Grade 10 math worksheets, practice and tests

Real Numbers

Sample Question

The number in the form of $8 p + 3$ where $p$ is whole number, is always

A. A perfect square

B. An odd number

C. An even number

D. Divisible by $3$

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Polynomials

Sample Question

If α and β are the zeros of polynomial x² - 11x + k, such that α² + β² = 65. Find the value of k.

A. 35

B. 24

C. 28

D. 21

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Linear Equations in Two Variables

Sample Question

For what value of $k$ , will the following pair of linear equations have infinitely many solutions?
$6 x + 3 y = 9$ and $(k + 9)x + 9 y = 2k + 9$

A. $6$

B. $12$

C. $8$

D. $9$

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Quadratic Equations

Sample Question

The sum of the n consecutive natural numbers starting from 4 is 85. Find the value of n.

A. 11

B. 9

C. 12

D. 10

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Arithmetic Progressions

Sample Question

The 8^th term of an arithmetic progression has the value 0. Which term of the AP is 3 times the 16^th element?

A. 30

B. 31

C. 33

D. 32

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Triangles

Sample Question

In a trapezium $ABCD$ , $O$ is the point of intersection of $AC$ and $BD$ . $AB || CD$ and $AB = 2 \times CD$ . If the area of $\Delta AOB = 52 \space cm^2$ , find the area of $\Delta COD$ .

A.
$14 \space cm^2$

B.
$13 \space cm^2$

C.
$16 \space cm^2$

D.
$15 \space cm^2$

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Coordinate Geometry

Sample Question

The points $A(10,-3)$ , $B(8,-3)$ , $C(9,0)$ , and $D(6,0)$ are the vertices of a parallelogram $ABCD.$ If $AB$ is the base, find the height of the parallelogram.

A.
$53 {\space} \text{units}$

B.
$13 {\space} \text{units}$

C.
$3 {\space} \text{units}$

D. None of these

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Trigonometry and its Applications

Sample Question

In right $\Delta ABC$ , $\angle B$ = $90^o$ , $AB$ = $2$ cm, and $BC$ = $2$ cm. Find $\angle C$ .

A.
$45^\circ$

B.
$90^\circ$

C.
$60^\circ$

D.
$30^\circ$

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Circles

Sample Question

Two concentric circles are of radii $8 \space cm$ and $r \space cm$ $( r > 8 )$ .A chord of the larger circle of length $51 \space cm$ , touches the smaller circle. What is the value of $r$ ?

A.
$53.46 \space cm$

B.
$13.37 \space cm$

C.
$26.73 \space cm$

D.
$\text{ None of these }$

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Area related to circles

Sample Question

The difference between circumference and diameter of a circular plot is $18 \space m$ . Find the area of the circular plot. $\left( \text{Assume } \pi = \dfrac{ 22 }{ 7 } \right)$

A.
$388.08 \space m^2$

B.
$13.2 \space m^2$

C.
$55.44 \space m^2$

D.
$60.48 \space m^2$

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Surface Area and Volume

Sample Question

A capsul is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsul is 26 mm and the diameter of the capsul is 12 mm then choose its correct surface area .

A. 452.57 mm²

B. 980.57 mm²

C. 1433.14 mm²

D. None of these

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Statistics

Sample Question

Find the arithmetic mean for the following data:

$\begin{align} \text { Age (in years) } \end{align}$ $15 - 19$ $20 - 24$ $25 - 29$ $30 - 34$ $35 - 39$ $40 - 44$
$\begin{align} \text { Number of people } \end{align}$ $13$ $11$ $14$ $23$ $21$ $19$

A.
$34.208 \space years$

B.
$26.208 \space years$

C.
$31.208 \space years$

D.
$31.338 \space years$

$\begin{align} \text { Age (in years) } \end{align}$	$15 - 19$	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$	$40 - 44$
$\begin{align} \text { Number of people } \end{align}$	$13$	$11$	$14$	$23$	$21$	$19$

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Probability

Sample Question

What is the probability that an integer in the set 1, 2, 3, ...122 is divisible by 2 and not divisible by 3?

A.
41
122

B.
40
119

C.
44
125

D.
44
119

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Full Year 10th Grade Review

Sample Question

2625 cans are stored in a warehouse in such a manner that there are 203 cans in the bottom row, 199 cans in the second row, 195 cans in the third row, and so on. How many rows of cans are there?

A. 15

B. 17

C. 13

D. 14

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Dice and Cubes

Sample Question

Faces of a cube are marked with 1,2,3,4,5 and 6. Two views of the cube are as shown below, if face 1 is opposite to face 2, what will be there on the top when 6 is at the bottom?

A. 5

B. 3

C. 4

D. Cannot be determined

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Venn Diagrams

Sample Question

Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports.

