6TH GRADE MATH PRACTICE PROBLEMS

Question 1 :

The sum of (-12) and (5) is

(A) 6         (B) 8         (C) -7

Solution :

  =  -12 + 5

Because the two terms are having opposite sings, we have to subtract and put greater number sign for the answer.

  =  -7

So, the answer is -7.

Question 2 :

The perimeter of the equilateral triangle is 18 cm. Find the length of each

(A) 5 cm           (B) 4 cm           (C) 6 cm

Solution :

Perimeter of equilateral triangle  =  18 cm

3a  =  18

a  =  18/3

a  =  6

So, the length of each side is 6 cm.

Question 3 :

How to express 5 ⋅ 5 ⋅ 5 using exponent?

(A) 10³         (B) 5³          (C) 2³

Solution :

5 ⋅ 5 ⋅ 5  =  5³

Question 4 :

What is the value of 0¹⁰

(A) 0         (B) 1         (C) 2

Solution :

The value of 0 power any thing is 0.

Question 5 :

A father is 30 years older than his son, and one year ago he was four times as old as his son. Find the father’s present ages.

(A) 53           (B) 12        (C) 41

Solution :

Let x be the present age of his son.

Age of father  =  30 + x

One year ago,

Son's age  =  x - 1

Father's age  =  30 + x - 1

Father's age  =  29 + x

29 + x  =  4(x - 1)

29 + x  =  4x - 4

4x - x  =  29 + 4

3x  =  33

x  =  11

Father's present age  =  30 + 11

=  43

So, the father's present age is 43 years.

Question 6 :

A perimeter of a square is 20 inches.Find the side length of the square.

(A) 10 inch        (B) 4 inch         (C) 5 inch

Solution :

Perimeter of square  =  20 inches

4a  =  20

a  =  20/4

a  =  5

So, the side length of square is 5 inches.

Question 7 :

A triangle has sides of lengths 19, 3 and 18 meters. What type of triangle is it ?

(A) Equilateral           (B)  Right           (C) Scalene

Solution :

The side lengths of triangle are 19, 3 and 18.

Verifying pythagorean theorem :

19²  ≠  18² + 3²

361  ≠  324 + 9

361 ≠ 333

It doesn't satisfy the above condition, it is not a right triangle. Because the measures are different, it is a scalene triangle.

Question 8 :

The measure of an angle is 77°. What is the measure of a supplementary angle ?

(A) 105°           (B) 103°           (C) 50°

Solution :

Two angles are supplementary when they add up to 180 degrees.

Let x be the other angle

77 + x  =  180

x  =  180 - 77

x  =  103°

So, the required angle is 103°.

Question 9 :

Find the 21^st term in the sequence 2, 4, 6, 8 . . .

(A) 10      (B) 42         (C) 20

Solution :

In the given sequence the common difference are same. So it is arithmetic progression.

General term in arithmetic progression :

t_n  =  a + (n - 1)d

a  =  2, d  =  4 - 2 ==>  2

t₂₁  =  2 + (21 - 1)2

t₂₁  =  2 + (20)2

t₂₁  =  2 + 40

t₂₁  =  42

So, the 21^st term of the sequence is 42.

Question 10 :

A train is travelling 1 kilometer in 1 minute and 20 seconds. If the train continues at this rate, how far will it travel in one hour?

(A) 10 miles        (B) 15 miles         (C) 45 miles 

Solution :

Time taken to cover the distance of 1 kilometer is 1 minute 20 seconds.

1 minute  =  60 seconds

So, time taken  =  60 + 20  ==>  80 seconds

Therefore, the rate of travel is 1 km/80 seconds.

To find the total distance traveled in one hour, simply form a conversion:

(1 km/80 sec) ⋅ 3600 sec/hour  =  45 km

Therefore, the total distance traveled in hour is 45 km.

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