Math for Grade 10 (Quick Topics) | Math Practice, Tests, Worksheets, Quizzes, Assignments

Real Numbers

Sample Question

3 + 10√3 is __________ number

A. a natural

B. a rational

C. an irrational

D. a whole

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Polynomials

Sample Question

If ^@\alpha^@ and ^@\beta^@ are the zeros of quadratic polynomial ^@x^2 + x-3^@, find the value of ^@\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }^@.

A.
^@\dfrac { 7 } { 27 } ^@

B.
^@\dfrac { 13 } { 27 } ^@

C.
^@\dfrac { 1 } { 3 } ^@

D.
^@\dfrac { 10 } { 27 } ^@

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Linear Equations in Two Variables

Sample Question

The sum of two number is 44 and their difference is 12. Find the numbers.

A. 28 and 17

B. 28 and 16

C. 29 and 17

D. 29 and 16

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Quadratic Equations

Sample Question

Find roots of quadratic equation ^@y^2 - 4 \sqrt{ 3}y - 15 = 0^@ = 0.

A.
^@-5 \sqrt{ 3} \space and \space 1 ^@

B.
^@5 \space and \space -\sqrt{ 3}^@

C.
^@ 5 \sqrt{ 3} \space and \space -\sqrt{ 3} ^@

D.
^@ -6 \sqrt{ 3} \space and \space 2 \sqrt{ 3} ^@

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Arithmetic Progressions

Sample Question

What are the values of ^@ g ^@ and ^@ h ^@ such that the numbers ^@ g, 20, 59, h ^@ form an AP?

A.
^@ g = -19 ^@ and ^@ h = 99 ^@

B.
^@ g = -18 ^@ and ^@ h = 98 ^@

C.
^@ g = -19 ^@ and ^@ h = 97 ^@

D.
^@ g = -19 ^@ and ^@ h = 98 ^@

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Triangles

Sample Question

In the given figure, ^@ DE \parallel BC^@, ^@AD = 5 \space cm^@, ^@DB = 20 \space cm^@, ^@AE = 6.5\space cm^@ and ^@DE = 2 \space cm^@. What is the ^@AC ^@ and ^@BC^@ ?

A.
^@ 32.5 \space cm \space \text{and} \space 12 \space cm ^@

B.
^@ 32.5 \space cm \space \text{and} \space 10 \space cm ^@

C.
^@ 33.5 \space cm \space \text{and} \space 10 \space cm ^@

D.
^@ 33.5 \space cm \space \text{and} \space 12 \space cm ^@

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Coordinate Geometry

Sample Question

Find the distance between the points ^@A(-9, 4)^@ and ^@B(-11, 16)^@.

A. 14.16 units

B. 12.16 units

C. 17.16 units

D. 15.66 units

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Circles

Sample Question

In the given figure, AB is the diameter of a circle with center ^@O^@ and ^@AT^@ is a tangent. If ^@\angle AOQ = 65^\circ ^@, find ^@\angle ATQ^@.

A.
^@ 32.5^\circ ^@

B.
^@ 57.5^\circ ^@

C.
^@ 52.5^\circ ^@

D.
^@ \text{ None of these } ^@

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Area related to circles

Sample Question

The given figure is a sector of a circle of radius ^@ 3.5 \space cm ^@. Find the perimeter of the sector. ^@\bigg(^@Take ^@ \pi = \dfrac { 22 }{ 7 }\bigg)^@

A.
^@ 8.83 \space cm ^@

B.
^@ 19.33 \space cm ^@

C.
^@ 28.83 \space cm ^@

D.
^@ \text { None of these } ^@

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Surface Area and Volume

Sample Question

Choose the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

A.
1
3
πr³

B.
1
5
πr³

C. 3πr³

D. None of these

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Statistics

Sample Question

If the mean of the following data is 27.3, find the value of x.
Class interval 0-10 10-20 20-30 30-40 40-50
Frequency 12 x 20 17 27

A. 24

B. 29

C. 20

D. 26

Class interval	0-10	10-20	20-30	30-40	40-50
Frequency	12	x	20	17	27

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Probability

Sample Question

A bag contains 5 red balls, 5 blue balls and 5 green balls. Ella draws 2 balls out of the bag. What is the probability that she gets a green ball and a red ball?

