Students should refer to ICSE Class 10 Mathematics Question Paper solved Set B given below which will help them to prepare for the upcoming ICSE Mathematics exams. Students should read ICSE Mathematics Class 10 Books to make sure they are completely prepared and should also refer to ICSE Class 10 Mathematics Solutions to understand all questions and their answers.

**ICSE Class 10 Mathematics Question Paper solved Set B**

*Answers to this Paper must be written on the answer sheet provided separately.You will not be allowed to write during the first 15 minutes.This time is to be spent in reading the question paper.The time given at the head of this Paper is the time allowed for writing the answers.Attempt seven questions in all. Part I is compulsory. All questions from Part I are to be attempted.A total of five questions are to be attempted from Part II.The intended marks for questions or parts of questions are given in brackets [ ].*

**ICSE Class 10 Mathematics Question Paper solved Set B****SECTION – A (40 Marks)***Attempt all the questions from this section.*

**Question 1****(a)** If b is the mean proportion between a and c, show that : [3]

a^{4} + a^{2}b^{2} + b^{4} / b^{4} + b^{2}c^{2} + c^{4} = a^{2} / c^{2}

**(b)** Solve the equation 4*x*^{2} − 5x−3=0 and give your answer correct to two decimal places. [4]

**(c)** AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. If the radius of the circle is 13 cm, find the distance between the two chords. [3]

**Answer 1**

**Question 2(a)** Evaluate without using trigonometric tables, [3]

**(c)** Jaya borrowed ₹ 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays ₹ 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt. [3]

**Answer 2**

**Question 3****(a)** The catalogue price of a computer set is ₹ 42000. The shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after the two successive discounts. Find : [3]

(i) the amount of sales tax a customer has to pay.

(ii) the total price to be paid by the customer for the computer set.

**(b)** P (1, –2) is a point on the line segment A(3, –6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B. [4]

**(c)** The marks of 10 students of a class in an examination arranged in ascending order is as follows : [3]

13, 35, 43, 46, x, x+4, 55, 61, 71, 80

If the median marks is 48, find the value of x. Hence find the mode of the given data.

**Answer 3**

**Question 4****(a)** What must be subtracted from 16x^{3} – 8x^{2} + 4x + 7 so that the resulting expression has 2x + 1 as a factor ? [3]

**(b)** In the given figure ABCD is a rectangle. It consists of a circle and two semi circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures. [4]

**(c)** Solve the following inequation and represent the solution set on a number line. [3]

**Answer 4**

**ICSE Class 10 Mathematics Question Paper solved Set B****SECTION – B (40 Marks)**

**Question 5****(a)**

**(b)** How much should a man invest in ₹ 50 shares selling at ₹ 60 to obtain an income of ₹ 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number. [3]

**(c)** Sixteen cards are labelled as a, b, c ……. m, n, o, p. They are put in a box and shuffled.

A boy is asked to draw a card from the box. What is the probability that the card drawn is : [3]

(i) a vowel.

(ii) a consonant.

(iii) none of the letters of the word median.

**Question 6****(a)** Using a ruler and a compass construct a triangle ABC in which AB = 7cm, ∠CAB=60° and AC = 5cm. Construct the locus of :

(i) points equidistant from AB and AC.

(ii) points equidistant from BA and BC.

Hence construct a circle touching the three sides of the triangle internally. [4]

**(b)** A conical tent is to accommodate 77 persons. Each person must have 16m^{3} of air to breathe. Given the radius of the tent as 7m find the height of the tent and also its curved surface area. [3]

**Answer 6**

**Question 7****(a) A page from a savings bank account passbook is given below :**

(i) Calculate the interest for the 6 months from January to June 2016, at 6% per annum.

(ii) If the account is closed on 1st July 2016, find the amount received by the account holder. [5]

**(b)** Use a graph paper for this question (Take 2 cm = 1 unit on both x and y axis)

(i) Plot the following points :

A (0, 4), B (2, 3), C (1, 1) and D (2, 0).

(ii) Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B’, C’, D’ respectively.

(iii) Join the points A, B, C, D, D’, C’, B’ and A in order, so as to form a closed figure. Write down the equation of the line of symmetry of the figure formed. [5]

**Answer 7****(a)**

**(b) **Coordinates of images of B, C and D are B’ (– 2, 3), C’ (– 1, 1) and D’ (–2, 0).

Equation of line of symmetry is x = 0.

**Question 8****(a)** Calculate the mean of the following distribution using step deviation method. [4]

**(b)** In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. If ∠BAQ = 30°, prove that : [3]

(i) BD is a diameter of the circle.

(ii) ABC is an isosceles triangle.

**(c)** The printed price of an air conditioner is ₹ 45,000/-. The wholesaler allows a discount of 10% to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find :

(i) VAT paid by the shopkeeper to the government.

(ii) The total amount paid by the customer inclusive of tax.

**Answer 8****(a)**

**(b)** (i) AB is the bisector of ∠CAQ.

∴ ∠CAB = ∠BAQ = 30°

AD is the bisector of ∠PAC

∴ ∠CAD = ∠PAD = (180° – 60°) /2 = 120° / 2 =60°

∴ ∠BAD = ∠BAC + ∠CAD = 30° + 60°= 90°

∴BD is a diameter of the circle.

(ii) ∠BAQ = ∠BCA = 30°

∴ AB is a chord and PQ tangent

∴ angle in the alternate segment are equal

∴ ΔABC is an isosceles triangle.

