Algebra 2
First Semester Final Exam
* Please DO NOT write on the test! *
1) The number 2. 7 belongs to which set of numbers?
(a) Natural numbers, Real numbers
(c) Rational numbers, Real numbers
(e) None of the above.
(b) Irrational numbers, Real numbers
(d) Integers, Rational numbers, Real numbers
2) Which of the following expressions is NOT equivalent to the others?
(a) 5(5n - 2) – 10n
(c) 15n – 10
(e) None of the above.
(b) 3(5n – 2) + 4
(d) 5(3n -2)
3) If f(x) = -2x2 + 7, what is f(-5)?
(a) 107
(c) 43
(e) None of the above.
(b) 57
(d) -43
4) What is the solution of the inequality 9 – 4x  -4(2 + x) + 3?
5
5
(a) x 
(b) x 
9
9
(c) All Real numbers
(d) No Real Numbers (No Solution)
(e) None of the above.
x
x
 6  0 or  1  0 ?
3
2
(b) -2  x  18
(d) No Real Numbers
5) What is the solution of the compound inequality
(a) x  -2 or x  18
(c) All Real Numbers
(e) None of the above.
6) Which of the following have the same solutions?
I. 4 x  7  8
III. 4x – 7 < 8 or 4x + 7 < -8
II. 4x – 7 < 8 and 4x - 7 < -8
IV. 4x – 7 < 8 and 4x - 7 > -8
(a) I and II
(c) I and IV
(e) None of the above.
(b) I and III
(d) I, III, and IV
7) Which are the solutions to x  4  2  5 ?
(a) -3 or 11
(c) -7 or 7
(e) None of the above.
(b) 3 or -11
(d) 1 or 7
Form A
8) Which relation is not a function?
(a)
(c)
{(0, 7), (2, 6), (5,8), (8, 9)}
{(4,3), (5,2), (1,10), (4,4)}
(b)
(d)
{(5, 6), (3, 6), (7, 6), (8, 6)}
{(1,4), (4,3), (3,5), (5, 7)}
(e) None of the above.


9) Which equation represents a line through (6, 1) that is perpendicular to y = 3x + 6?


(a) y = 3x – 17
(b) y = -3x + 19
1
1
(c) y  x  1
(d) y   x  3
3
3
(e) None of the above.
10) For the equation 5x – 4y = 20, which has value -5?
(a) the x-intercept
(c) the slope
(e) None of the above.
(b) the y-intercept
(d) the origin
11) Which equation does NOT represent a direct variation?
(a) y  3 
2
x
3
y 5

x 7
(e) None of the above.
(c)
(b) y 
x
7
(d) y – 5x = 0
12) Which of the following describes the graph of y   x  7 ?
(a)
(b)
(c)
(d)
(e)
A v-shape graph with vertex at (0, -7) that opens down
A v-shape graph with vertex at (0, 7) that opens down
A v-shape graph with vertex at (0, -7) that opens up
A v-shape graph with vertex at (0, 7) that opens up
None of the above.
13) What is the vertex of y  6 x  42  5 ?
(a) (-7, 5)
(c) (-42, 5)
(e) None of the above.
(b) (7, 5)
(d) (42, 5)
14) The graph of y  x  6 is translated 4 units left and 3 units down. What is the equation of the new
graph?
(a) y  x  2  3
(b) y  x  10  3
(c) y  x  10  3
(e) None of the above.
(d) y  x  10  3
15) Which point(s) are solutions of the inequality 7x + 5y ≥ 2?
I. (-2, -3)
II. (9, -1) and (0, 4)
(a) I
(c) III
(e) None of the above.
III. (0,-3) and (1, -5)
(b) II
(d) I and III
16) One equation of a system of equations is 12x – 3y = 6. Which of the following
equations would make the system inconsistent?
(a) y = -4x – 2
(c) y = -4x – 8
(e) None of the above.
17) What is the solution of the system?
(b) y = 4x – 8
(d) y = -12x - 6
5 x  6 y  24
2 x  3 y  9
(a) (6, -1)
(c) (-6, 1)
(e) None of the above.
(b) (6, 1)
(d) (-6, -1)
18) When you graph the inequality y ≤ -6x + 8, the boundary line (on the graph) should be _____, and the
shading should be _____ the line.
(a) dotted, above
(c) solid, above
(e) None of the above.
(b) dotted, below
(d) solid, below
19) Which function is NOT a quadratic function?
(a) y = (x – 17)(x – 2)
(c) y = -2x2 + x(2x + 3)
(e) None of the above.
(b) y = x2 + 3x – 16
(d) y = x(x – 4) - 6x2
20) What is the vertex of y = -x2 - 8x – 3?
(a) (-8, -3)
(c) (-4, 13)
(e) None of the above.
(b) (-8, 125)
(d) (-4, 45)
21) The vertices of a feasible region are (-5, 1), (0, 2), (0, 0), and (4, 2). For which
vertex is the maximum cost C = -6x + 3y found?
(a) (-5, 1)
(c) (0, 0)
(e) None of the above.
(b) (0, 2)
(d) (4, 2)

22) Simplify: 2 3   16

(a) 6  8i
(c) 5  4i
(e) None of the above.
(b) 6  6i
(d) 6  4i
23) Complete the square: x 2  6 x  ____ .
(a) 6
(c) 36
(e) None of the above.
(b) 9
(d) 3
24) Solve x 2  5 x  1  0 by using the Quadratic Formula.
5  29
2
5  21
(c)
2
(e) None of the above.
(a)
 5  21
2
 5  29
(d)
2
(b)
25) Rewrite y  x 2  10 x  3 in vertex form.
(a) y   x  5  28
(b) y   x  5  22
(c) y   x  5  103
(e) None of the above.
(d) y   x  5  28
2
2
2
2
26) Solve 9 x 2  6 x  1  64 .
(a) -11, 5
7
,3
3
(e) None of the above.
(c)
 65
, 21
3
7
(d) -3,
3
(b)
27) Write a Polynomial Function in Standard Form with the given zeroes at 2, -3, -2
(a) f x   x 3  3x 2  4 x  12
(c) f x   x 3  3x 2  4 x  12
(e) None of the above.
(b) f x   x 3  3x 2  4 x  12
(d) f x   x 3  x 2  8 x  12
28) Graph y = x 2 - 2x + 3. State the axis of symmetry and the minimum value.
29) Write an inequality for the graph below.
30) Factor: x2 – 5x – 24
31) Factor: 3x2 + 13x + 12
32) Sketch the graph of y  3x 3 ( x  4) 3 ( x  6) 2
33) Simplify: (5 + 2i)(6 - 4i)
34) Solve by factoring: x 2  4 x  12  0
35) Solve by Completing the Square: x 2  8 x  8  0
36) Solve using the Quadratic Formula: 3x 2  6 x  2  0
37) Write the polynomial in Standard Form. Classify it by its degree and by the number of terms:
3x 4  9 x 3  2 x 2  x  5 x 4  2 x 2
38) Write the product in standard form: x  32x  4x  1
39) Solve the equation: x 3  x 2  12 x  0
40) Write an equation of the line through (-1, -6) and (-2, 10) in slope-intercept form, standard form and
point-slope form.
Slope-intercept form is y  mx  b
Standard form is Ax  By  C
Point-slope form is y  y1  m( x  x1 )
Algebra 2
Form A
First Semester Final Exam
Name ______________________________
28. Axis of Symmetry _____________
33. _________________________
Minimum value _______________
34. x = ______________________
Graph Below
35. x = ______________________
36. x = ______________________
37. _________________________
Classify by degree _____________________
Classify by terms ______________________
38. _________________________________
29. _________________________
39. x = _____________________
30. _________________________
40. Slope intercept ___________________________
31. _________________________
Standard form ____________________________
32. Sketch below.
Point slope form ___________________________