# ICSE Mathematics 2020 Specimen Paper Class-10

**ICSE Mathematics 2020 Specimen** Paper Class-10 . **Specimen Mathematics** **ICSE** Class-10 Paper for 2020. Model **Specimen Paper** for **ICSE** Board Class-10 **Mathematics**. Hence by better practice and Model Sample Paper** ICSE** **Mathematics** **2020 Specimen** is very helpful for ICSE student appearing in 2020 exam of council.

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## ICSE Mathematics 2020 Specimen Paper Class-10

**MATHEMATICS**

**(Two hours and a half)**

Answers to this Paper must be written on the paper 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 all questions from Section A and any four questions from Section B.

All working, including rough work, must be clearly shown and must be done on the same

sheet as the rest of the answer.

Omission of essential working will result in loss of marks.

The intended marks for questions or parts of questions are given in brackets [ ].

Mathematical tables are provided.

**SECTION A (40 Marks)**

**Attempt all questions from this Section.**

#### Question 1

(a) Find the value of ‘k’ if 4?³− 2?² + ?? + 5 leaves remainder -10 when divided by 2? + 1. [3]
(b) Amit deposits ` 1600 per month in a bank for 18 months in a recurring deposit account. If he gets ` 31,080 at the time of maturity, what is the rate of interest per annum? [3]
(c) A shopkeeper bought an article with market price ₹ 1200 from the wholesaler at a discount of 10%. The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is 6%, then find:

(i) GST paid by the wholesaler.

(ii) Amount paid by the customer to buy the item.

#### Question 2

(a) Solve the following in equation and represent your solution on the real number

line:

(b) Find the 16th term of the A.P. 7, 11, 15, 19…. Find the sum of the first 6 terms. [3]
(c) In the given figure CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If ∠ABC = 93 and ∠DCE = 35

Find:

(i) ∠ADC

(ii) ∠CAD

(ii) ∠ACD [4]

#### Question 3

(a) Prove the following identity

#### Question 4

(a) A box consists of 4 red, 5 black and 6 white balls. One ball is drawn out at random. Find the probability that the ball drawn is:

(i) black

(ii) red or white [3]
(b) Calculate the median and mode for the following distribution:

(c) A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid

spheres each of radius 3.5 cm. Find the number of spheres formed. [4]

**SECTION B (40 Marks)**

**Attempt any four questions from this Section**

#### Question 5

(a) The 2nd and 45th term of an arithmetic progression are 10 and 96 respectively.

Find the first term and the common difference and hence find the sum of the first 15 terms. [3]

(c) With the help of a graph paper, taking 1cm=1unit along both x and y axis:

(i) Plot points A (0, 3), B (2, 3), C (3, 0), D (2, -3), E (0, -3)

(ii) Reflect points B, C and D on the y axis and name them as B’, C’ and D’ respectively.

(iii) Write the co-ordinates of B’, C’ and D’.

(iv) Write the equation of line B’ D’.

(v) Name the figure BCDD’C’B’B [4]

#### Question 6

(a) In ∆ ABC and ∆EDC, AB is parallel to ED. BD = 1/3BC and AB = 12.3 cm.

(i) Prove that ∆ABC ~∆EDC.

(ii) Find DE

(iii) Find: ???? ?? ∆???/???? ?? ∆??? [3]

(b) Find the ratio in which the line joining (-2, 5) and (-5, -6) is divided by the line y = -3. Hence find the point of intersection. [3]
(c) The given solid figure is a cylinder surmounted by a cone. The diameter of the base of the cylinder is 6 cm. The height of the cone is 4 cm and the total height of the solid is 25 cm. Take π = 22/7 .

Find the:

(i) Volume of the solid

(ii) Curved surface area of the solid

Give your answers correct to the nearest whole number. [4]

#### Question 7

(a) In the given figure, PAB is a secant and PT a tangent to the circle with centre O. If ∠ATP = 40, PA = 9 cm and AB = 7 cm.

Find:

(i) ∠APT

(ii) length of PT [3]
(b) The 1st and the 8th term of a GP are 4 and 512 respectively. Find:

(i) the common ratio

(ii) the sum of its first 5 terms. [3]
(c) The mean of the following distribution is 49. Find the missing frequency ‘a’.

#### Question 8

(a) Prove the following identity

(sinA + cosecA)2 + (cosA + secA)² = 5 + sec²A . cosec²A

(b) Find the equation of the perpendicular bisector of line segment joining A(4, 2) and B(-3, -5) [3]
(c) Using properties of proportion, find x : y if

#### Question 9

(a) The difference of the squares of two natural numbers is 84. The square of the

larger number is 25 times the smaller number. Find the numbers. [4]
(b) The following table shows the distribution of marks in Mathematics:

With the help of a graph paper, taking 2 cm = 10 units along one axis and 2 cm = 20 units along the other axis, plot an ogive for the above distribution and use it to find the:

(i) median.

(ii) number of students who scored distinction marks (75% and above)

(iii) number of students, who passed the examination if pass marks is 35%. [6]

#### Question 10

(a) Prove that two tangents drawn from an external point to a circle are of equal length. [3] (b)

From the given figure find the:

(i) Coordinates of points P, Q, R.

(ii) Equation of the line through P and parallel to QR. [3]
(c) Ms. Roy went to a departmental store and bought the following items. The GST rates and the quantity of each items and market price of each are given below:

Find the:

(i) The total amount of SGST paid.

(ii) The total amount of the bill.

#### Question 11

(a) Mr. Sharma receives an annual income of ` 900 in buying ` 50 shares selling at ` 80. If the dividend declared is 20%, find the:

(i) Amount invested by Mr. Sharma.

(ii) Percentage return on his investment. [3]
(b) Two poles AB and PQ are standing opposite each other on either side of a road 200 m wide. From a point R between them on the road, the angles of elevation of the top of the poles AB and PQ are 45° and 40°

respectively. If height of AB = 80 m, find the height of PQ correct to the nearest metre. [3]
(c) Construct a triangle PQR, given RQ = 10 cm, ∠PRQ = 75 and base RP = 8 cm.

Find by construction:

(i) The locus of points which are equidistant from QR and QP.

(ii) The locus of points which are equidistant from P and Q.

(iii) Mark the point O which satisfies conditions (i) and (ii). [4]

**ICSE Specimen Sample Paper for Class-10 Exam of Council**

**–: Also Try :–**

**Previous Year Solved Question Paper for ICSE Board**

**Mathematics for ICSE Class 10th (All Publication)**

**Physics for ICSE Class 10th (All Publication) **

**Chemistry for ICSE Class 10th (All Publication) **

**Biology for ICSE Class 10th (All Publication) **