its si m pl est f or m.
7
[ 2]
Q u esti o n 4
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) I n P ort u g al, Mi g u el b u y s a b o o k a b o ut pl a n ets.
T h e b o o k c osts € 3 4. 9 5.
I n E n gl a n d t h e s a m e b o o k c osts £ 2 7. 5 0.
T h e e x c h a n g e r at e is £ 1 = € 1. 1 7.
C al c ul at e t h e diff er e n c e i n p o u n ds ( £) b et w e e n t h e c ost of t h e b o o k i n P ort u g al a n d E n gl a n d.
[ 2]
12
( b) I n t h e b o o k, t h e dist a n c e b et w e e n t w o pl a n ets is gi v e n as 4. 0 7 × 1 0 kil o m etr es.
9
T h e s p e e d of li g ht is 1. 1 × 1 0 kil o m etr es p er h o ur.
C al c ul at e t h e ti m e t a k e n f or li g ht t o tr a v el fr o m o n e of t h es e pl a n ets t o t h e ot h er.
Gi v e y o ur a ns w er i n d a ys a n d h o urs.
[ 3]
( c) I n o n e of t h e pi ct ur es i n t h e b o o k, a r e ct a n gl e is dr a w n.
T h e r e ct a n gl e h as l e n gt h 9. 3 c m a n d wi dt h 5. 6 c m, b ot h c orr e ct t o o n e d e ci m al pl a c e.
(i)
W h at is t h e l o w er b o u n d f or t h e l e n gt h ?
(ii) W or k o ut t h e l o w er a n d u p p er b o u n ds f or t h e ar e a of t h e r e ct a n gl e.
8
[ 1]
[ 2]
Q u esti o n 5
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) A b d ull a h a n d J as mi n e b o u g ht a c ar f or $ 9 0 0 0.
A b d ull a h p ai d 4 5 % of t h e $ 9 0 0 0 a n d J as mi n e p ai d t h e r est.
(i) H o w m u c h di d J as mi n e p a y t o w ar ds t h e c ost of t h e c ar ?
[ 2]
(ii) Writ e d o w n t h e r ati o of t h e p a y m e nts A b d ull a h : J as mi n e i n its si m pl est f or m.
[ 1]
( b) L ast y e ar it c ost $ 2 2 5 6 t o r u n t h e c ar.
A b d ull a h, J as mi n e a n d t h eir s o n H e nri s h ar e t his c ost i n t h e r ati o 8 : 3 : 1.
C al c ul at e t h e a m o u nt e a c h p ai d t o r u n t h e c ar.
( c) (i) A n e w tr u c k c osts $ 1 5 0 0 0 a n d l os es 2 3 % of its v al u e e a c h y e a r .
C al c ul at e t h e v al u e of t h e tr u c k aft er t hr e e y e ars.
(ii) C al c ul at e t h e o v er all p er c e nt a g e l oss of t h e tr u c k’s v al u e aft er t hr e e y e ars.
9
[ 3]
[ 3]
[ 3]
Q u esti o n 6
9
( a)
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
7 2 = 2 × 2 × 2 × 3 × 3 writt e n as a pr o d u ct of pri m e f a ct ors.
Writ e t h e n u m b er 1 2 6 as a pr o d u ct of pri m e f a ct ors.
[ 2]
(ii) Fi n d t h e v al u e of t h e hi g h est c o m m o n f a ct or of 7 2 a n d 1 2 6.
[ 1]
(iii) Fi n d t h e v al u e of t h e l o w est c o m m o n m ulti pl e of 7 2 a n d 1 2 6.
[ 2]
(i)
( b) J o h n w a nts t o esti m at e t h e v al u e of π.
H e m e as ur es t h e cir c u mf er e n c e of a cir c ul ar pi z z a as 1 0 5 c m a n d its di a m et er as 3 4 c m, b ot h
c orr e ct t o t h e n e ar est c e nti m etr e.
C al c ul at e t h e l o w er b o u n d of his esti m at e of t h e v al u e of π .
Gi v e y o ur a ns w er c orr e ct t o 3 d e ci m al pl a c es.
3
( c) T h e v ol u m e of a c yli n dri c al c a n is 5 5 0 c m , c orr e ct t o t h e n e ar est 1 0 c m .
T h e h ei g ht of t h e c a n is 1 2 c m c orr e ct t o t h e n e ar est c e nti m etr e.
