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Gambridge IGCSE'*
CANDIDATE
NAME
CENTRE
NUMBER
CANDIDATE
NUMBER
MATHEMATICS
0580t22
Paper 2 Non-calculator (Extended)
February/March 2025
2 hours
You must answer on the question paper.
You will need: Geometrical instruments
INSTRUCTIONS
Answer all questions.
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
Write your name, centre number and candidate number in the boxes at the top of the page.
Write your answer to each question in the space provided.
Do not use an erasable pen or correction fluid.
Do not write on any bar codes.
Calculators must not be used in this paper.
You may use tracing paper.
You must show all necessary working clearly.
o
o
o
o
o
o
o
o
o
INFORMATION
The total rnark for this paper is 100.
The number of marks for each question or part question is shown in brackets [ ].
o
o
This document has 20 pages.
DC (DE/FC) 341757t2
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List of formulas
Areao A, of triangle, base b, height h.
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Area, A, of circle of radius r.
A=rr2
Ciroumference, C, of circle of radius r.
C=2rr
Curved surface areaoA, of cylinder of radius r,heighth.
A = Zrrh
Curved surface areao A, of cone of radius r, sloping edge /.
A = r.rl
Surface area, A, of sphere of radius r.
A = 4nr2
Volume, Z, of prism, cross-sectional areaA,length /.
V=Al
Volume, V, of pyramid, base area Aoheight h,
rt:!,at,
Volume, Z, of cylinder of radius r,height h.
V = rrzh
Volume, Z, of cone of radius r,heighth.
v
Volume, Z, of sphere of radius r.
y:tnt
For the equation
ax2+bx+c:O,where a*0,
=tn't
x = -o
xt[62
---Ta
a*
For the triangle shown,
abc
sinA sin,B sin C
a2 = b2 + c2 -2bccosA
1
Area = *absinC
./.
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Calculators must not be used in this paper.
1
Oranges cost 220 rupees per kilogram.
Work out the cost of 9kg of these oranges.
.. rupees [1]
2
Aryan goes on a journey.
He leaves home at 11 40 and amives at 14 18.
Find how many hours and minutes the journey took.
h.................... min [1]
3
A quadrilateral has one line of symmetry.
The diagonals of the quadrilateral cross at right angles.
Write down the mathematical name of the quadrilateral.
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V:4mp2
(a) Find Zwhen m = 10 and p =-3.
(b) Find the positive value ofp whenV = 3200 and m = 2.
p=
5
...........
Write these lengths in order of size, starting with the smallest.
0.03
m
2.9
cm
32mm
0.000 02km
smallest
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Work out the area of the trapezium.
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......... cm2 yz1
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Write down the inequality for x represented on the number line.
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Pryanka plays a game in which she can win, lose or draw.
The table shows the probability of her winning or losing a game.
Result of game
wln
lose
Probability
0.3
0.25
draw
(a) Complete the table.
l2l
(b) Pryanka plays this game L20 times.
Work out the expected number of games she wins.
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8.07
By writing each number correct to 1 significant figure, work out an estimate for D'
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Three regular polygons A, B and C meet at a point.
The interiorangles of thepolygons are inthe ratio a: b:
c:3:4:5.
Show that polygon C has twice the number of sides as polygon B.
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11 A company sells items either on a website or in shops.
The composite bar chart shows the percentage of sales on the website and in shops for January, February
and March.
F.
Z
TI
h
g
100
F
c
z
l_l sut", in shops
90
C
Sales on website
80
70
Percentage
of sales 50
40
30
20
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Jan
Feb
March
Month
11
(a) In April, ffi of the company's sales were on the website.
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On the grid, draw the bar for APril.
(b) In February, the company had sales of $3.5 million.
Work out the value of sales in shops in February.
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(c) In May, the company had sales of $6 million'
In June, the company had sales of $7'5 million'
Find the percentage increase in sales from May to June'
% 13)
(d) ln}O24,the company had total sales of $52 million'
Thiswasanincreaseof3OYoonthetotalsalesfor2023.
Work out the total sales in 2023.
12 (a) Write as a single fraction in its simplest form'
x 3x x*2
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(b) Factorise.
3x(a+4Y)-oY-4Y'
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16cm
The diagram shows a cylinder with radius r cm and height 16 cm.
A sphere has radius 3 cm.
The volume of the cylinder is equal to the volume of the sphere.
Find the value of r.
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A, B, C, D and E lie on a circle.
FG is atangentto the circle at C.
Angle BAD = 110o, angle ADB = 20o and angle BEC = 45o.
z
(a) Find angle,BCD.
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Give a geometrical reason for your answer.
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Angle BCD =
because
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x.
(b) (i) Find angle DBC.
=
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Angle DCG =
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Angle DBC
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=
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\-rzl
(a) Find the coordinates of point B.
) 121
( ...... .. . . .. . .......... ,
(b) Point C has coordinates (5, -2).
Findthe vedorei,.
a=l
)o,
(c) rt = 3Ei
rina lffl.
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16 The stem-and-leaf diagram shows the mass of each of 1 3 packets.
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Key: 3l 1 represents 31g
z
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x.
(a) Work out the interquartile range.
=
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Two of these packets are chosen at random.
Find the probability that the one packet has a mass of more than 50g and the other packet has a
mass of less than 50 g.
z
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17 Work out.
5
6+0.28
Give your answer as a flaction in its simplest form.
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The quadrilateral ACDE is formed by two right-angled triangles ABE and BCD.
AC = 17 cm, AE : lScm artd BD = 6cm.
(a) Show thatCD: 10cm.
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2
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z
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=
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(b) Find the perimeter of the quadrilateral ACDE.
Give your answer in the form p + k^[4.
B
F
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cm [4]
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(a) Simplify.
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(b) Rationalise the denominator and simplify.
2+ \/7
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2l (a) Write down the coordinates of the point where the graph of !: 5x-3
(
(b) A is the point (1,7) and.B is the point (5,15).
Find the equation of the perpendicular bisector of the line AB.
Give your answer in the form ! = mx* c.
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x.
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22 Acurvehasequation y=x3 +x2 -x.
rhe curve has a stationary point
*(+,-*).
(a) Find the coordinates of the other stationary point.
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(b) By sketching the graph of y = x3 +x2 -x, determine whether the stationary point
Ir s \. a maximum or a minimum.
l+,-*)is
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tu
tt
B
F.-
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'z
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x.
. (t)
T
t---
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trl
t--.
t
t-.=
z
o
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z
o
t
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=
L
(c) The equation *3 +*'-x = k has fewer than 3 solutions'
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ul
tt
Find the range of possible values for ft'
3
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z
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U)
E
F
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UJ
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Question 23 is printed on the next page.
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(b)
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z
u
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Find the value of x.
s
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c
c
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