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CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
1
Multiple Choice. Pick the answer that bests answers the question or completes the statement. Bubble in
the letter of your answer next to the corresponding number on the answer page. (1 point each)
1. ( x  3) 2 is equal to ____
a. x 2  6 x  9
b. x 2  6 x  9
c. x 2  9
d. x
2
9
2. Which of the following is not a method for finding the slope of a line?
a.
rise
run
b.
x  x1
y  y1
c.
y
x
d.
y1  y2
x1  x2
3. . A relation is a function if _____________ of the domain values are repeated.
a. all
b. none
c. some
d. any
4. When solving a linear system of equations, you are looking for which of the following?
a. Shaded Region
b. roots
c. Point(s) of Intersection
d. x intercepts
5. A linear system of equations made up of two intersecting lines has ________ solution(s).
a. no
6.
b. two
c. one
d. three
If the legs of a right triangle measure 5 and 12 inches respectively, the measure of the third side is
a. 144 in
c. 169 in 2
b. 13 in
d. 13
7. Which of the following is an equation of a circle?
a.
x  13  0
b. y  2 x 2  x  1
c. y 2  16 x
d. x 2  y 2  9
8. The vertex of a parabola that opens up will always be found at ______.
a. a y-intercept
b. an x-intercept
c. a maximum y
d. a minimum y
9. The set of all y values of a relation is called the _____.
a. range
b. domain
c. function
d. inverse
10. If a system of equations has one solution, then the equations will have _____.
a. the same slopes
b. different slopes
11. The parent function f ( x ) 
a. asymptote
x
c different y intercepts
d. both a and c
will be "V" shaped and have a(n) _____ at (0,0).
b. vertex
c. parabola
d. maximum
12. The Solution(s) of a Quadratic Equation is/are also sometimes called _____.
a. x-intercept(s)
b. Zero(s)
c. root(s)
d. all of these
13. The trinomial x 2  4 x  3 completely factored is _____.
a. ( x  1)( x  3)
b. ( x  1)( x  3)
c. x  22
d. none of these
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
2
14. Which equation graphs a parabola opening up and with a vertex at (3,-2).
a. y  ( x  3)2  2
b. f ( x)  0.5( x  3)2  2
c. g ( x)  ( x  3)2  2
d. h( x)  3x  1
15. The LOSE of y  2 x 2  8 x  12 is ______.
a. 2
b. y =2
c. x =-8
d. x = 2
16. All the solution(s) for 4 x 2  100  0 are ____
a. x  5
b. x  5
c. (0,5)
17. What is the Leading Coefficient (a) of
a. 3
b. 4
d. (5,0)
y  6 x 3  3x 2  4 x  5 ?
c. 6
d. 5
18. What is the constant of y  6 x 3  3x 2  4 x  5 ?
a. 3
b. 4
c. 6
d. 5
19. What is the degree of y  6 x 3  3x 2  4 x  5 ?
a. 3
b. 4
c. 6
d. 5
20. How many solutions does y  6 x 3  3x 2  4 x  5 have?
a. 3
b. 4
c. 6
21. In the Quadratic Formula, x 
a. domain
d. 5
 b  b 2  4ac
, b 2  4ac is called the ______.
2a
b. determinant
c. discriminant
d. dividend
22. If f ( x)  2 x  3  4 , what is f (2) ?
a.  3
b. 5
c. 11
d. 3
23. Given the Relation: { (0,5), (1,7), (2, 9), (5,15) }, which set below is the Range of the relation?
a. {1, 2, 3, 5}
b. { 0, 1, 2, 5 }
c. { 15, 5, 9, 2, 7, 1, 5, 0 }
d. { 5, 7, 9, 15 }
24 What is the y-intercept of the line determined by the linear equation 4 x  8 y  16 ?
a. (4,0)
b. (0,2)
c. ( 4,0)
25. What is the slope of the linear equation: y 
a. 
