Maths 0580 Revision Sheet
IF YOUR SCORE > 90%, THEN YOU ARE ALL SET FOR THE 0580 BOARDS!!
CREATED BY: PRASHOON BHATTACHARJEE
I have inten9onally made it very hard so that it is difficult for students to solve. The mark
scheme would contain all the solu9ons but details won’t be given as to how method marks
are given because this is not a proper exam sheet.
100 ques9ons are there in the sheet, for 455 marks.
Dura9on: 6 hours+ approximately
Spoiler alert: You may have already solved most of the ques9ons as these are picked from the
past papers only, but s9ll if you are able to solve them then that would be a great testament
to your skill because it is impossible to memorize so many ques9ons.
Enjoy !!!
1 Here is a shaded shape ABCD.
16
]
B
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BG16A
C D
O
The shape is made from a triangle and a sector of a circle, centre O and radius 6 cm.
OCD is a straight line.
AD = 14 cm
Angle AOD = 140°
Angle OAD = 24°
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Calculate the perimeter of the shape.
Give your answer correct to 3 significant figures.
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....................................................... cm
(Total for Question 16 is 5 marks)5 marks
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211 The total area of each of the following shapes is X.
] The area of the shaded part of each shape is kX.
For each shape, find the value of k and write your answer below each diagram.
NOT TO NOT TO
SCALE J SCALE
NOT TO F
SCALE I
O 72°
K
G
A B C D
H
AB = BC = CD Angle JOK = 72° EF = FG and EI = IH
k = ..................................... k = ..................................... k = .....................................
A
NOT TO NOT TO
SCALE SCALE
O B
The shape is a regular hexagon. The diagram shows a sector of a circle centre O.
Angle AOB = 90°
k = ..................................... k = .....................................
[10]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the
publisher will be pleased to make amends at the earliest possible opportunity.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2014 0580/42/M/J/14
83 The diagram shows a solid metal cuboid.
] The areas of three of the faces are marked on the diagram.
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The lengths, in cm, of the edges of the cuboid are whole numbers.
BG8A
27 cm2
15 cm2
45 cm2
The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.
Work out the greatest number of these cubes that can be made.
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5 marks
(Total for Question 8 is 5 marks)
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4 Point P has position vector s and point Q has position vector t.
(b)
] PQ is extended to point X such that PX : QX8 = 7: 3.
Find the position vector of X.
21
y
8
7
T
6
2
A
1
0 x
1 2 3 4 5 6 7 8
(a) Describe fully the single transformation that maps shape T onto shape A.
............................................................................................................................................................
................................................. [3]
............................................................................................................................................................ [2]
(b) On the grid, reflect shape T in the line y = x. [2]
5
22 A pipe is completely full of water.
Water flows through the pipe at a speed of 1.2 m/s into a tank.
The cross-section of the pipe has an area of 6 cm2.
Calculate the number of litres of water flowing into the tank in 1 hour.
........................................... litres [4]
© UCLES 2021 1521/42/M/J/21 [Turn over
© UCLES 2019 0580/21/O/N/19
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outside the
box
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6 Lunch
Choose one starter and one main course
AB19A
There are four starters and ten main courses to choose from.
Two of the starters and three of the main courses are suitable for vegans.
What percentage of the possible lunches have both courses suitable for vegans?
[3 marks]
Answer %
7
20 n is a positive integer.
Prove algebraically that 2n 2
3
n
( )
+ n + 6n n 2 − 1 is a cube number.
[3 marks]
AB20A
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IB/M/Nov18/8300/2H
8 A = (7,2)
B = (-5,8)
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13 The number of animals in a population at the start of year t is Pt
The number of animals at the start of year 1 is 400
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Given that
BG13A
Pt + 1 = 1.01Pt
work out the number of animals at the start of year 3
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2 marks
(Total for Question 13 is 2 marks)
14 y is inversely proportional to x3
y = 44 when x = a
Show that y = 5.5 when x = 2a
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(Total for Question 14 is 3 marks)
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[5 marks]
47) Every year a man is paid $500 more than the previous year. If he receives $17800 over four
years, what was he paid in the first year? [2 marks]
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3 Marks
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56) |x+1| = 5
Find the 2 values of x
x = ………………. , ……………….
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Without replacement
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82) dodecagon.
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He then travelled by plane to Geneva, depar?ng from New York at 22 15.
The flight path can be taken as an arc of a circle with diameter 4000 nau?cal mile with a sector angle of 50°.
The local ?me in Geneva is 6 hours ahead of the local ?me in New York.
Brad arrived in Geneva at 11 25 the next day.
To complete his journey Brad travelled to Chamonix via a helicopter.
The helicopter path can be described as the perimeter of a regular nonagon with side length 10 nau?cal miles.
The journey started at 13 00 and had an average speed of 100 knots/hr.
The local ?me in Chamonix is the same as the local ?me in Geneva.
Sum of interior angles of Nonagon = 1260°
1 nau?cal mile = 1.852 km
1 knot = 1.852km/h
………………………………….km/h [14]
100) f(x) = x5 + ax + z
A curve has equa?on y =f( f( f-1(x) ) ).
The turning points of the curve have coordinates (3, p) and (-3, a – p)
Work out the value of a, the value of p and the value of z.
Write 1 decimal place for final values of a, p, and z wherever applicable.
a = …………………….. , p = …………………….. , z = …………………….. [8]
