Question 1

Find the distance (in miles) traveled by a car which moves at speed $s$ (in mi/h) for two hours, then moves $10$ mi $/$ h slower for another two hours.

Accepted Answer

A)  $\frac { 14 } { 3 } s - \frac { 15 } { 2 }$ 
B)  $4 s - 20$ 
C)  $13 s - 15$ 
D)  $\frac { 17 } { 2 } s - \frac { 227 } { 2 }$ 
E)  $12 s - 1$ 
A)  $\frac { 14 } { 3 } s - \frac { 15 } { 2 }$ 
B)  $4 s - 20$ 
C)  $13 s - 15$ 
D)  $\frac { 17 } { 2 } s - \frac { 227 } { 2 }$ 
E)  $12 s - 1$

Question 2

Write an equation that expresses the statement that $V$ is proportional to the square root $x$ and inversely proportional to the square of $y$ .

Accepted Answer

@#LAT-DLM& , where @#LAT-DLM&

Question 3

Solve the equation. $( y - 3 ) ^ { 2 } = ( y + 3 ) ^ { 2 } - 6 y - 9$

Accepted Answer

A)  $3$ 
B)  $2$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 2 } { 3 }$ 
E)  $\frac { 3 } { 2 }$ 
A)  $3$ 
B)  $2$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 2 } { 3 }$ 
E)  $\frac { 3 } { 2 }$

Question 4

Perform the indicated operations and simplify. $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$

Accepted Answer

A)  $a ^ { 2 } x ^ { 2 } - y ^ { 2 }$ 
B)  $a ^ { 2 } x ^ { 4 } + a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$ 
C)  $a ^ { 2 } x ^ { 4 } - y ^ { 4 }$ 
D)  $a ^ { 2 } x ^ { 4 } - a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$ 
E)  $a ^ { 2 } x ^ { 4 } + y ^ { 4 }$ 
A)  $a ^ { 2 } x ^ { 2 } - y ^ { 2 }$ 
B)  $a ^ { 2 } x ^ { 4 } + a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$ 
C)  $a ^ { 2 } x ^ { 4 } - y ^ { 4 }$ 
D)  $a ^ { 2 } x ^ { 4 } - a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$ 
E)  $a ^ { 2 } x ^ { 4 } + y ^ { 4 }$

Question 5

Solve the equation $\frac { 1 } { s + a } + \frac { 2 } { s - a } = \frac { 5 } { s + c }$ for $c$ .

Accepted Answer

The answer of Solve the equation \(\frac { 1 }...

Question 6

Rationalize the denominator of the expression. $\frac { 1 } { 2 + \sqrt { 5 } }$

Accepted Answer

The answer of Rationalize the denominator of the expression. \(\frac...

Question 7

Let $S = \left\{ - 2 , - \sqrt { 3 } , 1 , \frac { 2 } { 3 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $10 \leq \frac { 5 } { 2 x }$ .

Accepted Answer

A) 
 $\varnothing$ 
B) 
 $\{ - 2 \}$ 
C) 
 $\{ - 2 , - \sqrt { 3 } \}$ 
D) 
 $\left\{ 1 , \frac { 5 } { 3 } , 2 \right\}$ 
E) 
 $S$ 
A) 
 $\varnothing$ 
B) 
 $\{ - 2 \}$ 
C) 
 $\{ - 2 , - \sqrt { 3 } \}$ 
D) 
 $\left\{ 1 , \frac { 5 } { 3 } , 2 \right\}$ 
E) 
 $S$

Question 8

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = 4 x ^ { 2 } - 12 x + 6$ .

Accepted Answer

A)  $[ 2,10 ]$ by
$[ - 10,10 ]$ 
B)  $[ - 1,4 ]$ by
$[ - 3,20 ]$ 
C)  $[ 5,10 ]$ by
$[ - 10,50 ]$ 
D)  $[ - 10,3 ]$ by
$[ 0,50 ]$ 
E)  $[ - 10,10 ]$ by
$[ - 20,20 ]$ 
A)  $[ 2,10 ]$ by
$[ - 10,10 ]$ 
B)  $[ - 1,4 ]$ by
$[ - 3,20 ]$ 
C)  $[ 5,10 ]$ by
$[ - 10,50 ]$ 
D)  $[ - 10,3 ]$ by
$[ 0,50 ]$ 
E)  $[ - 10,10 ]$ by
$[ - 20,20 ]$

Question 9

State the property of real numbers being used. $$x + 4 = 4 + x$$

Accepted Answer

A)  Commutative Property for addition 
B)  Commutative Property for multiplication 
C)  Associative Property for addition 
D)  Associative Property for multiplication 
E)  Distributive Property 
A)  Commutative Property for addition 
B)  Commutative Property for multiplication 
C)  Associative Property for addition 
D)  Associative Property for multiplication 
E)  Distributive Property

Question 10

Draw the square with vertices $A ( 1,2 )$ , $B ( 4,2 )$ , $C ( 4,5 )$ , and $D ( 1,5 )$ on a coordinate plane. Find the area of the square.

