6TH GRADE MATH PRACTICE QUIZ

(1)  Fill in the boxes.

(2)  A car travels 432 km on 48 liters of petrol. How far would it travel on 20 liters of petrol?

(3)  An electric pole, 24 meters high casts a shadow of 20 meters. Find the height of a tree. If it casts a shadow of 15 meters under similar conditions

(4)  A train 315 m long is running at 54 km/h.How much time will it take to cross a pole?

(5)  In an examination John secured 372 marks. If she secured 62% marks, find the maximum marks.

(6)  Factorize  9 m² + 4² -12 mn

(7)  Length of a rectangle is 8m less than twice its width. If the perimeter of the rectangle is 56m, find the length and width

(8)  The length of the sides of a right triangle are 6 cm and 8 cm. What is the length of its hypotenuse?

(9)  A rectangular lawn of length 40 m and width 25 m is to be surrounded externally by a path which is 2m wide. Find the area of the path.

(10)  Capacity of a tank is 60 m³. If the length and width of the tank are 5 m and 4 m respectively, find its depth.

6th grade worksheet - Solution

Question 1 :

Fill in the boxes.

Solution :

Let the two unknowns be "a" and "b"

90/165  =  -6/a

Since it is equivalent fraction, 

90(a)  =  -6(165)

In order to find the value of "a", we have to divide by 90 on both sides.

90a/90  =  -6(165)/90

a  =  -11

Like wise,

90/165  =  b/-55

Since it is equivalent fraction, 

90 (-55)  =  b (165)

By dividing 165 on both sides, we get

90(-55)/165  =  165b/165

b  =  -30

So, the answer is -11 & -30.

Question 2 :

A car travels 432 km on 48 liters of petrol. How far would it travel on 20 liters of petrol?

Solution :

Since the petrol consumption is getting decreased, number of km they traveled also will also get decrease.

Hence this come under direct variation.

So,

432 (20)  =  x (48)

By dividing 48 on both sides, we get

432(20) / 48  =  48x / 48

x  =  180 km

So, the answer is 180 km.

Question 3 :

An electric pole, 24 meters high casts a shadow of 20 meters. Find the height of a tree. If it casts a shadow of 15 meters under similar conditions

Solution :

Let x be the required length of pole

24/x  =  20/15

Multiply by x on both sides, we get

(24/x) x  =  4x/3

24  =  4x/3

Multiply by 3 on both sides,

24(3)  =  4x

Divide by 4 on both sides

24(3)/4  =  x

 6(3)  =  x 

x  =  18 m

Question 4 :

A train 315 m long is running at 54 km/h.How much time will it take to cross a pole?

Solution :

Given length of train = 315 m

That is distance travelled by the train to completely cross the pole = 315 m

Speed of train = 54 km/hr

= 54 x (5/18) = 15 m/sec

We know that, time taken = distance / speed

= 315/15

= 21 seconds

Thus the train takes 21 seconds to cross the pole.

Question 5 :

In an examination John secured 372 marks. If she secured 62% marks, find the maximum marks.

Solution :

Marks secured by John  =  372

Let the total marks be x. 

 62% of x   =  372 

(62/100) x   =  372

0.62 x  =  372

Dividing 0.62 on both sides, we get

0.62x / 0.62  =  372 / 0.62

x  =  600

Question 6 :

Factorize  9 m² + 4² -12 mn

Solution :

  =  9 m²  - 12 mn + 4²

  =  (3 m)²  - 2(3m)(2)  + 2²

The above line exactly matches with the algebraic identity a² - 2ab + b²

a² - 2ab + b²  =  (a - b)²

  =  (3m - 2)²

Question 7 :

Length of a rectangle is 8m less than twice its width. If the perimeter of the rectangle is 56m, find the length and width

Solution :

Let x be the width of the rectangle.

length  =  2x - 8

Perimeter of the rectangle  =  56 m

2(l + w)  =  56

2(2x - 8 + x)  =  56

2 (3x  - 8)  =  56

Divide by 2 on both sides, we get

3x - 8  =  56/2

3x - 8  =  28

Add 8 on both sides

3x  =  36

Divide by 3 on both sides

x  =  12 and  2x - 8  ==>  2(12) - 8  ==>  16 cm

So, the width is 12 cm and length is 16 cm.

Question 8 :

The length of the sides of a right triangle are 6 cm and 8 cm. What is the length of its hypotenuse?

Solution :

(hypotenuse)²  =  Sum of squares of other two sides

(hypotenuse)²  =  6² + 8²

  =  36  + 64

  =  100

Hypotenuse  =  √100  =  10 cm.

Question 9 :

A rectangular lawn of length 40 m and width 25 m is to be surrounded externally by a path which is 2m wide. Find the area of the path.

Solution :

Since the path surrounded externally, the length and width of rectangular portion including the path will be 4m more than the lawn.

length of path  = 40 + 2 + 2  =  44 m

width of path  =  25 + 2 + 2  =  29 m

Area of path  =  44(29)  -  40(25)

  =  1276  -  1000

  =  276m²

Question 10 :

Capacity of a tank is 60 m³. If the length and width of the tank are 5 m and 4 m respectively, find its depth.

Solution :

From the above information, we come to know that the tank is in the form of cuboid.

capacity of tank  =  60 m³

length x width x breadth  =  60

5 x 4 x depth  =  60

depth  =  60/20

depth  =  3 m

So, the answer is 3 m. 6th grade worksheet  6th grade worksheet

Answers

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.