Question 1

Find the product.
-$$n ^ { 2 } \left( 2 n - \frac { 1 } { 4 } \right) \left( 10 n + \frac { 1 } { 2 } \right)$$

Accepted Answer

A)  $20 n ^ { 4 } + \frac { 3 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
B)  $20 n ^ { 4 } - \frac { 3 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
C)  $20 n ^ { 4 } - \frac { 3 } { 2 } n ^ { 3 } + \frac { 1 } { 8 } n ^ { 2 }$ 
D)  $20 n ^ { 4 } - \frac { 7 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
A)  $20 n ^ { 4 } + \frac { 3 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
B)  $20 n ^ { 4 } - \frac { 3 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
C)  $20 n ^ { 4 } - \frac { 3 } { 2 } n ^ { 3 } + \frac { 1 } { 8 } n ^ { 2 }$ 
D)  $20 n ^ { 4 } - \frac { 7 } { 2 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$

Question 2

Determine the degree of the polynomial.
-$2 t ^ { 6 } + 3 t ^ { 3 } + 5 - 3 t ^ { 2 }$

Accepted Answer

A)  12 
B)  11 
C)  6
D) 4 
A)  12 
B)  11 
C)  6
D) 4

Question 3

Solve the problem.
-The radius of a right circular cone is given by the formula $\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } }$, where $\mathrm { V }$ is the volume and $\mathrm { h }$ is the height. If the volume is 1997 cubic inches and the height is 17 inches, what is the radius? Use $3.14$ for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  $6.1$ in. 
B)  $0.1 \mathrm { in }$. 
C)  $11.1 \mathrm { in } .$ 
D)  $10.6 \mathrm { in }$. 
A)  $6.1$ in. 
B)  $0.1 \mathrm { in }$. 
C)  $11.1 \mathrm { in } .$ 
D)  $10.6 \mathrm { in }$.

Question 4

Solve the problem.
-It is recommended that a woman who is pregnant should exercise such that her heart rate does not exceed 140 beats per minute. Use absolute value notation to write an expression that describes the
Difference between the heart rate achieved by each of the following pregnant women and the
Recommended maximum heart rate. Then evaluate that expression. (i) Abigail: 122 beats per minute
(ii) Mathilda: 144 beats per minute

Accepted Answer

A)  (i) Abigail: $| 140 - 122 | = - 18$
(ii) Mathilda: $| 140 - 144 | = - 4$ 
B)  (i) Abigail: $| 122 - 140 | = 18$
(ii) Mathilda: $| 144 - 140 | = 4$ 
C)  (i) Abigail: $122 - 140 = - 18$
(i) Mathilda: $144 - 140 = 4$ 
D)  (i) Abigail: $| 122 + 140 | = 262$
(ii) Mathilda: $| 144 + 140 | = 284$ 
A)  (i) Abigail: $| 140 - 122 | = - 18$
(ii) Mathilda: $| 140 - 144 | = - 4$ 
B)  (i) Abigail: $| 122 - 140 | = 18$
(ii) Mathilda: $| 144 - 140 | = 4$ 
C)  (i) Abigail: $122 - 140 = - 18$
(i) Mathilda: $144 - 140 = 4$ 
D)  (i) Abigail: $| 122 + 140 | = 262$
(ii) Mathilda: $| 144 + 140 | = 284$

Question 5

Find the product.
-$( n - 1 ) ( n - 1 ) ( n + 1 ) ( n + 1 )$

Accepted Answer

A)  $n ^ { 4 } - 2 n ^ { 2 } + 1$ 
B)  $n ^ { 4 } + 2 n - 1$ 
C)  $n ^ { 4 } - 2 n + 1$ 
D)  $n ^ { 4 } + 2 n ^ { 2 } - 1$ 
A)  $n ^ { 4 } - 2 n ^ { 2 } + 1$ 
B)  $n ^ { 4 } + 2 n - 1$ 
C)  $n ^ { 4 } - 2 n + 1$ 
D)  $n ^ { 4 } + 2 n ^ { 2 } - 1$

