# Express All Probability Answers As Percentages Name:______

Probability Review Guide

Topics

Express all probability answers as percentages.

1. You spin the spinner to the right and then flip a fair two-sided coin (heads/tails).

a. List the sample space for this chance experiment.

b. List the outcomes that make up the event “Spin an odd number and flip tails”?

c. What is the probability of spinning an odd number and flipping tails?

e. What is the probability of spinning a 3 or flipping heads? Round your answer to the nearest hundredth if necessary.

2. You asked a group of 26 students at school (16 were male) what type of party they used to enjoy going to when they were a child. Ten students said they liked to go to bowling parties, 4 of them were female. Complete a hypothetical two-way frequency table to display this information.

Male / Female / Total
Bowling
Pizza
Total

Assuming that the rest of the student body would vote following the same trend, find the following probabilities and round your answers to the nearest hundredth if necessary.

a. What is the probability:

i) that a randomly selected student would be female?

ii) that a randomly selected student would like a bowling party given that the student is male?

iii) that student was female given the selected student likes bowling parties?

c. What percentage of those students who liked pizza parties are female?

3. When a class is randomly selected in a high school, the probability that it is a core class is 0.82, the probability that the class is on the second floor of the school is 0.54, and the probability it is a core class and is on the second floor is 0.45. Let C be the event that it is a core class and S be the event that the class is on the second floor.

a) Complete a hypothetical 1000 two-way table below.

Core Class / Not a Core Class / Total
Second Floor
Not the Second Floor
Total

b) Use the mathematical notation for probability: intersection, union, complement, and conditional probability in your work to answer the following questions. What is the probability that a randomly selected class:

i) is not a core class?

ii) is a core class and is not on the second floor?

iii) is a core class or on the second floor?

iv) is a core class given it is on the second floor?

c) Are the events “a class is a core class” and “a class is on the second floor” independent? Clearly explain in complete sentences using mathematical reasoning and specific probabilities.

4. For the following questions, use the spinner below. All events on the spinner are equally likely.

a) If the spinner is spun four times, what is the probability that it will land on white all four times?

b) If the spinner is spun three times, what is the probability that it will never land on blue?

5. On any given winter day at FHS the probability that a student has the flu is 24%. The probability that a student has both a cough and the flu is about 14%. What is the probability that a student has a cough given they have the flu?

Topics

Graphing

Graph each function. Identifying the vertex, -intercepts(), -intercepts(), and axis of symmetry. Also state the domain and range for each function.

1) 2)

3) Solve by factoring.4) Solve by completing the square.

5)Solve using any method.6)Solve using the quadratic formula.

The function, , models the height of a ball that is thrown into the air. represents time in seconds and represent the height in feet.

7) What is the maximum height of the ball? Use the vertex to identify the maximum height.

8) How many seconds does the ball take to hit the ground? The height is 0 when the ball hits the ground. Set the function equal to zero and solve for .

Polynomials – Review Guide

Topics

Use the function to complete questions 1 – 4.

1. Given that is a factor of , factor completely.
1. Identify the zeros of .
1. What is the degree of the function?
1. Determine the end behavior of as and .
1. Sketch a graph of .
1. Solve for :
1. Given that is a factor of , find all solutions to the equation:

.

1. Let . Given that , what is a factor of ? Find all other factors. Then determine the zeros of .
1. Given that is a factor of , find the -intercepts of .
1. Let .
2. Find the zeros of . Also find the multiplicities.
1. Determine the end behavior of .
1. Given the polynomial function graphed to the right, what is a possible equation for the function?

Rational Functions – Review Guide

Topics

Simplify the following rational expressions.

1. 2.

Perform the addition/subtraction and simplify the following expressions.

1. 4.
1. 6.

Perform the multiplication/division and simplify the following expressions.

1. 8.
1. 10.

Solve the following rational equations. Make sure to check for extraneous solutions.

1. 12.

Square Roots and Radicals – Review Guide

Topics

Rewrite each of the following in simplest radical form.

1. 2. 3.
1. 5. 6.
1. 8. 9.

Rationalize the denominator and simplify the expression.

1. 11. 12.

Solve the equations and check for extraneous solutions.

1. 14.
1. 16.
1. 18.

Functions – Review Guide

Topics

Find the inverse of the following functions.

1. 2.
1. 4.

Use function composition to show whether or not the following functions are inverses.

1. , 6. ,

Use the following functions for all problems:

7. 8.

9. 10.

11. 12.

13. 14.

Exponential Functions – Review Guide

Topics

For each of the functions below, find

a) the parent function,

b) the transformations of the graph of the parent function to get the graph of the given function,

c) the domain, range, and asymptote.

1. 2.

a) a)

b)b)

c)c)

1. 4.

a) a)

b)b)

c)c)

Graph the functions with their parent functions on the same axis.

1. 6.

Use the properties of exponents to rewrite the following expressions.

7. 8.

9. 10.

Growth, Decay, and Logarithms – Review Guide

Topics

Use exponential growth and decay models to answer the following questions.

1. You decide to invest \$1000 into a retirement fund with an annual growth rate of 12%.
2. Write an equation for the amount of money, , in the account after years since 2017.
1. Determine the amount of money in the account in 2050.
1. You are hoping to be a millionaire when you retire. Determine what year you need to retire in order to have \$1,000,000.
1. The population of Midtown was 20,000 people in 2000. A CHS Algebra 2 student finds that the population is decreasing at a rate of 2.31%.
2. Determine an equation to model the population of Midtown.
1. What is the population in 2020?
1. When will the population reach 14,000?
1. How long will it take for the population to be half of what is was in 2000?

Condense/Expand the following logarithmic expressions.

1. 4.
1. 6.

Solve the following equations. Give an exact answer.

7. 8.

9. 10.

12. 13.

For each function given below, first determine the transformations of the parent function, , and then find the domain, range, and equation of the asymptote.

14. 15.

Topics not on this review that will be on the Final Exam:

• Unit 10: Trigonometry
• Unit 10.5: Graphing Sine and Cosine
• Unit 11: Sequences and Series