ICSE Maths Sem-2 Answer Key 2022 Solved Board Question Paper, Guess Your Marks

ICSE Maths Sem-2 Answer Key 2022 Solved Board Question Paper, Step by step solutions of ICSE Class-10 Mathematics Question Paper of Sem-2  for 2022 as council prescribe guideline. Visit official website CISCE for detail information about ICSE Class-10

ICSE Maths Sem-2 Answer Key 2022 Solved Board Question Paper

Board ICSE
Class 10th (X)
Subject Mathematics
Topic Semester-2 Answer Key
Syllabus On bifurcated syllabus (after reduction)
session 2021-22
Question Type MCQ (Sec- A) and Descriptive (Sec-B)
Total questions 6
Max mark 40

Section A

(Attempt all questions from this section)

Question 1:

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

(i) The probability of getting a number divisible by 3 in throwing a dice is :

(a) 1/6

(b) 1/3

(c) 1/2

(d) 2/3

Answer : (b) 1/3

(iii) The volume of a conical tent is 462 m³ and the area of the base is 154 m². the height of the cone is :

(a) 15 m

(b) 12 m

(c) 9 m

(d) 24 m

Answer : (c) 9 m

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

The median class for the given distribution is :

(a) 0 – 10

(b) 10 – 20

(c) 20 – 30

(d) 30 – 40

Answer : (c) 20 – 30

(iv) If two lines are perpendicular to one another then the relation between their slopes m1 and m2 is :

(a) m1 = m2

(b) m1 = 1/m2

(c) m1 = -m2

(d) m1 x m2 = -1

Answer : (d) m1 x m2 = -1

(v) A lighthouse is 80 m high. The angle of elevation of its top from a point 80 m away from its foot along the same horizontal line is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Answer : (b) 45°

(vi) The modal class of a given distribution always corresponds to the:

(a) interval with highest frequency

(b) interval with lowest frequency

(c) the first interval

(d) the last interval

Answer : (a) interval with highest frequency

(vii) The coordinates of the point P(-3,5) on reflecting on the x axis are:

(a) (3,5)

(b) (-3,-5)

(c) (3,-5)

(d) (-3,5)

Answer : (b) (-3,-5)

(viii) ABCD is a cyclic quadrilateral. If ∠BAD (2x+5)° and ∠BCD (x+10)° or then x is equal to:

(viii) ABCD is a cyclic quadrilateral. If ∠BAD (2x+5)° and ∠BCD (x+10)° or then x is equal to:

(a) 65°

(b) 45°

(c) 55°

(d) 5°

Answer : (c) 55°

(ix) A (1,4), B (4,1) and C (x,4) are the vertices of △ABC. f the centroid of the triangle is G (4.3) then x is equal to:

(a) 2

(b) 1

(c) 7

(d) 4

Answer : (c) 7

(x) The radius of a roller 100 cm long is 14 cm. The curved surface area of the roller is

(Take π = 22/7

(a) 13200 cm²

(b) 15400 cm²

(c) 4400 cm²

(d) 8800 cm²

Answer : (d) 8800 cm²

ICSE Sem-2 Math Board Question Paper PDF Solution Section A


Section B

(Attempt any three questions from this section)

Question 2 :

(i) Prove that :

1/(1 + sinθ) + 1/(1 – sinθ) = 2sec²θ

Sol–

icse math sem-2 sec-B question-2

(ii) Find a if A (2a+2,  3), B (7,4) and C (2a + 5,2) are collinear.

(iii) Calculate the mean of the following frequency distribution.

Calculate the mean of the following frequency distribution.

(iv) In the given figure O is the center of the circle. PQ and PR are tangent and ∠QPR = 70° calculate

Marks obtained by 100 students in an examination are given below.

(a) ∠QOR

(b) ∠QSR

Answer :      Please see PDF Solution at bottom

Question 3:

(i) A bag contains 5 white, 2 red and 3 black balls. A ball is drawn at random. What is the probability that the ball drawn is a red ball?

(ii) A Solid cone of radius 5 cm and height 9 cm is melted and made into small cylinders of radius of 0.5 cm and height 1.5 cm. Find the number of cylinders so formed.

(iii) Two lamp posts AB and CD each of height 100 m are on either side of the road. P is a point on the road between the two lamp posts. The angles of elevation of the top of the lamp posts from the point P are 60° and 40°. Find the distances PB and PD.

Two lamp posts AB and CD each of height 100 m are on either side of the road. P is a point on the road between the two lamp posts. The angles of elevation of the top of the lamp posts from the point P are 60° and 40°. Find the distances PB and PD.

(iv) Marks obtained by 100 students in an examination are given below.

Marks obtained by 100 students in an examination are given below.

Draw a histogram for the given data using a graph and find the mode.

Take 2 cm = 10 marks along one axis and 2 cm = 10 students along the other axis.

Answer :   Please see PDF Solution at bottom

Question 4: 

(i) Find a point P which divides internally the line segment joining the points A (-3,9) and B (1,-3) in the ratio 1:3.

(ii) A letter of the word SECOŃDARY is selected at random. What is the probability that the letter selected is not a vowel?

(iii) Use a graph paper for this question. Take 2cm- 1 unit along both the axes.

(a) Plot the points A(0,4), B(2,2), C(5,2) and D(4,0). E (0,0) is the origin.

(b) Reflect B, C, D on the y-axis and name then as B’, C’ and D’ respectively.

(c) Join the points ABCDD’C’B’ and A in order and give a geometrical name to the closed figure

(iv) A solid wooden cylinder is of radius 6 cm and height 16 cm. Two cones each of radius 2 cm and height 6 cm are drilled out of the cylinder. Find the volume of the remaining solid.

Take π = 22/7

 A solid wooden cylinder is of radius 6 cm and height 16 cm. Two cones each of radius 2 cm and height 6 cm are drilled out of the cylinder. Find the volume of the remaining solid.

Answer :   Please see PDF Solution at bottom

Question 5:

(i) Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 and AB = 5 cm cm, Find the length of CD.

(i) Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 and AB = 5 cm cm, Find the length of CD.

(ii) Line AB is perpendicular to CD. Coordinate of B, C and D are respectively (4,,0), (0, -1) and (4,3).

(ii) Line AB is perpendicular to CD. Coordinate of B, C and D are respectively (4,,0), (0, -1) and (4,3).

Find:

(a) Slope of CD

(b) Equation of AB

(iii) Prove that  :

(1 + sin θ)² + (1 – sinθ)²/2cos²θ = sec²θ + tan²θ

(iv) The name of the following distribution is 50. Find the unknown frequency.

Class Interval Frequency
0 – 20 6
20 – 40 f
40 – 60 8
60 – 80 12
80 – 100 8

Answer :   Please see PDF Solution at bottom

Question 6 :

(i) Prove that :

1 + tan²θ/(1 + secθ) = secθ

(ii) In the given figure A, B, and D are points on the circle with Centre O.

(ii) In the given figure A, B, and D are points on the circle with Centre O.

Given ∠ABC = 62°.

Find :

(a) ∠ADC

(b) ∠CAB

(iii) Find the equation of a line parallel to the line 2x + y -7 = 0 and passing through the intersection of the line x + y – 4 = 0 and 2x – y = 8.

(iv) Marks obtained by students in an examination are given below.

Marks obtained by students in an examination are given below.

Using graph paper draw an ogive and estimate the median marks. Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis.

Answer :  Please see PDF Solution at bottom


ICSE Sem-2 Math Board Question Paper PDF Solution Section B

— End of  ICSE Maths Sem-2 Answer Key 2022, Solved Board Question Paper  :-

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