NC MATH 1 EOC QUESTIONS WITH SOLUTIONS

Problem 91 :

Which sequence uses the algebraic expression 4n + 5 to describe the relationship between a term in the sequence and its position, n, in the sequence?

A. 4, 9, 14, 19, 24...               B. 4, 8, 12, 16, 20...

C. 9, 13, 17, 21, 25...             D. 9, 10, 11, 12, 13...

Solution:

4n + 5

When n = 1, 

= 4(1) + 5

= 4 + 5

= 9

When n = 2,

= 4(2) + 5

= 8 + 5

= 13

When n = 3,

= 4(3) + 5

= 12 + 5

= 17

So, option (C) is correct.

Problem 92 :

Which expression is equivalent to the following expression?

A. 5x² - 3x + 3              B. x² + 3x - 6

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

Solution:

So, option (C) is correct.

Problem 93 :

According to the graph, which statement best describes the slope?

A. As the distance traveled increases by 20, the amount of gas in the tank decreases by 3.

B. As the distance traveled decreases by 3, the amount of gas in the tank increases by 20.

C. As the distance traveled increases by 30, the amount of gas in the tank increases by 2.

A. As the distance traveled decreases by 20, the amount of gas in the tank decreases by 3.

Solution:

So, option (A) is correct.

Problem 94 :

Ryan is writing a composition for homework. He decides to keep track of the number of sentences he writes compared to the time in minutes he works. The graph below shows the data he collected.

At what rate does Ryan write his composition?

A. 0.5 sentence per minute          B. 1 sentence per minute

C. 1.5 sentences per minute        D. 2 sentences per minute

Solution:

Problem 95 :

Which of the following equations describes the same function in the table below?

Solution:

y - 8 = 5(x - 2)

y - 8 = 5x - 10

y = 5x - 10 + 8

y = 5x - 2

So, option (A) is correct.

Problem 96 :

What is the slope of the equation 2x - 5y = 10?

Solution:

2x - 5y = 10

-5y = -2x + 10

y = (2/5)x - 2

Slope = 2/5

So, option (B) is correct.

Problem 97 :

Brock is six feet tall. He climbs a ladder to paint some trim on his house. For each rung that he climbs, Brock is 1.2 feet higher above the ground. Which equation could you use to calculate the distance, d, from the top of Brock's head to the ground if r represents the number of ladder rung he has climbed?

A. d = 1.2r + 6

B. d = 1.2r

C. d = r + 6

D. d = 6r + 1.2

Solution:

Since, he is 6 feet tall, he starts with 6 feet above the ground and adding 1.2 each rung that he clibs.

So, y = mx + b

y = 1.2x + 6

So, option (A) is correct.

Problem 98 :

Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of greater length than the speech she gave the week before. The table below shows the lengths of several of her speeches.

If the trend continues, in which week will she give a 12-minute speech?

A. 22       B. 12        C. 15             D. 24

Solution:

Difference = 0.5

y = 0.5x + 1

12 = 0.5x + 1

11 = 0.5x

x = 22

So, option (A) is correct.

Problem 99 :

Dr. Chait is considering joining the Garden Club. If he pays a $25 membership fee, he can buy rosebushes from the club at a reduced price of $10  each. If he does not join the club, he can buy rosebushes from a local nursery for $15 each. The graph below compares the cost of buying rosebushes from the Garden Club and from the local nursery.

How many rosebushes will Dr. Chait have to buy from the Garden Club before he would begin to save money?

A. 5       B. 7         C. 25       D. 75

Solution:

10x + 25 = 15x

25 = 5x

x = 5

So, option (A) is correct.

Problem 100 :

The side length of a square is 4x³yz⁴ units. What is the area of the square?

A. 8x⁶y²z⁸ square units          B. 8x⁹yz¹⁶ square units

C. 16x⁶y²z⁸ square units        D. 16x⁹yz¹⁶ square units

Solution:

Side = 4x³yz⁴

area of the square = (side)²

= (4x³yz⁴)(4x³yz⁴)

= 16x⁶y²z⁸ square units

So, option (C) is correct.

Problem 101 :

Each month Jessie's phone bill includes a $25 basic fee plus a charge of $.07 per minute for the number of minutes of long-distance calls she makes. Which equation best describes the total amount of Jessie's monthly phone bill, t, in terms of m, the number of minutes of long-distance calls she makes?

A. t = 0.07 + 25m              B. t = 25 + 0.07m

C. t = 25(0.07m)                D. t = 25(7m)

Solution:

The phone bill is the sum of basic fee and the charge of long distance calls.

The charge of long distance call is 0.07m.

So, the phone bill is

t = 25 + 0.07m

So, option (B) is correct.

Problem 102 :

Shaniqua is constructing an isosceles triangle to use as a model in her Algebra class. The perimeter of her triangle is 24 inches. Shaniqua uses the equation b = 24 - 2s to find b, the length of the triangle's third side, in terms of s, the length of eah of its two congruent sides. What is her equation written in terms of s? 

Solution:

b = 24 - 2s

b - 24 = 2s

24 - b = 2s

s = (24 - b) / 2

So, option (D) is correct.