MAT 121 Final Exam Review Fall 2016
MAT 121 Final Exam Review Fall 2016
Chapter Three, Section 3.5
Solve the absolute value equation.
1.
2 x  6  2
2.
2 x  1  11
3.
z 1  2z
Solve the absolute value inequality. Write your answer in interval notation.
4.
12 x  30
5. 4 x  2  16
6.
2 x 1  3
1
MAT 121 Final Exam Review Fall 2016
Chapter Four, Section 4.1
Solve the system graphically. Check your answer.
1.
2x  y  4
x y 5
Solve the system of equations. Determine whether the system is consistent or inconsistent. If
the system is consistent, state whether the equations are dependent or independent.
2.
3.
4.
x  2y  3
2x  y  1
x y 3
2x  2 y  6
2 x  y  3
4x  2 y  2
Solve the system of equations. Check your answer.
1
1
x  y 1
2
8
5.
1
5
 x  y  1
2
6
2
MAT 121 Final Exam Review Fall 2016
3
Do the following.
a. Write a system of linear equations that models the situation.
b. Solve the resulting system.
6. Price: If 2 boxes of popcorn and 3 soft drinks cost $7 and 3 boxes of popcorn and 2 soft
drinks cost $8, find the price of a box of popcorn and the price of a soft drink.
Chapter Four, Section 4.2
Solve the system of equations by using substitution.
1.
x  2y  0
3x  2 y  1
Use elimination to solve the system.
2.
3.
4.
3x  20 y  67
2 x  5 y  47
2x  4 y  5
x  2 y  9
2x  y  2
4x  2 y  4
5. Coins: A sample of dimes and quarters totals $18. If there are 111 coins in all, how
many of each type of coin are there?
6. Airplane Speed: An airplane flies with the wind and travels 3000 miles in 5 hours. The
return trip into the wind requires 6 hours. Find the speed of the wind and of the airplane
in no wind.
7. Student Loans: A student takes out two loans to help pay for college. One loan is at 6%
interest, and the other is at 8% interest. The total amount borrowed is $4,000, and the
interest after 1 year for both loans is $264. Find the amount of each loan.
MAT 121 Final Exam Review Fall 2016
Chapter Five, Section 5.1
Identify the degree and leading coefficient of the polynomial.
1. 8 x 4  3x3  4 x  x5
Add the polynomials.
2.
 3x
3.
 5t
3
 4 x  3   5 x 2  4 x  12 
 3t    4t 4  3t 3  1
3
Subtract the polynomials.
4.
x
5.
5x
2
 3x  1   5 x 2  2 x  4 
4
 6 x3  x 2  5    x3  11x 2  9 x  3
Evaluate f  x  at the given x-value.
6.
f  x   2 x3  4 x  1
x 1
For the given f  x  and g  x  , find the following and simplify.
a.
b.
c.
d.
7.
 f  g  2
 f  g  1
 f  g  x 
 f  g  x 
f  x   3x2 , g  x   x 2  1
4
MAT 121 Final Exam Review Fall 2016
Chapter Five, Section 5.2
Multiply the monomials.
1.
 5 y z  4 x
2
2
yz 5 
Multiply the binomials.
2.
 2z 1 z  2
3.
x
2
 1 2 x 2  1
Multiply the polynomials.
4. 4 x  x 2  2 x  3
5.
 x  1  x 2  2 x  3
Simplify the expression.
6.
 3x y 
2
3 4
Multiply the expression.
7.
 x  4 x  4
8.
 x  7
9.
3x  x  1 x 1
2
5
MAT 121 Final Exam Review Fall 2016
Find fg  2 and  fg  x  .
10. f  x   x2  4x, g  x   x 2  5
Chapter Five, Section 5.3
Factor out the greatest common factor.
1. 6a 3b 2  15a 2b3
2. 15x 2  10 xy  25x 2 y 2
Use the zero-product property to solve the equation.
3. 3z  z  4  0
4.
 r 1 r  3  0
Solve the equation.
5. 5 x 2  x  0
6. 32 x 4  16 x3  0
Factor the polynomial.
7. x3  3x 2  2 x  6
8. 6 x3  4 x 2  9 x  6
6
MAT 121 Final Exam Review Fall 2016
Chapter Five, Section 5.4
Factor completely.
1. x 2  7 x  10
2. x 2  13 x  36
3. x 2  7 x  8
4. 6 x 2  7 x  5
5.
5 x3  x 2  6 x
Chapter Five, Section 5.5
Factor the expression, if possible.
1. x 2  36
2. 4 z 2  25
3. 49a 2  64b 2
4. 16x 4  y 4
Factor the expression.
5. x 2  2 x  1
6. 4 x 2  20 x  25
7. 9 z 2  24 z  16
8. 49a 2  28ab  4b 2
7
MAT 121 Final Exam Review Fall 2016
9.
4 x 4  4 x3 y  x 2 y 2
Factor the expression.
10. 27 x3  8
11. x3  8
Factor the expression completely.
12. 25 x 2  64
13. 3x 2  14 x  8
14. x 4  16 x3  64 x 2
Chapter Five, Section 5.6
Factor Completely.
1. 6 x3  13 x 2  15 x
2. 5 x 4  20 x3  10 x  40
3. x 4  2 x3  x  2
4. r 4  16
5. 3x5  27 x3  3 x 2  27
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MAT 121 Final Exam Review Fall 2016
9
Chapter Six, Section 6.1
Identify the domain of f . Write your answer in set-builder notation.
1.
x2  1
f  x  2
x  3x  2
Graph f  x  . Be sure to include any vertical asymptotes as dashed lines. State the domain of f
in set-builder notation.
2.
f  x 
1
x2
Evaluate f  x  at the given value of x.
3.
f  x 
3x
x 1
2
x2
Solve. Check your result.
4.
x
2x  5