Accepted Answer

The answer of Draw the square with vertices \(A (...

Question 11

Rationalize the denominator of the expression. $\frac { 5 - x } { \sqrt { 5 } + \sqrt { x } }$

Accepted Answer

The answer of Rationalize the denominator of the expression. \(\frac...

Question 12

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

Accepted Answer

A)  $z \leq - 1$ 
B)  $z \geq - 1$ 
C)  $z  - 1$ 
E)  $z = 0$ 
A)  $z \leq - 1$ 
B)  $z \geq - 1$ 
C)  $z  - 1$ 
E)  $z = 0$

Question 13

Factor the expression. $x ( n - y ) + ( x - 1 ) ( y - n )$

Accepted Answer

A)  $xn - y$ 
B)  $x + ( x - 1 ) ( y - n )$ 
C)  $n - y$ 
D)  $x + y$ 
E)  $x y$ 
A)  $xn - y$ 
B)  $x + ( x - 1 ) ( y - n )$ 
C)  $n - y$ 
D)  $x + y$ 
E)  $x y$

Question 14

Express the interest obtained after a year on an investment of $x$ dollars at $12 \%$ simple interest per year.

Accepted Answer

The answer of Express the interest obtained after a year...

Question 15

Perform the division and simplify. $\frac { x + 4 } { 9 x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + 8 x + 16 } { 3 x ^ { 2 } + 13 x - 10 }$

Accepted Answer

The answer of Perform the division and simplify. \(\frac {...

Question 16

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Accepted Answer

A) True 
 B)False

Question 17

Find the distance between $\pi$ and . $\pi - 1$

Accepted Answer

The answer of Find the distance between $\pi$ and ....

Question 18

Write an equation that expresses the statement.
Q varies directly as x.

Accepted Answer

The answer of Write an equation that expresses the statement.
Q...

Question 19

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { \sqrt { 64 x ^ { 6 } y ^ { 6 } } }$

Accepted Answer

The answer of Simplify the expression. Assume the letters denote...

Question 20

Determine an appropriate viewing rectangle for the equation $y = \left| 2 x ^ { 3 } - 1 \right| + x$ and use it to draw the graph.

Accepted Answer

The answer of Determine an appropriate viewing rectangle for the...

Find the distance (in miles) traveled by a car which moves at speed $s$ (in mi/h) for two hours, then moves $10$ mi $/$ h slower for another two hours.

Write an equation that expresses the statement that $V$ is proportional to the square root $x$ and inversely proportional to the square of $y$ .

Solve the equation. $( y - 3 ) ^ { 2 } = ( y + 3 ) ^ { 2 } - 6 y - 9$

Perform the indicated operations and simplify. $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$

Solve the equation $\frac { 1 } { s + a } + \frac { 2 } { s - a } = \frac { 5 } { s + c }$ for $c$ .

Rationalize the denominator of the expression. $\frac { 1 } { 2 + \sqrt { 5 } }$

Let $S = \left\{ - 2 , - \sqrt { 3 } , 1 , \frac { 2 } { 3 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $10 \leq \frac { 5 } { 2 x }$ .

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = 4 x ^ { 2 } - 12 x + 6$ .

State the property of real numbers being used. $x + 4 = 4 + x$

Draw the square with vertices $A ( 1,2 )$ , $B ( 4,2 )$ , $C ( 4,5 )$ , and $D ( 1,5 )$ on a coordinate plane. Find the area of the square.

Rationalize the denominator of the expression. $\frac { 5 - x } { \sqrt { 5 } + \sqrt { x } }$

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

Factor the expression. $x ( n - y ) + ( x - 1 ) ( y - n )$

Express the interest obtained after a year on an investment of $x$ dollars at $12 \%$ simple interest per year.

Perform the division and simplify. $\frac { x + 4 } { 9 x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + 8 x + 16 } { 3 x ^ { 2 } + 13 x - 10 }$

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Find the distance between $\pi$ and . $\pi - 1$

Write an equation that expresses the statement. Q varies directly as x.

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { \sqrt { 64 x ^ { 6 } y ^ { 6 } } }$

Determine an appropriate viewing rectangle for the equation $y = \left| 2 x ^ { 3 } - 1 \right| + x$ and use it to draw the graph.

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 1: Fundamentals

Find the distance (in miles) traveled by a car which moves at speed sss (in mi/h) for two hours, then moves 101010 mi /// h slower for another two hours.

Write an equation that expresses the statement that VVV is proportional to the square root xxx and inversely proportional to the square of yyy .

