Question 1

Evaluate the expression for the given value of x. expression: $6 x ^ { 2 } - 2 x + 5$ value: x = -3

Accepted Answer

A) -25 
B) 65 
C) -43 
D) 61 
E) -29 
A) -25 
B) 65 
C) -43 
D) 61 
E) -29

Question 2

Evaluate the expression. $| 3 - 7 |$

Accepted Answer

A) 4 
B) -4 
C) 10 
D) -10 
E) 21 
A) 4 
B) -4 
C) 10 
D) -10 
E) 21

Question 3

Use absolute value notation to describe the situation. The distance between u and -4 is no less than 6.

Accepted Answer

A)  $| u  - 4 |$ F1F1F1S1??F1F1F106 
B)  $| u  - 4 |$ F1F1F1S1???F1F1F106 
C)  $| u  - 4 |$ F1F1F1S1??F1F1F106 
D)  $| u  + 4 |$ F1F1F1S1??F1F1F106 
E)  $| u  + 4 |$ F1F1F1S1??F1F1F106 
A)  $| u  - 4 |$ F1F1F1S1??F1F1F106 
B)  $| u  - 4 |$ F1F1F1S1???F1F1F106 
C)  $| u  - 4 |$ F1F1F1S1??F1F1F106 
D)  $| u  + 4 |$ F1F1F1S1??F1F1F106 
E)  $| u  + 4 |$ F1F1F1S1??F1F1F106

Question 4

After 2 years, an investment of $500 compounded annually at an interest rate r will yield an amount of $500 ( 1 + r ) ^ { 2 }.$ Write this polynomial in standard form.

Accepted Answer

A) 1,000 + 1,000r 
B) 250,000 + 500,000r + 250,000r2 
C) 500 + 1,000r + 500r2 
D) 500r2 + 1,000r + 500 
E) 500r2 + 500r + 500 
A) 1,000 + 1,000r 
B) 250,000 + 500,000r + 250,000r2 
C) 500 + 1,000r + 500r2 
D) 500r2 + 1,000r + 500 
E) 500r2 + 500r + 500

Question 5

Which graph represents the inequality? $- 2 < x \leq 5$

Accepted Answer

A)    -2 5 
B)    -2 5 
C)    -2 5 
D)    -2 5 
E)    -2 5 
A)    -2 5 
B)    -2 5 
C)    -2 5 
D)    -2 5 
E)    -2 5

Question 6

Factor by grouping. 54u6 + 9u4 - 24u2 - 4

Accepted Answer

A) 9u4 - 4(6u2 + 1) 
B) (9u4 - 4)(6u2 + 1)2 
C) (9u4 - 4)2(6u2 + 1) 
D) (9u4 - 4)(6u2 + 1) 
E) (9u4 + 4)(6u2 - 1) 
A) 9u4 - 4(6u2 + 1) 
B) (9u4 - 4)(6u2 + 1)2 
C) (9u4 - 4)2(6u2 + 1) 
D) (9u4 - 4)(6u2 + 1) 
E) (9u4 + 4)(6u2 - 1)

Question 7

The number of committees consisting of exactly 3 people that can be formed from a group of n people is given by the polynomial $\frac { 1 } { 6 } n ^ { 3 } - \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 3 } n.$ Find the number of committees consisting of exactly 3 people that can be formed from a group of $24$ people. Round to the nearest whole number.

Accepted Answer

A) 2600 
B) 2016 
C) 2024 
D) 2120 
E) 2596 
A) 2600 
B) 2016 
C) 2024 
D) 2120 
E) 2596

Question 8

Write the following expression without absolute value symbols. $| 6 | - | 3 |$

Accepted Answer

A) 9 
B) -9 
C) 3 
D) 0 
E) -3 
A) 9 
B) -9 
C) 3 
D) 0 
E) -3

Question 9

On an expressway, the recommended safe distance between cars in feet is given by $0.014 v ^ { 2 } + 1.05 v - 4,$ where v is the speed of the car in miles per hour. Find the safe distance when $v = 85$ miles per hour. Round your answer to the nearest tenth.

Accepted Answer

A) 116.5 feet 
B) 186.4 feet 
C) 256.3 feet 
D) 279.6 feet 
E) 139.8 feet 
A) 116.5 feet 
B) 186.4 feet 
C) 256.3 feet 
D) 279.6 feet 
E) 139.8 feet

Question 10

Factor the trinomial. 8s2 + 22s + 15

Accepted Answer

A) (8s - 5)(s - 3) 
B) (8s + 5)(s + 3) 
C) (4s - 5)(2s + 3) 
D) (4s - 5)(2s - 3) 
E) (4s + 5)(2s + 3) 
A) (8s - 5)(s - 3) 
B) (8s + 5)(s + 3) 
C) (4s - 5)(2s + 3) 
D) (4s - 5)(2s - 3) 
E) (4s + 5)(2s + 3)

Question 11

Approximate the numbers and place the correct symbol () between them.

