This page shows questions in the Alg II Year 1 public release module at MSDE. Algebra 2
"Alg II Year 1"
Select from the list to explore. Read any associated passages and then interact with the questions here.
This is a question with 2 parts, including a multiple choice question that allows you to select only one option, and, a multiple choice question that allows you to select several options.
Consider the equation open parentheses x minus 2 close parentheses squared equals negative three x plus 6.
Part A
Which expression is a factor of both open parentheses x minus 2 close parentheses squared and negative three x plus 6?
Part B
What are the solutions of the equation open parentheses x minus 2 close parentheses squared equals negative three x plus 6?
Select all that apply.
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This is a multiple choice question that allows you to select several options.
Which value is a solution of the equation x squared equals fraction with numerator of 2 x and denominator of x plus 1?
Select all that apply.
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This is a multiple choice question that allows you to select several options.
Consider the function f of x equals log of x.
Which two transformations can be used to move the graph of f of x to the graph of the opposite of f of x plus 4?
Select all that apply.
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This is a question with 4 parts, including a multiple choice question that allows you to select several options, and, a multiple choice question that allows you to select only one option.
Part A
A company owns some shares of MStock. The accountant for the company models the stock's price per share, in dollars, as its value changes over several weeks. A graph of the model is shown.
Which statements are true about the value of the stock?
Select all that apply.
Part B
Which point shows the approximate lowest value of MStock?
Part C
The company also owns shares in NStock. The accountant for the company models the stock's price per share for NStock. The graphs of the models for NStock and MStock are shown.
After approximately what week is the value of NStock greater than the value of MStock?
Part D
In which week did both stocks reach their lowest values?
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This is a drag and drop question that allows you to select objects and place them in an appropriate answer space.
A unit circle with center P is shown. In circle P, angle J P K is a right angle, the measure of angle H P J equals one half the measure of angle J P K, and the measure of angle L P K equals the measure of angle H P J plus the measure of angle J P K.
Determine the values of angle L P K and the lengths of arc L M, arc H J, and arc J K.
Drag and drop each radian measure into the diagram.
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This is a multiple choice question that allows you to select only one option.
Gina rolled two number cubes, each numbered from 1 to 6, and calculated the sum of the two numbers landing face up. She repeated the process 100 times, and only once did she record a sum of 2. She suspected that the cubes might not be fair.
Gina reasoned that if the cubes were fair, the probability of rolling the sum of 2 is fraction with numerator of one and denominator of 36. For 100 rolls, 100 open parentheses fraction with numerator of one and denominator of 36 close parentheses is approximately equal to 2 point 8. She thought she should have seen the sum about two or three times in 100 rolls.
Under the assumption that the cubes are fair, she conducted a simulation to determine what is a plausible number of times to observe the sum in 100 rolls. The results of 50 trials of the simulation are shown in the table.
| Results of Simulation | |
| Observations of the Sum | Frequency out of 50 |
|---|---|
| no times | 4 |
| one time | 5 |
| two times | 10 |
| three times | 14 |
| four times | 10 |
| five times | 4 |
| six times | 2 |
| seven times | 1 |
Based on the results of the simulation, is there statistical evidence that Gina's number cubes are not fair?
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This is a question with 2 parts, including a test question that allows you to enter extended text in your response.
Part A
Three friends go to a store to rent games and movies. Calvin rents 3 movies and 2 games and spends a total of $25. Samantha rents 2 movies and 1 game and spends a total of $14.75.
If the rental fee for each game is the same and the rental fee for each movie is the same, determine how much their friend, Keith, will spend at the rental store to rent 1 movie and 2 games. Explain your answer.
Enter your answer and your explanation in the space provided.
Part B
A fourth friend, Beth, rents her movies and games from a different store. At this store, the rental fee for a movie is the same as the rental fee for a game. The total cost of renting 2 movies and 3 games is the same at both stores.
Determine the rental fee that Beth's store charges for each movie or game. Explain your answer.
Enter your answer and your explanation in the space provided.
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This is a test question that allows you to enter extended text in your response.
The table contains data about the fuel capacity, in gallons, and the weight, in pounds, for small motorcycles.
| Fuel Capacity (gallons) | Weight (pounds) |
|---|---|
| 0.5 | 84 |
| 1.0 | 131 |
| 1.1 | 139 |
| 1.3 | 145 |
| 1.7 | 176 |
| 2.0 | 212 |
| 2.1 | 227 |
| 2.2 | 219 |
| 2.5 | 253 |
| 2.6 | 263 |
- Give an equation for a linear regression model for these data to predict the weight from the fuel capacity. Identify the variables in your equation.
- Justify how well your linear equation fits the model by discussing a scatter plot of the data and the correlation coefficient in assessing the fit of your linear model.
- Use your model to predict the total weight of a small motorcycle that has a fuel capacity of 6 gallons, and discuss the usefulness of this prediction.
