GLENDALE ACADEMY INTERNATIONAL

MOCK TEST, OCTOBER 2020

GRADE X

Cambridge Assessment International Education

Cambridge International General Certificate of Secondary Education

CANDIDATE
NAME

CENTRE MARKS
NUMBER SECURED

MATHEMATICS 0580/22
Paper 2 (Extended) TIME: 1Hr 30min.

This document consists of 16 printed pages

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1. a) Calculate. Give your answer to 3 decimal places. [2]

b) Simplify [1]

c) Find the value of p when [1]

d) Find the value of w when [1]

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2. 2. a) Solve the inequality for positive integer values of x. [2]

b) w is inversely proportional to cube of t. w=50 when t=2. Find w when t=5 [2]

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3.a) The diagram shows two circles

Point D and E lie on the larger circle with centre O. Point O,B and C lie on small circle with
centre A.BOD is a straight line and angle BDE= x0
i) Find in terms of x expression for angle BOC [1]

ii) reflex angle BAC [2]

b) ABCD is a cyclic quadrilateral. Its angles are in the ratio

angleA: angleB:angle:C:angle D = 3:6:7:x.
Work out the size of the angle D. [2]

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4. a) The diagram shows two right angled triangle ABC and BCD.Show that AC is 18.1m correct
to 1 decimal place. [2]

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b) The diagram shows the entrance to a tunnel. The circular arc has a radius of 3m and centre O.
AB is horizontal and angle AOB = 120°.

During a storm the tunnel filled with water, to the level shown by the shaded area in the diagram.
(i) Calculate the shaded area. [3]

(ii) The tunnel is 50m long. Calculate the volume of water in the tunnel. [1]

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5. a) Solve the simultaneous equations. Show your Working [2]

b) Explain what your answer to part (a) tells you about the graphs of and
[1]

6. The population, P of a species of insect, t years after Ist Jamuary 2000, is given by the fomula

a) Jan says, “The multiplier is 0.85, so the population is decreasing by 85% each year.
Is Jan correct? Explain how you know. [1]

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b) Find the population on 1st January 2018 [2]

c) Find the number of whole years it takes for the population to fall below 20000 [2]

7. The are of a rectangulatr garden is 1677m2 correct to the nearest m2. The length of the garden
is 68.4m correct to 3 significant figures. Calculate the upper bound for the width of the garden.
Give your answer correct to 4 significant figures. [2]

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8.

M is the Mid point of AB

C is the Mid point of OB

Write the following vectors in terms of a,b and c. Give your answer in the simplest form.

[1]

[1]

[2]

b) Do the points A,N and C lie on the same straight line? Justify your answer using vectors.[3]

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9. 30 students were asked if they had a bicycle (B), a mobile phone (M) and a computer (C). The
results are shown in the Venn diagram.

(a) Work out the value of x. [1]

(b) Use set notation to describe the shaded region in the Venn diagram. [1]

(c) Find . [1]

(d) A student is chosen at random. (i) Write down the probability that the student is a member of
the set M’ [1]

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(ii) Write down the probability that the student has a bicycle. [1]

(e) Two students are chosen at random from the students who have computers. Find the
probability that each of these students has a mobile phone but no bicycle. [3]

10. a) The nth term of a sequence is 8n-3.

i) Write down the first two terms of this sequence. [1]

ii) Show that the number 203 is not in this sequence. [2]

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c)

The second term of this sequence is 20 and the third term is 50. The rule for finding the next
term is subtract y then multiply by 5. Find the value of y and work out the first term of the
sequence. [3]

11. The cumulative frequency diagram shows information about the trunk diameter, in metres, of
120
trees

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Find
(a) the inter-quartile range, [2]

(b) the 95th percentile, [1]

(c) the number of trees with a trunk diameter greater than 3 metres. [2]

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12. a) Simplify: [3]

b)

The equation of the line l in the diagram is y=5-x

a) The line cuts the y-axis at P. Write down the coordinates of P. [1]

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b) Write down the gradient of line l. [1]

13. a)There are three sets of traffic lights along a road.

If each light is green (G) for 40% of the time, what is the probability that a driver on this road is
not
stopped by any of these sets of lights? (Give your answer as a decimal.) [2]
P(GGG) =

b)The probability that Alexis selects a hard-centred chocolate from a box of chocolates is h .
She ate 4 chocolates and only one of them was hard-centred.

Which of these expressions shows the probability of this happening? [1]

14. Two solids are mathematically similar. The surface area of the smaller solid is 42π cm² The
surface area of the larger solid is 1512π cm² The height of the larger solid is 96cm. Work out the
height of the smaller solid. [3]

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15. The curve with equation is given. Determine the nature of each turning
point. [3]

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