A. 40

B. 44

C. 41

D. 43

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Number Series

Sample Question

Find the next term of given sequence.
25, 27, 30, 35, 42, 53, 66, ....

A. 86

B. 83

C. 90

D. 76

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Alphabet Problems

Sample Question

Which of the following is the next term in the series:
FZ, JX, NV, RT, ___

A. WQ

B. UR

C. VR

D. UQ

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NTSE_MAT

Sample Question

Find the next term of given sequence ..
11, 25, 47, 77, 115, , ....

A. 161

B. 153

C. 322

D. 168

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Grade 10 Math

Real Numbers

Sample Question

The number in the form of $8 p + 3$ where $p$ is whole number, is always

A. A perfect square

B. An odd number

C. An even number

D. Divisible by $3$

Polynomials

Sample Question

If α and β are the zeros of polynomial x² - 11x + k, such that α² + β² = 65. Find the value of k.

A. 35

B. 24

C. 28

D. 21

Linear Equations in Two Variables

Sample Question

For what value of $k$ , will the following pair of linear equations have infinitely many solutions?
$6 x + 3 y = 9$ and $(k + 9)x + 9 y = 2k + 9$

A. $6$

B. $12$

C. $8$

D. $9$

Quadratic Equations

Sample Question

The sum of the n consecutive natural numbers starting from 4 is 85. Find the value of n.

A. 11

B. 9

C. 12

D. 10

Arithmetic Progressions

Sample Question

The 8^th term of an arithmetic progression has the value 0. Which term of the AP is 3 times the 16^th element?

A. 30

B. 31

C. 33

D. 32

Trigonometry and its Applications

Sample Question

In right $\Delta ABC$ , $\angle B$ = $90^o$ , $AB$ = $2$ cm, and $BC$ = $2$ cm. Find $\angle C$ .

A.
$45^\circ$

B.
$90^\circ$

C.
$60^\circ$

D.
$30^\circ$

Constructions

Sample Question

A.

B.

C.

D.

Probability

Sample Question

What is the probability that an integer in the set 1, 2, 3, ...122 is divisible by 2 and not divisible by 3?

A.
41
122

B.
40
119

C.
44
125

D.
44
119

Full Year 10th Grade Review

Sample Question

2625 cans are stored in a warehouse in such a manner that there are 203 cans in the bottom row, 199 cans in the second row, 195 cans in the third row, and so on. How many rows of cans are there?

A. 15

B. 17

C. 13

D. 14

Dice and Cubes

Sample Question

Faces of a cube are marked with 1,2,3,4,5 and 6. Two views of the cube are as shown below, if face 1 is opposite to face 2, what will be there on the top when 6 is at the bottom?

A. 5

B. 3

C. 4

D. Cannot be determined

Venn Diagrams

Sample Question

Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports.

A. 40

B. 44

C. 41

D. 43

Number Series

Sample Question

Find the next term of given sequence.
25, 27, 30, 35, 42, 53, 66, ....

A. 86

B. 83

C. 90

D. 76

Alphabet Problems

Sample Question

Which of the following is the next term in the series:
FZ, JX, NV, RT, ___

A. WQ

B. UR

C. VR

D. UQ

NTSE_MAT

Sample Question

Find the next term of given sequence ..
11, 25, 47, 77, 115, , ....

A. 161

B. 153

C. 322

D. 168

A.	A perfect square
B.	An odd number
C.	An even number
D.	Divisible by $3$

A.	$14 \space cm^2$
B.	$13 \space cm^2$
C.	$16 \space cm^2$
D.	$15 \space cm^2$

A.	$53 {\space} \text{units}$
B.	$13 {\space} \text{units}$
C.	$3 {\space} \text{units}$
D.	None of these

A.	$53.46 \space cm$
B.	$13.37 \space cm$
C.	$26.73 \space cm$
D.	$\text{ None of these }$

A.	$388.08 \space m^2$
B.	$13.2 \space m^2$
C.	$55.44 \space m^2$
D.	$60.48 \space m^2$

A.	$34.208 \space years$
B.	$26.208 \space years$
C.	$31.208 \space years$
D.	$31.338 \space years$

Grade 10 Math

Real Numbers Sample Question The number in the form of 8p+38p+38 p + 3 where ppp is whole number, is always A.A perfect square B.An odd number C.An even number D.Divisible by 333

Polynomials Sample Question If α and β are the zeros of polynomial x2 - 11x + k, such that α2 + β2 = 65. Find the value of k. A.35 B.24 C.28 D.21

Linear Equations in Two Variables Sample Question For what value of kkk, will the following pair of linear equations have infinitely many solutions? 6x+3y=96x+3y=96 x + 3 y = 9 and (k+9)x+9y=2k+9(k+9)x+9y=2k+9(k + 9)x + 9 y = 2k + 9 A.666 B.121212 C.888 D.999