C al c ul at e t h e u p p er b o u n d of t h e r a di us of t h e c a n.
Gi v e y o ur a ns w er c orr e ct t o 3 d e ci m al pl a c es.
10
[ 4]
3
[ 5]
Q u esti o n 7
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
A s c h o ol h as 2 2 0 b o y s a n d 2 8 0 girls.
( a)
Fi n d t h e r ati o of b o y s t o girls, i n its si m pl est f or m.
( b) T h e r ati o of st u d e nts t o t e a c h ers is 1 0 : 1.
Fi n d t h e n u m b er of t e a c h ers.
[ 1]
[ 2]
( c) T h er e ar e 2 1 st u d e nts o n t h e s c h o ol’s c o m mitt e e.
T h e r ati o of b o y s t o girls is 3 : 4.
Fi n d t h e n u m b er of girls o n t h e c o m mitt e e.
[ 2]
( d) T h e c o m mitt e e or g a nis es a dis c o a n d s ells ti c k ets.
3 5 % of t h e s c h o ol’s st u d e nts e a c h b u y a ti c k et. E a c h ti c k et c osts $ 1. 6 0.
C al c ul at e t h e t ot al a m o u nt r e c ei v e d fr o m s elli n g t h e ti c k ets.
[ 3]
( e) T h e c ost of r u n ni n g t h e dis c o is $ 2 6 4.
T his is a n i n cr e as e of 1 0 % o n t h e c ost of r u n ni n g l ast y e ar’s dis c o.
C al c ul at e t h e c ost of r u n ni n g l ast y e ar’s dis c o.
[ 2]
11
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Number
Difficulty: Hard
Question Paper 5
Level
IGCSE
Subject
Maths (0580/0980)
Exam Board
CIE
Topic
Number
Paper
Paper 4
Difficulty
Hard
Booklet
Question Paper 5
Time allowed:
78 minutes
Score:
/68
Percentage:
/100
Grade Boundaries:
CIE IGCSE Maths (0580)
A*
>83%
A
67%
B
51%
C
41%
D
31%
CIE IGCSE Maths (0980)
9
>95%
8
87%
7
80%
6
69%
5
58%
4
46%
Q u esti o n 1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
C hris g o es t o a s h o p t o b u y m e at, v e g et a bl es a n d fr uit.
( a) (i) T h e c osts of t h e m e at, v e g et a bl es a n d fr uit ar e i n t h e r ati o
m e at : v e g et a bl es : fr uit = 2 : 2 : 3.
T h e c ost of t h e m e at is $ 2. 4 0.
C al c ul at e t h e t ot al c ost of t h e m e at, v e g et a bl es a n d fr uit.
[ 2]
(ii) C hris p a ys wit h a $ 2 0 n ot e.
W h at p er c e nt a g e of t h e $ 2 0 h as h e s p e nt ?
[ 2]
( b) T h e m ass es of t h e m e at, v e g et a bl es a n d fr uit ar e i n t h e r ati o
m e at : v e g et a bl es : fr uit = 1 : 8 : 3.
T h e t ot al m ass is 9 k g.
C al c ul at e t h e m ass of t h e v e g et a bl es.
2
[ 2]
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( c) C al c ul at e t h e c ost p er kil o gr a m of t h e fr uit.
[ 3]
( d) T h e c ost of t h e m e at, $ 2. 4 0, is a n i n cr e as e of 2 5 % o n t h e c ost t h e pr e vi o us w e e k.
C al c ul at e t h e c ost of t h e m e at t h e pr e vi o us w e e k.
3
[ 2]
Q u esti o n 2
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
Vr e ni t o o k p art i n a c h arit y w al k.
S h e w al k e d a dist a n c e of 2 0 kil o m etr es.
( a)
S h e r ais e d m o n e y at a r at e of $ 1 2. 5 0 f or e a c h kil o m etr e.
(i) H o w m u c h m o n e y di d s h e r ais e b y w al ki n g t h e 2 0 kil o m etr es ?
(ii) T h e m o n e y s h e r ais e d i n p a rt ( a)(i) w as
W or k o ut t h e t ot al m o n e y r ais e d.
5
5 2 of t h e t ot al m o n e y r ais e d.
(iii) I n t h e pr e vi o us y e ar t h e t ot al m o n e y r ais e d w as $ 2 4 5 0.
