In this 10th grade math worksheets 1, you will find 10 problems on math which are in the level of 10th grade.

Here is 10th grade math worksheets 1

**1. A rubber ball dropped from a height of 50 m rebounds at every impact from the floor to a height half of that from which is has fallen. Find the distance described by the time it comes to rest.**

Distance described in the 1^{st} impact = 50 m

Distance described in the 2^{nd} impact = 2[(1/2)x 50] = 2 x 25 m

Distance described in the 3^{rd} impact = 2[(1/2)x (25/2)] = 2 x (25/2) m

Distance described by the time it comes to rest = 50+2[25+(25/2)+(25/4)+............]

now we need to find the sum of infinite geometric series

Sum of infinite geometric series = a/(1 - r)

a = 25 r = t_{2}/t_{1}

r = (25/2)/(25)

r = (1/2)

S_{∞} = 25/[1- (1/2)]

= 25/(1/2) = 50

Distance described by the time it comes to rest = 50 + 2 [50]

= 50 + 100 = 150 m

So the correct answer for this question is 150 m option C

Distance described in the 2

Distance described in the 3

Distance described by the time it comes to rest = 50+2[25+(25/2)+(25/4)+............]

now we need to find the sum of infinite geometric series

Sum of infinite geometric series = a/(1 - r)

a = 25 r = t

r = (25/2)/(25)

r = (1/2)

S

= 25/(1/2) = 50

Distance described by the time it comes to rest = 50 + 2 [50]

= 50 + 100 = 150 m

So the correct answer for this question is 150 m option C

**2. A work was assigned to me on a Tuesday. I completed to work after 72 days.On what day, i completed the work.**

Tuesday corresponds to 2 in the clock.

Then, 2 + 72 = 74 which is divided by 7 and the remainder is 4

4 corresponds to Thursday.

So, I completed the work on Thursday.

So the correct answer for this question is Thursday option C

**3. The radius of the top of a bucket is 18 cm and that of the bottom is 6 cm.Its depth is 24 cm. Determine the capacity of the bucket.**

Volume of frustum cone = (1/3)π h(R

= (1/3)π (24)(18

= (1/3)π (24)(324 + 36 + 108)

= 8 π (468)

= 3744 π cm

So the correct answer is 3744 π cm

**4. A solid metal cylinder is 20 cm in height and has a radius of 1.5 cm. This is melted down and cast into spheres each of radius 1.5 cm.How many spheres each of radius 1.5 cm can be cast from the cylinder?**

height of the cylinder(h) = 20 cm

radius of cylinder(R) = 1.5 cm

radius of sphere (r) = 1.5 cm

Volume of cylinder = n x Volume of sphere

π R

(1.5)

(1/1.5) x (3/4) x 20 = n

n = (1/1.5) x 3 x 5

n = (5/0.5)

n = 10

So the correct answer is 10 option B

**5. In a higher secondary class, 66 play football,56 play hockey,63 play cricket,27 play both foot ball and hockey,25 play hockey and cricket,23 play cricket and foot ball and 5 do not play any game. if the strength of the class is 130.calculate the number who play all the three games.**

Let A,B and C be the number of students who play foot ball,hockey and cricket respectively.

Number of students who play foot ball = 66

Number of students who play hockey = 56

Number of students who play cricket = 63

Number of students who play football and hockey = 27

Number of students who play hockey and cricket = 25

Number of students who play cricket and football = 23

Number of students who do not play any game = 5

Let "x" be the number of students who play all the three game

Number of students who play any one of the games =

16+x+27-x+x+23-x+25-x+4+x+15+x

125 = 16 + 27 + 23 + 25 + 4 + 15 + x

125 - 110 = x

x = 15

Number of students who play all the three games = 15

So the correct answer is 15 option B

**6 . Determine the value of m if x + 1 is a factor of x
³ + m x
² + 19x + 12**

Let p(x) = x

x + 1 = 0

x = -1

Since(x + 1) is a factor p(-1)= 0

p(-1) = (-1)

0 = -1 + m - 19 + 12

0 = - 20 + 12 + m

0 = -8 + m

m = 8

So the correct answer is 8 option B

**7. Find the square root of (x² - 4) (x
² + x - 6) (x
²+ 5x + 6) **

= √(x

Now we are going to factorize the above quadratic equations

= √(x

= √(x + 2) (x - 2)(x + 3) (x - 2) (x + 2)(x + 3)

= (x + 2) (x - 2)(x + 3)

So the correct answer is (x + 2) (x - 2)(x + 3) option B

**8.The outer dimension of a bordered table are 2 cm and 108 cm. If the area of a table,excluding the border is 6400 cm²,how wide is the border?**

**9. Find the area of the triangle whose vertices are (4,5) (4,2) (-2,2)**

Now we have to take anticlockwise direction. So we have to take the points in the order

A (4,5) C (-2,2) and B (4,2)

Area of the triangle = (1/2) {x

x

y

Area of the triangle ACB = 1/2 {4(2-2) + (-2) (2-5) + 4 (5-2)}

= 1/2 {4 (0) + (-2) (-3) + 4 (3)}

= 1/2 {0 + 6 + 12}

= 1/2 {18}

= 18/2

= 9 Square Units.

Therefore the area of ACB = 9 square units.

So the correct answer is 9 square units

option B

**10.Find the equation of the straight line which joins the points A (5,1) and B (-2,2)**

Equation of the line joining two points

(y - y

x

y

(y - 1)/(2 - 1) = (x - 5)/(-2 - 5)

(y - 1)/1 = (x - 5)/(-7)

-7 (y - 1) = 1 (x - 5)

-7 y + 7 = x - 5

x + 7 y - 5 - 7 = 0

x + 7 y - 12 = 0

So the correct answer is x + 7 y - 12 = 0 option C

These are the questions on math prepared in 10th grade math worksheets 1 based on the curriculum of 10th grade

**Worksheet 1****Worksheet 2****Worksheet 3****W**orksheet 4**W**orksheet 5**W**orksheet 6**W**orksheet 7**W**orksheet 8**W**orksheet 9**W**orksheet 10**W**orksheet 11**W**orksheet 12**W**orksheet 13**W**orksheet 14**Worksheet 15**

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