Download Math Models Spring Final Exam Review

MMA Spring 2012 FINAL REVIEW Name___________________period______
1. Identify the slope and y-intercept y = 4x  5
2. Identify the rate of change and beginning value
3. Identify the x and y intercepts
y=
1
x7
2
x + 3y = -15
-5x + y = -10
2x + 3y = -12
-2x + 5y = -10
4. Laura’s cell phone plan costs $32 plus $.08 for every minute.
Identify the slope and the y –intercept._________________________
_________________________
Identify the independent and dependent variable.________________________
______________________
What is the equation that represents this scenario._________________________________________
5. Sean’s gym membership costs $270 for the year plus $ 3.00 for every towel he uses.
Identify the Rate of Change and the Base. _________________________
Identify the input and output. ___________________________
_________________________
________________________________
What is the equation that represents this scenario. _________________________________________
6. Sam gets $50 for Mowing the lawn. He wants to buy some (x) t-shirts for the summer. The shirts are $4.50
each he will spend no more than y dollars.
What is the Base_________ What is the rate_________ ( is it negative or positive)
What symbol means no more than_______________
What is the equation/inequality that represents this scenario. _________________________________________
7.
SOLVE FOR Y:
Identify m =______ and b=______
and sketch the graph
5x + 3y = -6
What is the slope and the base in this scenario:
8. Julie earns $14.75 an hour pulling weeds._______________________ ____________________
Write the equation_____________________________
9. Find the function values of the following:
10. Find the function values of the following:
4
g(s) =
s2
f(x) = -2x - 5
f(½ ) ___
f(-2)
f(4)
g(0)
______ g(-3)
g(6)
Find the x and y intercepts and sketch the graph.
11.(
,
) ( , ) 2x + 8y = 16
Write and solve the following linear functions.
12. John is paid $350 a month plus a 15% commission on the equipment he sells. If he sells $1200 worth of
equipment in a month, how much will he make?
What is the slope________what is the y-intercept____________
What is the independent variable________________________________________
What is the dependent variable_________________________________________
Equation:
Solution:
13. Jack earns $7.50 an hour at his job. How much will Jack make in a 8-hour work day?
What is the slope________what is the y-intercept____________
What is the independent variable________________________________________
What is the dependent variable_________________________________________
Equation:
Solution:
Write and graph the following linear functions.
14. Sara has 15 apps on her phone. Each week she buys 2 more.
What is the slope________what is the y-intercept____________
What is the independent variable________________________________________
What is the dependent variable_________________________________________
Equation
Graph
Write the equation of the lines parallel and perpendicular to the given information.
15.
m=½
(3,1)
Parallel equation:
Perpendicular equation: ________________________
16.
y = -3x + 5
Parallel equation:
(3,4)
Perpendicular equation: ________________________
Find the slope of a line given two points.
17. (0, 2) and (3, 4)
18. (-3, 4) and (5, 1)
Write the equation of the line given the table or graph.
19.
20.
Time
(seconds)
0
4.50
9.00
13.50
______________________________
21.
__ 2004 Summer Exit
The graph is the solution for which inequality?
23.
spend.
Distance
(meters)
25
75
125
175
_________________________________
22.
___ Which inequality best describes
the graph shown below?
Your parents say must save at least 85% of your graduation money and the rest you can
24.
You want to be in the top of your MMA class you must get no less than an 87% on this test to
achieve this goal.
25. y ≥ 2x – 4
26. y ≤ -½x + 5
27. -4x + 2y > 8
Write the system of equations:
28. The length of a rectangle is equal to 5 less than triple the width. Which system of equations can be used
to find the dimensions of the rectangle if the perimeter is 85 centimeters?
29. Karen bought some 2 neon fish and 6 angel fish at $6.75 for her new aquarium. Then Karen bought 5 neon
fish and 1 angel fish and spent $5.25. Write the system of equations to determine how much she spent on
each type of fish.