Question 6

Divide.
-$$\frac { 9 m ^ { 2 } + 67 m - 40 } { m + 8 }$$

Accepted Answer

A)  $9 m - 5$ 
B)  $m - 5$ 
C)  $9 m + 5$ 
D)  $9 m - 5 + \frac { 7 } { m - 5 }$ 
A)  $9 m - 5$ 
B)  $m - 5$ 
C)  $9 m + 5$ 
D)  $9 m - 5 + \frac { 7 } { m - 5 }$

Question 7

Find the product or quotient.
-$$\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }$$

Accepted Answer

A)  $z + 4$ 
B)  $\frac { z } { z ^ { 2 } + 13 z + 42 }$ 
C)  $\frac { \mathrm { z } + 4 } { \mathrm { z } }$ 
D)  $\frac { z + 4 } { z ^ { 2 } + 7 z }$ 
A)  $z + 4$ 
B)  $\frac { z } { z ^ { 2 } + 13 z + 42 }$ 
C)  $\frac { \mathrm { z } + 4 } { \mathrm { z } }$ 
D)  $\frac { z + 4 } { z ^ { 2 } + 7 z }$

Question 8

Find the product.
-$$( x + 4 y ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 64 y ^ { 3 }$ 
C)  $3 ( x + 4 y )$ 
D)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$ 
A)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 64 y ^ { 3 }$ 
C)  $3 ( x + 4 y )$ 
D)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$

Question 9

Evaluate the expression.
-$$\left| - \frac { 1 } { 7 } \right|$$

Accepted Answer

A)  $\pm \frac { 1 } { 7 }$ 
B)  0 
C)  $- \frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  $\pm \frac { 1 } { 7 }$ 
B)  0 
C)  $- \frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 7 }$

Question 10

Find the product.
-$$( 10 r - 11 ) ( 10 r + 11 )$$

Accepted Answer

A)  $100 r ^ { 2 } - 220 r - 121$ 
B)  $100 + 220 r - 121 r ^ { 2 }$ 
C)  $10 r ^ { 2 } - 121$ 
D)  $100 r ^ { 2 } - 121$ 
A)  $100 r ^ { 2 } - 220 r - 121$ 
B)  $100 + 220 r - 121 r ^ { 2 }$ 
C)  $10 r ^ { 2 } - 121$ 
D)  $100 r ^ { 2 } - 121$

Question 11

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$3 x ^{- 3}$

Accepted Answer

A)  $- 9 x$ 
B)  $- \frac { 1 } { 9 x }$ 
C)  $\frac { 1 } { 27 x ^ { 3 } }$ 
D)  $\frac { 3 } { x ^ { 3 } }$ 
A)  $- 9 x$ 
B)  $- \frac { 1 } { 9 x }$ 
C)  $\frac { 1 } { 27 x ^ { 3 } }$ 
D)  $\frac { 3 } { x ^ { 3 } }$

Question 12

Factor by any method.
-$$( q - 5 ) ^ { 2 } - 16$$

Accepted Answer

A)  $\left[ ( q - 5 ) ^ { 2 } + 4 \right] \left[ ( q - 5 ) ^ { 2 } - 4 \right]$ 
B)  $( q - 1 ) ^ { 2 }$ 
C)  $( q - 1 ) ( q - 9 )$ 
D)  $( q + 9 ) ( q - 9 )$ 
A)  $\left[ ( q - 5 ) ^ { 2 } + 4 \right] \left[ ( q - 5 ) ^ { 2 } - 4 \right]$ 
B)  $( q - 1 ) ^ { 2 }$ 
C)  $( q - 1 ) ( q - 9 )$ 
D)  $( q + 9 ) ( q - 9 )$

Question 13

Factor out the greatest common factor. Simplify the factors, if possible.
-$$5 x ^ { 3 } + 20 x$$