C al c ul at e t h e p er c e nt a g e i n cr e as e o n t h e pr e vi o us y e ar’s t ot al.
( b)
[ 1]
[ 2]
[ 2]
P art of t h e 2 0 kil o m etr es w as o n a r o a d a n d t h e r est w as o n a f o ot p at h.
T h e r ati o r o a d dist a n c e : f o ot p at h dist a n c e w as 3: 2.
(i)
W or k o ut t h e r o a d dist a n c e.
[ 2]
(ii) Vr e ni w al k e d al o n g t h e r o a d at 3 k m / h a n d al o n g t h e f o ot p at h at 2. 5 k m / h.
H o w l o n g, i n h o urs a n d mi n ut es, di d Vr e ni t a k e t o w al k t h e 2 0 kil o m etr es ?
[ 2]
(iii) W or k o ut Vr e ni’s a v er a g e s p e e d.
[ 1]
(i v) Vr e ni st art e d at 0 8 5 5. At w h at ti m e di d s h e fi nis h ?
( c) O n a m a p, t h e dist a n c e of 2 0 kil o m etr es w as r e pr es e nt e d b y a l e n gt h of 8 0 c e nti m etr es.
T h e s c al e of t h e m a p w as 1 : n .
C al c ul at e t h e v al u e of n .
4
[ 1]
[ 2]
Q u esti o n 3
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
( a) T h e s c al e of a m a p is 1: 2 0 0 0 0 0 0 0.
O n t h e m a p, t h e dist a n c e b et w e e n C air o a n d A d dis A b a b a is 1 2 c m.
(i) C al c ul at e t h e dist a n c e, i n kil o m etr es, b et w e e n C air o a n d A d dis A b a b a.
[ 2]
(ii) O n t h e m a p t h e ar e a of a d es ert r e gi o n is 1 3 s q u ar e c e nti m etr es.
C al c ul at e t h e a ct u al ar e a of t his d es ert r e gi o n, i n s q u ar e kil o m etr es.
[ 2]
( b) (i) T h e a ct u al dist a n c e b et w e e n C air o a n d K h art o u m is 1 5 8 0 k m.
O n a diff er e nt m a p t his dist a n c e is r e pr es e nt e d b y 3 1. 6 c m.
C al c ul at e, i n t h e f or m 1 : n , t h e s c al e of t his m a p.
[ 2]
(ii) A pl a n e fli es t h e 1 5 8 0 k m fr o m C air o t o K h art o u m.
It d e p arts fr o m C air o at 1 1 5 5 a n d arri v es i n K h art o u m at 1 4 0 3.
C al c ul at e t h e a v er a g e s p e e d of t h e pl a n e, i n kil o m etr es p er h o ur.
5
[ 4]
Q u esti o n 4
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
H ass a n s ells fr uit a n d v e g et a bl es at t h e m ar k et.
( a) T h e m ass of fr uit a n d v e g et a bl es h e s ells is i n t h e r ati o
fr uit : v e g et a bl es = 5 : 7.
H ass a n s ells 1. 3 3 t o n n e s of v e g et a bl es.
H o w m a n y kil o g r a m s of fr uit d o es h e s ell ?
( b) T h e a m o u nt of m o n e y H ass a n r e c ei v es fr o m s elli n g fr uit a n d v e g et a bl es is i n t h e r ati o
fr uit : v e g et a bl es = 9 : 8.
H ass a n r e c ei v es a t ot al of $ 7 6 5 fr o m s elli n g fr uit a n d v e g et a bl es.
C al c ul at e h o w m u c h H ass a n r e c ei v es fr o m s elli n g fr uit.
( c) C al c ul at e t h e a v er a g e pri c e of H ass a n’s fr uit, i n d oll ars p er kil o gr a m.
( d) (i) H ass a n s ells or a n g es f or $ 0. 3 5 p er kil o gr a m.
H e r e d u c es t his pri c e b y 4 0 %.
C al c ul at e t h e n e w pri c e p er kil o gr a m.
(ii) T h e pri c e of $ 0. 3 5 p er kil o gr a m of or a n g es is a n i n cr e as e of 2 5 % o n t h e pr e vi o us d a y’s pri c e.
C al c ul at e t h e pr e vi o us d a y’s pri c e.
