**Specimen ICSE Mathematics 2019 Class-10** . Sample **Specimen** **Mathematics** **ICSE** Class-10 **Paper** for **2019**. Model **Sample Paper** for **ICSE** Board Class-10 **Mathematics**. Hence by better practice and **Sample Paper ICSE** **Mathematics** 2019 is very helpful for ICSE student appearing in 2020 exam of council.

## Specimen ICSE Mathematics 2019 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 a and b if x-1 and x -2 are factors of x³-ax+b

(b) In the figure given below, ABCD is a parallelogram. E is a point on AB.CE intersects the diagonal BD at G and EF is parallel to BC.

If AE : EB = 1 : 2 find

(i) EF : AD

(ii) area of triangle BEF : area of triangle ABD [3]

(c) On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs 16.

Find the sum lent out, if the rate of interest in both cases is 8 % . [4]

#### Question 2

(a) Plot the points A(9,6) and B(5,9) on the graph paper. These two points are

the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6.

Complete the figure on the graph. Write down the geometrical name of

the figure. [3]

(b) In the diagram given below EDC. The tangent drawn to the circle at C makes an angle of 50° with AB produced. Find the measure of ∠ACB. [3]

(c) PQRS is a square piece of land of side 56 m. Two semicircular grass covered lawns are made on two of its opposite sides as shown in the figure.

Calculate the area of the uncovered portion. [4]

#### Question 3

#### Question 4

### SECTION B (40 Marks)

**Attempt any four questions from this Section**

#### Question 5

(b) In the diagram given below if AF = 21 cm, CE = 30 cm and FB = 7 cm.

Find the volume of the figure. [3]

(c) A man bought 200 shares each of face value Rs.10 at Rs. 12 per share. At the end of the year, the company from which he bought the shares declares a dividend of 15%. Calculate:

(i) the amount of money invested by the man

(ii) the amount of dividend he received

(iii) the percentage return on his outlay.

#### Question 6

(a) Solve the following quadratic equation for x and give your answer correct

to three significant figures:

2x²-4x-3=0 [3]

(b) An integer is chosen at random from 1 to 50. Find the probability that the

number is:

(i) divisible by 5

(ii) a perfect cube

(iii) a prime number

(c) Find x from the following equation using properties of proportion:

#### Question 7

(a) Bosco wishes to start a 200 m² rectangular vegetable garden. Since he has only 50 m barbed wire, he fences three sides of the rectangular garden letting his house compound wall act as the fourth side of the fence. Find the dimensions of the garden. [3]

(b) Construct a triangle ABC, with AB = 6 cm, BC = 7 cm and ABC = 60 .

Locate by construction the point P such that

(i) P is equidistant from B and C.

(ii) P is equidistant from AB and BC

(iii) Measure and record the length of PA. [3]

(c) A retailer buys a TV from a wholesaler for Rs 40000. He marks the price of the T.V. 15% above his cost price and sells it to a consumer at 5% discount on the marked price. If the sales are intra-state and the rate of GST is 12%, find:

(i) the marked price of the TV.

(ii) the amount which the consumer pays for the TV.

(in) the amount of tax (under GST) paid by the retailer to the Central Government.

(iv) the amount of tax (under GST) received by the State Government.

#### Question 8

(c) Prove that A(2, 1), B(0,3) and C(-2,1) are the three vertices of an isosceles right angled triangle. Hence find the coordinates of a point D, if ABCD is a square. [4]

#### Question 9

(a) A fair dice is rolled. Find the probability of getting

(i) 3 on the face of the dice

(ii) an odd number on the face of the dice

(iii) a number greater than 1 on the face of the dice. [3]

(b) A (4,2), B(6,8) and C (8,4) are the vertices of a triangle ABC. Write down the equation of the median of the triangle through A. [3]

(c) The angle of elevation of an aeroplane from a point P on the ground is 60° After 12 seconds from the same point P, the angle of elevation of the same

plane changes to 30°. If the plane is flying horizontally at a speed of

600 √3 km / h, find the height at which the plane is flying. [4]

#### Question 10

(a) The following table shows the distribution of the heights of a group of

students:

The following table shows the distribution of the heights of a group of a factory workers.

(i) Determine the cumulative frequencies.

(ii) Draw the cumulative frequency curve on a graph paper.

Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.

(iii) From your graph, write down the median height in cm. [6]

(b) The manufacturer sold a TV to a wholesaler for Rs.7000. The wholesaler

sold it to a trader at a profit of Rs.1000. If the trader sold it to the customer

at a profit of Rs.1500, find:

(i) the total VAT (value added tax) collected by the state

government at the rate of 5% .

(ii) the amount that the customer pays for the TV. [4]

#### Question 11

The equation of the line PQ is 3y – 3x + 7 = 0

(i) Write down the slope of the line PQ.

(ii) Calculate the angle that the line PQ makes with the positive direction of x-axis.

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