Accepted Answer

A)  $5 x ^ { 2 } ( x + 4 )$ 
B)  $5 x \left( x ^ { 2 } + 4 \right)$ 
C)  $5 x \left( x ^ { 2 } + 4 x \right)$ 
D)  $5 x \left( x ^ { 2 } + 15 x \right)$ 
A)  $5 x ^ { 2 } ( x + 4 )$ 
B)  $5 x \left( x ^ { 2 } + 4 \right)$ 
C)  $5 x \left( x ^ { 2 } + 4 x \right)$ 
D)  $5 x \left( x ^ { 2 } + 15 x \right)$

Question 14

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

Accepted Answer

A)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 15$ 
B)  $d ( R , S ) = - 1$ 
C)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 15$ 
D)  $d ( R , S ) = 1$ 
A)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 15$ 
B)  $d ( R , S ) = - 1$ 
C)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 15$ 
D)  $d ( R , S ) = 1$

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$( 10 \sqrt { 5 } + 3 \sqrt { 2 } ) ( 3 \sqrt { 5 } + 9 \sqrt { 2 } )$

Accepted Answer

A)  $30 \sqrt { 5 } + 27 \sqrt { 2 } + 99 \sqrt { 10 }$ 
B)  $30 \sqrt { 5 } + 27 \sqrt { 2 }$ 
C)  $204 + 99 \sqrt { 10 }$ 
D)  $96 + 99 \sqrt { 10 }$ 
A)  $30 \sqrt { 5 } + 27 \sqrt { 2 } + 99 \sqrt { 10 }$ 
B)  $30 \sqrt { 5 } + 27 \sqrt { 2 }$ 
C)  $204 + 99 \sqrt { 10 }$ 
D)  $96 + 99 \sqrt { 10 }$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }$$

Accepted Answer

A)  $- \frac { 7 x \sqrt { 2 x y } } { y ^ { 3 } }$ 
B)  $- \frac { 7 x } { y ^ { 2 } } \sqrt { \frac { 2 x } { y } }$ 
C)  $- \frac { 7 x ^ { 3 } \sqrt { 2 } } { y ^ { 5 } }$ 
D)  $- \frac { x \sqrt { 98 x y } } { y ^ { 3 } }$ 
A)  $- \frac { 7 x \sqrt { 2 x y } } { y ^ { 3 } }$ 
B)  $- \frac { 7 x } { y ^ { 2 } } \sqrt { \frac { 2 x } { y } }$ 
C)  $- \frac { 7 x ^ { 3 } \sqrt { 2 } } { y ^ { 5 } }$ 
D)  $- \frac { x \sqrt { 98 x y } } { y ^ { 3 } }$

Question 17

Simplify the expression.
-$\sqrt { ( z - 7 ) ^ { 2 } }$

Accepted Answer

A)  $| z - 7 |$ 
B)  $z - 7$ 
C)  $| z | - 7$ 
D)  $7 - z$ 
A)  $| z - 7 |$ 
B)  $z - 7$ 
C)  $| z | - 7$ 
D)  $7 - z$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { - \frac { 64 } { 27 } }$

Accepted Answer

A)  $\frac { 16 } { 9 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $- \frac { 64 } { 27 }$ 
A)  $\frac { 16 } { 9 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $- \frac { 64 } { 27 }$

Question 19

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-$\varnothing$________$\varnothing$

Accepted Answer

A) $\in$ 
B)   $\notin$ 
A) $\in$ 
B)   $\notin$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { 225 } + \sqrt { 81 }$$

Accepted Answer

A)  12 
B)  24 
C)  $3 \sqrt { 34 }$ 
D)  $2 \sqrt { 6 }$ 
A)  12 
B)  24 
C)  $3 \sqrt { 34 }$ 
D)  $2 \sqrt { 6 }$

Find the product. - $n ^ { 2 } \left( 2 n - \frac { 1 } { 4 } \right) \left( 10 n + \frac { 1 } { 2 } \right)$

