Algebra II HSemester 2 PracticeExam A

DRAFT

  1. Find the solution set of .
  2. What is the simplified form of the expression ?
  3. Simplify.
  4. b
  5. 1

  1. Let and . Which expression is equivalent to?
  2. If and , what is ?
  3. 47
  4. 92
  5. 139
  6. 407
  7. Let and . Which expression is equivalent to ?

  1. Which is the inverse of the function for ?
  2. What function is represented by this graph?

  1. Solve for x:
  2. x = –25
  3. x =
  4. x =
  5. x =
  6. You are trying to determine the height of a regular truncated pyramid that cannot be measured directly. The height h and slant height s of a truncated pyramid are related by the formula where and are the lengths of the upper and lower bases of the pyramid, respectively. If , , and , what is the height of the pyramid?
  7. 2
  8. 4
  9. Simplify the expression where .
  10. –7 + 5i
  11. –7 – i
  12. –5 + 5i
  13. 5 – 5i

  1. Whatfunction is represented by the graph?

  1. Which graph represents ?

  1. Which expression is equivalent to ?
  2. Which expression is equivalent to ?
  3. Solve the equation for x:

  1. Which is a solution for the equation ?
  2. Solve for x:
  3. x =
  4. x =
  5. x = 2
  6. no solution
  7. In the year 1995, about 20 million people used the Internet. Between 1995 and 2001, the number of people who used the internet grew by about 75% each year.

Which function best models the relationship between p, the number of people using the internet (in millions), and t, the number of years since 1995?


  1. What is the minimum or maximum of the quadratic function ?
  2. The value of w varies directly with x and inversely with y. If w = 5 when x = and y = , what is the value of w when
    x = 4 and y = ?
  3. 40
  4. 90
  5. 160

  1. What function is represented by the graph?
  1. Which of the following functions have an asymptote aty = 1?
  1. II only
  1. I and II only
  2. I and III only
  3. I, II, and III

  1. Simplify the expression .
  2. What is the solution set of?
  3. {–1, 3}
  4. {0, 4}
  5. {–1}
  6. What is the solution set of ?
  7. {–8, 2}
  8. {–8}
  9. {–4, 2}
  10. {–4}

  1. The harmonic meanh of a set of nnumbers is given by the formula

.

What is the harmonic mean of two positive numbers that differ by one if the smaller number is k?

  1. Given the system of linear equations:

Which expression below shows the solution to the system using matrices?


  1. What is the equation of the graph below?

  1. Which graph best represents the equation ?

  1. What is the equation for the graph below?

  1. Which graph best represents the graph of ?

  1. What equation represents the graph below?

  1. Which is the equation of a parabola?

  1. The charge for parking at an airport is $5 for time up to one hour, plus $2 for each additional hour (or portion of an hour) up to a maximum of $15. What graph represents this situation?

  1. Expand the expression .
  2. What is the series when written in summation notation?
  3. What equation is the sum of the 8 terms in the series ?

  1. Figure 1 shows a square with an area of 9 square units. In Figure 2, the first square has been divided into nine smaller congruent squares and the middle one removed. In Figure 3, each of the squares is again subdivided and the middle square removed. If the pattern continues, what is the area of Figure 6?

  1. What is the sum of the geometric series ?
  2. 3
  3. 4
  4. 9
  5. 12
  6. Which is a formulaof ageometric sequence when and ?
  7. Which is a formula of the arithmetic sequence 4, , 7, , …?

  1. Which is a recursive rule for the sequence 2, 4, 7, 11, 16, …?
  2. In the 1980’s, the standard configuration for a Wyoming license plate was a small number between 1 and 23, inclusive, followed by four digits with repetition allowed.

For example:

How many license plates were possible for the entire state of Wyoming in the 1980’s?

  1. 116,000
  2. 230,000
  3. 300,000
  4. 1,000,000

  1. A student will randomly choose four digits from the set {1, 2, 3, 4, 5, 6}, without replacement, and arrange them in the order they were chosen. How many different four-digit numbers can be made in this way?
  2. 15
  3. 24
  4. 360
  5. 720
  6. Which is a term of the expanded form of ?
  7. 1000a
  8. What is the coefficient of in the expansion of ?
  9. 4
  10. 8
  11. 24
  12. 32

  1. A cooler contains 8 cans of cola, 6 cans of ginger ale, 4 cans of root beer, and
    2 cans of orange soda. If a person reaches in the cooler and pulls out two cans at random, what is the probability that both cans will be ginger ale?
  2. Which of these measures are greatly influenced by extreme values?
  3. mean
  4. median
  5. interquartile range
  6. range
  1. IV only
  1. I and IV only
  2. II and III only
  3. I, III, and IV only

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

DRAFT

  1. The graph below shows the number of home runs hit by the 31 teams in a baseball league.

Which value could be the median number of home runs?

  1. 177
  2. 162
  3. 147
  4. 112

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

DRAFT

  1. What is the range of the function ?
  2. all real numbers

  1. What is the domain of the function ?

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

DRAFT

  1. What are the domain and range of the function ?
  2. Domain:
    Range:
  3. Domain:
    Range:
  4. Domain: all real numbers
    Range:
  5. Domain: all real numbers
    Range: all real numbers
  6. What are the domain and range of the function ?
  7. Domain:
    Range:
  8. Domain:
    Range:
  9. Domain:
    Range: all real numbers
  10. Domain:
    Range: all real numbers
  11. What are the horizontal asymptotes of the logistic growth function ?
  12. y = 0, y = 3
  13. y = 0, y = 6
  14. y = –2, y = 3
  15. y = –2, y = 6

  1. Which equation is represented in the graph below?

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

DRAFT

  1. What is the approximate local maximum of the function below?

  1. Which interval contains the local minimum of ?
  2. The function has no local minimum.
  3. What is assumed in the second step in a proof by mathematical induction?
  4. The statement is true for k = 0.
  5. The statement is true for n = 1.
  6. The statement is true for n = k.
  7. The statement is true for n = k + 1.

2008–20091

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

DRAFT

  1. In a proof by mathematical induction that for all positive integers n, what should be proven in the second step of the proof?
  2. 1 = 1

2008–20091

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

Free Response

DRAFT

  1. Use the functions and to answer the questions below.
  2. What are the domains and ranges of and ?
  1. Sketch the graph of on the grid provided.
  2. Are and inverse functions of each other? Provide evidence why or why not.
  1. Let . Find .
  1. The half-life of the radioactive isotope Barium-139 is 83 minutes. A scientist has 20 grams of
    Barium-139 at time t = 0.
  2. Write a function that expresses the quantity of Barium-139 as a function of t, the number of minutes after t = 0.

The half-life of Sodium-24 is 15 hours. The amount of Sodium-24 after t hours can be expressed as , where A0 is the initial amount of the isotope.

  1. If A0 = 10 grams, what amount, in grams, of Sodium-24 would remain after 100 hours? Leave your answer in terms of e.
  1. Write an equation for , the time required for 10 grams of Sodium-24 to decay to an amount A.

2008–20091GO ON

ClarkCountySchool DistrictRevised 07/22/2009

Algebra II HSemester 2 PracticeExam A

Free Response

DRAFT

  1. Use the function to answer the questions below.
  2. Sketch the graph of on the grid provided. Be certain to note any asymptotes and intercepts on the graph.
  1. The x-coordinate of any local maximum or minimumof can be found when. Find the x-coordinate(s) of all local extrema.
  1. Use the x-coordinates found in Part B to compute the y-coordinates of any local extrema of . Label any extrema on the graph.

2008–20091

ClarkCountySchool DistrictRevised 07/22/2009