Two-Year Algebra 2 B
Semester Exam Review
Two-Year Algebra 2 B Semester Exam Review 2015–2016
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Two-Year Algebra 2 B
Semester Exam Review Exam Formulas
b b 2 4ac If ax bx c 0, then x 2a 2
Factor Theorem: P a 0 if and only if x a is a factor of P x . Remainder Theorem: The remainder when a polynomial function P x is divided by x a is P a .
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Two-Year Algebra 2 B
Semester Exam Review
Unit 2, Topic 1 1.
An Algebra 2 class is asked to solve the radical equation
2x 5 x 1
Jack decides to solve this equation symbolically. Solve the equation and determine which solutions, if any, are extraneous.
In the following problems, i 1 and a bi represents a complex number where a and b are real numbers. 2.
What is the value of i i 2 i 3 i 4 ?
3.
Perform the following operations. Write your answer in the form a bi . a.
3 i 6 5i
b.
4 7i 2 6i
c.
3 2i 4 9i
d.
4 3i 4 3i
e.
7 5i
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Two-Year Algebra 2 B
4.
Semester Exam Review
One of the solutions of a quadratic equation q x 0 is x 4 . Complete the following: a.
__________________ is factor of q x
b.
The point ______ is the location of an x-intercept of the graph of q x .
c.
The second solution to the equation q x 0 is (always, sometimes, or never) real.
d.
5.
_______ is a zero of q x .
The solutions of a quadratic equation q x 0 are x 3 and x 7 . Complete the following. a.
__________________ and ______________ are the factors of q x .
b.
The points ______ and _______are the locations of an x-intercepts of the graph of q x .
c.
___________and ___________ are the zeros of q x .
6.
One solution of a quadratic equation with real coefficients is 5 3i . What is the other solution?
7.
One solution to a quadratic equation with real coefficients is 6i . What is the other solution?
8.
On the axes below, sketch the graph of a quadratic function with the stated roots.
a.
Two real roots
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b.
One double root
c.
Two imaginary roots
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Two-Year Algebra 2 B
9.
Semester Exam Review
Solve the following quadratic equations over the set of complex numbers. Show how you determined your solutions. a.
x 2 25
b.
x 3
c.
x 2 6 x 15
d.
5x2 2 x 3 0
e.
2 x 2 x 20 x 1
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Two-Year Algebra 2 B
Semester Exam Review
Unit 2, Topic 2
10.
Sketch a rough graph of a polynomial function that has each characteristic.
Degree is: a.
Leading Coefficient is:
Even
Positive
Odd
Negative
Even
Negative
Odd
Positive
Graph
b.
c.
d.
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Two-Year Algebra 2 B
11.
Semester Exam Review
Do the functions below have the same end behavior as f x x 4 , when x ? Write yes or no.
12.
a.
______ g x x 4 70 x 3
b.
______ h x x3
c.
______ k x 2 x
Do the functions below have the same end behavior as f x x 3 , when x ? Write yes or no. a.
______ g x x 3 200 x 2 50 90
b.
______ h x x 4
c.
______ j x log x
13.
Classify each function represented by the graph as even, odd, or neither even nor odd.
a.
___________
14.
The point 3,8 is on the graph of an even function. What are the coordinates of another
b.
__________
c.
__________
point on its graph? 15.
The graph of an even function has what symmetry?
16.
The point 5, 7 is on the graph of an odd function. What are the coordinates of another point on its graph?
17.
The graph of an odd function has what symmetry?
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Two-Year Algebra 2 B
18.
Semester Exam Review
Look at the graph of the polynomial function f x x( x 3) 2
a.
What is the degree of f ? _______
b.
As x , f x _______
c.
Write the zeros and their multiplicities.
d.
Give coordinates of the point where a relative maximum occurs. _______
e.
Give coordinates of the point where a relative minimum occurs. _______
f.
On what interval(s) is the function increasing? _____________________
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Two-Year Algebra 2 B
19.
Semester Exam Review
Look at the graph of g x ( x 1) 2 ( x 3) 2 below.
a.
What is the degree of g? _______
b.
As x , g x _______
c.
Write the zeros and their multiplicities.
d.
Give coordinates of the point where a relative maximum occurs. _______
e.
Give coordinates of the points where a relative minimum occurs.
f.
On what interval(s) is the function decreasing? _____________________
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Two-Year Algebra 2 B
20.