Accepted Answer

A) -3  3.25 
E) -3 > 3.75 
A) -3  3.25 
E) -3 > 3.75

Question 12

The compound interest formula can be rewritten as $P = \frac { A } { ( 1 + r / n ) ^ { n t } }$ Find the principal amount $P$ that could have been invested on the day you were born at 4.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

Accepted Answer

A) $243,354.47 
B) $389,367.15 
C) $292,025.36 
D) $194,683.58 
E) $316,360.81 
A) $243,354.47 
B) $389,367.15 
C) $292,025.36 
D) $194,683.58 
E) $316,360.81

Question 13

Perform the indicated operations below and simplify. $\frac { \left[ \frac { x ^ { 4 } } { ( x + 3 ) ^ { 3 } } \right] } { \left[ \frac { x ^ { 3 } } { ( x + 3 ) ^ { 4 } } \right] }$

Accepted Answer

A)  $x ( x + 3 ) ^ { 2 },$ $x \neq - 3$ 
B)  $x ^ { 2 } ( x + 3 ),$ $x \neq - 3,0$ 
C)  $x ( x + 3 ),$ $x \neq - 3,0$ 
D)  $x ( x + 3 ) ^ { 2 },$ $x \neq 0$ 
E)  $x ( x + 3 ),$ $x \neq - 3$ 
A)  $x ( x + 3 ) ^ { 2 },$ $x \neq - 3$ 
B)  $x ^ { 2 } ( x + 3 ),$ $x \neq - 3,0$ 
C)  $x ( x + 3 ),$ $x \neq - 3,0$ 
D)  $x ( x + 3 ) ^ { 2 },$ $x \neq 0$ 
E)  $x ( x + 3 ),$ $x \neq - 3$

Question 14

Write the rational expression in simplest form. $\frac { 120 v ^ { 4 } } { 15 v ^ { 5 } }$

Accepted Answer

A)  $\frac { 8 v ^ { 4 } } { v ^ { 5 } } , \quad v \neq 0$ 
B)  $\frac { 40 v } { 5 } , v \neq 0$ 
C)  $\frac { 24 } { 3 v } , \quad v \neq 0$ 
D)  $\frac { 8 } { v } , \quad v \neq 0$ 
E)  $\frac { 40 } { 5 v } , \quad v \neq 0$ 
A)  $\frac { 8 v ^ { 4 } } { v ^ { 5 } } , \quad v \neq 0$ 
B)  $\frac { 40 v } { 5 } , v \neq 0$ 
C)  $\frac { 24 } { 3 v } , \quad v \neq 0$ 
D)  $\frac { 8 } { v } , \quad v \neq 0$ 
E)  $\frac { 40 } { 5 v } , \quad v \neq 0$

Question 15

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form. $\left( y ^ { 2 } - 9 y + 4 \right) + \left( 8 y ^ { 2 } - y + 6 \right)$

Accepted Answer

A)  $- 7 y ^ { 2 } - 8 y + 10$ 
B)  $- 7 y ^ { 2 } - 10 y + 10$ 
C)  $9 y ^ { 2 } - 10 y - 2$ 
D)  $9 y ^ { 2 } - 8 y + 10$ 
E)  $9 y ^ { 2 } - 10 y + 10$ 
A)  $- 7 y ^ { 2 } - 8 y + 10$ 
B)  $- 7 y ^ { 2 } - 10 y + 10$ 
C)  $9 y ^ { 2 } - 10 y - 2$ 
D)  $9 y ^ { 2 } - 8 y + 10$ 
E)  $9 y ^ { 2 } - 10 y + 10$

Question 16

Find the special product. (4x - 9)2

Accepted Answer

A) 16x2 - 72x + 81 
B) 16x2 - 36x + 81 
C) 8x2 - 18 
D) 16x2 - 81 
E) 16x2 + 81 
A) 16x2 - 72x + 81 
B) 16x2 - 36x + 81 
C) 8x2 - 18 
D) 16x2 - 81 
E) 16x2 + 81

Question 17

Perform the addition and simplify. $\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }$

