Class 10 ICSE Term2 Maths Specimen 2022

BOARD -

CLASS -

SUBJECT -

ICSE

10th

MATHEMATICS

Paper Pattern for Written Term-I

TIME -

MARKS -

1 Hour 30 Minutes

Visit CISCE OFFICIAL PAGE for Regulations and Syllabus of Class 10th ICSE

Solved Specimen Paper Semester-2 2022

Question 1 [MATHEMATICS Specimen Paper Semester-2 2022]

Choose the correct answers to the questions from the given options. (Do not copy the question, Write the correct answer only.)

(i) The point (3,0) is invariant under reflection in:

The origin
x-axis
y-axis
both x and y axes

Solution

(ii) In the given figure, AB is a diameter of the circle with centre ‘O’. If ∠𝑪𝑪𝑪𝑪𝑪𝑪 = 55⁰ then the value of x is:

27.5⁰
55⁰
110⁰
125⁰

Solution

(iii)If a rectangular sheet having dimensions 22 cm x 11 cm is rolled along its shorter side to form a cylinder. Then the curved surface area of the cylinder so formed is:

968 cm²
424 cm²
121 cm²
242 cm²

Solution

(iv)If the vertices of a triangle are (1,3), (2, - 4) and (-3, 1). Then the co-ordinate of its centroid is:

(0, 0)
(0, 1)
(1, 0)
(1, 1)

Solution

(v)tan θ x √1-sin ² is equal to:

cos θ
sin θ
tan θ
cot θ

Solution

(vi)The median class for the given distribution is:

Class Interval	1 – 5	6-10	11-15	16-20
Cumulative Frequency	2	6	11	18

1 – 5
6 – 10
11-15
11 – 20

Solution

(vii)If the lines 7y = ax + 4 and 2𝑦 = 3 − 𝑥, are parallel to each other, then the value of ‘a’ is:

- 1
−7/2
-2/7
14

Solution

(viii)Volume of a cylinder is 330 cm ³ . The volume of the cone having same radius and height as that of the given cylinder is:

330cm³
165cm³
110cm³
220cm³

Solution

(ix)In the given graph, the modal class is the class with frequency:

Solution

(x)If the probability of a player winning a game is 0.56. The probability of his losing this game is:

0.56
1
0.44
0

Solution

Question 2 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).

Solution

(ii)Three rotten apples are accidently mixed with twelve good ones. One apple is picked at random. What is the probability that it is a good one?

Solution

(iii)In the given figure , AC is a tangent to circle at point B. ∆𝑬FD is an equilateral triangle and ∠𝑪BD = 𝟒0°. Find:

∠BFD

Solution

∠FBD
∠ABF

Solution

(iii)A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions are 35° and 𝟔0° respectively as shown in the diagram. If the distance of the object P from point Q is 50 metres, then find the distance between R and S correct to the nearest meter.

Solution

Question 3 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)In the given figure, PT is a tangent to the circle at T, chord BA is produced to meet the tangent at P. Perpendicular BC bisects the chord TA at C. If PA = 9cm and TB = 7cm, find the lengths of:

Solution

(ii)How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?

Solution

(iii)Prove that:

Solution

(iv)Use graph paper for this question, take 2 cm = 10 marks along one axis and 2 cm = 10 students along the other axis.
The following table shows the distribution of marks in a 50 marks test in Mathematics:

Draw the ogive for the above distribution and hence estimate the median marks.

Solution

Question 4 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)Find the equation of the perpendicular dropped from the point P (-1,2) onto the line joining A (1,4) and B (2,3).

Solution

(ii)Find the mean for the following distribution:

Solution

(iii)A solid piece of wooden cone is of radius OP = 7 cm and height OQ = 12 cm. A cylinder whose radius and height equal to half of that of the cone is drilled out from this piece of wooden cone. Find the volume of the remaining piece of wood.
(USE,𝜋=22/7)

Solution

(iv)Use a graph sheet for this question, take 2cm = 1 unit along both x and y axis:

Plot the points A (3,2) and B (5,0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.

Solution

Question 5 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)In the given figure, the sides of the quadrilateral PQRS touches the circle at A,B,C and D. If RC = 4 cm, RQ = 7 cm and PD = 5cm. Find the length of PQ:

Solution

(ii)Prove that:

Solution

(iii)In the given diagram, OA = OB, ∠OAB = 𝜃 and the line AB passes through point P (-3, 4).

Find:

Slope and inclination (𝜃) of the line AB

Solution

Equation of the line AB

Solution

(iv)Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis]

Solution

Question 6 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)A box contains tokens numbered 5 to 16. A token is drawn at random. Find the probability that the token drawn bears a number divisible by:

Solution

Neither by 2 nor by 3

Solution

(ii)A box contains tokens numbered 5 to 16. A token is drawn at random. Find the probability that the token drawn bears a number divisible by:

Solution

(iii)An aeroplane is flying horizontally along a straight line at a height of 3000 m from the ground at a speed of 160 m/s. Find the time it would take for the angle of elevation of the plane as seen from a particular point on the ground to change from 60⁰ to 45⁰. Give your answer correct to the nearest second.

