ICSE 10th Maths question paper - 2018 by Prasenjit Dutta | Practice Test to Test Your Knowledge
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ICSE 10th Maths question paper - 2018

ICSE 10th Maths question paper - 2018

This mock test includes actual ICSE Class 10 Maths board exam questions from the year 2018, helping students understand exam trends and practice real paper format

2025-08-19
Prasenjit Dutta Prasenjit Dutta
ICSE Class 10 Mathematics 2018 Grade 10

Duration

50 min

Questions

50

Marking

Negative

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Questions Preview

Find the values of 'x' and 'y' from the matrix equation: 2[x 7; 9 y-5]+[6 -7; 4 5]=[10 7; 22 15]

A
x = 4, y = 10
B
x = 2, y = 10
C
x = 2, y = 5
D
x = 4, y = 5

Sonia had a recurring deposit account in a bank and deposited ₹600 per month for 2½ years. If the rate of interest was 10% p.a., find the maturity value of this account.

A
₹20,000
B
₹18,500
C
₹20,325
D
₹18,825

Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random. What is the probability of getting a card which is a multiple of 6?

A
1/5
B
3/10
C
1/2
D
0

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the radius of the cylinder and its volume. (use π=22/7)

A
Radius = 21 cm, Volume = 34650 cm³
B
Radius = 14 cm, Volume = 15400 cm³
C
Radius = 42 cm, Volume = 138600 cm³
D
Radius = 21 cm, Volume = 11550 cm³

If (k-3), (2k+1) and (4k+3) are three consecutive terms of an A.P., find the value of k.

A
k = 1
B
k = -1
C
k = 2
D
k = 0

PQRS is a cyclic quadrilateral. Given ∠QPS=73°, ∠PQS=55° and ∠PSR=82°. Calculate ∠RQS and ∠PRQ.

A
∠RQS = 30°, ∠PRQ = 52°
B
∠RQS = 52°, ∠PRQ = 30°
C
∠RQS = 35°, ∠PRQ = 55°
D
∠RQS = 40°, ∠PRQ = 50°

If (x+2) and (x+3) are factors of x³+ax+b, find the values of 'a' and 'b'.

A
a = -19, b = 30
B
a = 19, b = -30
C
a = -19, b = -30
D
a = 19, b = 30

Prove that √sec²θ+cosec²θ=tanθ+cotθ. The expression on the left simplifies to which of the following?

A
sinθ + cosθ
B
secθ + cosecθ
C
tanθ + cotθ
D
sinθ cosθ

Using a graph paper, draw a histogram for the given distribution showing the number of runs scored by 50 batsmen and estimate the mode of the data. (Based on typical graphical representation)

A
Approximately 5500
B
Approximately 4500
C
Approximately 6500
D
Approximately 7500

Solve the following inequation, write down the solution set and represent it on the real number line: -2+10x ≤ 13x + 10 < 24+10x, x ∈ Z

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

If the straight lines 3x-5y=7 and 4x+ay+9=0 are perpendicular to one another, find the value of a.

A
a = -12/5
B
a = 12/5
C
a = 5/12
D
a = -5/12

Solve x²+7x=7 and give your answer correct to two decimal places.

A
x = 0.89 and x = -7.89
B
x = 0.82 and x = -7.82
C
x = 1.00 and x = -8.00
D
x = 0.95 and x = -7.95

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.

A
First term = 4, Common ratio = 2
B
First term = 2, Common ratio = 2
C
First term = 2, Common ratio = 4
D
First term = 1, Common ratio = 2

A man invests ₹22,500 in ₹50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate the number of shares purchased and the annual dividend received.

A
Number of shares = 450, Annual dividend = ₹2700
B
Number of shares = 500, Annual dividend = ₹3000
C
Number of shares = 450, Annual dividend = ₹3000
D
Number of shares = 500, Annual dividend = ₹2700

A(2,2), B(2,-2), C(0,-1) and D(0,1) are the vertices of a quadrilateral ABCD. If quadrilateral ABCD is reflected on the y-axis to form A'B'CD, what are the coordinates of A' and B'?

A
A'(-2,-2) and B'(-2,2)
B
A'(2, -2) and B'(2, 2)
C
A'(-2,2) and B'(-2,-2)
D
A'(2,2) and B'(2,-2)

Using properties of proportion, solve for x. Given that x is positive: (2x+√(4x²-1))/(2x-√(4x²-1))=4

A
x = 4/5
B
x = 5/8
C
x = 5/4
D
x = 3/4

Given A=[2 3; 5 7], B=[0 4; -1 7] and C=[1 0; -1 4], find AC+B²-10C.

