ICSE 10th Maths question paper - 2019 by Prasenjit Dutta | Practice Test to Test Your Knowledge
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ICSE 10th Maths question paper - 2019

ICSE 10th Maths question paper - 2019

This mock test includes actual ICSE Class 10 Maths board exam questions from the year 2019, helping students understand exam trends and practice real paper format

2025-08-19
Prasenjit Dutta Prasenjit Dutta
ICSE Class 10 Mathematics 2019 Grade 10

Duration

50 min

Questions

50

Marking

Negative

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Questions Preview

Solve the following inequation: 11x-4<15x+4≤13x+14, x ∈ W. Represent the solution on a real number line.

A
{0, 1, 2, 3, 4, 5}
B
{-2, -1, 0, 1, 2}
C
{-2, -1, 0, 1, 2, 3}
D
{-1, 0, 1, 2, 3}

A man invests ₹4500 in shares of a company which is paying 7.5% dividend. If ₹100 shares are available at a discount of 10%. Find the number of shares he purchases and his annual income.

A
Number of shares = 50, Annual income = ₹375
B
Number of shares = 45, Annual income = ₹337.5
C
Number of shares = 50, Annual income = ₹337.5
D
Number of shares = 45, Annual income = ₹375

In a class of 40 students, marks obtained by the students in a class test are given. Calculate the median and mode for the distribution. The data is as follows: Marks (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), Number of students (1, 2, 3, 3, 6, 10, 5, 4, 3, 3).

A
Median = 5, Mode = 6
B
Median = 6, Mode = 6
C
Median = 6, Mode = 5
D
Median = 5.5, Mode = 6

Prove that (cosecθ - sinθ)(secθ - cosθ)(tanθ + cotθ) = 1. Which of the following is the correct simplified expression?

A
sinθ cosθ
B
1
C
sinθ + cosθ
D
0

In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find the first term, common difference, and the sum of the first 20 terms.

A
First term = -1, common difference = 3, sum = 550
B
First term = 1, common difference = 3, sum = 580
C
First term = -1, common difference = 3, sum = 580
D
First term = 1, common difference = 2, sum = 420

Using the factor theorem, show that (x-2) is a factor of x³+x²-4x-4. Hence factorise the polynomial completely.

A
(x-2)(x+1)(x-2)
B
(x-2)(x+2)(x+1)
C
(x-2)(x-1)(x-2)
D
(x-2)(x+2)(x-1)

Simplify: sinA[sinA -cosA; cosA sinA] + cosA[cosA sinA; -sinA cosA]

A
[1 0; 0 1]
B
[sinA+cosA 0; 0 sinA+cosA]
C
[sinA -cosA; cosA sinA]
D
[0 1; 1 0]

M and N are two points on the X and Y axis respectively. P(3,2) divides the line segment MN in the ratio 2:3. Find the coordinates of M and N and the slope of the line MN.

A
M(7.5, 0), N(0, 5) and slope is -2/3
B
M(5, 0), N(0, 2.5) and slope is -1/2
C
M(7.5, 0), N(0, 5) and slope is -2/5
D
M(5, 0), N(0, 2.5) and slope is -1/2

A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the radius of the cylinder and its curved surface area.

A
Radius = 2 cm, Curved Surface Area = 401.92 cm²
B
Radius = 3 cm, Curved Surface Area = 602.88 cm²
C
Radius = 3 cm, Curved Surface Area = 401.92 cm²
D
Radius = 2 cm, Curved Surface Area = 602.88 cm²

The numbers K+3, K+2, 3K-7 and 2K-3 are in proportion. Find K.

A
K = 3
B
K = 5
C
K = 2
D
K = 4

Solve for x the quadratic equation x²-4x-8=0. Give your answer correct to three significant figures.

A
x = 5.46 or x = -1.46
B
x = 4.83 or x = -2.83
C
x = 5.24 or x = -1.24
D
x = 4.53 or x = -1.53

There are 25 discs numbered 1 to 25. A disc is drawn at random from the box. What is the probability that the number on the disc is an odd number, divisible by 2 and 3 both, and a number less than 16?

A
1/2, 1/12, 3/5
B
13/25, 2/25, 3/5
C
13/25, 4/25, 15/25
D
1/2, 1/12, 1/2

Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives ₹441 as interest at the time of maturity. Find the amount Rekha deposited each month.

A
₹200
B
₹220
C
₹240
D
₹250

In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC//AE. If ∠BAC=50° find ∠ACB, ∠EDC and ∠BEC. Hence prove that BE is also a diameter.

