## 10th grade math worksheets 1

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.

 (A) 150 m (B) 260 m (C) 50 m

jQuery UI Accordion - Default functionality
Distance described in the 1st impact = 50 m
Distance described in the 2nd impact = 2[(1/2)x 50] = 2 x 25 m
Distance described in the 3rd 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 = t2/t1
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 + 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.

 (A) Tuesday (B) Wednesday (C) Thursday

jQuery UI Accordion - Default functionality

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.

 (A) 5044 π cm2 (B) 3744 π cm2 (C) 1043 π cm2

jQuery UI Accordion - Default functionality Volume of frustum cone = (1/3)π h(R2 + r 2 + R r)

= (1/3)π (24)(182 + 6 2 + (18)(6))

= (1/3)π (24)(324 + 36 + 108)

= 8 π (468)

= 3744 π cm3
So the correct answer is 3744 π cm3 option B

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?

 (A) 20 (B) 10 (C) 15

jQuery UI Accordion - Default functionality 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 R2 h = n x (4/3) x π r 3
(1.5)2 x 20 = n x (4/3) x (1.5)3
(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.

 (A) 20 (B) 15 (C) 30

jQuery UI Accordion - Default functionality 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

 (A) 7 (B) 8 (C) 9

jQuery UI Accordion - Default functionality

Let p(x) = x3 + m x2 + 19 x + 12
x + 1 = 0
x = -1
Since(x + 1) is a factor p(-1)= 0
p(-1) = (-1)3 + m (-1) 2 + 19 (-1) + 12
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)

 (A) (x - 1) (x + 2) (x + 3) (B) (x - 2) (x + 2) (x + 3) (C) (x + 1) (x + 2) (x + 3)

jQuery UI Accordion - Default functionality

= √(x2 - 4) (x2 + x - 6) (x2 + 5 x + 6)
Now we are going to factorize the above quadratic equations
= √(x2 - 22) (x + 3) (x - 2) (x + 2)(x + 3)
= √(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?

 (A) 3 cm (B) 5 cm (C) 4 cm

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

 (A) 4 square units (B) 9 square units (C) 2 square units

jQuery UI Accordion - Default functionality 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) {x1(y2-y3) + x2(y3-y1) + x3(y1-y2}
x1 = 4 x2 = -2 x3 = 4
y1 = 5 y2 = 2 y3 = 2
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)

 (A) x + 3y - 12 = 0 (B) x + 5y - 15 = 0 (C) x + 7y - 12 = 0

jQuery UI Accordion - Default functionality

Equation of the line joining two points
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
x1 = 5 x2 = -2
y1 = 1 y2 = 2
(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  