A
[-15 40; 1 33]
B
[15 40; 1 33]
C
[-5 40; -9 73]
D
[-15 -40; -1 33]

Prove that (1+cot θ-cosecθ)(1+tanθ+secθ)=2. The expression on the left simplifies to which of the following?

A
0
B
1
C
2
D
sinθ

Find the value of k for which the following equation has equal roots: x²+4kx+(k²-k+2)=0

A
k = 1 or k = 2
B
k = 2/3 or k = -1
C
k = -2/3 or k = 1
D
k = 1/2 or k = -1/2

On a map drawn to a scale of 1:50,000, a rectangular plot of land ABCD has dimensions AB=6cm and BC=8cm. Find the actual length of the diagonal distance AC of the plot in km and the actual area of the plot in sq km.

A
Actual length = 5 km, Actual area = 12 sq km
B
Actual length = 5 km, Actual area = 16 sq km
C
Actual length = 6 km, Actual area = 12 sq km
D
Actual length = 6 km, Actual area = 16 sq km

A(2,5), B(-1,2) and C(5,8) are the vertices of a triangle ABC, 'M' is a point on AB such that AM:MB=1:2. Find the co-ordinates of 'M' and the equation of the line passing through the points C and M.

A
M(1,4) and equation y = x + 3
B
M(1,4) and equation y = x - 3
C
M(1,4) and equation y = 2x + 2
D
M(0,3) and equation y = x + 3

₹7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received ₹100 more. Find the original number of children.

A
30
B
40
C
50
D
60

If the mean of the following distribution is 24, find the value of 'a'.

A
a = 5
B
a = 8
C
a = 10
D
a = 12

Priyanka has a recurring deposit account of ₹1000 per month at 10% per annum. If she gets ₹5550 as interest at the time of maturity, find the total time for which the account was held.

A
2 years
B
3 years
C
4 years
D
5 years

In ΔPQR, MN is parallel to QR and PM/MQ=2/3. Find the ratio of the area of ΔOMN to the area of ΔORQ.

A
4:9
B
2:3
C
4:25
D
2:5

A solid consists of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 cm. The height of the cylinder and cone are each 4 cm. Find the total volume of the solid. (use π=22/7)

A
1540 cm³
B
1232 cm³
C
1024 cm³
D
1760 cm³

Use the Remainder theorem to factorize the polynomial: 2x³+3x²-9x-10.

A
(2x-5)(x-1)(x+2)
B
(2x+5)(x+1)(x-2)
C
(2x-5)(x+1)(x-2)
D
(2x+5)(x-1)(x-2)

The angle of elevation from a point P of the top of a tower QR, 50m high is 60° and that of the tower PT from a point Q is 30° Find the height of the tower PT, correct to the nearest metre.

A
17 m
B
20 m
C
25 m
D
15 m

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

If (7m+2n)/(7m-2n)=5/3, use properties of proportion to find m:n.

A
m:n = 4:7
B
m:n = 7:4
C
m:n = 2:3
D
m:n = 3:2

Find the equation of the line passing through the centroid G of the triangle with vertices A(-1,3), B(4,2), C(3,-2) and parallel to AC.

A
y = -5x/4 + 7/4
B
y = x - 2
C
y = 5x/4 - 3/4
D
y = -x + 2

Prove that (sinθ-2sin³θ)/(2cos³θ-cosθ)=tanθ. The expression on the left simplifies to which of the following?

A
cotθ
B
sinθ
C
tanθ
D
cosθ

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.

A
Vivek's age = 22, Amit's age = 25
B
Vivek's age = 25, Amit's age = 22
C
Vivek's age = 20, Amit's age = 27
D
Vivek's age = 27, Amit's age = 20

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.

A
95 m
B
100 m
C
105 m
D
110 m

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. Find the length of QR.

A
8 cm
B
10 cm
C
12 cm
D
16 cm

Find the value of 'x' for which x²+6x-10 = 0 and give your answer correct to two significant figures.

A
x = 1.4 or x = -7.4
B
x = 1.2 or x = -7.2
C
x = 1.0 or x = -7.0
D
x = 1.3 or x = -7.3