A.
105
27

B.
25
105

C.
105
24

D.
27
105

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Full Year 10th Grade Review

Sample Question

Simplify ^@ \sqrt { \dfrac{ 1 + \sin \theta } { 1 - \sin \theta } } + \sqrt { \dfrac{ 1 - \sin \theta } { 1 + \sin \theta } } ^@

A.
^@ 2 sec\theta ^@

B.
^@ 1 ^@

C.
^@ 2tan\theta ^@

D.
^@ 2 cosec\theta ^@

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Dice and Cubes

Sample Question

Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face F?

A. E

B. B

C. D

D. Cannot be determined

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Venn Diagrams

Sample Question

Which of following shows relation between Fruits, Apple and Grapes.

A.

B.

C.

D.

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Number Series

Sample Question

Find the next term of given sequence ..
23, 24, 28, 37, 53, ....

A. 83

B. 85

C. 78

D. 70

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Alphabet Problems

Sample Question

Which is the odd one out in this set
PN, PD, PX, PU

A. PU

B. PD

C. PN

D. PX

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NTSE_MAT

Sample Question

Which of the following is the next terms in the series given below?
EX, GW, IV, KU, ___

A. NS

B. LS

C. MT

D. LT

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Grade 10 Math

Real Numbers

Sample Question

3 + 10√3 is __________ number

A. a natural

B. a rational

C. an irrational

D. a whole

Polynomials

Sample Question

If ^@\alpha^@ and ^@\beta^@ are the zeros of quadratic polynomial ^@x^2 + x-3^@, find the value of ^@\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }^@.

A.
^@\dfrac { 7 } { 27 } ^@

B.
^@\dfrac { 13 } { 27 } ^@

C.
^@\dfrac { 1 } { 3 } ^@

D.
^@\dfrac { 10 } { 27 } ^@

Linear Equations in Two Variables

Sample Question

The sum of two number is 44 and their difference is 12. Find the numbers.

A. 28 and 17

B. 28 and 16

C. 29 and 17

D. 29 and 16

Quadratic Equations

Sample Question

Find roots of quadratic equation ^@y^2 - 4 \sqrt{ 3}y - 15 = 0^@ = 0.

A.
^@-5 \sqrt{ 3} \space and \space 1 ^@

B.
^@5 \space and \space -\sqrt{ 3}^@

C.
^@ 5 \sqrt{ 3} \space and \space -\sqrt{ 3} ^@

D.
^@ -6 \sqrt{ 3} \space and \space 2 \sqrt{ 3} ^@

Arithmetic Progressions

Sample Question

What are the values of ^@ g ^@ and ^@ h ^@ such that the numbers ^@ g, 20, 59, h ^@ form an AP?

A.
^@ g = -19 ^@ and ^@ h = 99 ^@

B.
^@ g = -18 ^@ and ^@ h = 98 ^@

C.
^@ g = -19 ^@ and ^@ h = 97 ^@

D.
^@ g = -19 ^@ and ^@ h = 98 ^@

Coordinate Geometry

Sample Question

Find the distance between the points ^@A(-9, 4)^@ and ^@B(-11, 16)^@.

A. 14.16 units

B. 12.16 units

C. 17.16 units

D. 15.66 units

Trigonometry and its Applications

Sample Question

tan(45° + θ) - cot(45° - θ) = ?

A. 0

B. 1

C. 2tanθ

D. 2cotθ

Circles

Sample Question

In the given figure, AB is the diameter of a circle with center ^@O^@ and ^@AT^@ is a tangent. If ^@\angle AOQ = 65^\circ ^@, find ^@\angle ATQ^@.

A.
^@ 32.5^\circ ^@

B.
^@ 57.5^\circ ^@

C.
^@ 52.5^\circ ^@

D.
^@ \text{ None of these } ^@

Constructions

Sample Question

A.

