Algebra I REVIEW – Unit 4 and Unit 5 Combined Test Name: ____________________

Unit 4 Lesson 1: Working with Polynomials – Add/Subtract/Multiply and then Classify Polynomials

Questions 1-2: Add and Subtract, as indicated, to simplfy each expression.

1. (3𝑥2 − 2𝑥 + 6) + (11𝑥2 − 2𝑥 + 4) 2. (𝑥4 + 2𝑥3 + 8) + (1 − 𝑥4 + 3𝑥3)

Questions 3-4: Find each product.

3. (𝑥 + 6)(4𝑥 − 5) 4. (𝑥 − 7)(2𝑥 + 1)

Unit 4 Lessons 2-5: Solve Quadratic Equations by Factoring

Questions 5-6: Factor each quadratic completely, if possible. If the quadratic cannot be factored write prime.

5. 𝑥2 − 2𝑥 − 15 6. 2𝑥2 + 18𝑥 + 36

Questions 7-9: Solve each equation by factoring.

7. 𝑥2 + 3𝑥 − 40 = 0 8. 𝑥2 + 6𝑥 = −9 9. 2𝑥2 − 6𝑥 − 20 = 0

Word Problem Practice: Use what you know about solving quadratic equations.

10. The length of a rectangle is 4 inches greater than its width. If the area is 60 square inches, what are the dimensions

of the rectangle? Write an equation to represent the area, then solve for the dimensions.

x

x + 4

Unit 4 Lesson 6: Graphs of Quadratic Functions

Questions 11-12: Complete a table, graph, and investigate the characteristics of the following functions:

11) 𝑦 = −𝑥2 + 6𝑥 − 8 12) 𝑦 = 𝑥2 − 4𝑥 + 8

State the following…

Domain: Domain:

Range: Range:

Zeros: Zeros:

Y–Intercept: Y–Intercept:

Vertex: Vertex:

Unit 4 Lesson 7: Solve Quadratics by Graphing

Questions 13-15: Identify the number of solutions and describe how the solutions can be seen on the graph.

13. 14. 15.

Maximum

or

Minimum

Maximum

or

Minimum

Unit 4 Lesson 8: Transformations

Questions 16-17: Change the standard form of the quadratic equation to vertex form, then describe the

transformations of the parent function 𝑓(𝑥) = 𝑥2.

16. 𝑔(𝑥) = 𝑥2 + 16𝑥 + 48 17. ℎ(𝑥) = 𝑥2 − 6𝑥 + 15

Questions 18-20: Describe the transformations of 𝑓(𝑥).

18. −𝑓(𝑥 + 5) − 2 19. 𝑓(𝑥 − 3) + 7 20. 𝑓(𝑥 + 1)

Unit 4 Lesson 9: Solve by Completing the Square

Questions 21-22: Identify the zeros of the function by completing the square and solving.

21. 𝑥2 − 8𝑥 + 12 = 0 22. 𝑥2 − 12𝑥 + 20 = 0

Check: Check:

Unit 4 Lesson 10: Solve Quadratic Equations by Using the Quadratic Formula

Questions 23-25: State the value of the discriminant then calculate the solution(s); rounding to the nearest tenth if

necessary.

23. 𝑥2 + 3𝑥 − 18 = 0 24. 3𝑥2 − 12𝑥 = −12 25. 5𝑥2 + 2𝑥 + 4 = 0

Discriminant: Discriminant: Discriminant:

Solution(s): Solution(s): Solution(s):

Unit 4 TASK: Comparing Quadratic Functions:

Questions 26-27: Compare properties of quadratic functions represented in different ways.

26. Compare the graph of f(x) to the graph of the function given by the equation 𝑔(𝑥) = 𝑥2 − 6𝑥 + 6. Which function

has a greater minimum value?

