Algebra IISemester 2 PracticeExam B

DRAFT

  1. Find the solution set of .
  2. Write the expression in exponential notation.
  3. Simplify.
  4. 2
  5. 4
  6. 8
  7. 12
  8. Let and . Find .
  9. Given and , what is ?
  10. –80
  11. –8
  12. 32
  13. 640

  1. Let and . Find.
  2. Which is the inverse of the function for ?
  3. , x ≥ 0
  4. ,x ≥ 0
  5. , x ≥ 0
  6. , x ≥ 0
  7. The graph below is the function .

What is the value of k?


  1. Solve for x:
  2. x = 5
  3. x =
  4. x =
  5. x =
  6. To compete in a sailboat race, a boat must satisfy the rule

,

where lis the length of the boat (in meters), s is the area of the sails (in square meters), and d is the volume of water displaced by the boat (in cubic meters).

A boat has a length of 21 meters and sail area of 400 square meters. What is its displacement?

  1. Simplify the expression where .
  2. –4+7i

  1. What graph represents the function ?

  1. Sketch the graph of.
  2. Simplify the expression.
  3. Which equation is equivalent to ?
  4. What is the solution of the equation?
  5. x = ±8
  6. x = ±9
  7. x = 64
  8. x = 81
  9. Solve for k:

  1. Solve for y:
  1. y = 0.01
  2. y = 0.1
  3. y = 1
  4. y = 10
  1. The relationship between an earthquake’s moment magnitude M and its energy released E (in ergs) is approximately defined by the function:

Find the amount of energy released by a magnitude 8.1 earthquake.

  1. What is the minimum or maximum of the quadratic function ?
  2. The value of z varies jointly with x and y. If z = 4 when x = 1 and y = 12, what is the value of z when x = 5 and y = –6?
  3. –90
  4. –10
  5. 2
  6. 8

  1. Sketch the graph of .
  2. Which best describes all asymptotes of the function ?
  3. x = 1, x = 2
  4. x = 1, y = 1
  5. x = 2, y = 0
  6. x = 2, y = 1
  7. Which expression is equivalent to?
  8. Solve for x:
  1. x = –3
  2. x = 1
  3. x = 2
  4. x = 3

  1. What is the solution set of ?
  2. {3, –1}
  3. {0, 4}
  4. {–1}
  5. The equation

describes the relationship between the focal length f of a thin lens, the distance do an object is from the lens, and the distance di the image is from the lens.

A lens has a focal length of
6 centimeters. How far is an object from a lens when its image is three times as far away?

  1. Given the system of linear equations

find the solution to the system using matrices by:

(1)writing in the form ,

(2)then computing ,

(3)and finally computing .

  1. Identify and graph the conic section:
  1. Identify and graph the conic section:
  1. Identify and graph the conic section:
  1. Identify and graph the conic section:
  1. What type of conic section is represented by the graph of ?
  2. circle
  3. ellipse
  4. hyperbola
  5. parabola
  6. Which is the equation of a parabola?

  1. Graph the function:
  1. Expand the expression .
  2. What is the series when written in summation notation?
  3. What equation is the sum of thefirst 15 terms in the series 2 + 5 + 8 + 11 + …?

  1. A box of paper clips begins with 270 clips. A person takes one-third of the clips and passes the box to a second person who takes one-third of the remaining clips. Another person then takes one third of the remaining clips. How many clips remain when a fourth person receives the box?
  2. 10
  3. 80
  4. 90
  5. 120
  6. What is the sum of the infinite geometric series ?
  7. Write the formula of an arithmetic sequence when and .
  8. Which is a formula of the geometric sequence 0.04, 0.2, 1, 5, …?
  9. Write a recursive rule for the sequence
    1, 2, 5, 14, 41, 122, …

  1. Postal codes in Canada consist of three letters and three digits, in an alternating pattern, beginning with a letter. For example, T1J4A5.

Any digit is allowed in the 2nd, 4th, and 6th places. The letters D, F, I, O, Q, and U are not allowed in the 1st, 3rd, or 5th places. Additionally, the letters W and Z are not allowed in the 1st place.

How many possible Canadian postal codes exist?

  1. Three students are chosen at random from a group of five. How many different combinations of three students are possible?
  2. 10
  3. 20
  4. 60
  5. 120
  6. What is the expanded form of ?
  7. What is the coefficient of in the expansion of ?
  8. 12
  9. 18
  10. 36
  11. 54

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra IISemester 2 PracticeExam B

DRAFT

  1. A group of students consists of
    3 freshmen, 4 sophomores, 5 juniors, and 2 seniors. If two students are chosen at random from the group, what is the probability that neither student is a junior?
  2. Which measure(s) of central tendency are generally affected by outliers?
  3. The list below shows the low temperatures for a North Dakota city over a 10-day period.

11, 17, 17, 12, 1, 2, 18, 17, 26, 28

Create a box-plot that represents the data.

2008–20091

ClarkCountySchool DistrictRevised 07/22/2009

Algebra IISemester 2 PracticeExam B

Free Response

DRAFT

  1. Use the function to answer the questions below.
  2. What are the domain and range of ?
  1. Derive.
  1. Sketch the graph of on the same set of axes.
  1. If , find .
  1. The value A of an investment earning Ipercent annual interest compounded quarterly can be modeled by the function , where A0 is the initial value of the investment and t is the length of the investment in years.
  2. The amount $3000 is deposited into an investment earning 8% annual interest. What is the value of the investment after 10 years? (Leave your answer as an expression; do not complete the computation.)
  1. Write an equation for , the time required for an investment to reach a value of A.
  1. Using your answer from Part B, how much time will a $1000 investment need to be an account earning 10% interest to double its value? (Leave your answer as an expression; do not complete the computation.)

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra IISemester 2 PracticeExam B

Free Response

DRAFT

  1. Use the functionsand to answer the questions below.
  2. Let . Find.
  1. Solve .
  1. Sketch the graph of on the grid provided. Be certain to note any asymptotes and intercepts on the graph.

2008–20091

ClarkCountySchool DistrictRevised 07/22/2009