6
[ 3]
[ 2]
[ 2]
[ 2]
[ 2]
Q u esti o n 5
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
F ati m a a n d M o h a m m e d e a c h b u y s a bi k e.
( a)
F ati m a b u y s a cit y- bi k e w hi c h h as a pri c e of $ 1 2 0.
S h e p a ys 6 0 % of t his pri c e a n d t h e n p a ys $ 1 0 p er m o nt h f or 6 m o nt hs.
(i) H o w m u c h d o es F ati m a p a y alt o g et h er ?
[ 2]
(ii) W or k o ut y o ur a ns w er t o p a rt ( a)(i) as a p er c e nt a g e of t h e ori gi n al pri c e of $ 1 2 0.
[ 2]
( b) M o h a m m e d p a ys $ 1 5 9. 1 0 f or a m o u nt ai n- bi k e i n a s al e.
T h e ori gi n al pri c e h a d b e e n r e d u c e d b y 1 4 %.
C al c ul at e t h e ori gi n al pri c e of t h e m o u nt ai n- bi k e.
[ 2]
( c) M o h a m m e d’s h ei g ht is 1 6 9 c m a n d F ati m a’s h ei g ht is 1 5 6 c m.
T h e fr a m e si z es of t h eir bi k es ar e i n t h e s a m e r ati o as t h eir h ei g hts.
T h e fr a m e si z e of M o h a m m e d’s bi k e is 5 2 c m.
C al c ul at e t h e fr a m e si z e of F ati m a’s bi k e.
[ 2]
( d) F ati m a a n d M o h a m m e d ar e m e m b ers of a s c h o ol t e a m w hi c h t a k es p art i n a bi k e ri d e f or c h arit y.
(i) F ati m a a n d M o h a m m e d ri d e a t ot al dist a n c e of 3 6 k m.
T h e r ati o dist a n c e F ati m a ri d es : dist a n c e M o h a m m e d ri d es is 1 1 : 9.
W or k o ut t h e dist a n c e F ati m a ri d es.
(ii)
T h e dist a n c e of 3 6 k m is o nl y
C al c ul at e t his t ot al dist a n c e.
7
2
23
[ 2]
of t h e t ot al dist a n c e t h e t e a m ri d es.
[ 2]
Q u esti o n 6
1
H e a d t o s a v e m y e x a ms. c o. u k f or m or e a w es o m e r es o ur c es
A tr ai n st art s it s j o ur n e y wit h 2 4 0 p a s s e n g er s.
1 4 4 of t h e p ass e n g ers ar e a d ults a n d t h e r e st ar e c hil dr e n.
( a) Writ e t h e r ati o
A d ults : C hil dr e n i n it s l o w e st t er m s.
[ 2]
( b) At t h e fir st st o p, 3 7 21 % of t h e a d ults a n d 13 of t h e c hil dr e n g et off t h e tr ai n.
2 0 a d ults a n d x c hil dr e n g et o nt o t h e tr ai n.
T h e t ot al n u m b er of p ass e n g ers o n t h e tr ai n i s n o w 2 0 0.
(i)
H o w m a n y c hil dr e n g ot off t h e tr ai n ?
[ 1]
(ii)
H o w m a n y a d ults g ot off t h e tr ai n ?
[ 1]
(iii)
H o w m a n y a d ult p ass e n g ers ar e o n t h e tr ai n a s it s et s off a g ai n ?
[ 1]
(i v)
W h at i s t h e v al u e of x ?
[ 1]
( c) Aft er a s e c o n d st o p, t h er e ar e 3 0 0 p ass e n g ers o n t h e tr ai n a n d t h e r ati o
Me n:
W o m e n: C hil dr e n
i s 6 : 5 : 4.
C al c ul at e t h e n u m b er of c hil dr e n n o w o n t h e tr ai n.
( d)
[ 2]
O n T u es d a y t h e tr ai n j o ur n e y t o o k 7 h o urs a n d 2 0 mi n ut es a n d b e g a n at 1 3 5 3.
(i)
(ii)
At w h at ti m e di d t h e tr ai n j o ur n e y e n d ?
T u es d a y’ s ti m e of 7 h o urs 2 0 mi n ut es w as 1 0 % m or e t h a n M o n d a y’s j o ur n e y ti m e.
H o w m a n y mi n ut es l o n g er w as T u e s d a y’ s j o ur n e y ?
8
[ 1]
[ 2]