Question 1

Factor the trinomial, if possible.
-$$u ^ { 2 } - 3 u v - 70 v ^ { 2 }$$

Accepted Answer

A)  prime 
B)  $( u + 7 v ) ( u - 10 v )$ 
C)  $( u - 7 v ) ( u + v )$ 
D)  $( u - 7 v ) ( u + 10 v )$ 
A)  prime 
B)  $( u + 7 v ) ( u - 10 v )$ 
C)  $( u - 7 v ) ( u + v )$ 
D)  $( u - 7 v ) ( u + 10 v )$

Question 2

Find the sum or difference.
-$$\left( 6 x ^ { 4 } - 8 x ^ { 2 } + x \right) - \left( 9 x ^ { 3 } + 6 x ^ { 2 } + 3 x \right) + \left( 3 x ^ { 2 } - x \right)$$

Accepted Answer

A)  $2 x ^ { 5 } + 7 x ^ { 4 } - 3 x$ 
B)  $6 x ^ { 4 } - 9 x ^ { 3 } - 11 x ^ { 2 } - 3 x$ 
C)  $6 x ^ { 4 } + 9 x ^ { 3 } - 17 x ^ { 2 } - 3 x$ 
D)  $6 x ^ { 4 } - 9 x ^ { 3 } - 9 x ^ { 2 } + 3 x$ 
A)  $2 x ^ { 5 } + 7 x ^ { 4 } - 3 x$ 
B)  $6 x ^ { 4 } - 9 x ^ { 3 } - 11 x ^ { 2 } - 3 x$ 
C)  $6 x ^ { 4 } + 9 x ^ { 3 } - 17 x ^ { 2 } - 3 x$ 
D)  $6 x ^ { 4 } - 9 x ^ { 3 } - 9 x ^ { 2 } + 3 x$

Question 3

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$7 c ^ { 5 } + 7 c ^ { 4 } + 2 c ^ { 3 }$

Accepted Answer

A)  Binomial 
B)  Monomial 
C)  Trinomial 
D)  None of these 
A)  Binomial 
B)  Monomial 
C)  Trinomial 
D)  None of these

Question 4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { y } { 5 } } { \frac { 9 } { y + 4 } }$$

Accepted Answer

A)  $\frac { 9 y } { 5 ( y + 4 ) }$ 
B)  $45 y ( y + 4 )$ 
C)  $\frac { y + 4 } { 45 y }$ 
D)  $\frac { y ( y + 4 ) } { 45 }$ 
A)  $\frac { 9 y } { 5 ( y + 4 ) }$ 
B)  $45 y ( y + 4 )$ 
C)  $\frac { y + 4 } { 45 y }$ 
D)  $\frac { y ( y + 4 ) } { 45 }$

Question 5

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( - 3 x ^ { 6 } y \right) \left( - 3 x ^ { 2 } y ^ { 5 } \right)$$

Accepted Answer

A)  $9 x ^ { 8 } y ^ { 6 }$ 
B)  $9 x ^ { 12 } y ^ { 5 }$ 
C)  $- 9 x ^ { 8 } y ^ { 5 }$ 
D)  $- 6 x ^ { 8 } y ^ { 5 }$ 
A)  $9 x ^ { 8 } y ^ { 6 }$ 
B)  $9 x ^ { 12 } y ^ { 5 }$ 
C)  $- 9 x ^ { 8 } y ^ { 5 }$ 
D)  $- 6 x ^ { 8 } y ^ { 5 }$

Question 6

Evaluate the expression for x = -2, y = 3, and a = -4.
-$4 x ^ { 2 } - 3 y - a$

Accepted Answer

A)  9 
B)  8 
C)  11 
D)  5 
A)  9 
B)  8 
C)  11 
D)  5

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 54 a ^ { 2 } b } { c ^ { 2 } } }$$

