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
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NAME: DATE: Algebra 2: MOCK MIDTERM #2 - Mr. Gino's … · NAME: _____ DATE: _____ Algebra 2: MOCK MIDTERM #2 ... Perform the given operation and express as a single rational expression
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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: