# Final Review 2 and Answers ```1st SEMESTER FINAL 2 REVIEW
Your first semester final will test your mastery of the material we have covered thus far. You may want to review
your notes, and work through the many chapter tests in the text. The problems here demonstrate the breadth of the
material that you will see in the exam. THIS REVIEW IS A STARTING POINT FOR YOUR STUDIES. You
will want to study more deeply in the areas you have difficulty with.
Is the given point an element of the solution set for the system of equations? Support your answer.
2x  3y  0
2 x  3 y  11
1) (3,-2)
2) (-4,1)
 x  y  4
x  5y  9
Use elimination to solve the system:
x  3y  1
2 x  5 y  23
3)
4)
3 x  3 y  3
 x  y  5
Use substitution to solve the system:
x  4 y  18
3 x  2 y  5
5)
6)
2 x  3 y  11
5 x  y  13
Use Cramer’s rule to solve they system:
2x  3y  7
3 x  4 y  14
7)
8)
 x  2 y  4
5 x  2 y  21
Use an Augmented Matrix to solve the system:
x  2 y  11
2 x  3 y  17
9)
10)
2 x  3 y  17
3x  4 y  24
Solve the system of equations:
x yz 6
2 x  3 y  z  4
11) 2 x  y  3 z  9
3 x  y  z  2
12) x  2 z  4
4 x  3 y  z  2
13) What does the solution to a system of equations represent?
14) If 30 gumballs can be purchased for 3 dollars, write a function that represents the cost in cents of ‘d’ dozen
gumballs.
15) If a supersonic jet can travel 30 miles per minute, write a function that represents the distance traveled in ‘h’
hours.
Does the set of points represent a linear function?
16)  2, 2 ,  3, 1 ,  4, 4 , 5, 7 
17)
 4, 2 ,  0, 4 ,  4,6 ,  12,10
18) What is 3  2 y  5  3 x in slope intercept form?
19) What is y y  4 
2
 x  1 in standard form?
3
Graph the point or plane:
20) 4 x  5 y  z  20
21) 2 x  5 y  4 z  80
22) (6, 4,8)
Write the function g  x  that is a result of each transformation:
23) Parent function f  x   x2 is vertically compressed by a factor of 1/3, translated right 4 units and up 6 units.
24) Parent function f  x   x is vertically stretched by a factor of 6, translated left 3 units and down 7 units.
25) Parent function f  x   x3 is vertically flipped, translated left 6 units and down 4 units.
Find the maximum or minimum of the function:
26) f  x   x2  6x  3
27) g  x   2 x2  2 x  4
Write the function in vertex form:
28) f  x   x2  8x  7
29) g  x   x2  4 x  5
Write a quadratic function in standard form having zeros of:
 1
2
30)  5 and   
31)  6 and  
 3
5
Find the x- and y-intercepts of the graphs of the equations below.
32) y  4 x  3
33) y  6 x 2  11x  10
34) y  3 x  9
35) y  x3  x 2  4 x  4
Sketch the graph of each function (label the vertex and y-intercept). Name the domain and range.
2
3
36) y   x  4   5 37) y  2 x  3  5
38) y  2  x  1  4
39) y  2 x  3  4
40) A ball is kicked from the ground into the air with an initial velocity of 60 fps. The height of the ball, h  t  , after
t seconds is given by h  t   16t 2  60t . a) How long is the ball in the air? b) How long is the ball in the air before
it starts down? c) How high does the ball go? d) Sketch a graph of the parabola, label completely and clearly.
41) Using the same information from problem 40, the ball is instead kicked from the roof of a 10 ft tall building.
a) What is the new parabolic equation? b) How long will the ball stay in the air this time?
42) When a model rocket was launched it traveled a horizontal distance of 400 ft and reached a maximum height of
900 ft. . Sketch the path of the rocket, find an equation of the parabola that models the flight of the rocket, and state
the domain and range.
43) A popular mixture of potpourri includes pine needles and lavender. If pine needles cost \$1.50 per ounce and
lavender costs \$4.00 per ounce, how much of each ingredient should be mixed to make 80 ounces of the potpourri
that is worth \$200?
44) The cost of 3.2 lbs of carrots and 2 lbs of peas is \$7.36. The cost of 1.8 lbs of carrots and 2.5 lbs of peas is
\$5.35. What is the cost per pound for the carrots and peas?
45) Given the roots of 3, -2, 1, and -1, write and graph the polynomial equation. (Include all intersects on graph)
46) Using matrix multiplication, find the total collected for adult tickets and student tickets for the 3 performances.
Student
Thu
\$5
\$2.50
Fri
\$7.50
\$4.25
Sat
\$9
\$5.75
Thur
Fri
Sat
67
196
245
Student
104
75
154
1) No
2) Yes
3) (4,-1)
4) (-4,3)
5) (-2,5)
6) (-3,-2)
1
 26 1 

7)  ,  , D  7, Dx  26, Dy  1
8)  4,   , D  14, Dx  14, Dy  7
2
 7 7 

9) (-1,-5)
10) (-4,3)
11) (1,2,-3) 12) (-2,-1,3)
13) The values that work in both equations, or the point of intersection of the graphs
14) C  d   120d
15) D  h   1800h
16) Yes
17) Yes
3
18) y   x  1
2
1
2
23) g  x    x  4   6
3
26) Minimum: 6
19) 2 x  3 y  14
20 – 22) See graphs in class
24) g  x   6 x  3  7
25) g  x     x  6   4
27) Maximum:
9
2
28) f  x    x  4   9
29) g  x    x  2   9
30) f  x   3x 2  14 x  5
31) f  x   5x 2  28x  12
2
2
3 
32) x-int:  , 0 
y-int:  0, 3
4 
34) x-int:  3,0 
y-int:  0,3
36) Domain: x  R Range: y  5
38) Domain: x  R Range: y  R
40) a) 3.75 sec
b) 1.875 sec
2
41) a) h  t   16t  60t  10
5   2 
33) x-int:  , 0  ,   ,0  y-int:  0, 10
2   3 
35) x-int:  2,0 ,  2,0  ,  1,0  y-int:  0, 4 
37) Domain: ( ,  )
Range: [5, )
39) Domain: [3,  )
Range: [4, )
c) 56.25 ft
d) See graph in class
b) 3.91 sec
9
2
Range: 0  h  900
 d  200   900 Domain: 0  d  200
400
48 oz of pine needles, 32 oz of lavender
Carrots cost \$1.75/lb, Peas cost \$.88/lb
y   x  3 x  2  x  1 x  1