Algebra II Honors2011–2012 Semester 1
Free Response Practice Exam A
- The graphs of the polynomial functions and are shown. The domain of both and is the set of real numbers. All zeros of both and can be observed in the graph.
(a)Justify why one of the functions is a 4th degree polynomial and why the other is not.
(b)Justify why one of the functions has a positive lead coefficient and why the other has a negative lead coefficient.
(c)What are the zeros of and ?
(d)Justify why the zeros of and can be the same even though they have different degrees.
- Answer the questions below.
(a)Complete the table and describe the pattern.
Power of i / / / / / / / /Simplified Form
(b)Evaluate .
(c)Solve the equation.
(d)Find the product of the solutions of the equation in part (c).
- A company is making three industrial cleaners A, B, and C. Cleaner A contains 70% of its weight in water, 26% in active chemicals, and 4% in a non-active ingredient to give the cleaner a pleasant smell. Cleaner B has 72% water, 25% active chemicals, and 3% of a non-active ingredient.
Cleaner C has 73% water and 27% active chemicals. Suppose the company is using 5500 grams of water, 2000 grams of the active ingredient, and 130 grams of the inactive ingredient.
(a)Use matrices to organize the given information.
(b)Solve the system to find how many grams the company can make of each cleaner.
2011–20121
Clark County School DistrictRevised 05/26/2011
Algebra II Honors2011–2012 Semester 1
Free ResponsePractice Exam B
- The graph of the polynomial function is shown. The domain of is the set of real numbers. All zeros can be observed in the graph.
(a)What is the degree of ? Justify your answer.
(b)Approximate the absolute minimum of ?
(c)Approximate the maximum value of on the interval ?
(d)Define the range of .
- Use the graph to answer the questions.
(a)Classify the roots of each function as real
or non-real.
(b)What are the domain and range of ?
(c)Describe how to use the graphs to find the value of c when each parabola has the equation .
(d)What are the roots of the equation ?
- A set of low voltage landscape lights are sold in three different packages. Package One contains a transformer, 25 feet of wire, and 5 lights. Package One sells for $20. Package Two contains a transformer, 50 feet of wire, and 15 lights. Package Two sells for $35. Package Three contains a transformer, 100 feet of wire, and 20 lights. Package Three costs $50.
(a)Use matrices to organize the given information.
(b)Solve the system and find the unit price of the transformer, one light, and one foot of wire.
2011–20121
Clark County School DistrictRevised 05/26/2011
Algebra II Honors2011–2012 Semester 1
Free ResponsePractice Exam C
- Use the function .
(a)Describe the end behavior of as and .
(b)Define all zeros of and the y-intercept.
(c)Sketch the graph of the polynomial.
(d)What are the local maximum and local minimum values of ?
(e)What are the domain and range of ?
- Answer the questions regarding quadratic equations.
(a)Sketch a graph of a quadratic equation that has imaginary solutions.
(b)Justify why the equation has complex solutions.
(c)Write a quadratic equation in standard form when the solutions are .
(d)Write a quadratic equation in standard form when the solutions are .
(e)Write a quadratic equation in standard form when the solutions are .
- A marching band director is using matrices to track the positions of musicians during a performance. At one time in the event, two musicians are at positions and on a field (see diagram). Their positions can be expressed by the matrix .
(a)After executing a move, the two musicians are positions and , respectively.Write a matrix B that shows the positions of the two musicians after the move.
(b)The move executed by the musicians is defined by a third matrix, R, such that B = RA. Find matrix R.
(c)A third musician begins the move at the point .
What is the third musician’s position after the move?
2011–20121
Clark County School DistrictRevised 05/26/2011