Class 10 ICSE Term2 Maths Specimen 2022

Paper Pattern for Written Term-I

Visit CISCE OFFICIAL PAGE for Regulations and Syllabus of Class 10th ICSE

Solved Specimen Paper Semester-2 2022

Question 1 [MATHEMATICS Specimen Paper Semester-2 2022]

Choose the correct answers to the questions from the given options. (Do not copy the question, Write the correct answer only.)

(i) The point (3,0) is invariant under reflection in:

Solution

(ii) In the given figure, AB is a diameter of the circle with centre ‘O’. If ∠𝑪𝑪𝑪𝑪𝑪𝑪 = 55⁰ then the value of x is:

Solution

(iii)If a rectangular sheet having dimensions 22 cm x 11 cm is rolled along its shorter side to form a cylinder. Then the curved surface area of the cylinder so formed is:

Solution

(iv)If the vertices of a triangle are (1,3), (2, - 4) and (-3, 1). Then the co-ordinate of its centroid is:

Solution

(v)tan θ x √1-sin 2 is equal to:

Solution

(vi)The median class for the given distribution is:

Solution

(vii)If the lines 7y = ax + 4 and 2𝑦 = 3 − 𝑥, are parallel to each other, then the value of ‘a’ is:

Solution

(viii)Volume of a cylinder is 330 cm 3 . The volume of the cone having same radius and height as that of the given cylinder is:

Solution

(ix)In the given graph, the modal class is the class with frequency:

Solution

(x)If the probability of a player winning a game is 0.56. The probability of his losing this game is:

Solution

Question 2 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).

Solution

(ii)Three rotten apples are accidently mixed with twelve good ones. One apple is picked at random. What is the probability that it is a good one?

Solution

(iii)In the given figure , AC is a tangent to circle at point B. ∆𝑬FD is an equilateral triangle and ∠𝑪BD = 𝟒0°. Find:

Solution

Solution

Solution

Question 3 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)In the given figure, PT is a tangent to the circle at T, chord BA is produced to meet the tangent at P. Perpendicular BC bisects the chord TA at C. If PA = 9cm and TB = 7cm, find the lengths of:

Solution

(ii)How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?

Solution

(iii)Prove that:

Solution

(iv)Use graph paper for this question, take 2 cm = 10 marks along one axis and 2 cm = 10 students along the other axis. The following table shows the distribution of marks in a 50 marks test in Mathematics:

Draw the ogive for the above distribution and hence estimate the median marks.

Solution

Question 4 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)Find the equation of the perpendicular dropped from the point P (-1,2) onto the line joining A (1,4) and B (2,3).

Solution

(ii)Find the mean for the following distribution:

Solution

(iii)A solid piece of wooden cone is of radius OP = 7 cm and height OQ = 12 cm. A cylinder whose radius and height equal to half of that of the cone is drilled out from this piece of wooden cone. Find the volume of the remaining piece of wood. (USE,𝜋=22/7)

Solution

(iv)Use a graph sheet for this question, take 2cm = 1 unit along both x and y axis:

Solution

Question 5 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)In the given figure, the sides of the quadrilateral PQRS touches the circle at A,B,C and D. If RC = 4 cm, RQ = 7 cm and PD = 5cm. Find the length of PQ:

Solution

(ii)Prove that:

Solution

(iii)In the given diagram, OA = OB, ∠OAB = 𝜃 and the line AB passes through point P (-3, 4).

Find:

Solution

Solution

(iv)Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis]

Solution

Question 6 [MATHEMATICS Specimen Paper Semester-2 2022]

(i)A box contains tokens numbered 5 to 16. A token is drawn at random. Find the probability that the token drawn bears a number divisible by:

Solution

Solution

(ii)A box contains tokens numbered 5 to 16. A token is drawn at random. Find the probability that the token drawn bears a number divisible by:

Solution

Solution

(iv)Given that the mean of the following frequency distribution is 30, find the missing frequency ‘f’

Solution

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(v)tan θ x √1-sin ² is equal to:

(viii)Volume of a cylinder is 330 cm ³ . The volume of the cone having same radius and height as that of the given cylinder is:

(iv)Use graph paper for this question, take 2 cm = 10 marks along one axis and 2 cm = 10 students along the other axis.
The following table shows the distribution of marks in a 50 marks test in Mathematics:

(iii)A solid piece of wooden cone is of radius OP = 7 cm and height OQ = 12 cm. A cylinder whose radius and height equal to half of that of the cone is drilled out from this piece of wooden cone. Find the volume of the remaining piece of wood.
(USE,𝜋=22/7)