1
2
b.
1
2
d. (0,2)
1
x  2?
2
c.  4
d.
4
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
3
26. Which ordered pair(s) are all the y-intercept(s) of the equation: y  x 2  2 x  1?
a. (0,1)
b. (0,0)
c. (1,0)
d. (0,-1) and (0,2)
27. If one acute angle of a right triangle is 35 , what is the measure of the other acute angle?
a. 45
b. 55
c. 145
d. not possible to determine
28. Both parabolas and absolute value graphs have ____
a. a vertex
29. When is
b. symmetry
c. maximums
d. a and b
x  1 not positive?
a. x  0
b. x  4
c. x  1
30. In the quadratic formula, x 
a. equation of the LOS
d. never
b
represents _____
2a
b. Minimum
c. x coordinate of the vertex
d. both a and c
31. What is the radius of the circle graphed by the equation: ( x  1)2  y 2  25 ?
a. 25
c.  25
b. 5
d. 625
32. The solution for a system of equations, will make ____________ equations true when you check.
a. neither
b. one
c. both
33. The square root of a number is the same as raising the number to the
a.
b.
(1/2) power
b. second power
c. (1/3) power
 2
34. Which system of equations represents the matrix equation:  2

a.
2x  3y  6
 5 y   x  10
b.
2 x  4 y  12
 5y  x  6
c.
4   x  12 

 3  y   6  ?
 2 x  4 y  12
2x  3y  6
35. The boundary line of the graph of 2 x  3 y  6 will be ______.
a. solid
b. dashed
c. vertical
d. horizontal
c. (3,0)
d. (0,2)
36. The x intercept of 2 x  3 y  6 is _____.
a. (3,0)
b. (0,3)
d.
 x  2y  6
4 x  5 y  12
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
( x  3)
37. The domain of y 
, will be any real number _______.
( x  2)
a. except  2
b. except 3
c. except 2
d. no restrictions on domain
38.
39.
40.
41. Which equation below will graph a line perpendicular to y 
a. y 
3
x4
2
b. f ( x) 
3
x2
2
c. h( x ) 
2
x  9?
3
2
x
3
d. 
2
x5 y
3
42. The solution for the inequality: 3  5  2x  11 is _____.
a. 1  x  3
b. x  1
c.  3  x  1
d. No solution
43. The square of any nonzero real number b, b 2 , will always result in an answer that is _____.
a. a positive number
b. a negative number
c. zero
d. either a or c
44. The midpoint of the segment with endpoints (4,7) and (6,5) is _____.
a. (1,6)
b. (5,1)
c. (1,1)
d. (5,6)
45. The vertex of y  2( x  3) 2  4 is
a.
(3,-4)
b. (3,4)
46. The y-intercept of y  2( x  3) 2  4 is
a. 4
b. (0,-14)
c. (0,4)
d. (0,0)
c. (-14,0)
d. (3,4)
c. up
d. down
47. The graph of y  2( x  3) 2  4 will open
a.
Right
b. Left
4
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
5
Answer the questions below in the space provided. Your written answer should include algebraic terminology
and facts to justify your answer. (2 points each)
1. Simplify: (1pt)
4b(2.3) 2 (1.45)(0)(0.34) x 3  12 0 (2ez )
2. Solve the system of equations. Show work. No graphing!!! (2pts)
2 x  3 y  7
yx4
3. Write the equation of a circle with center at (3,-4) and with a radius of 6. Show work. (2pts)
Write the equation of each graph below on the appropriate line provided. (1pt each)
5.
6.
5. ___________________________________
6. ___________________________________
Solve. Show work. (2pts each)
8.
25x 2 100  y
9.
3x  8  5  3
10. Write and solve a system of equations for the problem below. Show work. (5pts)
You have $18,000 to invest in three types of stocks. You expect annual returns on Stock X to be 10%,
stock Y to be 9% and Stock Z to be 6%. You want the combined investment in Stock Y and Stock Z to be
twice the amount invested in Stock X. How much should you invest in each type of stock to obtain an
average return of 8% for all of your investments?
