Name:
________________________________________________
Subject: IGCSE Mathematics (0580)
Time Allowed: 2 Hours
Sample Paper 2 – Non-Calculator – Version 2
INSTRUCTIONS/RULES:
●
Calculators must not be used in this paper.
●
Answer all the questions
●
Total Marks for this paper is 100.
●
All the diagrams are not to scale, unless otherwise indicated.
Threshold for this paper (set by the exam maker):
Grade
A*
A
B
C
D
E
Min. Mark
77
66
55
42
32
20
This exam consists of 20 printed pages. Any blank pages are indicated.
Page 2
List of formulas
Page 3
Page 4
1
(a) Write down the appropriate equations in the boxes for the graphs shown below.
[3]
Page 5
(b) On the graphs below, label the maximum points as 𝑀 and minimum points as 𝑋.
[5]
!
#
(c) State the exact value of " sin(450°) − " cos(540°) + 𝑡𝑎𝑛$ (45°).
.................................................... [4]
2
𝑎 = 𝑎% + 𝑗𝑡 is a formula that links acceleration, time and jerk together.
Given that an object at time, 𝑡 = 4 s had 𝑎% = 5 m/s2 and has 𝑎 = 7 m/s2, calculate the jerk, 𝑗, of the
object with correct units.
.................................................... unit ....................... [3]
Page 6
3
It is given that 𝑥 and 𝑦 are two different prime numbers.
(a) Find the HCF (Highest Common Factor) of 𝑥 and 𝑦.
................................................... [1]
(b) Find the LCM (Least Common Multiple) of 𝑥 and 𝑦.
................................................... [1]
4
A length is measured as 5 meters, correct to the nearest meter.
State the upper bound and lower bound for this length.
Upper bound ....................................................
Lower bound ................................................... [2]
5
On a cold day in Pittsburg, the temperature was 8 °C during the day. During nighttime, the
temperature drops down to −8 °C.
Calculate the temperature difference between the daytime and nighttime.
................................................... °C [1]
6
The University of Cambridge campus spans an area of 6,170,000 m2.
Work out how much the university of Cambridge campus spans in an area of km2.
................................................... km2 [1]
7
Express √63 in the form 𝑘√𝑛, where 𝑘 and 𝑛 are positive integers.
................................................... [2]
8
Page 7
At X Notes, a company dedicated to educational content creation, there are three types of roles:
Contributors, Interns, and Ambassadors. In the company, the number of Contributors to Interns
follows a ratio of 3:2, and the number of Interns to Ambassadors follows a ratio of 2:1.
In total, there are 300 individuals across all three roles.
(a) Calculate the number of individuals in each role.
Ambassadors
....................................................
Contributors
....................................................
Interns
................................................... [4]
(b) An individual is chosen at random from the Contributors and another individual is chosen at
random from the Ambassadors.
Calculate the probability that both chosen individuals are from Asia, given that there are
50 contributors, 30 Interns, and 20 Ambassadors that are from the Asia.
............................................ [3]
Page 8
(c) Complete the pie chart to represent the number of people in different roles who are from Asia.
Label each sector of the pie chart with the role type it represents and the angle of that sector.
180°
[3]
(d) (i) An ambassador at X notes gets paid $600 monthly and works 10 hours per week.
Assuming that there are 4 weeks (or 28 days) in a month, work out the hourly salary rate of
an ambassador at X notes.
............................................ [3]
(ii) The interns have an hourly payrate that is 1.5 times more than ambassadors. An intern works
the same amount of time as an ambassador.
Work out the weekly salary of an intern.
............................................ [3]
Page 9
9
Work out the exact cross-sectional area of a hemisphere with radius 7 cm.
............................................ [2]
10 It is given that 3& + 3& + 3& + 3& + 3& + 3& + 3& + 3& + 3& = 3' .
Find 𝑚 in terms of 𝑛.
............................................ [2]
(
(
11 Given that 3𝑎 + $) = 2, determine the value of a 9𝑎* + +)! + 2 without solving for 𝑎.
...................................................... [2]
12 Complete the statements below.
It is given that (𝑦 − 5) is directly proportional to 𝑥. When the graph of (𝑦 − 5) is plotted against 𝑥, it
(
is a ................................... line with a gradient of *.