Accepted Answer

A)  $\frac { 3 a \sqrt { 6 b } } { c }$ 
B)  $\frac { a \sqrt { 54 b } } { c }$ 
C)  $\frac { 3 \sqrt { 6 a ^ { 2 } b } } { c }$ 
D)  $\frac { 9 a \sqrt { 6 b } } { c }$ 
A)  $\frac { 3 a \sqrt { 6 b } } { c }$ 
B)  $\frac { a \sqrt { 54 b } } { c }$ 
C)  $\frac { 3 \sqrt { 6 a ^ { 2 } b } } { c }$ 
D)  $\frac { 9 a \sqrt { 6 b } } { c }$

Question 8

Solve the equation
-$$\frac { x ^ { 2 } + 13 x + 32 } { x + 5 }$$

Accepted Answer

A)  $x + 8 - \frac { 8 } { x + 5 }$ 
B)  $x + 8 + \frac { 8 } { x + 5 }$ 
C)  $x + 9$ 
D)  $\frac { x + 8 } { x + 5 }$ 
A)  $x + 8 - \frac { 8 } { x + 5 }$ 
B)  $x + 8 + \frac { 8 } { x + 5 }$ 
C)  $x + 9$ 
D)  $\frac { x + 8 } { x + 5 }$

Question 9

Evaluate the expression.
-$- | 9 |$

Accepted Answer

A)  9 
B)  -9 
C)  0 
D)  $\pm 9$ 
A)  9 
B)  -9 
C)  0 
D)  $\pm 9$

Question 10

Factor by any method.
-$12 ( m - 5 ) ^ { 2 } - 7 ( m - 5 ) - 12$

Accepted Answer

A)  $( 3 m + 9 ) ( 4 m + 8 )$ 
B)  $( 3 m + 4 ) ( 4 m + 3 )$ 
C)  $( 3 m - 19 ) ( 4 m - 17 )$ 
D)  $( 3 m + 18 ) ( 4 m + 24 )$ 
A)  $( 3 m + 9 ) ( 4 m + 8 )$ 
B)  $( 3 m + 4 ) ( 4 m + 3 )$ 
C)  $( 3 m - 19 ) ( 4 m - 17 )$ 
D)  $( 3 m + 18 ) ( 4 m + 24 )$

Question 11

Solve the problem.
-$$( 6 p + 5 ) ( 6 p - 5 )$$

Accepted Answer

A)  $p ^ { 2 } - 25$ 
B)  $36 p ^ { 2 } + 60 p - 25$ 
C)  $36 p ^ { 2 } - 25$ 
D)  $36 p ^ { 2 } - 60 p - 25$ 
A)  $p ^ { 2 } - 25$ 
B)  $36 p ^ { 2 } + 60 p - 25$ 
C)  $36 p ^ { 2 } - 25$ 
D)  $36 p ^ { 2 } - 60 p - 25$

Question 12

Factor by any method.
-$$10 a ^ { 3 } - 4 a ^ { 2 } b + 25 a b ^ { 2 } - 10 b ^ { 3 }$$

Accepted Answer

A)  $\left( 10 a ^ { 2 } + 5 b ^ { 2 } \right) ( a - 2 b )$ 
B)  $\left( 2 a ^ { 2 } + 5 b \right) ( 5 a - 2 b )$ 
C)  $\left( 2 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a - 2 b )$ 
D)  $\left( 2 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a + 2 b )$ 
A)  $\left( 10 a ^ { 2 } + 5 b ^ { 2 } \right) ( a - 2 b )$ 
B)  $\left( 2 a ^ { 2 } + 5 b \right) ( 5 a - 2 b )$ 
C)  $\left( 2 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a - 2 b )$ 
D)  $\left( 2 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a + 2 b )$

Question 13

Evaluate the expression.
-$$\left( - \frac { 27 } { 64 } \right) ^ { - 2 / 3 }$$

Accepted Answer

A)  $- \frac { 9 } { 16 }$ 
B)  $\frac { 9 } { 16 }$ 
C)  $\frac { 16 } { 9 }$ 
D)  not a real number 
A)  $- \frac { 9 } { 16 }$ 
B)  $\frac { 9 } { 16 }$ 
C)  $\frac { 16 } { 9 }$ 
D)  not a real number