A
∠ACB = 40°, ∠EDC = 130°, ∠BEC = 40°
B
∠ACB = 50°, ∠EDC = 120°, ∠BEC = 50°
C
∠ACB = 40°, ∠EDC = 120°, ∠BEC = 40°
D
∠ACB = 50°, ∠EDC = 130°, ∠BEC = 50°

The first and last term of a Geometrical Progression (G.P.) are 3 and 96 respectively. If the common ratio is 2, find 'n' the number of terms and the sum of the n terms.

A
n=5, sum=100
B
n=6, sum=189
C
n=6, sum=120
D
n=5, sum=99

A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid. The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm. Give your answer correct to the nearest whole number.

A
85 cm³
B
95 cm³
C
100 cm³
D
110 cm³

In the given figure, AC is a tangent to the circle with centre O. If ∠ADB=55°, find x and y. Give reasons for your answers. (This question requires a diagram to be solved. We will provide a text-based description of the solution.)

A
x = 35°, y = 70°
B
x = 45°, y = 80°
C
x = 55°, y = 70°
D
x = 35°, y = 55°

The model of a building is constructed with the scale factor 1:30. If the height of the model is 80 cm, find the actual height of the building in meters. If the actual volume of a tank at the top of the building is 27 m³, find the volume of the tank on the top of the model.

A
Actual height = 24 m, Model volume = 1000 cm³
B
Actual height = 2.4 m, Model volume = 1000 cm³
C
Actual height = 24 m, Model volume = 2700 cm³
D
Actual height = 2.4 m, Model volume = 2700 cm³

Given [4 2; -1 1]M = 6I, where M is a matrix and I is unit matrix of order 2x2. Find the order of matrix M and the matrix M itself.

A
Order 2x2, M = [2 4; -1 4]
B
Order 2x2, M = [1 1; 2 4]
C
Order 2x2, M = [1 -2; 1 4]
D
Order 2x2, M = [1 2; 1 -4]

The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.

A
First term = 2 or 24, Common difference = 12 or -12
B
First term = 4 or 22, Common difference = 10 or -10
C
First term = 2 or 22, Common difference = 12 or -10
D
First term = 4 or 22, Common difference = 12 or -10

The vertices of a ΔABC are A(3,8), B(-1,2) and C(6,-6). Find the slope of BC and the equation of a line perpendicular to BC and passing through A.

A
Slope = -8/7, Equation y - 8 = 7/8(x - 3)
B
Slope = 8/7, Equation y - 8 = -7/8(x - 3)
C
Slope = 8/7, Equation y - 8 = 7/8(x - 3)
D
Slope = -8/7, Equation y - 8 = -7/8(x - 3)

The data on the number of patients attending a hospital in a month are given. Find the average (mean) number of patients by using the shortcut method. Assume the mean as 45. The data is as follows: Number of patients (10-20, 20-30, 30-40, 40-50, 50-60, 60-70), Number of Days (5, 2, 7, 9, 2, 5).

A
38.21
B
42.50
C
45.00
D
39.29

Using properties of proportion solve for x, given (√5x+√2x-6) / (√5x-√2x-6) = 4.

A
x = 4
B
x = 3
C
x = 2
D
x = 1

Sachin invests ₹8500 in 10%, ₹100 shares at ₹170. He sells the shares when the price of each share rises by ₹30. He invests the proceeds in 12% ₹100 shares at ₹125. Find the sale proceeds, the number of ₹125 shares he buys, and the change in his annual income.

A
Sale proceeds = ₹10000, Number of shares = 80, Change in income = ₹-200
B
Sale proceeds = ₹10000, Number of shares = 80, Change in income = ₹200
C
Sale proceeds = ₹9000, Number of shares = 72, Change in income = ₹100
D
Sale proceeds = ₹9000, Number of shares = 72, Change in income = ₹-100

A man observes the angle of elevation of the top of the tower to be 45°. He walks towards it in a horizontal line through its base. On covering 20 m the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.

A
47 m
B
50 m
C
55 m
D
60 m

Using the Remainder Theorem find the remainders obtained when x³+(kx+8)x+k is divided by x+1 and x-2. Hence find k if the sum of the two remainders is 1.

A
k = 1
B
k = -1
C
k = -2
D
k = 2

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

A
27 and 30
B
24 and 27
C
30 and 33
D
21 and 24

In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC//AE. If ∠BAC=50° find ∠ACB, ∠EDC and ∠BEC. Hence prove that BE is also a diameter.

A
∠ACB = 40°, ∠EDC = 130°, ∠BEC = 40°
B
∠ACB = 50°, ∠EDC = 120°, ∠BEC = 50°
C
∠ACB = 40°, ∠EDC = 120°, ∠BEC = 40°
D
∠ACB = 50°, ∠EDC = 130°, ∠BEC = 50°

The 4th term of an A.P. is 22 and the 15th term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms.

