CAMBRIDGE INTERNATIONAL
DATE: 18-10-2024
MOCK-1
DURATION:120mins
GRADE: 10
SUBJECT – MATHEMATICS
MARKS:100
_____________________________ Paper 2 Non-calculator___________________________
Name: ___________________________
Roll number: ___________
MATHEMATICS 0580/22
Paper 2 Non-calculator (Extended)
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 answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary working clearly.
INFORMATION
● The total mark for this paper is 100.
● The number of marks for each question or part question is shown in brackets [ ].
Page 1 of 18
List of formulas
Page 2 of 18
1.
Work out the area of the trapezium.
_______________ cm2
[2]
x = ___________________
[2]
2.
AB = BC and ABD is a straight line.
Find the value of x.
3.
Workout
Give your answer as a fraction in its simplest form.
Page 3 of 18
____________________
[3]
4.
Describe fully the single transformation that maps triangle T onto triangle U.
__________________________________________________________________
__________________________________________________________________
5.
[3]
The line y = 3x – 2 crosses the y-axis at G.
Write down the coordinates of G.
( _______, _______ )
[1]
6a.
i.
Find 2p + q .
[2]
Page 4 of 18
ii.
Find the exact value of |p|.
Give your answer as a surd in its simplest form.
________________
[2]
b.
A is the point (4, 1) and
Find the coordinates of B.
(_______, ________)
7.
a.
A, B, C and D lie on the circle, centre O.
TA is a tangent to the circle at A.
Angle ABC = 131° and angle ADB = 20°.
Find
angle ADC
Page 5 of 18
[1]
b.
c.
d.
8.
9.
a.
b.
Angle ADC =___________
[1]
Angle AOC =___________
[1]
Angle BAT =___________
[1]
Angle OAB =___________
[1]
y = _________________
[3]
______________ cm
[1]
angle AOC
angle BAT
angle OAB
h2 = x2 + 2y2
Rearrange the formula to make y the subject.
Ella’s height is 175 cm, correct to the nearest 5 cm.
Write down the upper bound of Ella’s height.
Rafael’s height is 161 cm, correct to the nearest cm.
Work out the upper bound of the difference between Ella’s height and Rafael’s
height.
Page 6 of 18
________________ cm
[2]
10.
a.
b.
By drawing suitable lines and shading the unwanted regions, find the region, R,
where
x ⩾ 2, y ⩾ x and 2x + y ⩽ 8 .
[5]
The point P lies in the region R.
The coordinates of P are (a, b).
Write down the largest possible value of a + b.
___________________
Page 7 of 18
[1]
11.
a.
Triangle ABC is mathematically similar to triangle PQR.
The area of triangle ABC is 15 cm2.
Work out the area of triangle PQR.
___________ cm2
b.
[2]
The triangles are the cross-sections of prisms which are also mathematically
similar.
The volume of the smaller prism is 300 cm3.
Calculate the length of the larger prism.
_______________ cm
[3]
12a. A cylinder with radius 2 cm and height h cm has the same volume as a sphere with
radius 3 cm.
Find the value of h.
h = ____________________
Page 8 of 18
[3]
b.
A solid metal cube has sides with length 20 cm.
The cube is melted down and made into 40 solid spheres, each of radius r cm.
Show that
[3]
c.
A solid cylinder has radius x cm and height
cm.
The surface area of a sphere with radius R cm is equal to the total surface area of
the cylinder.
Find an expression for R in terms of x.
13.
a.
f(x) = 3x + 2 g(x) = x2 + 1
Find h(3).
R = ___________________
[3]
______________
[1]
h(x) = 4x
Page 9 of 18
b.
c.
d.
e.
Find fg(1).
______________
[2]
___________________
[3]
x = ________________
[2]
f –1(x) = ______________
[2]
Find gf(x) in the form ax2 + bx + c.
Find x when f(x) = g(7).
Find f –1(x).
Page 10 of 18
f.
Find
Give your answer as a single fraction, in terms of x, in its simplest form.
g.
14.
______________________
[3]
x = __________________
[1]
Find x when h–1(x) = 2.
P = 210 × 38 × 75 .
Write 12P 2 as a product of prime factors.
Page 11 of 18
_____________________
[2]
15.
In the diagram, O is the origin, OT = 2TD and M is the midpoint of TC.
OC = c and OD = d.
Find the position vector of M.
Give your answer in terms of c and d in its simplest form.
_____________________
16.
Find the value of n.
Page 12 of 18
[3]
n = ___________________
[2]
17.
Rationalise the denominator, giving your answer in its simplest form.
[3]
18.
a.
23, 17, 11, 5, ....
Write down the next number in this sequence.
____________________
Page 13 of 18
[1]
b.
Find the nth term of this sequence.
__________________
[2]
________________
[3]
19.
In the diagram, AB and CD are parallel.
The lines CB and AD intersect at X.
AB = 3.0 cm, AX = 2.0 cm, BX = 2.7 cm and CD = 7.5 cm.
Find the length of BC.
Page 14 of 18
20.
The diagram shows the speed–time graph for part of a car journey.
Calculate the total distance travelled during the 10 seconds.
_________________m
21.
[2]
y is inversely proportional to x2 .
When x = 3, y = 2.
Find y when x = 2.
y = _______________
Page 15 of 18
[3]
22.
Simplify.
[4]
23.
A night bus runs from 21 50 to 05 18 the next day.
Work out the number of hours and minutes that the night bus runs.
_______ h __________ min
24.
a.
b.
[1]
There are 20 cars in a car park and 3 of the cars are blue.
James wants to draw a pie chart to show this information.
Find the angle of the sector for the blue cars in this pie chart.
________________
[2]
_______________
[1]
One of the 20 cars is picked at random.
Find the probability that this car is not blue.
Page 16 of 18
25.
The line y = 2x-5 intersects the line y = 3 at the point P.
Find the coordinates of the point P.
(________ , ________)
26.
The bearing of B from A is 107°.
Calculate the bearing of A from B.
___________________
27.
[2]
[2]
x is an integer.
Complete the Venn diagram.
[2]
Page 17 of 18
28.
Find the highest common factor (HCF) of 28x5 and 98x3 .
________________
29.
[2]
A train, 1750 metres long, is travelling at 55 km/h.
Calculate how long it will take for the whole train to completely cross a bridge that
is 480 metres long.
Give your answer in seconds, correct to the nearest second.
___________________ s
Page 18 of 18
[3]