NAME: ________________________________________________________ DATE: _____________

Algebra 2: MOCK MIDTERM #1

Part I Directions: Answer all questions from this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Record your answers on the scantron provided using a #2 pencil.

1. When and d is a positive integer, the expression is equivalent to

1)

2)

3)

4)

2. Given i is the imaginary unit, in simplest form is

1)

2)

3)

4)

3. Which factorization is incorrect?

1)

2)

3)

4)

4. Which graph has the following characteristics?

• three real zeros

• 𝑎𝑠 𝑥 → −∞, 𝑓(𝑥) → −∞

• 𝑎𝑠 𝑥 → ∞, 𝑓(𝑥) → −∞

1)

3)

5. The solution set for the equation is

1)

2)

3)

4)

6. The zeros for are

1)

2)

3)

4)

2)

4)

7. A solution of the equation is

1)

2)

3)

4)

8. The expression is equivalent to

1)

2)

3)

4)

9. Which value is in the domain of the function graphed below, but is not in its range?

1) 0

2) 2

3) 3

4) 7

10. Which value of k will make a perfect square trinomial?

1)

2)

3)

4)

11. The expression is equivalent to

1)

2)

3)

4)

12. Sally’s high school is planning their spring musical. The revenue, R, generated can be determined by

the function , where t represents the price of a ticket. The production cost, C, of the

musical is represented by the function . What is the highest ticket price, to the nearest

dollar, they can charge in order to not lose money on the event?

1)

2)

3)

4)

13. The expression is equivalent to

1)

2)

3)

4)

14. What are the center and radius of the circle whose equation is 5𝑥2 + 5𝑦2 + 20𝑥 = 25?

1) and 1

2) and 1

3) and 3

4) and 3

15. Which equation represent the graph of a parabola that is congruent to the parabola shown below?

1) 𝑦 =1

10𝑥2 + 3

2) 𝑦 =1

5𝑥2 + 5

3) 𝑥 =1

10𝑦2

4) 𝑥 =1

20𝑦2 + 1

16. The focal length, F, of a camera’s lens is related to the distance of the object from the lens, J, and the

distance to the image area in the camera, W, by the formula below.

When this equation is solved for J in terms of F and W, J equals

1)

2)

3)

4)

17. The table below shows the cost of mailing a postcard in different years. During which time interval

did the cost increase at the greatest average rate?

1) 1898-1971

2) 1971-1985

3) 1985-2006

4) 2006-2012

18. Which list of ordered pairs does not represent a one-to-one function?

1)

2)

3)

4)

19. Which transformation of moves the graph 7 units to the left and 3 units down?

1)

2)

3)

4)

20. The product of and expressed in simplest radical form is

1)

2)

3)

4)

21. Which relation does not represent a function?

1)

3)

22. The expression is equivalent to

1)

2)

3)

4)

23. What is the total number of points of intersection of the graphs of the equations and

?

1) 1

2) 2

3) 3

4) 0

24. If , then is equal to

1)

2)

3)

4)

2)

4)

Part II Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

25. For the function 𝑓(𝑥) = (𝑥 − 3)3 + 1, find 𝑓−1(𝑥).

26. If a model rocket is launched vertically upward from ground level with an initial velocity of 128 feet

per second, then its height h after t seconds is given by the equation ℎ(𝑡) = −16𝑡2 + 128𝑡 (if air

resistance is neglected). At what time(s), to the nearest hundredth, will the rocket be 100 feet above

the ground?

27. If and , determine in simplest form.

28. The directrix of the parabola has the equation . Find the coordinates of the

focus of the parabola.

29. Solve for x:

30. What is the solution set of the equation ?

31. Write in form, where y is a real number.

32. Solve algebraically for the exact values of x:

Part III Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

33. Solve the following system of equations algebraically for all values of a, b, and c.

−3𝑎 − 𝑏 − 3𝑐 = −8

−5𝑎 + 3𝑏 + 6𝑐 = −4

−6𝑎 − 4𝑏 + 𝑐 = −20

34. The graph below is of a fourth-degree polynomial function 𝒇.

State the intervals where 𝒇 < 𝟎.

State the zeros of 𝒇.

Write a formula for 𝒇, in factored form. Be sure the formula satisfied 𝒇(𝟐) = −𝟏𝟓

35. Rewrite the expression (4𝑥2 + 5𝑥)2 − 5(4𝑥2 + 5𝑥) − 6 as a product of four linear factors.

36. Solve the system of equations shown below algebraically.

Part IV Answer the question in this part. Each correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For the question in this part, a correct numerical answer with no work shown will receive only 1 credit.

37. Consider the polynomial function 𝑔(𝑥) = 𝑥4 + 2𝑥3 + 10𝑥2 + 18𝑥 + 9 and its graph below.

a. Based on the appearance of the graph, what does the real solution to the equation

𝑥4 + 2𝑥3 + 10𝑥2 + 18𝑥 + 9 = 0 appear to be?

b. Prove algebraically that your answer is in fact a zero of 𝑦 = 𝑔(𝑥).

c. Find the two complex number zeros of 𝑦 = 𝑔(𝑥).

d. Write 𝑔 as a product of four linear factors.