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 :

What is the smallest number by which 256 may be divided so that the quotient is perfect cube?

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

Solution :

To find the number required to divide 256 such that the quotient is a perfect cube, we have to decompose 256 into prime factors.

 =  ∛256  =  ∛(2⋅2⋅2⋅2⋅2⋅2⋅2⋅2)When we group the prime factors inside the cube root as triples, we left over with 2⋅ 2. That is 4.  Hence 4 is the smallest number required to divide 256 so that the quotient is a perfect cube. Let us look into the solution of next problem on "8th grade math worksheet 4 answer".

Question 2 :

How many digits are there in the square root of 4456321?

(A) 2 digits        (B) 4 digits      (C) 3 digits

Solution :

Square root of 1 digit and 2 digit number contains 1 digit.

Square root of 3 and 4 digit number contains 2 digits.

Square root of 5 and 6 digit number contains 3 digits.

Square root of 7 and 8 digit number contains 4 digits. Let us look into the solution of next problem on "8th grade math worksheet 4 answer".

Question 3 :

Find the value of 3x3 - 4x2 + x - 5 when x = -3

(A) -54                 (B) -71               (C) -32

Solution :

Let f(x)  =  3x3 - 4x2 + x - 5

x  =  - 3

f(-3)  =  3(-3)3 - 4(-3)2 + (-3) - 5

=  3(9) - 4(9) - 3 - 5

=  27 - 36 - 3 - 5

=  27 - 44

=  -17

Question 4 :

The perimeter of a rectangle is 52 cm. If its width is 2 cm more than one-third of its length, find the dimensions of rectangle.

(A) 12 cm x 4 cm    (B) 18 cm x 8 cm      (C) 15 cm x 9 cm

Solution :

Perimeter of a rectangle  =  52 cm

2(length + width)  =  52 ==>  l + w  =  26

Let "x" be the length

width  =  (x/3) + 2

x + (x/3) + 2  =  26

[(3x + x)/3]  + 2 =  26

4x / 3  =  24

4x  =  24 (3)

x  =  6(3) ==>  18 cm

Width  =  (18/3) + 2

=  6 + 2  =  8 cm

Hence the required dimension is 18 cm x 8 cm.

Question 5 :

What must be added to each of the numerator and the denominator of the fraction 7/11 to make it equal to 3/4

(A) 9                    (B) 5             (C) 12

Solution :

Let "x" be the required number to be added to both numerator and denominator of the fraction.

(7 + x) / (11 + x)  =  3/4

4(7 + x)  =  3(11 + x)

28 + 4x  =  33 + 3x

4x - 3x  =  33 - 28

x  =  5

Hence 5 is the required number to be added to make the fraction 7/11 as 3/4.

Question 6 :

A line which intersects two or more lines at a distinct points is called a ____________

(A) concurrent       (B) Intersecting     (C) Transversal

Solution :

A line which intersects two or more lines at a distinct points is called a concurrent.

Question 7 :

The opposite angles of a cyclic quadrilateral are _______________

(A) Supplementary    (B) Complementary (C) None of these

Solution :

The sum of opposite angles of a cyclic quadrilateral is 180 degree.

Question 8 :

In triangle ABC is inscribed in a circle with center O and BC is a diameter, if angle BAC is 50°, find angle ABC. (A)  50°           (B)  40°           (C)  48°

Solution :

In the right triangle ABC,

<A + <B + <C =  180

50 + <B + 90  =  180

140 + <B  =  180

<B  =  180 -  140

<B  =  40

Question 9 :

The circumference of a circle is 44 cm.Find its area (use π=22/7)

(A) 154 cm2      (B) 130 cm2      (C) 145 cm2

Solution :

Circumference of a circle =   44 cm

2πr  =  44

⋅ (22/7) ⋅ r  =  44

r  =  7

Area of circle  =  πr2

=  (22/7)  (7)2

=  154 cm2

Question 10 :

The volume of a right circular cylinder is 1100 cm3 and the radius of its base is 5 cm. Calculate its curved surface area.

(A) 410 cm2        (B) 125 cm2          (C) 440 cm2

Solution :

Volume of a right circular cylinder  =  1100 cm3

πr2 h =  1100 cm3

Here r = 5

(22/7) ⋅ (5)2 ⋅ h  =  1100

h  = 2/7

Curved surface area of cylinder  =  2 πr h

=  2 ⋅ (22/7) ⋅ 5 ⋅ (2/7)

=  440 cm2

Hence the curved surface area of cylinder is  440 cm2 After having gone through the stuff given above, we hope that the students would have understood "8th grade math worksheet 4 answer"

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