Solve the equation. (y−3)2=(y+3)2−6y−9( y - 3 ) ^ { 2 } = ( y + 3 ) ^ { 2 } - 6 y - 9(y−3)2=(y+3)2−6y−9

Perform the indicated operations and simplify. (αx2−y2)(αx2+y2)\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)(αx2−y2)(αx2+y2)

Solve the equation 1s+a+2s−a=5s+c\frac { 1 } { s + a } + \frac { 2 } { s - a } = \frac { 5 } { s + c }s+a1​+s−a2​=s+c5​ for ccc .

Rationalize the denominator of the expression. 12+5\frac { 1 } { 2 + \sqrt { 5 } }2+5​1​

Let S={−2,−3,1,23,2}S = \left\{ - 2 , - \sqrt { 3 } , 1 , \frac { 2 } { 3 } , 2 \right\}S={−2,−3​,1,32​,2} . Use substitution to determine which of the elements of SSS satisfy the inequality 10≤52x10 \leq \frac { 5 } { 2 x }10≤2x5​ .

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation y=4x2−12x+6y = 4 x ^ { 2 } - 12 x + 6y=4x2−12x+6 .

State the property of real numbers being used. x+4=4+xx + 4 = 4 + xx+4=4+x

Draw the square with vertices A(1,2)A ( 1,2 )A(1,2) , B(4,2)B ( 4,2 )B(4,2) , C(4,5)C ( 4,5 )C(4,5) , and D(1,5)D ( 1,5 )D(1,5) on a coordinate plane. Find the area of the square.

Rationalize the denominator of the expression. 5−x5+x\frac { 5 - x } { \sqrt { 5 } + \sqrt { x } }5​+x​5−x​

Write the following statement in terms of inequalities. ZZZ is greater than or equal to −1- 1−1 .

Factor the expression. x(n−y)+(x−1)(y−n)x ( n - y ) + ( x - 1 ) ( y - n )x(n−y)+(x−1)(y−n)

Express the interest obtained after a year on an investment of xxx dollars at 12%12 \%12% simple interest per year.

Perform the division and simplify. x+49x2−4÷x2+8x+163x2+13x−10\frac { x + 4 } { 9 x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + 8 x + 16 } { 3 x ^ { 2 } + 13 x - 10 }9x2−4x+4​÷3x2+13x−10x2+8x+16​

State whether the inequality is true or false. −110>−1100- \frac { 1 } { 10 } > - \frac { 1 } { 100 }−101​>−1001​

Find the distance between π\piπ and . π−1\pi - 1π−1

Write an equation that expresses the statement. Q varies directly as x.

Simplify the expression. Assume the letters denote any real numbers. 64x6y63\sqrt [ 3 ] { \sqrt { 64 x ^ { 6 } y ^ { 6 } } }364x6y6​​

Determine an appropriate viewing rectangle for the equation y=∣2x3−1∣+xy = \left| 2 x ^ { 3 } - 1 \right| + xy=​2x3−1​+x and use it to draw the graph.

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Find the distance (in miles) traveled by a car which moves at speed $s$ (in mi/h) for two hours, then moves $10$ mi $/$ h slower for another two hours.

Write an equation that expresses the statement that $V$ is proportional to the square root $x$ and inversely proportional to the square of $y$ .

Solve the equation. $( y - 3 ) ^ { 2 } = ( y + 3 ) ^ { 2 } - 6 y - 9$

Perform the indicated operations and simplify. $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$

Solve the equation $\frac { 1 } { s + a } + \frac { 2 } { s - a } = \frac { 5 } { s + c }$ for $c$ .

Rationalize the denominator of the expression. $\frac { 1 } { 2 + \sqrt { 5 } }$

Let $S = \left\{ - 2 , - \sqrt { 3 } , 1 , \frac { 2 } { 3 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $10 \leq \frac { 5 } { 2 x }$ .

Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = 4 x ^ { 2 } - 12 x + 6$ .

State the property of real numbers being used. $x + 4 = 4 + x$

Draw the square with vertices $A ( 1,2 )$ , $B ( 4,2 )$ , $C ( 4,5 )$ , and $D ( 1,5 )$ on a coordinate plane. Find the area of the square.

Rationalize the denominator of the expression. $\frac { 5 - x } { \sqrt { 5 } + \sqrt { x } }$

Write the following statement in terms of inequalities. $Z$ is greater than or equal to $- 1$ .

Factor the expression. $x ( n - y ) + ( x - 1 ) ( y - n )$

Express the interest obtained after a year on an investment of $x$ dollars at $12 \%$ simple interest per year.

Perform the division and simplify. $\frac { x + 4 } { 9 x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + 8 x + 16 } { 3 x ^ { 2 } + 13 x - 10 }$

State whether the inequality is true or false. $- \frac { 1 } { 10 } > - \frac { 1 } { 100 }$

Find the distance between $\pi$ and . $\pi - 1$

Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 3 ] { \sqrt { 64 x ^ { 6 } y ^ { 6 } } }$

Determine an appropriate viewing rectangle for the equation $y = \left| 2 x ^ { 3 } - 1 \right| + x$ and use it to draw the graph.