A
First term = 10, common difference = 4, sum = 192
B
First term = 4, common difference = 10, sum = 192
C
First term = 10, common difference = 4, sum = 176
D
First term = 4, common difference = 10, sum = 176

If b is the mean proportion between a and c, show that (a⁴+a²b²+b⁴)/(b⁴+b²c²+c⁴)=a²/c²

A
The proof is not possible
B
The proof is correct as the left side simplifies to a²/c²
C
The proof is correct as the left side simplifies to 1
D
The proof is correct as the left side simplifies to b²

Solve the equation 4x²-5x-3=0 and give your answer correct to two decimal places.

A
x = 1.69 and x = -0.44
B
x = 1.76 and x = -0.51
C
x = 1.50 and x = -0.50
D
x = 1.25 and x = -0.25

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.

A
17 cm
B
15 cm
C
20 cm
D
10 cm

Evaluate without using trigonometric tables: sin²28°+sin²62°+tan²38°-cot²52°+(1/4)sec²30°

A
2
B
4/3
C
5/3
D
1

Jaya borrowed Rs. 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.

A
Rs. 22,000
B
Rs. 22,500
C
Rs. 23,000
D
Rs. 24,000

The catalogue price of a computer set is Rs. 42,000. 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 the total price to be paid by the customer for the computer set.

A
Rs. 38,154
B
Rs. 37,288
C
Rs. 36,000
D
Rs. 38,154.60

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.

A
(-3, 4)
B
(3, -4)
C
(-2, 4)
D
(2, -4)

The marks of 10 students of a class in an examination arranged in ascending order is as follows: 13, 35, 43, x, x+4, 55, 61, 71, 80. If the median marks is 48, find the value of x.

A
46
B
44
C
42
D
40

What must be subtracted from 16x³-8x²+4x+7 so that the resulting expression has 2x+1 as a factor?

A
4
B
2
C
-1
D
5

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.

A
10.7 cm²
B
10.0 cm²
C
11.0 cm²
D
11.2 cm²

Solve the following inequation and represent the solution set on a number line. -8½ < -½-4x ≤ 7½,x∈I

A
The solution set is { -1, 0, 1, 2, ... }
B
The solution set is { -2, -1, 0, 1, ... }
C
The solution set is { 2, 3, 4, ... }
D
The solution set is { -2, -1, 0, 1, 2}

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

A
Investment = Rs. 2700, Yield = 8%
B
Investment = Rs. 2700, Yield = 9%
C
Investment = Rs. 3000, Yield = 8%
D
Investment = Rs. 3000, Yield = 9%

Sixteen cards are labeled 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 a vowel?

A
5/16
B
3/16
C
1/4
D
1/2

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.

A
Height = 32 m, Curved Surface Area = 704 m²
B
Height = 32 m, Curved Surface Area = 700 m²
C
Height = 24 m, Curved Surface Area = 704 m²
D
Height = 24 m, Curved Surface Area = 700 m²

The marks obtained by 120 students in an English test are given below. Draw the ogive and hence, estimate the median marks, the number of students who did not pass the test if the pass percentage was 50, and the upper quartile marks. Data is as follows: Marks (0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100), No. of students (5, 9, 16, 22, 26, 18, 11, 6, 4, 3).

A
Median = 46.5, Students not passed = 44, Upper Quartile = 60
B
Median = 47.5, Students not passed = 45, Upper Quartile = 62
C
Median = 45, Students not passed = 44, Upper Quartile = 60
D
Median = 46.5, Students not passed = 45, Upper Quartile = 62

A man observes the angle of elevation of the top of the tower to be 45°. He walks towards it in a horizontal line through its base. On covering 20 m the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.

A
27.3 m
B
27 m
C
47 m
D
50 m

Using the Remainder Theorem, find the remainders obtained when x³ + (kx+8)x + k is divided by x+1 and x-2. Hence find k if the sum of the two remainders is 1.

A
k = -2
B
k = 2
C
k = -1
D
k = 1

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

A
24 and 27
B
27 and 30
C
30 and 33
D
21 and 24

A man deposits Rs 900 per month in a recurring deposit account for a period of 5 years. If he gets Rs 5415 as interest at the time of maturity, find the rate of interest per annum.

A
6%
B
8%
C
10%
D
12%

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.

A
10.7 cm²
B
10.0 cm²
C
11.0 cm²
D
11.2 cm²

Given that the polynomial x³ + (k-2)x² + 4x + 6 is exactly divisible by x-2. Find the value of k and hence factorize the polynomial completely.

A
k= -11, (x-2)(x+3)(x-1)
B
k= -11, (x-2)(x-3)(x+1)
C
k= 1, (x-2)(x+3)(x-1)
D
k= 11, (x-2)(x-3)(x+1)