EOC Review

Structure and operations

100

Mrs. Lynch asks her students to express (x^1/5)⁴ in exponential form. The table shows the responses of four students. 

Bernie x^5/4

Cheyenne x^4/5 

Lindsay 4x⁵

Wyatt 5x4

Cheyenne 

200

Ms. Glick drew two line segments on the chalkboard. The first line segment was 168 cm long and the other was 5 feet 2 inches long. If 1 inch = 2.54 cm, approximately how many inches longer was the first line segment than the second?

4 inches 

300

Consider the expression. 

2x(x+3y) + 5(2x-z)

How many terms does the expression have when simplified completely?

4 Terms

400

Find the remainder when 

p(x)=-2x⁵+x⁴+5x³+4x+1 is divides by (x-2).

1

500

What are the solutions to the equation 

y=4x²+14x+6?

x= - 3

x= - 1/2

Equations and Inequalities

100

A bakery sells muffins and cookies. One day, the bakery sold 40 items and earned $70. Each muffin costs $2 and each cookie costs $1.50.

If x represents the number of muffins and  represents the number of cookies sold, which matrix correctly represents a system of equations used to find the price per type of item?

 ⌈1    1    ⎮   40 ⌉

 ⌊2 1.50   ⎮   70 ⌋

200

A veterinarian's office offers boarding for cats and dogs. Boarding a cat costs $20 per night, while boarding a dog costs $25 per night. 

If the veterinarian's office boards 18 total animals in one night and earns a total of $400, which equations can be used to find the number of cats, x, and dogs, y, that were boarded? 

x + y = 18

20x + 25y = 400

300

What makes a relation a function

Each input (x-value) is pared with exactly one output (y-value)

400

f (x) = ⎮ x - 2 ⎮ 

what is f (-1)

f (- 1) = 3

500

Describe the end behavior of f (x) = - 3x³. 

as x t → - infinity y → + infinity. 

as x → + infinity, y → - infinity 

Functions

100

Factor x² - 9 

( x - 3 ) ( x + 3 ) 

200

Find the zeros of x² - 5x + 6 

x = 2

x = 3

300

Divide ( 2x³ + 4x ) by ( 2x ) 

x² + 2 

400

Describe the transformation. 

- 3 ⎮ x + 2 ⎮ - 1 

Reflection x - axis 

Vertical stretch by a factor of 3 

2 units left 

1 unit down 

500

Given f (x) = x^2.   Write the combination of functions as a new function.  

1. Reflect f (x) over the x - axis 

2. 3 units right.

3. 7 units down. 

f (x) = - ( x - 3 ) ²  - 7 

Statistics and Probability

100

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is chosen at random, what is the probability it is blue?

3 / 10 

200

A teacher recorded the quiz scores of a student: 70, 80, 90, and 60.

What is the median score?

75

300

A school wants to know how students feel about the cafeteria food. They survey students who are currently eating lunch in the cafeteria.

1. What type of bias might be present in this survey?
2. Explain why this could lead to misleading results.
3. Suggest one way to improve the survey.

1. Selection bias

2. The survey only includes students who choose to eat in the cafeteria. Students who bring lunch or avoid the cafeteria (possibly because they dislike the food) are not included, which can skew the results.

3. Survey a random sample of all students in the school, not just those in the cafeteria.

400

Test scores are normally distributed with a mean of 70 and a standard deviation of 10. Using the Empirical Rule, what percent of scores fall between 60 and 80?

60 to 80 is within 1 standard deviation 

of the mean → 68%

500

Two students tracked how many hours they studied over 5 days.

• Student A: 2, 4, 6, 8, 10
• Student B: 6, 6, 6, 6, 6

1. Find the mean for each student.

2. Without fully calculating, determine which student has the greater standard deviation.

1. Student A mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 6
    Student B mean = (6 + 6 + 6 + 6 + 6) ÷ 5 = 6

2. Student A has the greater standard deviation.

Extra bonus Points

100

perform the indicated operation: 

( 3x² + 5x - 2 ) + ( 2x² - 3x + 7 ) 

5x² + 2x + 5

200

A bacteria population is modeled by the following data:

• Day 0: 100 bacteria
• Day 1: 150 bacteria
• Day 2: 225 bacteria
• Day 3: 338 bacteria

1. Does this data show exponential growth?
2. Explain how you can tell using the pattern in the table.

1. Yes, the data shows exponential growth.
2. Each day the population is multiplied by about the same factor (approximately 1.5):

• 100 × 1.5 = 150
• 150 × 1.5 = 225
• 225 × 1.5 ≈ 338
  Since the values increase by a constant ratio, it represents exponential growth.

300

Given the quadratic equation: 2x² - 7x - 4 = 0 

Solve with the quadratic formula. 

x = - 1/2 

x = 4

400

Solve using the elimination method:

3x + 2y = 16

5x - 2y + 24

( 5 , 1/2 ) 

500

Solve by substitution: 

y = 2x + 3 

4x + y = 19

( 8/3 , 25/3)