# EOC GRADE 8 MATH PRACTICE WITH SOLUTIONS

Problem 41 :

The density of an object can be found using the formula D = m/v.

• m is the mass of the object
• v is the volume of the object

Which formula could be used to determine the volume of an object?

Solution:

So, option (C) is correct.

Problem 42 :

John collected data on the number of new movies produced in different years.

Suppose that the number of movies made in 2005 was 595, and the number made in 2010 was 895.

What is the average rate of change in the number of new movies between 2005 and 2010?

A. 50 movies per year   B. 60 movies per year

C. 300 movies per year

Solution:

Let, slope = rate of change

So, option (B) is correct.

Problem 43 :

Yanice need to solve the problem below using the quadratic formula.

x2 + 8x + 7 = -8

Which use of the following shows the quadratic formula being used correctly to determine the solutions for this problem?

Solution:

x2 + 8x + 7 = -8

x2 + 8x + 15 = 0

So, option (D) is correct.

Problem 44 :

What is the range of the relation shown in the graph below?

A. All y ≤ 5    B. All x ≤ 5    C. All values of y

D. All values of x

Solution:

The graph is located below the y = 5.

(i.e) y ≤ 5

So, option (A) is correct.

Problem 45 :

The surface area, S, of a cylinder is calculated using the formula S = 2πrl + 2πr2. Which equation is equivalent to this formula solved for l, the length of the cylinder?

Solution:

S = 2πrl + 2πr2

S - 2πrl = 2πr2.

So, option (D) is correct.

Problem 46 :

Rogelio divides a trinomial by a monomial, as shown below.

Which of the following is the correct result?

A. x3 + 9x2 + 15x           B. x4 + 3x2 + 5x

C. x3 + 3x + 5                 D. 3x4 + 9x2 + 5

Solution:

So, option (C) is correct.

Problem 47 :

Patrick compared the slope of the function g(x) = -2x- 8 to the slope of the linear function shown in the table below. Let m = the slope of g(x) and n = the slope of h(x).

Which statement is true?

A. m < n      B. m > n        C. m = n

Solution:

Let m is the slope of g(x).

g(x) = -2x - 8

m = -2

When,

h(x) = mx + b

h(-3) = -3m + b = 1 (method of undetermined coefficients)

h(-2) = -2m + b = -2

h(0) = 0(m) + b = -8

b = -8

Put b = -8 into -3m + b = 1

-3m - 8 = 1

-3m = 9

m = -3

h(x) = -3x - 8

n = -3

-2 > -3

m > n

So, option (B) is correct.

Problem 48 :

Shelly has been asked to factor the following expression completely.

36y - 81x2y

Which answer choice shows her completely factored expression?

A. y(6 + 9x)(6 - 9x)            B. 9y(2 + 3x)(2 - 3x)

C. y(36 - 81x2)                   D. 9y(4 - 9x2)

Solution:

= 36y - 81x2y

= 9y(4 - 9x2)

= 9y(2 + 3x)(2 - 3x)

So, option (B) is correct.

Problem 49 :

The function below can be used to describe the path of a bird flying through the air.

f(x) = x2 - 4x - 32

Which of the following shows the correct factorization of this function f(x) = 0?

A. (x + 4)(x + 8) = 0             B. (x + 4)(x - 8) = 0

C. (x - 4)(x - 8) = 0               D. (x - 4)(x + 8) = 0

Solution:

f(x) = x2 - 4x - 32

x2 - 8x + 4x - 32 = 0

x(x - 8) + 4(x - 8) = 0

(x + 4)(x - 8) = 0

So, option (B) is correct.

Problem 50 :

Yanet needs to simplify the expression below before she substitutes values for x and y.

A. x9y5          B. x24y16        C. x6y3 + x3y2         D. x15y8 + x6y4

Solution:

So, option (D) is correct.

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