B.

C.

D.

Surface Area and Volume

Sample Question

Choose the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

A.
1
3
πr³

B.
1
5
πr³

C. 3πr³

D. None of these

Statistics

Sample Question

If the mean of the following data is 27.3, find the value of x.
Class interval 0-10 10-20 20-30 30-40 40-50
Frequency 12 x 20 17 27

A. 24

B. 29

C. 20

D. 26

Probability

Sample Question

A bag contains 5 red balls, 5 blue balls and 5 green balls. Ella draws 2 balls out of the bag. What is the probability that she gets a green ball and a red ball?

A.
105
27

B.
25
105

C.
105
24

D.
27
105

Full Year 10th Grade Review

Sample Question

Simplify ^@ \sqrt { \dfrac{ 1 + \sin \theta } { 1 - \sin \theta } } + \sqrt { \dfrac{ 1 - \sin \theta } { 1 + \sin \theta } } ^@

A.
^@ 2 sec\theta ^@

B.
^@ 1 ^@

C.
^@ 2tan\theta ^@

D.
^@ 2 cosec\theta ^@

Dice and Cubes

Sample Question

Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face F?

A. E

B. B

C. D

D. Cannot be determined

Venn Diagrams

Sample Question

Which of following shows relation between Fruits, Apple and Grapes.

A.

B.

C.

D.

Number Series

Sample Question

Find the next term of given sequence ..
23, 24, 28, 37, 53, ....

A. 83

B. 85

C. 78

D. 70

Alphabet Problems

Sample Question

Which is the odd one out in this set
PN, PD, PX, PU

A. PU

B. PD

C. PN

D. PX

NTSE_MAT

Sample Question

Which of the following is the next terms in the series given below?
EX, GW, IV, KU, ___

A. NS

B. LS

C. MT

D. LT

A.	^@\dfrac { 7 } { 27 } ^@
B.	^@\dfrac { 13 } { 27 } ^@
C.	^@\dfrac { 1 } { 3 } ^@
D.	^@\dfrac { 10 } { 27 } ^@

A.	^@-5 \sqrt{ 3} \space and \space 1 ^@
B.	^@5 \space and \space -\sqrt{ 3}^@
C.	^@ 5 \sqrt{ 3} \space and \space -\sqrt{ 3} ^@
D.	^@ -6 \sqrt{ 3} \space and \space 2 \sqrt{ 3} ^@

A.	^@ g = -19 ^@ and ^@ h = 99 ^@
B.	^@ g = -18 ^@ and ^@ h = 98 ^@
C.	^@ g = -19 ^@ and ^@ h = 97 ^@
D.	^@ g = -19 ^@ and ^@ h = 98 ^@

A.	^@ 32.5 \space cm \space \text{and} \space 12 \space cm ^@
B.	^@ 32.5 \space cm \space \text{and} \space 10 \space cm ^@
C.	^@ 33.5 \space cm \space \text{and} \space 10 \space cm ^@
D.	^@ 33.5 \space cm \space \text{and} \space 12 \space cm ^@

A.	^@ 32.5^\circ ^@
B.	^@ 57.5^\circ ^@
C.	^@ 52.5^\circ ^@
D.	^@ \text{ None of these } ^@

A.	^@ 8.83 \space cm ^@
B.	^@ 19.33 \space cm ^@
C.	^@ 28.83 \space cm ^@
D.	^@ \text { None of these } ^@

A.	^@ 2 sec\theta ^@
B.	^@ 1 ^@
C.	^@ 2tan\theta ^@
D.	^@ 2 cosec\theta ^@

Grade 10 Math

Real Numbers Sample Question 3 + 10√3 is __________ number A.a natural B.a rational C.an irrational D.a whole

Polynomials Sample Question If ^@\alpha^@ and ^@\beta^@ are the zeros of quadratic polynomial ^@x^2 + x-3^@, find the value of ^@\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }^@. A.^@\dfrac { 7 } { 27 } ^@ B.^@\dfrac { 13 } { 27 } ^@ C.^@\dfrac { 1 } { 3 } ^@ D.^@\dfrac { 10 } { 27 } ^@