Accepted Answer

A)  $\frac { 7 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$ 
B)  $\frac { 7 x - 43 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$ 
C)  $\frac { 7 x + 47 } { ( x + 9 ) ( x + 8 ) ( x + 1 ) }$ 
D)  $\frac { 7 x - 47 } { ( x - 9 ) ( x + 8 ) ( x - 1 ) }$ 
E)  $\frac { 7 } { 2 \left( x ^ { 2 } - 12 x + 32 \right) }$ 
A)  $\frac { 7 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$ 
B)  $\frac { 7 x - 43 } { ( x - 9 ) ( x - 8 ) ( x + 1 ) }$ 
C)  $\frac { 7 x + 47 } { ( x + 9 ) ( x + 8 ) ( x + 1 ) }$ 
D)  $\frac { 7 x - 47 } { ( x - 9 ) ( x + 8 ) ( x - 1 ) }$ 
E)  $\frac { 7 } { 2 \left( x ^ { 2 } - 12 x + 32 \right) }$

Question 18

Completely factor the expression. -4q3 + 15q2 + 54q

Accepted Answer

A) -q(q + 6)(4q - 9) 
B) -q(q - 6)(4q + 9) 
C) (-q2 + 6q)(4q + 9) 
D) (-q2 - 6q)(4q - 9) 
E) (q + 6)(-4q2 - 9q) 
A) -q(q + 6)(4q - 9) 
B) -q(q - 6)(4q + 9) 
C) (-q2 + 6q)(4q + 9) 
D) (-q2 - 6q)(4q - 9) 
E) (q + 6)(-4q2 - 9q)

Question 19

Factor the sum or difference of cubes. 27q3 + 1

Accepted Answer

A) (3q - 1)3 
B) (3q + 1)3 
C) (3q + 1)(9q2 - 3q + 1) 
D) (3q + 1)(9q2 + 3q + 1) 
E) (3q - 1)(9q2 - 3q + 1) 
A) (3q - 1)3 
B) (3q + 1)3 
C) (3q + 1)(9q2 - 3q + 1) 
D) (3q + 1)(9q2 + 3q + 1) 
E) (3q - 1)(9q2 - 3q + 1)

Question 20

Factor out the common factor. 8v(5v + 3) + (5v + 3)

Accepted Answer

A) (5v + 3)8v 
B) (5v + 3)8v + 1 
C) (5v + 3)8v - 1 
D) (5v + 3)(8v + 1) 
E) (5v + 3)(8v - 1) 
A) (5v + 3)8v 
B) (5v + 3)8v + 1 
C) (5v + 3)8v - 1 
D) (5v + 3)(8v + 1) 
E) (5v + 3)(8v - 1)

Evaluate the expression for the given value of x. expression: $6 x ^ { 2 } - 2 x + 5$ value: x = -3

Evaluate the expression. $| 3 - 7 |$

Use absolute value notation to describe the situation. The distance between u and -4 is no less than 6.

After 2 years, an investment of $500 compounded annually at an interest rate r will yield an amount of $500 ( 1 + r ) ^ { 2 }.$ Write this polynomial in standard form.

Which graph represents the inequality? $- 2 < x \leq 5$

Factor by grouping. 54u6 + 9u4 - 24u2 - 4

Write the following expression without absolute value symbols. $| 6 | - | 3 |$

On an expressway, the recommended safe distance between cars in feet is given by $0.014 v ^ { 2 } + 1.05 v - 4,$ where v is the speed of the car in miles per hour. Find the safe distance when $v = 85$ miles per hour. Round your answer to the nearest tenth.

Factor the trinomial. 8s2 + 22s + 15

Approximate the numbers and place the correct symbol (< or >) between them.

The compound interest formula can be rewritten as $P = \frac { A } { ( 1 + r / n ) ^ { n t } }$ Find the principal amount $P$ that could have been invested on the day you were born at 4.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

Perform the indicated operations below and simplify. $\frac { \left[ \frac { x ^ { 4 } } { ( x + 3 ) ^ { 3 } } \right] } { \left[ \frac { x ^ { 3 } } { ( x + 3 ) ^ { 4 } } \right] }$

Write the rational expression in simplest form. $\frac { 120 v ^ { 4 } } { 15 v ^ { 5 } }$

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form. $\left( y ^ { 2 } - 9 y + 4 \right) + \left( 8 y ^ { 2 } - y + 6 \right)$

Find the special product. (4x - 9)2

Perform the addition and simplify. $\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }$

Completely factor the expression. -4q3 + 15q2 + 54q

Factor the sum or difference of cubes. 27q3 + 1

Factor out the common factor. 8v(5v + 3) + (5v + 3)

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Exam 1: Fundamental Concepts of Algebra

Evaluate the expression for the given value of x. expression: 6x2−2x+56 x ^ { 2 } - 2 x + 56x2−2x+5 value: x = -3

Evaluate the expression. ∣3−7∣| 3 - 7 |∣3−7∣

Use absolute value notation to describe the situation. The distance between u and -4 is no less than 6.