(c) MP = 45,000

Discount amount to the shopkeeper = 10/100 × ₹ 45,000

SP = 45,000 – 4,500 = ₹ 40,500

Sales tax for the shopkeeper = 12/100 × 40,500 = ₹ 4,860

Discount amount to the customer = 5/100 × 45,000 = ₹ 2,250

SP = 45,000 – 2,250 = `42,750

Sales tax for the customer = 12/100 × 42,750 = ₹ 5,130

(i) VAT paid by the shopkeeper = 5,130 – 4,860 = ₹ 270

(ii) Amount paid by customer = 42,750 + 5130 = ₹ 47,880

**Question 9****(a)** In the figure given, O is the centre of the circle. ∠DAE = 70°. Find giving suitable reasons, the measure of : [4]

(i) ∠BCD

(ii) ∠BOD

(iii) ∠OBD

**(b)** A(–1, 3) , B(4, 2) and C(3, –2) are the vertices of a triangle. [3]

(i) Find the coordinates of the centroid G of the triangle.

(ii) Find the equation of the line through G and parallel to AC.

**(c)** Prove that [3]

**Answer 9(a)**

∴ ∠DAE = ∠BCD (ext. ∠ of a cyclic quad. is equal to interior opp. ∠)

(i) ∠DAE = ∠BCD = 70°

(ii) ∠BOD = 2 ∠BCD = 140°

(angle at centre is twice the angle on other segment)

(iii) In ΔOBD, OB = OD (radii of circle)

∴ ∠OBD = ∠ODB = x° (say) (at least 2 correct reasons)

x° + x° +140° = 180° (sum of angles of a triangle = 180°)

∴ ∠OBD = x° = 20°

**(b)** Centroid G = [ (-1 + 4 + 3 / 3), (3 + 2 – 2 / 3) ] = G(2,1)

Slope of AC = (-2 – 3) / (3 +1) = -5/4

Equation of line through G and parallel to AC :

y – 1 = −5/4 (x – 2)

5x + 4y = 14

**(c)** sinθ(1 – 2sin^{2}θ ) / cosθ(2cos^{2}θ – 1)

= sinθ(sin^{2}θ + cos^{2}θ – 2sin^{2}θ) / cosθ[2cos^{2}θ – (sin^{2}θ + cos^{2}θ)]

= sinθ(cos^{2}θ – sin^{2}θ) / cosθ[cos^{2}θ – sin^{2}θ]

= tanθ.

**Question 10****(a)** The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages. [4]

**(b)** The daily wages of 80 workers in a project are given below. [6]

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = ₹ 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate :

(i) the median wage of the workers.

(ii) the lower quartile wage of workers.

(iii) the number of workers who earn more than ₹ 625 daily.

**Answer 10****(a)** Let the age of Vivek be x years And that of Amit be 47 – x years

∴ x (47 – x) = 550

47x – x^{2} = 550

Or x^{2} – 47x + 550 = 0

(x – 25) (x – 22) = 0

∴ x = 25 or x = 22 (not possible)

∴ Vivek’s age is x = 25 years, and Amit’s age is 47 – 25 = 22 years

**(b)** c.f : 2, 8, 20, 38, 62, 75, 80

(For smooth S curve plotted with upper boundaries)

(i) Median =N^{th }/ 2 term = 40^{th} term = ₹ 605

(ii) Q_{1} = Nth / 4 term = 20^{th} term = ₹ 550

(iii) No. of workers who earn more than ₹ 625

= 80 – 52 = 28 (± 3)

**Question 11****(a)** The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number. [4]

**(b)** PQR is a triangle. S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm [3]

(i) Prove ΔPQR ∼ ΔSPR

(ii) Find the length of QR and PS

(iii) area of ΔPQR / area of ΔSPR

**(c)** Mr. Richard has a recurring deposit account in a bank for 3 years at 7.5% p. a. simple interest. If he gets ₹ 8325 as interest at the time of maturity, find : [3]

(i) The monthly deposit

(ii) The maturity value.

**Answer 11****(a)** tan 60° = 60/AD

AD = 60/tan 60° [tan 60° = 3 ]

= 60/√3 = 60 × √3 / 3

= 20 √3

= 20 × 1.732

= 34.640 m

tan 45° = CD/DB ∴ 1 = CD/DB tan 45° = 1

CD = DB = 60 m

∴ AB = AD + DB

= 34.640 + 60

= 94.640 = 95 m

**(b)** (i) In ΔPQR and ΔSPR

∠PSR = ∠QPR

∠ R is common to both

∴ 3rd angle is equal

∴ DPQR ∼ SPR (AAA)

Hence sides are proportional.

(ii) ∴ QR/PR = PQ/PS = PR/SR

QR/6 = 8/PS = 6/3

∴ QR = 6 × 2

QR = 12 cm

PS = 8/2 = 4

∴ PS = 4 cm

(iii) ΔPQR / ΔSPR = 6^{2 }/ 3^{2}

ΔPQR/ΔSPR = 2^{2 }/ 1 = 4/1

**(c)** Let monthly deposit be ₹ x

Qualifying sum = (x)(36)(36 1) / 2

Interest = (x)(36)(37)(7.5) / 2(100)(12)

₹ 8325 = (x)(9)(37) / 80

x = ₹ 2000

Maturity Value = 2000 × 36 + 8325 = ₹ 80,325.