Linear Equations in Two Variables Sample Question The sum of two number is 44 and their difference is 12. Find the numbers. A.28 and 17 B.28 and 16 C.29 and 17 D.29 and 16

Quadratic Equations Sample Question Find roots of quadratic equation ^@y^2 - 4 \sqrt{ 3}y - 15 = 0^@ = 0. A.^@-5 \sqrt{ 3} \space and \space 1 ^@ B.^@5 \space and \space -\sqrt{ 3}^@ C.^@ 5 \sqrt{ 3} \space and \space -\sqrt{ 3} ^@ D.^@ -6 \sqrt{ 3} \space and \space 2 \sqrt{ 3} ^@

Arithmetic Progressions Sample Question What are the values of ^@ g ^@ and ^@ h ^@ such that the numbers ^@ g, 20, 59, h ^@ form an AP? A.^@ g = -19 ^@ and ^@ h = 99 ^@ B.^@ g = -18 ^@ and ^@ h = 98 ^@ C.^@ g = -19 ^@ and ^@ h = 97 ^@ D.^@ g = -19 ^@ and ^@ h = 98 ^@

Coordinate Geometry Sample Question Find the distance between the points ^@A(-9, 4)^@ and ^@B(-11, 16)^@. A.14.16 units B.12.16 units C.17.16 units D.15.66 units

Trigonometry and its Applications Sample Question tan(45° + θ) - cot(45° - θ) = ? A.0 B.1 C.2tanθ D.2cotθ

Circles Sample Question In the given figure, AB is the diameter of a circle with center ^@O^@ and ^@AT^@ is a tangent. If ^@\angle AOQ = 65^\circ ^@, find ^@\angle ATQ^@. A O B T Q 65° A.^@ 32.5^\circ ^@ B.^@ 57.5^\circ ^@ C.^@ 52.5^\circ ^@ D.^@ \text{ None of these } ^@

Constructions Sample Question A. B. C. D.

Surface Area and Volume Sample Question Choose the maximum volume of a cone that can be carved out of a solid hemisphere of radius r. A B O r r V A. 13 πr3 B. 15 πr3 C.3πr3 D.None of these

Statistics Sample Question If the mean of the following data is 27.3, find the value of x.Class interval0-1010-2020-3030-4040-50Frequency12x201727 A.24 B.29 C.20 D.26

Probability Sample Question A bag contains 5 red balls, 5 blue balls and 5 green balls. Ella draws 2 balls out of the bag. What is the probability that she gets a green ball and a red ball? A. 10527 B. 25105 C. 10524 D. 27105

Full Year 10th Grade Review Sample Question Simplify ^@ \sqrt { \dfrac{ 1 + \sin \theta } { 1 - \sin \theta } } + \sqrt { \dfrac{ 1 - \sin \theta } { 1 + \sin \theta } } ^@ A. ^@ 2 sec\theta ^@ B. ^@ 1 ^@ C. ^@ 2tan\theta ^@ D. ^@ 2 cosec\theta ^@

Dice and Cubes Sample Question Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face F? A.E B.B C.D D.Cannot be determined

Venn Diagrams Sample Question Which of following shows relation between Fruits, Apple and Grapes. A. B. C. D.

Number Series Sample Question Find the next term of given sequence ..23, 24, 28, 37, 53, .... A.83 B.85 C.78 D.70

Alphabet Problems Sample Question Which is the odd one out in this setPN, PD, PX, PU A.PU B.PD C.PN D.PX

NTSE_MAT Sample Question Which of the following is the next terms in the series given below?EX, GW, IV, KU, ___ A.NS B.LS C.MT D.LT

Real Numbers

Sample Question

3 + 10√3 is __________ number

A. a natural

B. a rational

C. an irrational

D. a whole

Polynomials

Sample Question

If ^@\alpha^@ and ^@\beta^@ are the zeros of quadratic polynomial ^@x^2 + x-3^@, find the value of ^@\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }^@.