Quadratic Equations Sample Question The sum of the n consecutive natural numbers starting from 4 is 85. Find the value of n. A.11 B.9 C.12 D.10

Arithmetic Progressions Sample Question The 8th term of an arithmetic progression has the value 0. Which term of the AP is 3 times the 16th element? A.30 B.31 C.33 D.32

Trigonometry and its Applications Sample Question In right ΔABCΔABC\Delta ABC , ∠B∠B\angle B = 90o90o 90^o , ABABAB = 222 cm, and BCBC BC = 222 cm. Find ∠C∠C\angle C. A.45∘45∘ 45^\circ B.90∘90∘ 90^\circ C.60∘60∘60^\circ D.30∘30∘30^\circ

Constructions Sample Question A. B. C. D.

Probability Sample Question What is the probability that an integer in the set 1, 2, 3, ...122 is divisible by 2 and not divisible by 3? A. 41122 B. 40119 C. 44125 D. 44119

Full Year 10th Grade Review Sample Question 2625 cans are stored in a warehouse in such a manner that there are 203 cans in the bottom row, 199 cans in the second row, 195 cans in the third row, and so on. How many rows of cans are there? A.15 B.17 C.13 D.14

Dice and Cubes Sample Question Faces of a cube are marked with 1,2,3,4,5 and 6. Two views of the cube are as shown below, if face 1 is opposite to face 2, what will be there on the top when 6 is at the bottom? A.5 B.3 C.4 D.Cannot be determined

Venn Diagrams Sample Question Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports. A.40 B.44 C.41 D.43

Number Series Sample Question Find the next term of given sequence.25, 27, 30, 35, 42, 53, 66, .... A.86 B.83 C.90 D.76

Alphabet Problems Sample Question Which of the following is the next term in the series:FZ, JX, NV, RT, ___ A.WQ B.UR C.VR D.UQ

NTSE_MAT Sample Question Find the next term of given sequence ..11, 25, 47, 77, 115, , .... A.161 B.153 C.322 D.168

Real Numbers

Sample Question

The number in the form of $8 p + 3$ where $p$ is whole number, is always

A. A perfect square

B. An odd number

C. An even number

D. Divisible by $3$

Polynomials

Sample Question

If α and β are the zeros of polynomial x² - 11x + k, such that α² + β² = 65. Find the value of k.

A. 35

B. 24

C. 28

D. 21

Linear Equations in Two Variables

Sample Question

For what value of $k$ , will the following pair of linear equations have infinitely many solutions?
$6 x + 3 y = 9$ and $(k + 9)x + 9 y = 2k + 9$

A. $6$

B. $12$

C. $8$

D. $9$

Quadratic Equations

Sample Question

The sum of the n consecutive natural numbers starting from 4 is 85. Find the value of n.

A. 11

B. 9

C. 12

D. 10

Arithmetic Progressions

Sample Question

The 8^th term of an arithmetic progression has the value 0. Which term of the AP is 3 times the 16^th element?

A. 30

B. 31

C. 33

D. 32

Trigonometry and its Applications

Sample Question

In right $\Delta ABC$ , $\angle B$ = $90^o$ , $AB$ = $2$ cm, and $BC$ = $2$ cm. Find $\angle C$ .

A.
$45^\circ$

B.
$90^\circ$

C.
$60^\circ$

D.
$30^\circ$

Constructions

Sample Question

A.

B.

C.

D.

Probability

Sample Question

What is the probability that an integer in the set 1, 2, 3, ...122 is divisible by 2 and not divisible by 3?

A.
41
122

B.
40
119

C.
44
125

D.
44
119

Full Year 10th Grade Review

Sample Question

2625 cans are stored in a warehouse in such a manner that there are 203 cans in the bottom row, 199 cans in the second row, 195 cans in the third row, and so on. How many rows of cans are there?

A. 15

B. 17

C. 13

D. 14

Dice and Cubes

Sample Question

Faces of a cube are marked with 1,2,3,4,5 and 6. Two views of the cube are as shown below, if face 1 is opposite to face 2, what will be there on the top when 6 is at the bottom?

A. 5

B. 3

C. 4

D. Cannot be determined

Venn Diagrams

Sample Question

Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports.

A. 40

B. 44

C. 41

D. 43

Number Series

Sample Question

Find the next term of given sequence.
25, 27, 30, 35, 42, 53, 66, ....

A. 86

B. 83

C. 90

D. 76

Alphabet Problems

Sample Question

Which of the following is the next term in the series:
FZ, JX, NV, RT, ___

A. WQ

B. UR

C. VR

D. UQ

NTSE_MAT

Sample Question

Find the next term of given sequence ..
11, 25, 47, 77, 115, , ....

A. 161

B. 153

C. 322

D. 168