Name: __________________________________________
Algebra 2 Honors - Final Exam Review (Semester 1)
1. Which point shows the location of
(3 − i) − (4 − 3i) ?
a.
b.
c.
d.
3. Factor 64k 3 + 27c 3
a. (4 k+ 3c )(4 k+ 3c )(4 k+ 3c )
b. (4k + 3c )(16k 2 – 12k c + 9c 2 )
c. (4k + 3c )(16k 2 – 24k c + 9c 2 )
d. (4k – 3c )(16k 2 + 12k c + 9c 2 )
point A
point B
point C
point D
4. Which of the following is equivalent to
a.
b.
c.
2. Consider the system:
d.
4 8
+ i
3 3
4 8
− − i
5 5
4 8
+ i
5 5
4 8
− + i
3 3
4x − 2y = 12
y = kx − 6
Select the value of k for which the system has
infinitely many solutions.
a. 2
b. -2
c. 6
d. 1
5. Factor: 12w 2 z + 16wz − 128z
a. 4z(3w + 8)(w − 4)
b. 4(w + 8z)(w − 4z)
c. 4(3w − 8)(w + 4)
d. 4z(3w − 8)(w + 4)
1
8
?
2 − 4i
9. Which of the following most accurately describes
2
the translation from the graph y = (x − 4 ) − 2 to
6. To solve the equation x 2 + 12x = 4 by completing
the square, which equation would be part of the
solution?
a. (x + 12) 2 = 4
b.
c.
d.
2
the graph y = (x + 9 ) + 3 ?
a. down 2 and right 4
b. up 5 and left 13
c. up 5 and right 13
d. down 3 and left 9
(x + 6) 2 = 40
(x + 12) 2 = 40
(x + 6) 2 = 4
10. Choose the equation that fits the graph below.
7. Factor 9x4 – 49y2
a. (3x2 + 7y)(3x2 + 7y)
b. (3x + 7y)(3x – 7y)
c. (3x2 – 7y)(3x2 – 7y)
d. (3x2 + 7y)(3x2 – 7y)
8. Choose which of the following equations would
produce the widest, vertically compressed graph.
2
a. y = 2 (x + 1 ) − 5
1
2
b. y = (x + 1 ) − 5
2
c.
d.
y = (x + 2 ) + 3
b.
y = −3 (x + 2 ) + 3
c.
y = −3 (x − 2 ) + 3
1
2
y = − (x + 3 ) + 2
3
d.
2
y = 3 (x + 1 ) − 5
1
2
y = (x + 1 ) − 5
3
2
2
a.
2
2
12. Which graph shows the solution to the inequalities:
y ≥ 2x − 4 and 2y − x ≤ 2 ?
11.
2a + 3 8a 4 + 8a 3 + 2a 2 − 14a − 33
a.
4a 3 + 2a 2 – 4a + 13 −
6
2a + 3
b.
4a 3 – 2a 2 + 4a – 13 −
6
2a + 3
c.
4a 3 + 2a 2 – 4a + 13 +
6
2a + 3
d.
4a 3 – 2a 2 + 4a – 13 +
6
2a + 3
a.
b.
c.
d.
13. What are the x-intercepts of the graph of
y = 3x 2 − x − 10 ?
–6 and 5
a.
5
b.
2 and − 3
c.
d.
3
6 and –5
5
−2 and 3
15. What is the solution to the system of equations
shown below?
ÏÔÔ
ÔÔ −4x + 4y + 4z = −16
ÔÔ
Ô
ÌÔ −2x + 5y + 5z = −14
ÔÔÔ
ÔÔ −3x − 2y + z = −5
Ó
a. no solution
b. (–5, –1, −8)
c. (2, –1, –1)
d. infinitely many solutions
14. Which is the graph of y = (x – 3) 2 – 3?
a.
b.
Ê
ˆ
Ê
ˆ
16. ÁÁ 3c 2 − 6c + 4 ˜˜ + 3ÁÁ 4c 2 − 5c − 8 ˜˜ =
Ë
¯
Ë
¯
2
a. 15c − 21c − 20
b. −c 2 − c + 12
c. −9c 2 + 9c + 28
d. 15c 2 + 9c − 20
c.
d.
17. Find the zeros of f(x) = x 2 + 3x − 18
a. x = 6, x = –3
b. x = –6, x = –3
c. x = 6, x = 3
d. x = –6, x = 3
4
22. Find all of the x-intercepts of
f(x) = x 3 + 4x 2 − x − 4 . State your answers as
coordinate points.
18. Select the point that lies in the solution set for the
system:
ÏÔÔ
¸
ÔÔ −6x + 7y < −9 ÔÔÔÔ
ÌÔÔ
˝Ô
ÔÓ −2x + 8y > 6 ÔÔ˛
a.
b.
c.
d.
(–6, –7)
(4, 2)
(–9, 1)
(–4, –1)
23. Write the series 2 + 6 + 10 + 14 in sigma notation
19. Which polynomial represents
(x 2 − x − 5) (−x − 2) ?
a.
b.
c.
d.
3
24. Factor the polynomial 12x 3 − 8x 2 − 3x + 2
2
–x – x + 7x –10
–x 3 + 3x 2 + 3x –10
–x 3 + 3x 2 + 3x + 10
–x 3 – x 2 + 7x + 10
1 2
x − 3x − 3 , write TRUE
2
or FALSE for each statement.
25. Given the equation y =
The vertex is the minimum value _______
20. Milkshakes at the movie theater cost $2 for a small
and $3 for a large. If 31 milkshakes are sold today
for a total profit of $76, how many small
milkshakes were sold?
The graph is vertically stretched compared to the
graph of y = −2x 2 − 3x − 3 _______
The graph is vertically compressed compared to the
graph of y = x 2 − 3x − 3 _______
21. Solve and check for extraneous solutions:
12
3
=
2
x + 2x − 15 x + 5
5
26. Solve 2n 2 − 7n + 9 = 0
32. Find the vertex of f(x) = x 2 + 6x + 7
27. Write an equation for the nth term of the sequence
5,15,25,35,...
33. Find the product of (5 + 2i) and (7 + 8i)
34. Solve: || 18 − 3y || = 3
28. Factor 16x + 24x + 9
2
29. Simplify i
35. Simplify:
37
30. Find the sum of the infinite geometric series:
5 5 5 5
5+ + + +
...
2 4 8 16
2x 2 + 5x + 3 x 2 + 2x + 1
÷
8x − 12
4x 2 − 9
36. Solve 3(x + 4) 2 + 4 = 112
31. If f(x) = 5x − 3, find f(−5)
6