Determine the degree of the polynomial. - $2 t ^ { 6 } + 3 t ^ { 3 } + 5 - 3 t ^ { 2 }$

Find the product. - $( n - 1 ) ( n - 1 ) ( n + 1 ) ( n + 1 )$

Divide. - $\frac { 9 m ^ { 2 } + 67 m - 40 } { m + 8 }$

Find the product or quotient. - $\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }$

Find the product. - $( x + 4 y ) ^ { 3 }$

Evaluate the expression. - $\left| - \frac { 1 } { 7 } \right|$

Find the product. - $( 10 r - 11 ) ( 10 r + 11 )$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $3 x ^{- 3}$

Factor by any method. - $( q - 5 ) ^ { 2 } - 16$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 x ^ { 3 } + 20 x$

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

Simplify the expression. Assume all variables represent positive real numbers. - $( 10 \sqrt { 5 } + 3 \sqrt { 2 } ) ( 3 \sqrt { 5 } + 9 \sqrt { 2 } )$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }$

Simplify the expression. - $\sqrt { ( z - 7 ) ^ { 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - \frac { 64 } { 27 } }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. - $\varnothing$ ________ $\varnothing$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 225 } + \sqrt { 81 }$

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 12: Review of Basic Concepts

Find the product. - n2(2n−14)(10n+12)n ^ { 2 } \left( 2 n - \frac { 1 } { 4 } \right) \left( 10 n + \frac { 1 } { 2 } \right)n2(2n−41​)(10n+21​)

Determine the degree of the polynomial. - 2t6+3t3+5−3t22 t ^ { 6 } + 3 t ^ { 3 } + 5 - 3 t ^ { 2 }2t6+3t3+5−3t2

Find the product. - (n−1)(n−1)(n+1)(n+1)( n - 1 ) ( n - 1 ) ( n + 1 ) ( n + 1 )(n−1)(n−1)(n+1)(n+1)

Divide. - 9m2+67m−40m+8\frac { 9 m ^ { 2 } + 67 m - 40 } { m + 8 }m+89m2+67m−40​

Find the product or quotient. - z2+8z+12z2+13z+42÷z2+2zz2+11z+28\frac { z ^ { 2 } + 8 z + 12 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 11 z + 28 }z2+13z+42z2+8z+12​÷z2+11z+28z2+2z​

Find the product. - (x+4y)3( x + 4 y ) ^ { 3 }(x+4y)3

Evaluate the expression. - ∣−17∣\left| - \frac { 1 } { 7 } \right|​−71​​

Find the product. - (10r−11)(10r+11)( 10 r - 11 ) ( 10 r + 11 )(10r−11)(10r+11)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 3x−33 x ^{- 3}3x−3

Factor by any method. - (q−5)2−16( q - 5 ) ^ { 2 } - 16(q−5)2−16

Factor out the greatest common factor. Simplify the factors, if possible. - 5x3+20x5 x ^ { 3 } + 20 x5x3+20x

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

Simplify the expression. Assume all variables represent positive real numbers. - (105+32)(35+92)( 10 \sqrt { 5 } + 3 \sqrt { 2 } ) ( 3 \sqrt { 5 } + 9 \sqrt { 2 } )(105​+32​)(35​+92​)

Simplify the expression. Assume all variables represent positive real numbers. - −98x3y5- \sqrt { \frac { 98 x ^ { 3 } } { y 5 } }−y598x3​​

Simplify the expression. - (z−7)2\sqrt { ( z - 7 ) ^ { 2 } }(z−7)2​

Simplify the expression. Assume all variables represent positive real numbers. - −64273\sqrt [ 3 ] { - \frac { 64 } { 27 } }3−2764​​

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. - ∅\varnothing∅ ________ ∅\varnothing∅

Simplify the expression. Assume all variables represent positive real numbers. - 225+81\sqrt { 225 } + \sqrt { 81 }225​+81​