Question 14

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { 1 } { \sqrt { 5 } } + \frac { 5 } { \sqrt { 20 } } - \frac { 3 } { \sqrt { 45 } }$$

Accepted Answer

A)  $\frac { 1 } { 2 } \sqrt { 5 }$ 
B)  $\frac { 1 } { 2 } \sqrt { 35 }$ 
C)  $- \frac { 17 } { 30 } \sqrt { 5 }$ 
D)  $\frac { 17 } { 30 } \frac { 1 } { \sqrt { 5 } }$ 
A)  $\frac { 1 } { 2 } \sqrt { 5 }$ 
B)  $\frac { 1 } { 2 } \sqrt { 35 }$ 
C)  $- \frac { 17 } { 30 } \sqrt { 5 }$ 
D)  $\frac { 17 } { 30 } \frac { 1 } { \sqrt { 5 } }$

Question 15

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$$\left( 5 m ^ { 3 } z ^ { 4 } \right) \left( 4 m ^ { 2 } z ^ { 2 } \right)$$

Accepted Answer

A)  $20 m z ^ { 5 }$ 
B)  $20 m ^ { 5 } \mathrm { z }$ 
C)  $20 m ^ { 5 } z ^ { 6 }$ 
D)  $20 m z ^ { 6 }$ 
A)  $20 m z ^ { 5 }$ 
B)  $20 m ^ { 5 } \mathrm { z }$ 
C)  $20 m ^ { 5 } z ^ { 6 }$ 
D)  $20 m z ^ { 6 }$

Question 16

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$- ( - 5 ) ^ { - 1 }$$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B)  $- 5$ 
C)  $- \frac { 1 } { 5 }$ 
D)  5 
A)  $\frac { 1 } { 5 }$ 
B)  $- 5$ 
C)  $- \frac { 1 } { 5 }$ 
D)  5

Question 17

Use set notation, and list all the elements of the set.
-The first two natural numbers.

Accepted Answer

A)  {1, 2} 
B)  {0, 1, 2} 
C)  {0, 2} 
D)  {0, 1} 
A)  {1, 2} 
B)  {0, 1, 2} 
C)  {0, 2} 
D)  {0, 1}

Question 18

Find the distance between two points given their coordinates.
-Find the distance between points R and S on a number line, with coordinates 8 and -7, respectively.

Accepted Answer

A)  d(R, S) = -1 
B)  d(R, S) = 15 
C)  d(R, S) = -15 
D)  d(R, S) = 1 
A)  d(R, S) = -1 
B)  d(R, S) = 15 
C)  d(R, S) = -15 
D)  d(R, S) = 1

Question 19

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- 7 x ^ { 0 }$

Accepted Answer

A)  0 
B)  1 
C)  -7 
D)  -1 
A)  0 
B)  1 
C)  -7 
D)  -1

Question 20

Factor by grouping.
-$$x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$$

Accepted Answer

A)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$ 
B)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$ 
C)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
D)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$ 
A)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$ 
B)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$ 
C)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
D)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$

Factor the trinomial, if possible. - $u ^ { 2 } - 3 u v - 70 v ^ { 2 }$

Find the sum or difference. - $\left( 6 x ^ { 4 } - 8 x ^ { 2 } + x \right) - \left( 9 x ^ { 3 } + 6 x ^ { 2 } + 3 x \right) + \left( 3 x ^ { 2 } - x \right)$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $7 c ^ { 5 } + 7 c ^ { 4 } + 2 c ^ { 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { y } { 5 } } { \frac { 9 } { y + 4 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 3 x ^ { 6 } y \right) \left( - 3 x ^ { 2 } y ^ { 5 } \right)$

Evaluate the expression for x = -2, y = 3, and a = -4. - $4 x ^ { 2 } - 3 y - a$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 54 a ^ { 2 } b } { c ^ { 2 } } }$

