# Algebra II Semester 1 Practice Exam B

Algebra II Semester 1 Practice Exam B

Note: Some of Questions 1–60 on this practice exam are free-response.

1. To which set(s) of numbers does belong?
1. Evaluate for , and .
2. Which is a simplified form of the expression

?

1. What is the value of n if ?
2. Rewrite the linear equation below to solve for the x-coordinate, .
1. Which is a solution for y in the equation ?

1. Rewrite the absolute value inequality as a compound inequality for .
2. or
3. no solution
4. Which of the following expresses all of the solutions for the compound inequality below?

or

1. or
2. no solution
3. all real numbers
1. In the year 2000 the average price of a home in Clark County was \$197,000. By the year 2007, the average price of a home was \$323,000.

Which is a linear model for the price of a home, P, in Clark County in terms of the year, t? Let t = 0 correspond to the year 2000.

1. Which of the following is a function?
2. {(6, –5), (6, 2), (2, –1)}
3. {(–2, 6), (3, 6), (6, 6)}
4. What is the domain of the following relation?
1. {–3, –2, 0}
2. {–2, 1, 5}
3. {–5, –1, 2}
4. {0, 2, 3}
1. Write the standard form of the equation of the line that passes through the point and is perpendicular to the line .
2. Write an equation in point-slope form of the line that passes through the point and has a slope of .

1. Calculate the slope of a line that passes through the points and .
1. A traveler is in the desert. When the drive begins at 11:00 a.m. the temperature is F. When the traveler returns at 4:00 p.m., the temperature is F. What is the average rate of change in the temperature?
2. F per hour
3. F per hour
4. F per hour
5. F per hour
6. Determine if the following lines are parallel, perpendicular, or neither.
1. Graph the linear equation .

1. The value of varies directly with x, and when What is the value of x when ?
1. Evaluate for the piecewise function:
1. Solve the following linear system:
1. (–4,0)
2. (2, 9)
3. infinitely many solutions
4. no solution

1. What is the value of x in the solution of the following system of linear equations?
1. no solution
1. What is the y-coordinate of the solution to the following system of equations?

1. Graph the system of inequalities.

1. A jar contains 24 coins made up of quarters and dimes. When 3 quarters and 4 dimes are removed, the total value of the coins remaining in the jar is \$2.75. How many quarters and dimes were originally in the jar?
1. Using linear programming procedures, the equation is to be maximized subject to the following constraints.

The grid may be used to graph the feasible region.

What is the maximum value for the objective function?

1. 88
2. 78
3. 73
4. 53

1. A school fundraiser sells different sizes of gift baskets with a varying assortment of nuts and chocolates. A small basket contains 2 packages of nuts and 3 packages of chocolates. A big basket contains 5 packages of nuts and 8 packages of chocolates. The profit on the nuts is \$1 per package, and the profit on chocolate is \$2 per package.

Which shows the use of matrices to find the total profit for each size of basket?

1. Which is the difference , given that and ?

1. Given and , find the product BA.
2. not possible
3. Calculate the determinant.
1. 18
2. 20
3. 26
4. 58
1. Solve for x and y:
1. Which graph from a graphing calculator represents the function ? (Assume the scale on each graph is one unit per tick mark.)

1. Solve the quadratic equation by factoring.
2. no solution
3. What is the solution set of
4. Which is one of the appropriate steps in finding solutions for when solved by completing the square?

1. Which shows the solutions for , using the quadratic formula?
2. Use the discriminant to determine the number and type of solutions of the equation
3. 1 real solution, 1 imaginary solution
4. no real solutions, 2 imaginary solutions
5. 2 real solutions
6. 1 real solution, no imaginary solutions
7. Solve the quadratic equation .

1. Write the expression as a complex number in standard form.

1. Which of the following graphs from a graphing calculator represents the graph of ? (Assume the scale on each graph is one unit per tick mark.)

1. A coin is dropped from a balcony located 300 feet above the street. How many seconds later will it hit the street?

Use the formula where is the height (in feet) of the coin after seconds and is the coin’s initial height.

1. Which graph represents the polynomial function ? (Assume the scale on each graph is one unit per tick mark.)

1. Sketch a graph of the polynomial .

1. Multiply the following polynomials.
1. Solve the polynomial equation .
1. Factor the polynomial .

1. Which is the set of all real zeros of the polynomial function ?
2. According to the Fundamental Theorem of Algebra, how many complex solutions does the polynomial have?
1. According to the Remainder Theorem, which of the following is the remainder when the polynomial is divided by ?

1. Which of the following describes the end behavior of the graph of as ?

2008–20091GO ON

Clark County School DistrictRevised 07/22/2009

Algebra II Semester 1 Practice Exam B

1. Which best represents the graph of the polynomial function as shown on a graphing calculator? (Assume the scale on each graph is one unit per tick mark.)

2008–20091

Clark County School DistrictRevised 07/22/2009

Algebra II Semester 1 Practice Exam B

Free Response

1. Use the graph below of the cubic function .
1. Given , , and , write the equation for the function .
1. Describe the end behavior of as .
1. Compare the graph of to , and list all intercepts of .

1. The quadratic function, , has these characteristics:

axis of symmetry: x = 1
domain:
range:

1. Sketch the graph of and write the equation for it in vertex form.

1. How many x-intercepts does the graph of have? Verify your answer using the discriminant.

2008–20091GO ON

Clark County School DistrictRevised 07/22/2009

Algebra II Semester 1 Practice Exam B

Free Response

1. The final grade in a class is a weighted average of three components: tests, quizzes, and homework. The matrices below represent the weights of the various components and the current percentages of each component for two students in the class.

WeightsCurrent Scores

1. Find the product of the two matrices. Explain what the product represents.
1. A different teacher’s grading system uses total points. In this teacher’s class, a student’s final percentage is computed by finding the sum of the points for the test, quiz, and homework components, then taking that sum as a percentage of 200 total points.

The matrices below represent the test, quiz, and homework scores for three students. Show how to compute each student’s final percentage using matrix arithmetic.

2008–20091

Clark County School DistrictRevised 07/22/2009