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This page shows questions in the Alg II Integrated Mathematics public release module at MSDE. Algebra 2
"Alg II Integrated Mathematics"

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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?

  1. A.
    2
  2. B.
    3
  3. C.
    x plus 2
  4. D.
    x minus 2
  5. E.
    open parentheses x minus 2 close parentheses squared

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.

  1. A.
    x equals negative 3
  2. B.
    x equals negative 2
  3. C.
    x equals negative 1
  4. D.
    x equals zero
  5. E.
    x equals 1
  6. F.
    x equals 2
  7. G.
    x equals 3

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

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?

  1. A.
    The size of the population in 2010 is indicated by the x-intercept.
  2. B.
    The size of the population in 2010 is indicated by the y-intercept.
  3. C.
    The rate of change per year is indicated by the x-intercept.
  4. D.
    The rate of change per year is indicated by the y-intercept.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

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?

  1. A.
    zero point zero four five natural log of 2
  2. B.
    fraction with numerator of the natural log of 2 and denominator of zero point zero four five
  3. C.
    natural log of the fraction with numerator of 2 and denominator of zero point zero four five
  4. D.
    natural log of the fraction with numerator of zero point zero four five and denominator of 2

Part C

Which interval contains the numbers of years when the amount in the account will first reach $5,000?

  1. A.
    16 is less than t which is less than 20
  2. B.
    20 is less than t which is less than 24
  3. C.
    24 is less than t which is less than 28
  4. D.
    28 is less than t which is less than 32

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.

$

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.