MATH 1 EOC REVIEW QUESTIONS WITH SOLUTIONS

Problem 21 :

A quadrilateral has vertices located at (-3, -5), (4, 2), (4, 1) and (2, -1). Which best describes the figure?

A. rhombus    B. rectangle         C. trapezoid

Solution:

This is trapezoid.

So, option (C) is correct.

Problem 22 :

A school opened with 100 students. The number of students has increased by 25% each year since the school opened. Which function can be used to determine the number of students at the school x years after it opened? 

A. f(x) = 0.25x + 100         B. f(x) = 100(0.25)^x

C. f(x) = 100(1.25)^x

Solution:

Given, a = 100, r = 0.25

y = a(1 + r)^t

y = 100(1 + 0.25)^x

y = 100(1.25)^x

So, option (C) is correct.

Problem 23 :

Jenna cut a piece of cloth several times. The table below shows the number of pieces of cloth she had after making several cuts.

Which equation could be used to determine the number of pieces of cloth,y, Jenna had after making x cuts?

A. y = 2x         B. y = 2^x          C. y = x²

Solution:

By observing the values of y

2, 4, 8, 16, ......

It is geometric function, so it will create exponential function.

Every exponential function will be in the form, y = ab^x

Multiplication factor (b) = 4/2 = 2

y = a(2)^x -----(1)

Choosing any point from table and applying in the exponential function.

(1, 2)

2 = a(2)¹

a = 1

By applying the value of a in (1), we get

y = 1(2)^x

y = 2^x

So, option (B) is correct.

Problem 24 :

A teacher surveyed 160 students to see how many students leave school during lunch. The results of the survey are shown in the relative frequency table below.

what percent of the boys surveyed leave school during lunch?

A. 13%          B. 24%        C. 31%

Solution:

From the table, we can find

• Number of boys leave school = 0.125(160) ==> 20
• Number of girls leave school = 0.1875(160) ==> 30
• Number of boys stay at school = 0.40625 ==> 65
• Number of girls stay at school = 0.28125(160) ==> 45
  

Percentage of boys = (20/160) x 100%

= 12.5%

= 13%

So, option (A) is correct.

Problem 25 :

A liquid is evaporating. The amount of a liquid remaining, in liters, after x weeks is modeled by the equation

y = 100(0.78)^3x

What percent of the liquid evaporates per week?

A. 47%       B. 53%       C. 78%

Solution:

y = 100(0.78)^3x

y = 100[(0.78)³]^x

y = 100(0.474)^x

y = 100(47.4/100)^x

= 47%

So, option (A) is correct.

Problem 26 :

The function y = 45x + 6 can be used to determine the cost for a person to purchase x tickets to a correct. A person can purchase up to 8 tickets. What is an appropriate domain for the function?

A. all integers ≤ 8          B. all positive integers ≤ 8

C. all positive real numbers ≤ 8

Solution:

It is known that the part of the tickets cannot be sold so, x can take only integers values.

Also, the number of tickets cannot be negative. So, x can take only positive integers values.

The maximum number of tickets that a person can purchase is 8. So, x ≤ 8.

So, option (B) is correct.

Problem 27 :

The table below shows monthly pet expenses based on the number of pets owned.

Using the line of best fit for the data in the table, what is the predicted monthly expense for owing 3 pets?

A. $66          B. $76          C. $80

Solution:

Solution :

y = 26.8x - 4

When x = 3

y = 26.8(3) - 4

y = 80.4-4

y = 76.4

So, answer B is correct.

Problem 28 :

A clothing store sells pants and shirts.

• The store can buy up to a total of 500 pants and shirts each month.
• The store wants to buy at least as many shirts as pants.
• The store wants to buy at least 100 pants each month.

Which system of inequalities represents the constraints on the number of shirts, s, and number of pants, p, the store buys each month?

C. s + p ≤ 500

     s ≥ p

     p ≥ 100

Solution:

The store can buy up to a total of 500 pants and shirts each month.

s + p ≤ 500

The store wants to buy at least as many shirts as pants.

s ≥ p

The store wants to buy at least 100 pants each month.

p ≥ 100

So, option (C) is correct.

Problem 29 :

What is the area of the rectangle below?

A. 5x + 4      B. 6x² + 14x - 12         C. 6x² - 22x - 12

Solution:

Given, length = 3x - 2

width = 2x + 6

Area of rectangle = length × width

A = (3x - 2) (2x + 6)

= 6x² + 18x - 4x - 12

A = 6x² + 14x - 12

So, option (B) is correct.

Problem 30 :

A sequence is shown below.

10, 12, 14, 16, ...

Which function can be used to determine the nth number in the sequence?

A. F(n) = n + 2     B. F(n) = 2n + 8     C. F(n) = 2n + 10

Solution:

a = 10

d = 2

F(n) = a + (n - 1)d

= 10 + (n - 1) 2

= 10 + 2n - 2

F(n) = 2n + 8

So, option (B) is correct.