Solve by graphing:
30.
x  2y  8
3x  y  7
The solution is where the two lines cross.
Solve for y.
31.
y  2x 1
2x  4 y  4
(
,
)
The solution is where the two lines cross.
(
,
Graph the following linear inequalities Hint: dashed or solid Hint: shade above or below
34.
32.
The solution is the commonly shaded region.
Solve by substitution: HINT: get one variable alone.
35.
y  6x
x  y  28
x coordinate =________
y coordinate =________
The solution is the commonly shaded region.
36.
3 x  y  1
2 x  3 y  24
(
,
)
)
Solve by the elimination method with addition and subtraction.
37.
38.
3x  2 y  7
3 x  5 y  45
3 x  13 y  9
5x  2 y  1
(
x coordinate =________
,
)
y coordinate =________
List the rules of transformation for each of the following parts of a quadratic equation y = a(x – h) + k
39.
a:________________________ _________________________ ___________________
h: ____________________________________
k:_____________________________________
40. What is the Quadratic parent function:__________________
List ALL of the ways the given function is different from the quadratic parent function.
41. f(x) = 1 x2 – 5
42. f(x) = 2(x - 4)2 - 8
3
1.
2.
3.
1.
2.
Write the new equations given the following changes.
43. If “a” in this quadratic function is f(x) = -2x2 – 4 is increased by 3 what will new equation look like?
44. If “c” in this quadratic function is f(x) = ½ x2 – 4 is changed to 0 what will the new equation look like?
1 2
1
x – 2 to g(x) = x2 + 5 create a wider parabola or narrower parabola or same size?
4
4
1 2
1
46. Does going from f(x) = x – 2 to g(x) = x2 + 5 create a wider parabola or narrower parabola or same size?
4
6
47. Which function has the widest graph?
(A) y  2 x 2
(B) y  x 2
(C) y  0.5 x 2
(D) y   x 2
45. Does going from f(x) =
48. Which function has the narrowest graph?
(A) y  2 x 2
(B) y  x 2
(C) y  0.5 x 2
(D) y   x 2
1
49. (2005 October Exit) How does the graph of y = 5x differ from the graph of y = x2__________________
5
2
2
50. (2004 10 Grade) How does the graph of y = x differ from the graph of y = x − 8___________________
2
th
51. What are the zeros of the following equation:
y  x 2  4 x  12 ?
52. What are the roots of the following equation:
y  x2  4 ?
53. Find the solutions of f(x) = x2 – 8x + 15 by using a graph or table in your calculator.
54. Find the root(s), zeros, x-intercepts, solutions from the graph and table below.
Then find the y- intercept, if posssible.
55.
56.
57.
x- intercepts
___________
__________
y-intercept__________
x- intercept
___________
x
y
-2
0
-1
0
1
2
3
-5
-8
-9
-8
-5
4
0
58.
x- intercepts __________
______________
y-intercept__________
x
0
1
2
3
4
6
y
4
0
-2
-2
0
10
x- intercepts _________
______________
y-intercept___________
59. Write the GCF.
___________ ( x3  4 x5 ) ____________  8a 3b3  18a 2b  __________ 3x5 - 12x4 + 6x3 _________13x  5 y 2
Write the GCF and in Parentheses write what is left.
To check: multiply your answer and see if you get the original problem.
60.___________(
) 6x5y2 -
61.___________(
)  4r
2
28x3y 3
yz 2  18r 3 z 5  6ryz 
Factor.
62. x2 + 8x +16
63. x2 – 13x + 40
64. x2 – x – 12
65. x2 + 2x – 48
66. x2 – 25
67. 6x2 + 5x +1
68. If the landing strip at the airport has an area of 9x2 – 121, what is the length and width?
69. The AHS parking lot has an area of x2 + 9x + 20. What is the length and width of the parking lot?
Simplify each radical expression.
70.
54
71.
24
72.
48