x 5 x 5
5.
2x
x4

x2 x2
MAT 121 Final Exam Review Fall 2016
Use f  x  and g  x  to evaluate each of the following.
 f  g 3
 f  g  2
 fg 5
 f / g  0
a.
b.
c.
d.
6.
f  x   2x 1, g  x   4x2
Use f  x  and g  x  to find each of the following.
 f  g  x 
 f  g  x 
 fg  x 
 f / g  x 
a.
b.
c.
d.
7.
f  x   x2  4, g  x   6 x
Chapter Six, Section 6.2
Simplify the rational expression.
1.
x5
x  2 x  15
2.
x 2  3x  10
x2  6 x  5
2
Multiply or divide. Leave your answer in factored form when appropriate.
3.
x2 x3

x x4
4.
x 2  2 x  35 x3  x 2

2 x3  3x 2 2 x  14
10
MAT 121 Final Exam Review Fall 2016
5.
x2  x
x

2x  6 x  3
6.
x 2  3x  2 x 2  x  2

x2  5x  6 x2  2 x  3
Chapter Six, Section 6.3
Add or subtract. Leave your answer in factored form when appropriate.
1.
3
1
 2
x  2 x  1 x  3x  2
2.
3x
3y
 2
x  y x  2 xy  y 2
3.
1
2
x

 2
x 1 x 1 x 1
2
Find  f  g  x  and  f  g  x  .
4.
f  x 
1
x
, g  x 
x 1
x 1
Chapter Six, Section 6.4
Solve. Check your result.
1.
3
1
6

 2
5t t  1 5t  5t
2.
12
2
x


x 9 x 3 3 x
2
11
MAT 121 Final Exam Review Fall 2016
Chapter Six, Section 6.5
Simplify the complex fraction. Leave your answer in factored form when appropriate.
1.
1
x 3
1
3

x x3
2.
1
1

x x 1
2
1

x 1 x 1
3.
1
1
 2
x  2x 1 x  2x 1
 x  1 x  1
2
Chapter Six, Section 6.6
Let y be directly proportional to x.
a. Find the constant of proportionality k.
b. Use y  kx to find y when x  7.
1. y  6 when x  3
Let y be inversely proportional to x.
a. Find the constant of proportionality k.
k
b. Use y  to find y when x  10.
x
2. y  5 when x  4
Let z vary jointly with x and y.
a. Find the constant of proportionality k.
b. Use z  kxy to find z when x  5 and y  7.
3. z  6 when x  3 and y  8
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MAT 121 Final Exam Review Fall 2016
Chapter Six, Section 6.7
Divide.
1.
50 x 4  25 x 2  100 x
25 x
2.
10 x y
3
2
 5x2 y3   5x2 y 2 
Divide.
4 x3  8 x 2  x  2
3.
x2
4.
2 x3  x 2  5
x2
2 x 4  x3  5 x 2  4 x  12
2 x2  x  3
5.
Use synthetic division to divide.
6.
 2x
4
 3x 2  4    x  2 
Chapter Seven, Section 7.1
Evaluate the expression by hand, if possible. Variables represent any real number.
16
25
1.
2.
3
64
If possible, evaluate the functions at the given value(s) of the variable.
3.
f  x   x2  x
x  4, 3
13
MAT 121 Final Exam Review Fall 2016
4.
f  x   3 5x  2
x  5, 2
Find the domain of f . Write your answer in interval notation.
5.
f  x   2x  4
6.
f  x   3x 2  4
Chapter Seven, Section 7.2
Use radical notation to write each expression.
1. 71/2
2. x 5/6
Use rational exponents to write each expression.
3.
4.
3
 x  1
1
x 1
Write each expression in radical notation. Evaluate the expression by hand when possible.
1/2
4
5.  
9
6.
4 
1/2 3
Use a positive rational exponent to write the expression.
7.
49x
3
x2
14
MAT 121 Final Exam Review Fall 2016
15
Use positive rational exponents to simplify the expression. Assume that all variables are positive.
y3  3 y 2
8.
9.
 x6 
 
 27 
2/3
Chapter Seven, Section 7.3
Simplify the expression. Assume that all variables are positive.
2  50
1.
2.
4  3 16
3
a 2b
b
3.
3
4.
5.
3
54
2
3x  12 x
Use properties of polynomials to simplify the expression. Assume all radicands are positive.
6.
x4 x4
7.
x2  4x  4
x2
Simplify the radical expression by factoring out the largest perfect nth power.
8.
8n3
MAT 121 Final Exam Review Fall 2016
16
27x 2
9.
y3
Simplify the expression. Let all variables be positive and write your answer in radical notation.
3
10.
4
83 4
11.
4
27  3 9  3
Chapter Seven, Section 7.4
Write the terms as like radicals, if possible. Assume that all variables are positive.
1.
7,
28,
3
2.
3
16,
3.
3
8 xy ,
63
54
3
x4 y 4
If possible, simplify the expression. Assume that all variables are positive.
4. 7  4 7
5.
3
16  3 3 2
6. 8  4 3
7.
9 18  2 8
8.
2 3 16  3 2  2
9.
4x  8  x  2
10.
25x3  x3
MAT 121 Final Exam Review Fall 2016
8x2 3 x2

27
8
11.
3
12.
8 5 4 5

7
2
13.
15 8 2 2

4
5
Find  f  g  x  and  f  g  x  .
14. f  x   3 4 x  4, g  x   5 x  1
Multiply and simplify.
15.

16.
3  7 3  7 
17.