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
11. Solve by factoring. Show work. (2pts)
12. Solve
6
y  x 2  3x  40
y  2 x2  12 x  16 by using the quadratic formula. Show work. (3pts)
Let f ( x )  1  3 x and g ( x)  2 x  1 , find: (show substitution) (2pt each)
13. f (2)
14. f ( x)  g ( x)
15. g ( f ( x))
16. g (0)
Simplify. Show work. (1 pt each)
17.  3( x  2)  3x  4
19.
 16
21. (4  3i )( 2  4i )
23.
16  6  (2) 2
18. (12  i )  (4  3i )
20. (2 x  3) 2
22. ( x  4)( x  4)
24.
49
25. Solve the inequality and graph the solution on the number line. (2pts)
3 x 1  9
____________________________________________________
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
7
Solve each equation for real number solutions. Without graphing. Show work. (2pts each)
27. 3x 2  25  2
26. 5 x  3  2(9  x)
28. x 2  7 x  42  5 x  6
29. Graph, f ( x)   x 2  4 x  4 on the coordinate plane provided. Show work and make a table
with enough points to show symmetry and the vertex. Show how you obtained the vertex. (4pts)
x
y
Use a graphing calculator to find the indicated information for this entire page. Round to the nearest hundredth if
necessary.
30. Solve the system of equations:
31. y  2 x 2  3x  9
2 x  3 y  12
y  3  4x
.
Solution(s): _______________________ (2pts)
a. Zeros: ________________________________________(2pts)
b. Vertex: _____________
(1pt)
c. y-intercept: ______________ (1pt)
32. Find the solution(s) for the system of equations. (2pts)
f ( x)   x 2  5 x  2
g ( x) 
5
x2
2
Solution(s): _____________________________________
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
8
33. Make a scatter plot with the given data in the table showing the height of a plant over 21 days of measuring.
Make a line of best fit for the data and use it for questions 34 - 38. (1 pt each)
Show Mr. Crowley the scatter plot with line of best fit. ____ (1pt)
Day
1
5
9
17
21
Height (cm)
4
6
8
14
16
Make a line of best fit for the data and use it for questions 34 - 38. (1 pt each) Round to the nearest tenth.
34.
35.
36.
37.
38.
Write the equation of the line of best fit: _______________________________________
What is the slope of the line of best fit? ________________
What does the slope of the line of best fit mean?
Based on the line of best fit, how tall will the plant be on the 25th day?
How did you find your answer for 37?
Graph each equation on the coordinate plane provided:
(2pts)
39. ( x  2) 2  ( y  3) 2  9
40. Graph the inequality on the coordinate plane provided. (2pts)
y
3
x 1
2
41. Write and solve a system of equations for the word problem. Show work. (4 pts)
The Warner Theatre sold 250 tickets for the 5pm showing of “The Babe”. They sold youth tickets for $6
each and adult tickets for $8.50 each and collected a total of $1990. How many of each kind of ticket was
sold
CP Algebra II Practice Final Exam 2017
Name: ____________________________________ kc
9
{  3 x 2  10, x  3
42. Evaluate the compound function: f ( x)  {
{ x  20, x  3
for f (20)
(1pt)
Use f ( x)  x 5  2 x 3  5x 2  4 numbers 45 -49. (1pt each)
45. What is the degree of this polynomial function? _______________
46. What is the leading coefficient of this polynomial function? _______________
47. What is the constant of this polynomial function? _______________
48. What is the y-intercept of this polynomial function? _________________
49. Write all real solutions for this polynomial function: ____________________________________________
(2pts)
x  0,
50. Maximize the objective function: A  3x  2 y given the constraints:
y0
x  3 y  15
4 x  y  16
. Show work. (5pts)