A.
^@\dfrac { 7 } { 27 } ^@

B.
^@\dfrac { 13 } { 27 } ^@

C.
^@\dfrac { 1 } { 3 } ^@

D.
^@\dfrac { 10 } { 27 } ^@

Linear Equations in Two Variables

Sample Question

The sum of two number is 44 and their difference is 12. Find the numbers.

A. 28 and 17

B. 28 and 16

C. 29 and 17

D. 29 and 16

Quadratic Equations

Sample Question

Find roots of quadratic equation ^@y^2 - 4 \sqrt{ 3}y - 15 = 0^@ = 0.

A.
^@-5 \sqrt{ 3} \space and \space 1 ^@

B.
^@5 \space and \space -\sqrt{ 3}^@

C.
^@ 5 \sqrt{ 3} \space and \space -\sqrt{ 3} ^@

D.
^@ -6 \sqrt{ 3} \space and \space 2 \sqrt{ 3} ^@

Arithmetic Progressions

Sample Question

What are the values of ^@ g ^@ and ^@ h ^@ such that the numbers ^@ g, 20, 59, h ^@ form an AP?

A.
^@ g = -19 ^@ and ^@ h = 99 ^@

B.
^@ g = -18 ^@ and ^@ h = 98 ^@

C.
^@ g = -19 ^@ and ^@ h = 97 ^@

D.
^@ g = -19 ^@ and ^@ h = 98 ^@

Coordinate Geometry

Sample Question

Find the distance between the points ^@A(-9, 4)^@ and ^@B(-11, 16)^@.

A. 14.16 units

B. 12.16 units

C. 17.16 units

D. 15.66 units

Trigonometry and its Applications

Sample Question

tan(45° + θ) - cot(45° - θ) = ?

A. 0

B. 1

C. 2tanθ

D. 2cotθ

Circles

Sample Question

In the given figure, AB is the diameter of a circle with center ^@O^@ and ^@AT^@ is a tangent. If ^@\angle AOQ = 65^\circ ^@, find ^@\angle ATQ^@.

A.
^@ 32.5^\circ ^@

B.
^@ 57.5^\circ ^@

C.
^@ 52.5^\circ ^@

D.
^@ \text{ None of these } ^@

Constructions

Sample Question

A.

B.

C.

D.

Surface Area and Volume

Sample Question

Choose the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

A.
1
3
πr³

B.
1
5
πr³

C. 3πr³

D. None of these

Statistics

Sample Question

If the mean of the following data is 27.3, find the value of x.
Class interval 0-10 10-20 20-30 30-40 40-50
Frequency 12 x 20 17 27

A. 24

B. 29

C. 20

D. 26

Probability

Sample Question

A bag contains 5 red balls, 5 blue balls and 5 green balls. Ella draws 2 balls out of the bag. What is the probability that she gets a green ball and a red ball?

A.
105
27

B.
25
105

C.
105
24

D.
27
105

Full Year 10th Grade Review

Sample Question

Simplify ^@ \sqrt { \dfrac{ 1 + \sin \theta } { 1 - \sin \theta } } + \sqrt { \dfrac{ 1 - \sin \theta } { 1 + \sin \theta } } ^@

A.
^@ 2 sec\theta ^@

B.
^@ 1 ^@

C.
^@ 2tan\theta ^@

D.
^@ 2 cosec\theta ^@

Dice and Cubes

Sample Question

Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face F?

A. E

B. B

C. D

D. Cannot be determined

Venn Diagrams

Sample Question

Which of following shows relation between Fruits, Apple and Grapes.

A.

B.

C.

D.

Number Series

Sample Question

Find the next term of given sequence ..
23, 24, 28, 37, 53, ....

A. 83

B. 85

C. 78

D. 70

Alphabet Problems

Sample Question

Which is the odd one out in this set
PN, PD, PX, PU

A. PU

B. PD

C. PN

D. PX

NTSE_MAT

Sample Question

Which of the following is the next terms in the series given below?
EX, GW, IV, KU, ___

A. NS

B. LS

C. MT

D. LT