Here we are going to see 10 practice questions of mixed topics. We have been preparing this set of questions in order to test how you understood the topics.

## Practice questions of mixed topics in 8th grade math

Question 1 :

Find the smallest number by which 3087 should be multiplied to obtain a perfect cube.

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

Solution :

 =  ∛(3 ⋅ 3 ⋅ 7 ⋅ 7 ⋅ 7)Hence 3 is the smallest number to be multiplied to obtain a perfect cube.

Question 2 :

11025 students are sitting in a lawn in such a way that there are many students in a row as there are rows in lawn. Find the number of rows in the lawn.

(A)   205              (B)   105           (C)   115

Solution :

From the given information, we come to know that the number of rows in the lawn is equal to the number of students in a row.

So, we have to find the square root of 11025

Hence the number of rows in the lawn is 105.

Let us look into the solution of next problem on "8th grade math worksheet 2 answer".

Question 3 :

Evaluate (243) -2/5

(A)   1/5             (B)   1/7           (C)   1/9

Solution :

(243) -2/5

243  =  3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3  =  35

(243) -2/5    =  (35)-2/5

=  3-2

=  1/3=  1/9

Question 4 :

Evaluate (52 + 122)1/2

(A)  17          (B)   15         (C) 13

Solution :

(52 + 122)1/2 =  (52 + 122)1/2

=  (25 + 144)1/2

=  169

=  √(13 ⋅ 13)

=  13

Question 5 :

If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2

(A)  35        (B)  45         (C)  55

Solution :

(a + b + c)2  =  a2 + b2 + b2 + 2ab + 2bc + 2ca

(a + b + c)2  =  a2 + b2 + b2 + 2(ab + bc + ca)

92  =  a2 + b2 + b2 + 2(23)

81  =  a2 + b2 + b2 + 46

81 - 46  =  a2 + b2 + b2

a2 + b2 + b =  35

Question 6 :

What is the degree of the polynomial 4 + 3x - 7 x3 + 5 x4

(A)  4         (B)  3        (C)  1

Solution :

The highest power of the polynomial is know as degree.

Hence the degree of the polynomial is 4.

Question 7 :

Solve the following 3x / (2x - 5) = 12/5

(A)  40 kg     (B)  36 kg     (C)  50 kg

Solution :

3x / (2x - 5) = 12/5

5(3x)  =  12 (2x - 5)

15 x  =  24 x - 60

15 x - 24x  =  -60

-9x  =  -60

x  =  60/9

=  20/3

Question 8 :

The numerator of a rational number is less than its denominator by the number 3. if the numerator becomes three times and the denominator is increased by 20, the new fraction became 1/8. Find the required fraction.

(A)  1/3                (B)   1/2              (C)   1/4

Solution :

Let x = denominator

x-3 = numerator

3 (x - 3) / (x + 20) = 1/8

(3x - 9) / (x + 20) = 1/8

8(3x - 9) = (x + 20)

24 x - 72  =  x + 20

Subtract both sides by x

24x - x  - 72  =  20

23x  =  20 + 72

x  =  92/23  =  4 (denominator)

Numerator  =  4 - 3  =  1

Hence the required fraction is 1/4.

Question 9 :

In a circle with center O and the radius 13 cm, AB is a chord of length 24 cm.Find the distance between the chord and the center.

(A)  6 cm               (B)   8 cm              (C)   5 cm

Question 10 :

Find the value of x ° if the lines AB and CD are parallel to each other

(A)   0°               (B)   180°            (C)   225°

Solution :

x  =  360 - (45 + 30)

x  =  360 - 75

x  =  285

Hence the required angle is 285

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