x 3

ab  3

x 2

ab  3

Rationalize the denominator.
18.
5
3 5
19.
2
52
20.
1
7 6
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MAT 121 Final Exam Review Fall 2016
18
Chapter Seven, Section 7.5
If possible, evaluate each root function f at the given x-values. When the result is not an integer,
approximate it to the nearest hundredth.
1.
f  x  3 1 x,
x  5, x  2
Use radical notation to write f  x  .
2.
f  x   x2/3
If possible, evaluate f  x  at the given values of x. When appropriate, approximate the answer to
the nearest hundredth.
3.
f  x   x4/3
x  8, x  27
For the given f  x  and g  x  , evaluate each expression.
a.
b.
c.
d.
4.
 f  g  2
 f  g  x 
 fg  x 
 f / g  x 
f  x   9 x  18, g  x   4 x  8
Chapter Seven, Section 7.6
Solve the equation symbolically. Check your results.
1.
2t  4  4
2.
x 1  3  4
3. 2 x  2  1  5
4.
3
2z  4  2
MAT 121 Final Exam Review Fall 2016
5.
6.
19
5z 1  z  1
x 1  x  4 1
Solve.
7.
 4  2x
8.
 x  1
3
2
 100
8
If the sides of a triangle are a, b, and, c and they satisfy a 2  b2  c 2 , the triangle is a right
triangle. Determine whether the triangle with the given sides is a right triangle.
9.
a  5 b  9 c  14
A right triangle has legs a and b with hypotenuse c. Find the length of the missing side.
10. a  3, c  8
Find the distance between the points.
11.
 1, 2 ,  4, 10
Chapter Seven, Section 7.7
Use i to write the expression.
1.
144
2.
18
Write the expression in standard form.
3.
5  3i    2  3i 
4.
 2  7i   1  2i 
MAT 121 Final Exam Review Fall 2016
5.
1  2i  6  i 
6.
3  5i 3  5i 
7.
2  i
2
Write the expression in standard form.
8.
3  2i
1  4i
9.
7  4i
3  2i
Chapter Eight, Section 8.1
Find the vertex of the parabola.
1.
f  x   2x2  6x  3
20
MAT 121 Final Exam Review Fall 2016
Do the following for the given f  x  .
a.
Identify the vertex and axis of symmetry on the graph of y  f  x  .
b. Graph y  f  x  .
c. Evaluate f  2 and f (3).
2.
f  x   2 x2  4 x 1
Find the minimum y -value on the graph of y  f  x  .
3.
f  x   2x2  2x  3
Find the maximum y -value on the graph of y  f  x  .
4.
f  x   2 x2  x  5
5. Height Reached by a Baseball: A baseball is hit into the air, and its height h in feet
after t seconds is given by h  t   16t 2  64t  2.
a. What is the height of the baseball when it is hit?
b. After how many seconds does the baseball reach its maximum height?
c. Determine the maximum height of the baseball.
21
MAT 121 Final Exam Review Fall 2016
Chapter Eight, Section 8.2
Do the following.
a. Sketch a graph of the equation.
b. Identify the vertex.
c. Compare the graph of y  f  x  to the graph of y  x 2 . (State any transformations
used.)
1.
f  x  
1
2
 x  3  1
2
Do the following.
a. Find the vertex on the graph of the equation.
b. Write the equation in vertex form.
2. y  4 x 2  8x  5
3. y  2 x 2  4 x  1
Write the equation in vertex form by completing the square. Identify the vertex.
4. y  x 2  2 x  3
5. y  3x 2  6 x  1
22
MAT 121 Final Exam Review Fall 2016
23
Chapter Eight, Section 8.3
Solve by factoring.
1. x 2  2 x  35  0
2. 6 x 2  x  1  0
Use the square root property to solve.
3. 5 x 2  64  0
4.
 2 x  1
2
5
Solve by completing the square.
5. x 2  2 x  24
6.
4 x2  8x  7  0
7. Falling Object: How long does it take for a toy to hit the ground if it is dropped out of a
window 60 feet above the ground? Does it take twice as long as it takes to fall from a
window 30 feet above the ground?
Chapter Eight, Section 8.4
Solve by using the quadratic formula. If there are no real solutions, say so.
1. x 2  6 x  16  0
2. 4 x 2  x  1  0
MAT 121 Final Exam Review Fall 2016
Do the following for the given equation.
a. Evaluate the discriminant.
b. How many real solutions are there?
3. x 2  4 x  4  0
Solve the equation. Write complex solutions in standard form.
4. x 2  80  0
5. x 2  x  2  0
6.
2 x 2  3x  4  0
Solve by completing the square.
7.
x2  2 x  4  0
8.
2 x2  4 x  6  0
24