# 6th GRADE MATH WORKSHEETS 1

In this page 6th grade math worksheets 1, you will find 10  questions in various topic of math.  You may try each questions on your own and you may check the answer immediately by using the submit button. This question paper will be in the form of quiz.

On this webpage, we give 6th grade math worksheets 1 online test  which can be taken by any one without any login credentials. At the end of the test,  students can check their score instantly and also they can view detailed answer for all the questions. We hope, this online practice test will be a great boost for the students. We give detailed solution for every question of this worksheet. If you find it difficult to do any problem,please click the link view solution for each question. You will get detailed solution.

1. Fill in the boxes. (A) -2 & -15

(B) -11 & -30

(C) -30 & -11

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

(A) 180 km

(B) 130 km

(C) 152 km

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

(A) 15 m

(B) 17 m

(C) 18 m

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

(A) 15 seconds

(B) 21 seconds

(C) 30 seconds

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

(A) 500

(B) 600

(C) 700

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

(A) 16 m & 12 m

(B) 16 m & 11 m

(C) 12 m & 16 m

7. Factorize  9m² -12 m n  + 4 n²

(A) (3m+2n) (3m+2n)

(B) (3m+2n) (3m-2n)

(C) (3m-2n) (3m-2n)

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

(A) 6 cm

(B) 10 cm

(C) 5 cm

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

(A) 266 m2

(B) 255 m2

(C) 276 m2

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

(A) 3 m

(B) 5 m

(C) 7 m

jQuery UI Accordion - Default functionality

1. -11 & -30
2. 180 km
3. 18 m
4. 21 seconds
5. 600
6. (3m-2n) (3m-2n)
7. 16 m & 12 m
8. 10 cm
9. 276 m2
10. 3 m

 Question 1 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Here the given fractions are equal. Let "x" be the denominator of the second fraction 90/165 = -6/x 90 x = -6 x 165 from this we have to find the value of "x" so, x = (-6 x 165)/90 x = -990/90 x = -11 Let "y" be the numerator of the third fraction 90/165 = y/-55 90 (-55) = y x 165 y = 90(-55)/165 y = -4950/165 y = -30 So the correct answer for this question is -11 & -30 option B Question 2 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} The car covers the distance 432 km by consuming 48 liters of petrol.Now we have to find the number of km covered by the car using 20 liters of petrol. Since it is direct variation, 432 x 20 = x x 48 8640 = 48 x 8640/48 = x x = 180 km So the correct answer for this question is 180 km option A Question 3 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Now we need to find the length of the tree when it casts a shadow of 15 meters Since it is direct variation, 24 x 15 = x x 20 360 = 20 x 360/20 = x x = 18 m So the correct answer for this question is 18 m option C Question 4 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Now,we are going to use the formula to find time Time = Distance/Speed Length of the train = distance covered by the train = 315 m Speed of the train = 54 km/hr To convert the speed from km/hr to m/second we have to multiply by 5/18                           = 54 x (5/18)                          = 15 m/sec Time = 315/15         = 21 seconds So the correct answer for this question is 21 seconds option B Question 5 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Marks secured by John = 372 Let "x" be the maximum marks 62 % of x = 372 (62/100) x x = 372 x = 372 x (100/62) x = 37200/62 x = 600 So,the maximum mark is 600. So the correct answer for this question is 600 option B Question 6 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Let "x" be the breadth of the rectangle So,length of the rectangle = 2 x - 8 Perimeter of the rectangle = 56 m Perimeter of a rectangle = 2 (length + breadth) 2 (2 x - 8 + x) = 56 2 (3x - 8) = 56 6 x - 16 = 56 6 x = 56 + 16 6 x = 72 x = 72/6 x = 12 breadth of the rectangle = 12 m length of the rectangle = 2 (12) - 8                          = 24 - 8                          = 16 m So the correct answer for this question is 12 m & 16 m option C Question 7 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Here 9 can be written as 32 and 4 can be written as 22 = 32m2 - 2 (6 m n) + 22n2 = (3 m)2 - 2 (3 m)(2 n) + (2 n)2 This exactly matches the algebraic identity a2 - 2 a b + b2 So, we shall written it as (3 m - 2 n)2 Therefore the factors are (3 m - 2 n) (3 m - 2 n) So the correct answer for this question is (3 m - 2 n) (3 m - 2 n) option C Question 8 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Here we need to find the length of the hypotenuse side In any right triangle the square of hypotenuse side is equal to the sum of squares of other two sides. Length of other two sides are 6 cm and 8 cm respectively (Hypotenuse side)2 = 62 + 82                    = 36 + 64                    = 100 hypotenuse side = √ 100                     = 10 cm So the correct answer for this question is 10 cm option C Question 9 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Width of the path = 2 m Length of rectangular lawn = 40 m Breadth of the rectangular lawn = 25 m Area of path = Area of large rectangle - area of small rectangle Area of a rectangle = Length x breadth          = (44 x 29) - (40 x 25)          = 1276 - 1000          = 276 m2 So the correct answer for this question is 276 m2 option C Question 10 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given information we come to know that the tank is in the form of cuboid Volume of the tank = 60 kl Length x breadth x height = 60 length of the tank = 5 m breadth of the tank = 4 m From this we have to find the height 5 x 4 x h = 60 20 x h = 60 h = 60/20 h = 3 m So the correct answer for this question is 3 m option A 