NAME: ________________________________________________________ DATE: _____________

Algebra 2: MOCK MIDTERM #2

Part I

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. Which statement is true about the graphs of f and g shown below?

1) f is a relation and g is a function.

2) f is a function and g is a relation.

3) Both f and g are functions.

4) Neither f nor g is a function.

2. The domain of is the set of all real numbers

1) greater than 2

2) less than 2

3) except 2

4) between and 2

3. When is multiplied by its conjugate, the result is

1)

2)

3) 5

4) 13

4. If is solved by completing the square, one of the steps in the process is

1)

2)

3)

4)

5. If and , what is ?

1)

2)

3)

4)

6. Which expression is equivalent to ?

1)

2)

3)

4)

7. The expression is equivalent to

1)

2)

3)

4)

8. If and , what is the value of the expression , when ?

1) 0

2)

3)

4)

9. If f(x) = and g(x)= , what is (𝑔 − 𝑓)(𝑥)?

1)

2)

3)

4)

10. The equation is equivalent to

(1)

(2)

(3)

(4)

11. The graph of is shown to the right.

Which function could represent the graph of ?

1)

2)

3)

4)

12. Factor completely:

1) 3)

2) 4)

4x2 -24x+ 4y2 + 72y = 76

4 x-3( )2+ 4 y+9( )

2= 76

4 x-3( )2+ 4 y+9( )

2=121

4 x-3( )2+ 4 y+9( )

2=166

4 x-3( )2+ 4 y+9( )

2= 436

13. Which equation represents a parabola with a focus of and a directrix of ?

1)

2)

3)

4)

14. The expression is equivalent to

1)

2)

3)

4)

15. The expression is equivalent to

1)

2)

3)

4)

16. For which equation will ?

1)

2)

3)

4)

17. When , what is the value of ?

1)

2)

3) 3

4)

18. What is the value of when ?

1)

2)

3)

4)

19. Given the functions , , and shown below:

The correct list of functions ordered from greatest to least by average rate of change over the interval

is

1) , ,

2) , ,

3) , ,

4) , ,

20. The expression is equivalent to

1)

2)

3)

4)

21.

22.

23.

24.

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. Express in simplest form.

26. Solve the equation algebraically for all values of x.

27. Apply the properties of exponents to verify that the given statement 2𝑛+2 − 2𝑛 = 3 ∙ 2𝑛 is an identity

for integer values of 𝑛.

28. Given the function 𝑦 = 𝑓(𝑥), graph 𝑔(𝑥) = −𝑓(𝑥 + 1) + 2. Indicate all transformations performed in the correct order.

29. Perform the given operation and express as a single rational expression in simplest form:

30. The graph of function ℎ(𝑥) is given below. Determine if 𝑥 + 1 is a factor of ℎ(𝑥).

Justify your answer.

31. Determine if the function 𝑓(𝑥) =4𝑥2+2

𝑥 is even, odd, or neither. Justify your answer.

32. Show that the set of ordered pairs (x, y) in the table below satisfied a cubic relationship. Find the

value of a in the equation 𝒚 = 𝒂𝒙𝟑 + 𝒃𝒙𝟐 + 𝒄𝒙 + 𝒅 that all of the ordered pairs satisfy.

x 0 1 2 3 4 5

y 2 1 6 23 58 117

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 system algebraically:

2𝑥 − 𝑦 − 𝑧 = 15

4𝑥 + 5𝑦 + 2𝑧 = 10 −𝑥 − 4𝑦 + 3𝑧 = −20

34. Solve algebraically for all values of x:

35. Consider the polynomial function 𝑓(𝑥) = 𝑥3 + 𝑏𝑥2 − 13𝑥 + 10. If 𝑓(1) = 0, find all zeroes of 𝑓.

36. Solve the following systems of equations 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. Perform the indicated operations and simplify: