SAMPLE SEMESTER EXAM Chapter One: Equations & Inequalities

SAMPLE SEMESTER EXAM Chapter One: Equations & Inequalities

SAMPLE SEMESTER EXAM
Advanced Algebra & Trigonometry
Name _____________________________________
Chapter One: Equations & Inequalities
21
5
Leave answers in reduced improper fraction form!
Directions: Evaluate each expression if: a = -2, b = 3, c =
1. a – 2b + 3c
2. 2a   b  3 
3. a  3 b2   a  c
4.
2
3b  2a
5c
Directions: Simplify Completely
5. -4(3x + y) – 2(x – 5y)
6. 6(9a – 3b) – 8(2a + 4b)
Directions: Solve each equation or inequality
7. 3(2x + 3) – 4(3x – 6) = 15
9. 8 
x
3
5
8.
x  12 3 x x  6


5
4
2
10. 2 x 
18  x
5
Directions: Solve for the variable indicated
11. 2k – 3m = 16, for “k”
12. A 
1
h  a  b , for “h”
2
Directions: Solve and Check.
13. 3 x  4  21
14. 3 3 x  2  12  6
Directions: Solve and graph on the number line
15. 6x – 1 > 17 OR 8x  6  10
16. 2  5  x  3   9
17. 2 x  7  1
18. 3 x  6  8  17
Chapter Two: Linear Relations & Functions
Directions: Find each value if f(x) = -3x + 2 and g(x) = x2 – 4
19. f(-2)
20. f(2a)
21. 3[g(-1)]
Directions: Answer
22. Write in Standard form:
2
3
1
y x 0
3
4
6
23. Find the slope of the line that goes through the points (1, 4) and (-2, 9)
24. Find the equation of the line that goes through the points (1, 4) and (-2, 9)
25. Find the equation of the line that passes through the point (4, 2) that is
perpendicular to the line y = -2x + 3.
26. Find the equation of the line that passes through the point (4, 2) that is
parallel to the line y = -2x + 3.
Directions: Graph
27. 2x + 3y = 24
Identify the slope, y-int & x-int
 x if x  2

28. f  x    x  2 if  2  x  2
5 if x  2

29. y = (x + 2)2 – 3
Describe the transformation of this
function in relation to the parent function
y = x2
30. y  3 x  1  2
Chapter Three: Systems of Equations & Inequalities
Directions: Solve by using the Method of Elimination
31. y  3x  13
1
y  x5
3
Directions: Solve by using the Method of Substitution
32. 3y – 5x = 0
2y – 4x = -2
Directions: Solve by Graphing
33. 3x + 4y = 8
x – 3y = -6
Directions: Graph the system of inequalities. Name the vertices of the feasible region and
then find the max and/or minimum values of the function for the region.
34. 3  x  6
y  3 x  12
y  2 x  6
f(x, y) = 4x – 2y
Directions: Use the matrices below to simplify #35-37
9 1
A 

1 2
35. 2B + 3A
 1 4
B

3 7 
36. CA
 3 4 


C   1 2 
 5 2 
37. AB – BA
Directions: Solve the System using either Elimination/Substitution –OR- Cramer’s Rule.
38. 5x + 2y = 4
3x + 4y + 2z = 6
7x + 3y + 4z = 29
Chapter Four: Quadratic Functions & Relations
Directions: Solve each quadratic equation using the method indicated.
39. Graph: 2x2 – 4x – 5 = 0
40. Factor: 6x2 – 31x + 5 = 0
41. Factor: x2 + 2x = 8
42. Complete the Square: x2 – 2x + 8 = 0
43. Complete the Square: 2x2 + 4x – 3 = 0
Directions: Find the Discriminant, determine the Nature of the roots then solve using the
Quadratic Formula
44. x2 – 4x – 45 = 0
45. 2x2 + 5x + 9 = 0
Directions: Solve each inequalitiy by the method indicated.
46. Graph: y > x2 – 6x + 8
47. Algebraically: Write answer in {set} or (interval) notation
2x2 + 3x – 20 > 0
Direction: Write each answer in simplest “i” form
4i
48. (3 – 4i) – (9 – 5i)
49.
4i
50. (6 + 5i)(3 – 2i)
Chapter Five: Polynomials & Polynomial Functions
Directions: Simplify. Assume that no variable equals 0.
51. (3x2y-3)(-2x3y5)
 x2 y 3 
54. 
4 
 xy 
52. 4y(3xy – y)
 4x
3
3a4 b3 c
6a2 b5c3
2
55. (4x2 – 6x + 5) – (6x2 + 3x – 1)
Directions: Use Long Division
57.
53.
56. (x + y)(x2 + 2xy – y2)
Directions: Use Synthetic Division

 8 x2  13 x  20   2 x  5
58.
 3x
3

 16x2  9x  24   x  5 
Directions: Describe the end behavior of the graph. Then determine whether it represents
an even or odd degree polynomial function and find the number of zeros.
59.
Directions: Evaluate.
60. Find p(-3) if p  x  
2 3 1 2
x  x  5x
3
3
61. Find 3f(a – 4) – 2g(a) if f(x) = x2 + 3x and g(x) = 2x2 – 3x + 5
Directions: Use the function f(x) = x3 – 2x2 – 3x for #62-65
62. Graph:
63. Estimate the x-coordinates at with the relative max & min occur
64. State the zeros of the function.
65. State the domain and range of the function.
ANSWER KEY TO SAMPLE EXAM
Advanced Algebra & Trigonometry
18. See Graphs
29 11
35. 

 9 20 
52. 12xy2 – 4xy
19. 8
 23 5 


3 
36.  7
 47 9 
53.
20. -6a + 2
 1 34 
37. 

 27 1 
x2
54. 2
y
21. -9
38. (2, -3, 6)
55. -2x2 – 9x + 6
5. -14a + 6b
22. 9x – 8y = 2
39. x = -1, 3
See Graphs
56. x3 + 3x2y + xy2 – y3
6. 38a – 50b
23. m  
1
40. x  ,5
6
57. 2x2 + x – 4
7. 3
5
17
24. y   x 
3
3
41. x = -4, 2
58. 3 x2  x  4 
8. 12
1
25. y  x
2
42. x  1 i 7
59.
as " x "  , f(x)  
as " x "  , f(x)  
9. x < 25
26. y = -2x + 10
43. x 
1.
23
5
2. 32
92
3.
5
4.
25
4
10. x < -2
5
3
27. m   23 , b  8,
x  int  12 See Graphs
2  10
2
44. Disc: 196
Nature: 2 real
Ans: x = -5, 9
45. Disc: -47
Nature: 2 comp
5  i 47
Ans: x 
4
a2
2b2 c2
60. 0
61. –a2 – 9a + 2
11. k 
16  3m
2
28. See Graphs
12. h 
2A
a b
29. See Graphs
46. See Graphs
1
63. x   ,2
2
13. x = 3, 11
30. See Graphs
47. See Graphs
64. x = -1, 0, 3
14. 
31. (-3, 4)
48. -6 + i
15. See Graphs
32. (3, 5)
49.
16. See Graphs
33. (0, 2) See Graphs
50. 28 + 3i
17. 
34. See Graphs
51. -6x5y2
4  16i
17
4
x5
62. See Graphs
65. D :  ,  
R :  ,  
15.
29.
16.
18.
27.
30.
33.
28.
46.
3
, 3)
2
Min = -20 (-2, 6)
34. Max = 0 @ (
47.
39.
62.