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5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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Student: _____________________Date: _____________________
Instructor: Virginia DavisCourse: Foundations for College Math(1)
Assignment: Final Exam Review Ch10,11
Simplify by factoring. Assume that all variables under radicals represent nonnegative numbers.
x10
Select the correct choice below and, if necessary, fill in the answer box that completes your choice.
A. =x10
(Type an exact answer, using radicals as needed.)B. The square root is not a real number.
Find the root. Assume that the variable represents a nonnegative real number.
8 x32
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Simplify your answer.)8 x32 =
B. The root is not a real number.
Simplify the radical. Assume that all variables represent positive real numbers.
3 − 27x9y6
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. =3 − 27x9y6
B. The radical does not represent a real number.
Simplify the radical. Assume that all variables represent positive real numbers.
6 a66b6
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 6 a66b6 =
B. The root is not a real number.
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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Use radical notation to rewrite the expression.
1211 2
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. (Simplify your answer. Type an exact answer, using radicals as needed.)1211 2 =
B. The answer is not a real number.
Use rational exponents to simplify each radical. Assume that all variables represent positive numbers.
12 a4b4
=12 a4b4
(Simplify your answer. Type an exact answer, using radicals as needed.)
Use the quotient rule to simplify.
54
54=
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Simplify your answer.)
Use the quotient rule to simplify.
249
249
=
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Simplify your answer.)
Simplify by factoring.
24
24 = (Type an exact answer, using radicals as needed.)
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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Use the quotient rule to divide, then simplify, if possible.
9
3
9
3=
(Type an exact answer, using radicals as needed. Simplify your answer.)
Solve.
x − 5 = 2
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution(s) is(are) x . = (Use a comma to separate answers as needed.)
B. The solution set is .
Solve.
= 65x − 9
Select the correct choice below and fill in any answer boxes present in your choice.
A. x = (Simplify your answer. Use a comma to separate answers as needed.)
B. There is no solution.
Find the length of the unknown side of the triangle.
20 ft
5 ft
The length of the unknown side of the triangle is ft. (Simplify your answer. Type an exact answer, using radicals as needed.)
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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Find the length of the unknown side of the given triangle.
3 m6 m
The side is m. (Simplify your answer. Type an exact answer, using radicals as needed.)
Subtract.
(5 + 7 ) − (9 − 8 )
(5 + 7 ) − (9 − 8 ) = (Simplify your answer. Type your answer in the form a b .)+
Subtract.
(5 − 9 ) − (3 − 6 )
(Simplify your answer. Type your answer in the form a + b .)(5 − 9 ) − (3 − 6 ) =
Perform the indicated operation.
(7 + 4 )(7 − 4 )
The answer is . (Simplify your answer. Type your answer in the form a b .)+
Multiply.
( i )5 + 6 2
( i )5 + 6 2 = (Simplify your answer. Type your answer in the form a + b .)
Use the square root property to solve the equation. The equation has real number solutions.
(x + 1)2 = 16
x = (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
Use the square root property to solve the equation. The equation has real number solutions.
(x − 1)2 = 20
x = (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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Use the square root property to solve the equation.
x + 92 = 0
x = (Type an exact answer, using radicals as needed. Express complex numbers in terms of . Use a comma to separate answers as needed.)
Use the quadratic formula to solve the equation. The equation has real number solutions.
y7 = 4y2 + 3
y = (Type a simplified answer, using fractions and radicals as needed. Use a comma to separate answers as needed.)
Use the quadratic formula to solve the equation.
x + 7x − 2 = 02
x = (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
Use the quadratic formula to solve the equation.
x x 02 + 4 + 8 =
The solution(s) is/are x .= (Simplify your answer. Type an exact answer, using radicals and as needed. Use a comma to separate answers as needed.)
Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.
f(x) = − 3(x − 5) + 42
Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
The vertex is . (Type an ordered pair.)
The axis of symmetry is . (Type an equation.)
20 16 12 8 4 4 8 12 16 20
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5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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26. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.
f(x) = x + 6x + 52
The vertex is . (Simplify your answer. Type an ordered pair.)
Does the graph open upward or downward?
The parabola opens ward.upThe parabola opens ward.down
Find any xintercepts of the graph.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The xintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
B. There is no xintercept.
Find any yintercepts of the graph.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The yintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
B. There is no yintercept.
Use the graphing tool to graph the function.
10 8 6 4 2 2 4 6 8 10
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5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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27. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.
f(x) = − x − 6x − 52
The vertex is . (Simplify your answer. Type an ordered pair.)
Does the graph open upward or downward?
The parabola opens ward.downThe parabola opens ward.up
Find any xintercepts of the graph.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The xintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
B. There is no xintercept.
Find any yintercepts of the graph.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The yintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
B. There is no yintercept.
Use the graphing tool to graph the function.
10 8 6 4 2 2 4 6 8 10
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5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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28. Find the vertex of the graph of the quadratic function shown below. Determine whether the graph opens upward or downward, find the yintercept, approximate any xintercepts to one decimal place, and sketch the graph.
f(x) = 12x − 24x + 132
The vertex is . (Simplify your answer. Type an ordered pair.)
Does the graph open upward or downward?
The parabola opens ward.upThe parabola opens ward.down
What is the yintercept of the graph?
(Type an ordered pair. Use a comma to separate answers as needed.)
Approximate any xintercepts of the graph. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The xintercept(s) is(are) . (Type an ordered pair. Round to one decimal place as needed. Use a comma to separate answers as needed.)
B. There are no xintercepts.
Choose the correct graph below.
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B.
5 5
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5 5
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D.
5 5
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5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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1. A. =x10 x5 (Type an exact answer, using radicals as needed.)
2. A. (Simplify your answer.)8 x32 = x4
3. A. =3 − 27x9y6 − 3x y3 2
4. A. 6 a66b6 = a b11
5. A. (Simplify your answer. Type an exact answer, using radicals as needed.)1211 2 = 11
6. 3 ab
7. 5
2
8. 2
7
9. 2 6
10. 3
11. A. The solution(s) is(are) x . = 9 (Use a comma to separate answers as needed.)
12. A. x = 9 (Simplify your answer. Use a comma to separate answers as needed.)
13. 5 17
14. 3 3
15. − 4 + 15
16. 2 − 3
17. 65
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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18. − 11 + 60
19. 3, − 5
20. 1 + 2 ,1 − 25 5
21. 3 , − 3
22. 1, 34
23. ,− 7 − 57
2− 7 + 57
2
24. − 2 + 2 , − 2 − 2
25.
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(5,4)
x = 5
26. ( − 3, − 4)
The parabola opens ward.up
A. The xintercept(s) is(are) .( − 5,0),( − 1,0) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
A. The yintercept(s) is(are) .(0,5) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
5/19/2016 Final Exam Review Ch 10,11-Virginia Davis
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27. ( − 3,4)
The parabola opens ward.down
A. The xintercept(s) is(are) .( − 5,0),( − 1,0) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
A. The yintercept(s) is(are) .(0, − 5) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
10 8 6 4 2 2 4 6 8 10
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28. (1,1)
The parabola opens ward.up
(0,13)
B. There are no xintercepts.
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