NC MATH 1 EOC WORKSHEET WITH SOLUTIONS

Problem 71 :

The sum of two binomials is 5x² - 6x. If one of the binomials is 3x² - 2x. What is the other binomials?

A. 2x² - 4x             B. 2x² - 8x

C. 8x² + 4x             D. 8x² - 8x

Solution:

Given, sum of two binomial = 5x² - 6x

One binomial = 3x² - 2x

Let the other binomial be a.

a + 3x² - 2x = 5x² - 6x

a = 5x² - 6x - 3x² + 2x

a = 2x² - 4x

So, option (A) is correct.

Problem 72 :

A. -2        B. -1        C. 1           D. 2

Solution:

So, option (B) is correct.

Problem 73 :

The equation of line 6x + 5y = 3, and the equation of line is 5x - 6y = 0. Which statement about the two lines is true?

A. Lines j and q have the same y-intercept.

B. Lines j and q are parallel.

C. Lines j and q have the same x-intercept.

D. Lines j and q are perpendicular.

Solution:

Find the slope of line j:

6x + 5y = 3

5y = -6x + 3

y = (-6/5)x + (3/5)

Slope m₁ = -6/5

Find the slope of line q:

5x - 6y = 0

6y = 5x

y = (5/6)x

Slope m₂ = 5/6

Compare the two slopes, we have

m₁ = -6/5 and m₂ = 5/6

The slopes are inverse reciprocal, that means, that the lines are perpendicular. So, option (D) is correct.

Problem 74 :

(4x² - 2x + 8) - (x² + 3x - 2) = 

A. 3x² + x + 6              B. 3x² + x + 10

C. 3x² - 5x + 6             D. 3x² - 5x + 10

Solution:

= (4x² - 2x + 8) - (x² + 3x - 2) 

= 4x² - 2x + 8 - x² - 3x + 2

= 3x² - 5x + 10

So, option (D) is correct.

Problem 75 :

Which best represents the graph of y = 2x - 2?

Solution:

y = 2x - 2

When x = 0,

y = -2

When y = 0,

x = 1

So, option (A) is correct.

Problem 76 :

The data in the table show the cost of renting a bicycle by the hour, including a deposit.

A. c = 5h       B. c = 1/5h + 5       C. c = 5h + 5     D. c = 5h - 5

Solution:

When h = 2, then c = 15

When h = 5, then c = 30

Equation is c = kh + b

 15 = 2k + b

30 = 5k + b

So, the equation is c = 5h + 5.

So, option (C) is correct.

Problem 77 :

Harry determined that every time he tapped his wand the sound increased 4 decibels. He noticed that after tapping his wand three times, the sound measured 34 decibels. Which equation best represents the sound when w represents a move of the wand and s represents the loudness of the sound?

A. s = 4w - 22                  B. s = 4w + 22

C. s = 4w - 43                  D. s = 4w = 43

Solution:

If each tap increases sound by 4, that means the slope m = 4.

One data pint (x, y) = (3, 34)

y = mx + b

34 = 4(3) + b

34 = 12 + b

b = 22

s = 4w + 22

So, option (B) is correct.

Problem 78 :

The total cost f(d) in dollars of renting a sailboat for d days is given by the function 

f(d) = 120 + 60d

If the total cost was $360, for how many days, d, was the sailboat rented?

A. 2         B. 4           C. 6            D. 8

Solution:

f(d) = 120 + 60d

360 = 120 + 60d

60d = 240

d = 4 days

So, option (B) is correct.

Problem 79 :

Given the system of equations below:

3x - 2y = 12

4x - y = 11

What is the value of y in the solution?

A. -3       B. -2        C. 2       D. 3

Solution:

3x - 2y = 12 ---> (1)

4x - y = 11

(2) × -2 ==> -8x + 2y = -22 ---> (2)

Adding (1) and (2), we get

-5x = -10

x = 2

By applying x = 2 in (1),

3(2) - 2y = 12

6 - 2y = 12

-2y = 6

y = -3

So, option (A) is correct.

Problem 80 :

Which expression is equivalent to x⁶x²?

A. x⁴x³        B. x⁵x³         C. x⁷x³            D. x⁹x³

Solution:

x⁶x² = x⁸

A. x⁴x³ = x⁷

B. x⁵x³ = x⁸

C. x⁷x³ = x¹⁰

D. x⁹x³ = x¹²

So, option (B) is correct.