Enter your answer and your explanation in the space provided.
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This is test content.
The functions h of d, g of y, and f of m each represent the balance of a savings account that is opened with an initial balance of a dollars, with no additional deposits of withdrawals.
- f of m equals a open parentheses one point zero zero zero eight raised to the power of m close parentheses where m is the number of months since the account was opened
- g of y equals a open parentheses one point zero one raised to the power of y close parentheses where y is the number of years since the account was opened
- h of d equals a open parentheses one point zero zero zero zero five raised to the power of d close parentheses where d is the number of days since the account was opened
If the time period is the same for all three accounts, order the functions from greatest to least growth rate.
Drag and drop the functions into the correct order.
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This is a multiple choice question that allows you to select several options.
When graphed in the xy-coordinate plane, which equations will intersect the graph of y equals two raised to the power of x in the interval 0 is less than x which is less than 1?
Select all that apply.
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This is a multiple choice question that allows you to select several options.
Select the values that are the solutions to the equation x squared minus 14 x plus 50 equals 0.
Select all that apply.
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This is a test question that allows you to enter extended text in your response.
Mark solved the equation in the box, using the steps shown.
Is the solution x equals 4 correct? State yes or no, and justify your answer.
Enter your answer and your justification in the space provided.
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This is a multiple choice question that allows you to select several options.
In the equation shown, p is a constant. If the equation has no real solutions, which could be the value of p?
2 x squared plus p x plus 4 equals zero
Select all that apply.
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This is a multiple choice question that allows you to select several options.
Which expressions are equivalent to the given expression for all positive values of x, y, and z?fraction with numerator of x squared y cubed z to the five halves power and a denominator of x to the negative fourth power y to the fifth power z squared
Select all that apply
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This is a question with 2 parts, including a fill in the blank question that allows you to enter only numbers, and, a multiple choice question that allows you to select only one option.
The size of the population of a certain city was 25,000 in 2010 and decreased by 4% each year afterward.
Part A
The size of the population, y, can be modeled by an exponential function of the form y equals a open parenthesis b to the power of x close parenthesis, where x represents the number of years since 2010 and a and b are constants. What is the value of b?
Enter your answer in the box.
Part B
Suppose the equation representing the size of the population is graphed in the xy-coordinate plane. Which statement is true?
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This is a question with 4 parts, including a fill in the blank question that allows you to enter only numbers, and, a multiple choice question that allows you to select only one option.
Wesley deposits $2,000 in an account that earns 4.5% annual interest compounded continuously. If no other deposits or withdrawals are made, the amount, A, in dollars, in the account after t years can be modeled by the function A of t equals two thousand e raised to the zero point zero four five t power.
Part A
What is the average rate of change, in dollars per year, of the amount in the account over the first two years? Give your answer to the nearest whole number.
Enter your answer in the box.
$ per year
Part B
The solution to the equation four thousand equals two thousand e raised to the zero point zero four five t power gives the number of years it will take for the amount in the account to reach $4,000. What is the solution to the equation expressed as a logarithm?
Part C
Which interval contains the numbers of years when the amount in the account will first reach $5,000?
Part D
If Wesley wants to have $5,000 in the account after 15 years, how much should he deposit initially, assuming the same interest rate? Give your answer to the nearest whole number of dollars.
Enter your answer in the box.
$
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This is a question with 3 parts, including a fill in the blank question that allows you to enter only numbers.
Two functions are shown.f of x equals x squared
g of x equals 3 minus xFill in each coefficient to complete the definition of 2 f of the quantity 1 minus x end quantity minus 3 g of x.
2 f of the quantity 1 minus x end quantity minus 3 g of x equals blank x squared plus blank x plus blank mathematics expression or equation mathematics expression or equation
This is a test question that allows you to enter extended text in your response.
A function f of x is defined as f of x equals x squared plus x minus 6.
Determine
- the x-intercepts
- the y-intercept
- the coordinates of any maximum or minimum, and
- intervals of increase and decrease
Enter your answers in the space provided. Enter only your answers.
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This is a question with 3 parts, including a multiple choice question that allows you to select only one option, and, a question with drop-down menus from which you must select an option to fill in the blank.
The graph shows the median percent cloud cover per month for 12 months for the city of Tampa, Florida.
Because the cloud cover tends to be cyclical in nature, a sine function was used to model the relationship between median percent cloud cover and month. With the number 1 representing the month of January, the model c equals 55 plus 9 sine open parenthesis zero point nine eight m plus zero point 7 4 close parenthesis predicts the median percent cloud cover for month number m.
Part A
Which constant in the model gives the best representation of the average of the median percent cloud cover for the year?
Part B
The median percent cloud cover for the month of September was 58%. How does the model predict the amount of cloud cover for September?
Select from the drop-down menus to correctly complete the sentence.
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