After 2 years, an investment of $500 compounded annually at an interest rate r will yield an amount of 500(1+r)2.500 ( 1 + r ) ^ { 2 }.500(1+r)2. Write this polynomial in standard form.

Which graph represents the inequality? −2<x≤5- 2 < x \leq 5−2<x≤5

Factor by grouping. 54u6 + 9u4 - 24u2 - 4

Write the following expression without absolute value symbols. ∣6∣−∣3∣| 6 | - | 3 |∣6∣−∣3∣

On an expressway, the recommended safe distance between cars in feet is given by 0.014v2+1.05v−4,0.014 v ^ { 2 } + 1.05 v - 4,0.014v2+1.05v−4, where v is the speed of the car in miles per hour. Find the safe distance when v=85v = 85v=85 miles per hour. Round your answer to the nearest tenth.

Factor the trinomial. 8s2 + 22s + 15

Approximate the numbers and place the correct symbol (< or >) between them.

The compound interest formula can be rewritten as P=A(1+r/n)ntP = \frac { A } { ( 1 + r / n ) ^ { n t } }P=(1+r/n)ntA​ Find the principal amount PPP that could have been invested on the day you were born at 4.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

Perform the indicated operations below and simplify. [x4(x+3)3][x3(x+3)4]\frac { \left[ \frac { x ^ { 4 } } { ( x + 3 ) ^ { 3 } } \right] } { \left[ \frac { x ^ { 3 } } { ( x + 3 ) ^ { 4 } } \right] }[(x+3)4x3​][(x+3)3x4​]​

Write the rational expression in simplest form. 120v415v5\frac { 120 v ^ { 4 } } { 15 v ^ { 5 } }15v5120v4​

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form. (y2−9y+4)+(8y2−y+6)\left( y ^ { 2 } - 9 y + 4 \right) + \left( 8 y ^ { 2 } - y + 6 \right)(y2−9y+4)+(8y2−y+6)

Find the special product. (4x - 9)2

Perform the addition and simplify. 2x2−17x+72+5x2−7x−8\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }x2−17x+722​+x2−7x−85​

Completely factor the expression. -4q3 + 15q2 + 54q

Factor the sum or difference of cubes. 27q3 + 1

Factor out the common factor. 8v(5v + 3) + (5v + 3)

Equations and Inequalities

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Limits and Derivatives

Applications of the Derivative

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Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

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Evaluate the expression for the given value of x. expression: $6 x ^ { 2 } - 2 x + 5$ value: x = -3

Evaluate the expression. $| 3 - 7 |$

After 2 years, an investment of $500 compounded annually at an interest rate r will yield an amount of $500 ( 1 + r ) ^ { 2 }.$ Write this polynomial in standard form.

Which graph represents the inequality? $- 2 < x \leq 5$

Write the following expression without absolute value symbols. $| 6 | - | 3 |$

On an expressway, the recommended safe distance between cars in feet is given by $0.014 v ^ { 2 } + 1.05 v - 4,$ where v is the speed of the car in miles per hour. Find the safe distance when $v = 85$ miles per hour. Round your answer to the nearest tenth.

The compound interest formula can be rewritten as $P = \frac { A } { ( 1 + r / n ) ^ { n t } }$ Find the principal amount $P$ that could have been invested on the day you were born at 4.5% annual interest compounded monthly to make you a millionaire on your 21st birthday.

Perform the indicated operations below and simplify. $\frac { \left[ \frac { x ^ { 4 } } { ( x + 3 ) ^ { 3 } } \right] } { \left[ \frac { x ^ { 3 } } { ( x + 3 ) ^ { 4 } } \right] }$

Write the rational expression in simplest form. $\frac { 120 v ^ { 4 } } { 15 v ^ { 5 } }$

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form. $\left( y ^ { 2 } - 9 y + 4 \right) + \left( 8 y ^ { 2 } - y + 6 \right)$

Perform the addition and simplify. $\frac { 2 } { x ^ { 2 } - 17 x + 72 } + \frac { 5 } { x ^ { 2 } - 7 x - 8 }$