Algebra IIFirst Semester FinalExam ReviewDec. 2010Name
Unit 1.1
1. Using the word bank, list all the possible names for x and y.
Inputrangeoutput
Dependent variableeffectdomain
CauseIndependent variable
XY
List the domain and range and determine if it is a function.
2. {(-9, -2), (2, 4), (3, -7), (8, 1), (10, 0), (5, 6)}
Domain: ______Range: ______Function: yes / no
Evaluate:
3. when w = -8 and z = 34. when x = 2 and y = -1
Simplify:
5. 6.
Evaluate the function for the indicated value.
7. ; f(-4)8. ; g(27)
Simplify:
9. 10.
Consider the graph shown.
11. How would you determine if the data shown represented a function?
12. Is the shown relation a function?
Determine if the relation is a function.
12. Function / Not a function
(Circle one)
Unit 1.2
Solve for x.
1. 2.
3. 4.
Find the x and y intercepts.
5. 6.
Rules for graphing inequalities:
≤≥
Line:
Shade:
7.Which inequality best describes the graph shown below?
A y > −x + 5
B y < −x + 5
C y < −x + 5
D y > −x + 5
2003 Exit
8.Which graph best represents all the pairs of numbers (x, y) such that x + y < −6?
F G H J
Unit 1.3
Write the following formulas:
1. slope-intercept form2. point-slope form
3. For , write in slope-intercept form.
Find the slope of the line.
4.5.2y = 4x - 6
6. If the slope of the line were changed to 5, what would the new equation be?
7. Line r passes through ( 1, -3) and is perpendicular to . What is the equation of line r?
8. What is the equation: m = 2/3 and through ( -4 , -1 )
2006 February Exit
Write the equation of the line that is perpendicular to the graph shown and
passes through the point (0, 3).
Write an equation in slope intercept form of each line described.
1. slope 2; y intercept 52. slope ½ ; passes through (4, -1)
12. Karen is paid a salary of $2000 a month plus a commission of 15% of the value of the jewelry she sells. Find the value of the jewelry Karen must sell in a month to earn at least $5,000.
Unit 2.1
Write the system of equations. Don’t solve!
1. Your teacher gives you a test worth 100 points with 34 questions. Each question is worth either 2 points or 4 points. Write a system of equations to determine the number of 2 point and 4 point questions on the test.
2. Tom bought 12 student tickets and 4 adult tickets to the football game for $56. Renee bought 4 student tickets and 8 adult tickets for $52. Write the system of equations that will determine the cost of adult tickets and the student tickets that they bought.
3. Juan bought 40 drinks, all either cola or root beer. The cola was equal to four times the number of cans of root beer. Write a system of equations to determine the number of cans of cola and root beer he bought.
4. The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters?
5. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?
Unit 2.2A
1. Explain what the following terms mean:
A. Independent systemB. Inconsistent systemC. Dependent system
Solve by substitution:
2. 3.
Solve by the elimination method.
4. 5.
6. In the system of equations 4x + 2y = 10 and 3x + 7y = -18, which expression can be correctly substituted for y in the equation 3x + 7y =-18?
(A) 10 – 2x(B) 10 + 2x(C) 5 – 2x(D) 5 + 2x
7. Use substitution or elimination to solve these equations. Show your work
6x + y = -2
6x + 2y = 2
8. Use substitution to determine if the given ordered pair is a solution for the system of equations.
Unit 2.2B
Use graphing to solve each system of equations.
1.3x - 4y = 20
y - 2x = 0
2. Graph the system of inequalities.
3. The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store?
(A) 2e – u = 220(B) 2e – u = 220(C) 2e – 2u = 440(D) e – 2u = -220
e – u = -175 e + u = 175 e – u = -175 e – u = 175
4. Solve the system you chose from #3 with your best method.Write your solution as an ordered pair.
Unit 2.3
Describe the transformations:
1. 2.
3. 4.
5. 6. f(x) = 3x2 - 2
7. Linear or Quadratic:8. Linear or Quadratic:
X / Y-1 / -1
0 / 2
1 / 5
2 / 8
3 / 11
Explain______Explain______
X / Y-1 / -2
0 / -4
1 / -2
2 / 4
3 / 14
For the graph, indicate whether the data is discrete or continuous. Then list the elements of the domain and range.
9. Type:
Domain
Range:
10. Type:
Domain
Range:
Unit 3.1
Graph and label (vertex, roots, axis of symmetry) of the following:
1. x2 + 5 2. (x + 3)2 – 7 3. – ½ (x – 4)2 – 7
Find the axis of symmetry and vertex of the following. Show your work!!!
4. 2x2 – 4x + 55. x2 + 6x – 7
Find the roots/x-intercepts/zeros/solutions when y=0 from the graphs and tables below. (Write answer in ordered pair(s).)
x / y-3 / 1
-2 / 0
-1 / 1
0 / 4
-1 / 9
-2 / 16
7. 8.
Find the following information for the given equation.
6. y = ¾ (x + 2)2 - 3
Opens:
AOS:
Vertex:
X-intercepts:
Unit 3.2
Factor the following expressions using the methods for GCF, difference of perfect squares, a = 1, or a > 1.
1. x2 – 252. 16x2 – 4
3. 7x3 + 21x24. x2 + 9x + 20
5. x2 + 8x + 156. 3x3 + 2x
7. 4x2 – 35x + 498. 5x2 + 19x + 12
12. A rectangle has an area of x2 – 25. Write expressions for the length of each side.
Unit 3.3
Find the solutions to the following quadratic functions.
1. x2 – 1 = 02. x2 + 9x +14 = 0
3. -20x2 – 49x – 30 = 04 5x2 + 7x + 2 = 0
5. 9x2 – 6x + 1 = 06. 4x – 12 = 0
7. A rectangle has an area of x2 + 4x – 5. Find expressions for the length and the width of the rectangle.
For each question, identify the type and number of roots using the discriminant and then solve to find the roots.
8) -x2 - 5x + 69) 8x2 + 10x – 3
# roots:# roots:
Type:Type:
Solution:Solution:
10) 3x2 − 4x – 1
# roots:
Type:
Solution:
Factor by Grouping.
11) r2 – rq + 4r – 4q12) 24x3 + 8x2 – 9x - 3