When 𝑦 is plotted against 𝑥, it has the equation ......................................................
[3]
Page 10
𝐶
13
8 cm
𝐴
𝐵
10 cm
(a) Work out the area of the triangle 𝐴𝐵𝐶 shown above.
............................................ [2]
(b) State the number of lines of symmetry of the triangle 𝐴𝐵𝐶 above.
............................................ [1]
(c) The triangle 𝑋𝑌𝑍 is a similar triangle to triangle 𝐴𝐵𝐶.
𝑍
𝑑 cm
𝑋
𝑌
15 cm
Work out the area of triangle 𝑋𝑌𝑍.
............................................ [3]
Page 11
(d) Triangle 𝐴𝐵𝐶 and triangle 𝐸𝐹𝐺 are plotted on the grid below.
𝑦
16
G
15
14
13
12
11
10
E
F
9
C
8
7
6
5
4
3
A
B
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
(i) Describe fully, the single transformation that occurs when triangle 𝐴𝐵𝐶 is transformed to
triangle 𝑋𝑌𝑍.
......................................................................................................................................................
................................................................................................................................................ [2]
(ii) Work out the exact distance moved by each point when triangle 𝐴𝐵𝐶 is transformed to
triangle 𝑋𝑌𝑍.
...................................... [2]
17
𝑥
Page 12
14 Simplify
),-./,-).
), ! -).,
, ensuring that your final answer is in terms of 𝑎 and 𝑥 only.
........................................... [5]
15 Write down 7,510,000 in standard form.
........................................... [1]
Page 13
16 The denominator of a positive fraction is 1 more than the numerator.
!
The sum of the positive fraction and its reciprocal is *.
Find the positive fraction.
........................................... [5]
Page 14
*
17 The graph below has the equation 𝑦 = 𝑎(𝑥 + 𝑏) + 𝑐.
Work out the value of 𝑎, 𝑏 and 𝑐.
𝑎=
....................................................
𝑏=
....................................................
𝑐=
................................................... [4]
Page 15
18 The mass, correct to the nearest kilogram, of each of the 11 packets of rice is shown below.
7
6
10
26
9
11
10
11
12
16
11
(a) Find the mode.
............................................... kg [1]
(b) Find the median.
............................................... kg [2]
(c) Give a reason why the mean would be an unsuitable average to use.
....................................................................................................................................................... [1]
19
101°
𝑥°
Work out the value of 𝑥.
............................................... [2]
Page 16
20
𝐾
𝒃
𝑂
𝑋
𝒂
𝐽
𝑂𝐾𝐽 is a triangle.
𝑋 is a point on 𝐾𝐽 so that 𝐾𝑋 : 𝑋𝐽 = 1 : 5.
𝑂 is the origin, QQQQ⃗
𝑂𝐽 = a and QQQQQQ⃗
𝑂𝐾 = b.
Find the position vector of 𝑋.
Give your answer in terms of a and b in its simplest form.
................................................. [3]
21 Factorise 𝑥 * + 6𝑥 + 5.
................................................. [2]
Page 17
22 Find the set of values of ℎ such that:
- the perimeter of the trapezium below is 50 cm
- the area spanned by the trapezium is greater than 50 cm2
3 cm
(3 + 2ℎ) cm
(5 − ℎ) cm
ℎ cm
7 cm
................................................. [4]
Page 18
23 The net of a cylinder is shown below.
𝑙 cm
3𝜋 cm
4𝜋 cm
(a) Work out the exact value of the length, 𝑙 cm.
.............................................. [3]
(b) Work out the surface area of this cylinder in terms of 𝜋.
.............................................. [3]
(c) Work the volume of this cylinder in terms of 𝜋.
.............................................. [2]
Page 19
24 Aaryan oscillates a string.
A horizontal line intersects the piece of the string Aaryan is oscillating at 4 points and divides it into
five parts, as shown below.
If the piece of string is intersected in this way by 19 parallel lines, each of which intersects it at
4 points, determine the number of parts into which the string will be divided.
.............................................. [4]
Page 20
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