Fourth Quarter Exam Review
Name ______________________________
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. Classify –4x4 – 3x2 by degree and by number of terms.
a. quintic binomial
c. quintic trinomial
b. quartic binomial
d. quartic trinomial
2. Classify –5x5 – 8x4 – 2x3 by degree and by number of terms.
a. cubic binomial
c. quartic trinomial
b. quintic trinomial
d. quadratic binomial
3. Zach wrote the formula w(w – 1)(2w + 3) for the volume of a rectangular prism he is designing, with width w, which is
always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number
of terms.
4. Write the expression (x + 5)(x – 3) as a polynomial in standard form.
a. x2 + 2x – 15
c. x2 – 8x + 2
b. x2 + 8x – 15
d. x2 + 8x – 8
5. Write 2x3 + 8x2 – 24x in factored form.
a. 2x(x – 2)(x – 6)
c. 6x(x – 2)(x + 2)
b. –2x(x + 2)(x + 6)
d. 2x(x + 6)(x – 2)
6. Find the zeros of y = x(x – 5)(x – 2).
a. x = -5, -2, 0
c. x = 2, 5
b. x = -5, 2, 5
d. x = 0, 2, 5
7. Write a polynomial function in standard form with zeros at 1, 5, and –3.
a.
y = x3 – 3x2 – 13x + 15
c.
y = x3 + 8x2 – 30x – 16
b.
y = x3 + 15x2 – 3x – 13
d.
y = x3 – 3x2 – 13x – 16
8. Find the zeros of y = (x – 3)4(x + 4)3 and state the multiplicity.
a.
b.
c.
d.
x = 3 multiplicity 4, 3 multiplicity –4
x = 4 multiplicity 3, 3 multiplicity –4
x = 4 multiplicity 3, –4 multiplicity 3
x = 3 multiplicity 4, –4 multiplicity 3
9. A model for the height of a toy rocket shot from a platform is y = -16x2 + 80x + 10, where x is the time in seconds and y
is the height in feet. Find the zeros of the function.
10. Divide 3x3 – 3x2 – 4x + 3 by x + 3.
A. 3x2 – 12x + 32
C. 3x2 + 6x – 40
B. 3x2 – 12x + 32, R: -93
D. 3x2 + 6x – 40, R: 99
11. Find the real-number root of: √
A.
B.
12. Simplify the radical expression:
D.
C. 6g3
D. 6g4
C. 9x10y4
D. 3x10y4
√
B. 36g4
A. 36g3
C.
13. Simplify the radical expression: √
A. 3x5y2
B. 9x5y2
14. Multiply and simplify if possible: √
A.
√
√
B. √
15. Simplify √
C.
√
D. not possible
. Assume that all variables are positive.
A.
√
C.
B.
√
D. none of these
16. Multiply and simplify √
A.
√
. Assume that all variables are positive.
√
C.
B. √
√
D. none of these
17. Divide and simplify:
A.
√
√
√
B.
√
√
18. Rationalize the denominator of the expression:
C. √
√
√
D.
√
√
A.
√
C.
B.
√
D.
√
√
√
√
19. Add if possible:
√
√
A.
C.
√
B.
D. not possible to simplify
√
20. Subtract if possible:
√
√
A.
√
C. 1
B. √
D. not possible to simplify
21. A garden has width √
and length √
. What is the perimeter of the garden in simplest radical form?
A.
√
units
C. 91 units
B.
√
units
D.
22. Simplify:
√
√
A.
√
B.
√
√
units
√
√
C.
√
D. none of these
23. Simplify:
A. 512
24. Multiply: (
B. 4,096
C. 16
D. √
√ )
A.
√
C.
√
B.
√
D.
√
25. Multiply:
√
√
√
√
B. –3
√
A.
26. Write the exponential expression
A.
27. Write the radical expression
A.
D.
C.
D.
√
in radical form.
B. √
√
C. 17
√
in exponential form.
√
B.
C.
D.
B. –8
C. 4
D. –6
28. Solve the equation: √
A. 14
√
29. Solve the equation:
A. 11
B. 15; –1
C. –3
D. 1; –1
B. 5
C. 11
D. –11
30. Solve the equation:
A. –5, 11
√
31. Solve and check for extraneous solutions:
A.

B. 1
2
C.
3
1 and 
2
D. 1
3
32. Solve and check for extraneous solutions:
A. 7
B. 2
6
3
33. Let
C.
and
B. –8x – 8
D. 6
4
7
C. –8x – 4
D. 2x – 8
. Find f(x) – g(x).
and
A. 2x – 5
C. 4x – 1
B. 2x + 5
35. Let
A.
C.
B.
D.
. Find (f ◦ g )(-5).
and
B. –53
A. 23
D. 2x – 1
. Find 2f(x) – 3g(x).
and
36. Let
1
. Find f(x) + g(x).
A. 2x – 4
34. Let

C. –9
D. 3
37. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
0
4
9
10
y
3
2
7
–1
38. Find the inverse of y = 7x2 – 3.
A.
C.
√
B.
D.
√
√
39. Police can estimate the speed of a vehicle before the brakes are applied using the formula
, where s is
the speed in miles per hour and d is the length of the vehicle’s skid marks. What was the approximate speed of
a vehicle that left a skid mark measuring 100 feet?
A. about 29 miles per hour
C. about 48 miles per hour
B. about 10 miles per hour
D. about 43 miles per hour
40. For the function
A. 14
, find (f ◦f -1)(5).
C. –5
B. 5
41. The velocity of sound in air is given by the equation
t is the temperature in degrees Celsius.
√
D. 25
, where v is the velocity in meters per second and
A. Find the temperature when the velocity of sound in air is 318 meters per second. Round the answer to the
nearest degree.
B. Find the velocity of sound in meters per second when the temperature is 20°C. Round the answer to the
nearest meter per second.
42. Consider the equation √
.
A. Solve the equation and check for extraneous roots. Explain your steps.
43. Consider the relation s given by the values in the table.
x
–5
–3
–1
1
y
–6
–2
–2
–6
A. Find the inverse of relation s
B. Graph s and its inverse.
C. Describe the relationship between the line y = x and the graphs of s and its inverse.
D. Is the relation s a function? How do you know?
E. Is the inverse of s a function? How do you know?
44. Rationalize the denominator for the expression
45. Consider the function
√
A. Find the domain of f.
B. Find
.
C. Find the domain of
D. Is
a function?
.
.
√
√
√
. Explain your steps.