27. Which function is shown in the graph? Identify 2 characteristics to support your reasoning.

A) 𝑝(𝑥) = 𝑥2 + 2𝑥 + 18

B) 𝑞(𝑥) = 𝑥2 − 4𝑥 + 2

C) 𝑟(𝑥) = 𝑥2 + 8𝑥 + 18

Unit 5 TASK: Comparing Functions Graphically:

Questions 28-30: Identify the function family (Linear, Quadratic, or Exponential) for each question and describe two

characteristics that justify your reasoning.

28. 29. 𝑦 = 𝑥2 + 5𝑥 + 6 30.

f(x)

Questions 31-33: Match the Characteristics with the graph.

A) Range: −∞ < 𝑦 < ∞ B) Asymptote: 𝑦 = 3 C) Minimum: (2, 4)

31. __________________ 32. __________________ 33. __________________

Question 34: Identify the model that BEST represents each situation:

MODEL: ______________________ _______________________ _______________________

Questions 35-37: Match the Characteristics with the graph.

A) 𝐷𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑓𝑜𝑟 (−∞, ∞) B) 𝐷𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑓𝑜𝑟 (−∞, 3) C) 𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔 𝑓𝑜𝑟 (−∞, ∞)

35. __________________ 36. __________________ 37. __________________

Situation A) Annie is saving money for college.

She deposited $1000 into a savings

account and she expects it to

double every 5 years.

Situation B) Marcus throws a football straight up into the air. After it reaches its maximum height of 20 feet, it descends back to the ground.

Situation C) Ben works at a T-shirt shop. He has

20 shirts done and is printing the

rest of the T-shirt order at 3 shirts

per minute.

Unit 5 Lesson 1: Even and Odd Functions:

Questions 38-40: Identify whether each function is Even, Odd, or Neither and justify based on symmetry.

38. 39. 𝑦 = 4𝑥3 + 5𝑥2 40.

Unit 5 Lesson 2: Comparing Linear and Exponential functions:

Questions 41-42: Identify the parameters in the context of the problem situation.

41. Sam is draining his 2000 gallon pool at 42. Tessa is saving money to purchase a used car.

15 gallons per minute. This situation can She deposits $850 is savings that will earn 3%

modeled by the function: 𝑓(𝑥) = −15𝑥 + 2000 interest. This situation can be modeled by

𝑔(𝑥) = 850(1.03)𝑥

Question 43-45: Match the Equation with the graph and identify the key characteristics.

A) 𝑟(𝑥) = −3𝑥 + 5 B) 𝑠(𝑥) = 5(3)𝑥 C) 𝑡(𝑥) = 5𝑥 − 3

43. __________________ 44. __________________ 45. __________________

Unit 5 Lesson 3: Stretch, Shrink, and Comparing Transformations

Question 46: Describe the transformations of h(x) = −1

2x2 + 4 from the parent quadratic function.

Question 47: Consider the functions f(x) and g(x):

𝑓(𝑥) = 𝑥2 − 6𝑥 + 13 𝑔(𝑥) =1

2𝑥 + 1

47. Describe transformations of f(x) and g(x) that will make both functions

pass through the point (2, 3)? Write the transformation in function notation.

Unit 5 Lesson 4: Comparing Average Rates of Change: Questions 48-50: Calculate the average rate of change for each function over the intervals [0, 2] and [3, 4], then determine wheter the function is Linear or Exponential based on your calculations. 48. Rate for r(x): 49. Rate for s(x): 50. Which statement BEST describes the comparison of the y-values for r(x) and s(x)? Add to the table of values to justify your answer.

A) The values of s(x) will eventually exceed the values of r(x) over the interval [0, 5]

B) The values of r(x) will always exceed values of s(x)

Unit 5 Lesson 5: Writing a Model Question 51: Zach enjoys hiking. At lunch time he is 10 miles from his campsite. When he starts off hiking after lunch, he is hiking at 3 miles per hour. Part A) Linear or Exponential? Use a recursive process to determine how far Zach is from his campsite after hiking for 2 hours after lunch. Part B) Write a model to represent this situation and use the model to determine how far Zach is from his campsite after hiking 4 hours after lunch. Part C) How much more time does Zach need to reach his destination that is 25 miles from his campsite? Give evidence to support your answer.

g(x)

f(x)