Download Algebra 2 Semester 1 Review

Semester 1 Exam Review
There are 60 multiple choice questions from modules 1 - 4 on this exam. Each question is
worth 2 points for a total of 120 points. You must score a 72 on this exam (60%) in order to
receive credit.
1. Which of the following is NOT an example of a RATIONAL number?
a. 5.25
b. ¼
c. 10
d. 2.3333
2. The name of an algebraic property and an example are given. Which one is
INCORRECT?
a. Associative Property of Multiplication 5(3+2)=5(5)
b. Commutative Property of Addition 4+3=3+4
c. Identity Property of Multiplication 4*1=4
d. Reflexive Property of Equality a=a
3. Simplify the expression:
2  3  32 
8  22
4. Write the following in equation form: Be able to select the best equation for the following
word problem. The sum of three consecutive even integers is 18. Do not solve.
5. When solving the equation
x 1
 4  12 what is NOT be a possible first step?
3
a. Adding a 4 to both sides.
b. Multiplying each term on both sides by a 3.
c. adding a 1 to both sides
6. What is the solution to the inequality -3(x-1) < -x+4
7. What is the solution to the combined inequalities -7 <x+2 <7?
8. Solve the literal equation -Ax + By = C for x.
9. If y varies directly as x and y = 4 when x = 2, what is y when x = 5?
10. If f(x) = 2x and g(x) = x+3, what is f[g(20] = ?
11. Write the equation -2x + y = 12 in slope-intercept form.
12. Write the equation of the line that passes through the points (2,5) and (6,-1).
13. What does the graph of y = -2x+4 look like?
14. What does the graph of the equation y = 2 look like?
15. Write the equation of the line that is perpendicular to the line 3x - 2y = 6 and passes
through the point (-1,2).
16. Simplify: (3x3 z 5 )2
17. Simplify: 2 x 2 (3x  2 y )
18. Multiply and simplify (y + 5)(2y – 1)
19. How many terms will there be in your answer when you multiply and simplify (3x  1)3 .
20. What is the remainder when you divide  3x3  2 x  6    x  1 .
21. What is the greatest common factor for the polynomial: 4 xy 2  2 y  8 x 2 y .
22. Determine if the following is a perfect square trinomial: 9 x 2  12 xy  4 y 2 .
23. Determine if the following is a perfect square trinomial: 25 x 2  20 x  16 .
24. Factor x 6  343
25. Factor x 2  2 x  24
26. Factor 6 x 2  x  2
27. Factor a 2b  3a 2  2b  6
28. Solve by Factoring 2 x 2  x  3  0
29. Solve for x: 3x 2  12
30. Simplify: 3 18x3  5x 8x
31. Simplify:
169a3b2
32. Divide and rationalize the denominator for:


33. Multiply and Simplify: 3 2  2 4 2  6
25ab 4
12a 4b

34. Be able to solve for x using the quadratic formula. 3 x 2  2 x  7
35. What is the vertex of this parabola? What direction does the parabola open?
y  2( x  1)2  6
36. If the vertex of a parabola is (3,2) what is the equation for the axis of symmetry?
(Assume the parabolas opens up)
37. Simplify:
25
38. Simplify: i 7
39. What is the conjugate of the complex number 6 – 2i?
40. Simplify: (3  2i )(2  i)
41. If a quadratic equation has 2 identical rational roots, how many times will its graph
intersects the x-axis?
42. What is the value of the discriminate: 3 x 2  4 x  5  0
43. If the value of a discriminant is a positive perfect square, what does that tell us about the
type and number of roots?
44. With a tail wind, a plane traveled 600 mi in 4 hours. With a head wind, the plane traveled
the same distance in 7 hours. Write a system of equations that could be used to solve this
problem to determine the wind speed? Do not solve.
 3 5 7 1
45. Solve: x  


 2 0  3 2
46. What are the dimensions of the resulting matrix found by multiplying a 4 by 2 matrix and
a 2 by 1 matrix? What about a 3 by 1 and a 3 by 1?
0 2 1 
47. Evaluate the discriminate:  2 1 4 
 1 3 2 
48. Describe the graph: y 
2
x2
3
49. What expression will you substitute for x in the second equation?
x  2y 1
3x  4 y  6
1
x2
50. How many solutions will this system of equations have?
2
y  3 x  1
y
Answers:
1.
2.
3.
4.
5.
C
A
6
(x) + (x+2) + (x+4) = 18
C
1
6. x > 2
7. -9 < x < 5
8. x = (C – BY) /- A
9. k = 2. y = 10
10. 46
11. y = 2x + 12
3
x+8
2
13. dot at (0,4) and (1,2) – straight line connecting
12. y =
14. horizontal line at 2
2
4
x
3
3
6 10
16. 9x z
15. y =
17. 6 x 3  4 x 2 y
18. 2y 2  9y  5
19. 4
20. -11
21. 2y
22. yes
23. no
24. ( x 2  7)( x 4  7 x 2  49)
25. (x + 6)(x – 4)
26. (3x – 2)(2x + 1)
27. (a2  2)(b  3)
28.
29.
30.
31.
x = -3/2 and x = 1
2
19x 2x
13ab a
32.
5b 3ab
6a 2
33. 36  26 2
34.
2  2 22
6
35. vertex (-1, -6), opens down
36. y  ( x  3)2  2
37. 5i
38. –i
39. 6 + 2i
40. 8 + i
41. 1
42. 76
43. 2 real rational roots
44. 4(r + t) = 600 and 7(r-t) = 600
 4 6 
45. x = 

5 2
46. 4 by 1, not possible
47. 7
48. y int = -2. slope is 2/3, dotted line, shaded above
49. x = -2y + 1
50. 1