Semester Exam Review
The graph of a polynomial function f x with leading coefficient 2 is shown below.
Write a function equation represented by the graph. f x _______________________
21.
The graph of a polynomial function g x with leading coefficient
1 is shown below. 2
Write a function equation represented by the graph. g x _______________________
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Two-Year Algebra 2 B
22.
23.
Semester Exam Review
Let f x x 2 2 x 7, g x 2 x 2 9, and h x 5 x 3 . a.
Write f g x as a polynomial in standard form.
b.
Write f g x as a polynomial in standard form.
c.
What is the degree of the product f g x ?
d.
What is the degree of the product g h x ?
e.
Write f h x as a polynomial in standard form.
Jillian divides x 3 8 x 2 7 x 1 by x 9 and gets a quotient of x 2 x 2 with a remainder of 19. a.
Is x 9 a factor of x 3 8 x 2 7 x 1 ? Justify your answer.
b.
If f x x 3 8 x 2 7 x 1 , what is the value of f 9 ?
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Two-Year Algebra 2 B
24.
Semester Exam Review
Look at the long division below. x2 x 7 x 8 x 3 7 x 2 x 56 x3 8 x 2 0 x 0 x 2 x 56 x2 8x 0 7 x 56 7 x 56 0
a.
If P x x 3 7 x 2 x 56 , what is P 8 ?
b.
What is the x-intercept of the graph of P x x 3 7 x 2 x 56 ?
c.
What is a factor of x 3 7 x 2 x 56 ?
d.
Write a factorization of x 3 7 x 2 x 56 .
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Two-Year Algebra 2 B
25.
Semester Exam Review
A polynomial function of degree 4 has the following properties.
A negative leading coefficient. Roots of 3 (multiplicity 1), 1 (multiplicity 1), and 4 (multiplicity 2).
Make a rough sketch of a function with these properties below.
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Two-Year Algebra 2 B
Semester Exam Review
Unit 2, Topic 3
The graph of f x
1 is shown below. x
Unit 2, Topic 3
26.
The graphs below are transformations of y
a.
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1 . Write the equation for each graph. x
b.
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Two-Year Algebra 2 B
Semester Exam Review
27.
Graph the following.
a.
y 3
28.
Write the least common multiple of the denominators in each equation, then solve the equations. Check for extraneous solutions.
a.
1 x 1
7 5 x3 x2
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b.
b.
y 2
1 x3
10 1 x x 2 x
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Two-Year Algebra 2 B
29.
30.
Semester Exam Review
A house with a total wall surface area of 4,500 square feet is to be painted. Each painter can paint 300 square feet of surface in one hour. a.
How long will it take one painter to paint the house?
b.
Complete the blank. The number of hours that it takes to paint the house varies _____________ as the number of painters.
c.
Let n be the number of painters assigned to this job, and let H represent the total number of hours it will take for the paint job to be complete. Use your answer to part a) to write an equation relating H and n.
d.
How many hours will it take if 4 painters are assigned to this job?
Write an equation relating the variables in this situation. The number of hours, H, to drive 200 miles varies inversely as the speed of the car, s, in miles per hour.
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Two-Year Algebra 2 B
31.
a.
Show that the functions f and g below are equivalent. f x 2
32.
Semester Exam Review
1 x3
g x
2x 7 x3
b.
What are the equations of the asymptotes of the graphs?
a.
Show that the functions h and z are equivalent. h x 5
b.
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1 x4
z x
5 x 21 x4
What are the equations of the asymptotes of the graphs?
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Two-Year Algebra 2 B
33.
34.
Semester Exam Review
Brianna bakes cakes. The average cost, C, in dollars, to make x pound cakes in a day is 250 6x given by the formula C . x a.
If Brianna bakes 10 pound cakes in one day, what was her average cost per pound cake made?
b.
One day, Brianna’s average cost to make each pound cake was $11. Write and solve an equation to determine how many pound cakes she made that day.
Brandi makes fruitcakes. She always gives 2 fruit cakes a day to charity. The average 500 8 x , where x is the cost per fruitcake sold, S, in dollars, is given by the formula S x2 number of fruitcakes made. a.
One day, Brandi made 22 fruitcakes. What was the average cost per fruitcake sold?
b.
On another day, the average cost per fruitcake sold was $18.75. Write and solve an equation to determine how many fruitcakes she made.
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