Solve the equation - $\frac { x ^ { 2 } + 13 x + 32 } { x + 5 }$

Evaluate the expression. - $- | 9 |$

Factor by any method. - $12 ( m - 5 ) ^ { 2 } - 7 ( m - 5 ) - 12$

Solve the problem. - $( 6 p + 5 ) ( 6 p - 5 )$

Factor by any method. - $10 a ^ { 3 } - 4 a ^ { 2 } b + 25 a b ^ { 2 } - 10 b ^ { 3 }$

Evaluate the expression. - $\left( - \frac { 27 } { 64 } \right) ^ { - 2 / 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 1 } { \sqrt { 5 } } + \frac { 5 } { \sqrt { 20 } } - \frac { 3 } { \sqrt { 45 } }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $\left( 5 m ^ { 3 } z ^ { 4 } \right) \left( 4 m ^ { 2 } z ^ { 2 } \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- ( - 5 ) ^ { - 1 }$

Use set notation, and list all the elements of the set. -The first two natural numbers.

Find the distance between two points given their coordinates. -Find the distance between points R and S on a number line, with coordinates 8 and -7, respectively.

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 7 x ^ { 0 }$

Factor by grouping. - $x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Factor the trinomial, if possible. - u2−3uv−70v2u ^ { 2 } - 3 u v - 70 v ^ { 2 }u2−3uv−70v2

Find the sum or difference. - (6x4−8x2+x)−(9x3+6x2+3x)+(3x2−x)\left( 6 x ^ { 4 } - 8 x ^ { 2 } + x \right) - \left( 9 x ^ { 3 } + 6 x ^ { 2 } + 3 x \right) + \left( 3 x ^ { 2 } - x \right)(6x4−8x2+x)−(9x3+6x2+3x)+(3x2−x)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 7c5+7c4+2c37 c ^ { 5 } + 7 c ^ { 4 } + 2 c ^ { 3 }7c5+7c4+2c3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - y59y+4\frac { \frac { y } { 5 } } { \frac { 9 } { y + 4 } }y+49​5y​​

Simplify the expression. Assume all variables represent nonzero real numbers. - (−3x6y)(−3x2y5)\left( - 3 x ^ { 6 } y \right) \left( - 3 x ^ { 2 } y ^ { 5 } \right)(−3x6y)(−3x2y5)

Evaluate the expression for x = -2, y = 3, and a = -4. - 4x2−3y−a4 x ^ { 2 } - 3 y - a4x2−3y−a

Simplify the expression. Assume all variables represent positive real numbers. - 54a2bc2\sqrt { \frac { 54 a ^ { 2 } b } { c ^ { 2 } } }c254a2b​​

Solve the equation - x2+13x+32x+5\frac { x ^ { 2 } + 13 x + 32 } { x + 5 }x+5x2+13x+32​

Evaluate the expression. - −∣9∣- | 9 |−∣9∣

Factor by any method. - 12(m−5)2−7(m−5)−1212 ( m - 5 ) ^ { 2 } - 7 ( m - 5 ) - 1212(m−5)2−7(m−5)−12

Solve the problem. - (6p+5)(6p−5)( 6 p + 5 ) ( 6 p - 5 )(6p+5)(6p−5)

Factor by any method. - 10a3−4a2b+25ab2−10b310 a ^ { 3 } - 4 a ^ { 2 } b + 25 a b ^ { 2 } - 10 b ^ { 3 }10a3−4a2b+25ab2−10b3

Evaluate the expression. - (−2764)−2/3\left( - \frac { 27 } { 64 } \right) ^ { - 2 / 3 }(−6427​)−2/3

Simplify the expression. Assume all variables represent positive real numbers. - 15+520−345\frac { 1 } { \sqrt { 5 } } + \frac { 5 } { \sqrt { 20 } } - \frac { 3 } { \sqrt { 45 } }5​1​+20​5​−45​3​

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - (5m3z4)(4m2z2)\left( 5 m ^ { 3 } z ^ { 4 } \right) \left( 4 m ^ { 2 } z ^ { 2 } \right)(5m3z4)(4m2z2)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −(−5)−1- ( - 5 ) ^ { - 1 }−(−5)−1