Deck 12: Review of Basic Concepts and Skills

Question 1

Evaluate/simplify the expression. | -2.5 |

Answer 1

2.5

Question 2

Use the following to answer questions :
List all the numbers in the set that are elements of R.

Answer 2

Question 3

Evaluate without a calculator, using the order of operations. -6² + 12 - | 5 - 12 | -

A) -98
B) 32
C) 46
D) -40

Answer 3

-40

Question 4

Perform the operation indicated mentally or using pencil/paper. (9)(-6)(0)

A) 3
B) 0
C) 54
D) -54

Question 5

Perform the operation indicated mentally or using pencil/paper.

Question 6

Use the following to answer questions :
List all the numbers in the set that are elements of Q.

A)
B)
C)
D)

Question 7

Use a descriptive variable and an inequality symbol (<, >, $\ge$ , $\le$ ) to write a model for the statement. The Smith family will spend at least $16,500 on home improvements.

A) Let a represent the amount. a < $16,500.
B) Let a represent the amount. a $\le$ $16,500.
C) Let a represent the amount. a > $16,500.
D) Let a represent the amount. a $\ge$ $16,500.

Question 8

Use the following to answer questions :
Graph the elements of the set on a number line.

Question 9

State true of false. If false, state why.

Question 10

Evaluate/simplify the expression.

A) 10
B) -10
C)
D)

Question 11

Use the following to answer questions :
Rewrite the elements of the set in order from smallest to largest.

A)
B)
C)
D)

Question 12

Convert to decimal form and graph by estimating the number's location between two integers.

Question 13

Use the following to answer questions :
List all the numbers in the set that are elements of H.

A)
B)
C)
D)

Question 14

Perform the operation indicated mentally or using pencil/paper. -16 - (-20)

A) 36
B) -4
C) 4
D) -36

Question 15

Evaluate without the aid of a calculator.

A)
B)
C)
D)

Question 16

Use the following to answer questions :
List all the numbers in the set that are elements of Z.

Question 17

Use the following to answer questions :
List all the numbers in the set that are elements of W.

Question 18

Evaluate/simplify the expression. - | -16 |

A) -16
B) 16
C)
D)

Question 19

Use the following to answer questions :
List all the numbers in the set that are elements of N.

Question 20

Evaluate without a calculator, using the order of operations.

Question 21

Simplify by combining like terms. 4x + 14x² - 9x - 5x²

A) -9x² - 5x
B) 9x² + 5x
C) 9x² - 5x
D) 18x² - 14x

Question 22

Translate the phrase into an algebraic expression.
the difference between a number and two is squared

Question 23

Evaluate without a calculator, using the order of operations.

A) -35
B) 35
C) 20
D) -20

Question 24

Evaluate 4x - 2y given x = 3 and y = -1.

Question 25

Evaluate 4x²y given x = -3 and y = 5.

Question 26

Rewrite the expression using the associative property of multiplication and simplify if possible.

Question 27

Translate the phrase into an algebraic expression.
five times the sum of a number and six, decreased by four

Question 28

Create a mathematical model using descriptive variables.
The speed of the truck was three miles per hour more than the speed of the car.

Question 29

Identify the number of terms in the expression and the coefficient of each term.
-5x² + x - 6

Question 30

Create the indicated algebraic expression. Use descriptive variables. The length of a rectangular lawn is 8 ft more than three times the width of the lawn. Express the length of the lawn in terms of the width.

A) 3 + w + 8
B) 3(w + 8)
C) 8w + 3
D) 3w + 8

Question 31

Evaluate 3y² + 4y - 5 given y = -5.

A) -100
B) 50
C) -60
D) 90

Question 32

Translate the phrase into an algebraic expression. seven less than twice a number

A) 2(7 - n)
B) 7 - 2n
C) 2(n - 7)
D) 2n - 7

Question 33

Evaluate given y = -5.

Question 34

Simplify by combining like terms.
-8z - z - 4z

Question 35

Translate the phrase into an algebraic expression. six fewer than a number

A) 6 - n
B) n - 6
C) n / 6
D) n + 6

Question 36

Evaluate given x = 5 and y = -3.

A) 1
B)
C)
D)

Question 37

Rewrite the expression using the commutative property of addition and simplify if possible.
-9 + 5

Question 38

Simplify by removing all grouping symbols and combining like terms.
2a + (-8a)

Question 39

Simplify by removing all grouping symbols and combining like terms. (10a - 10b + c) - (a - b - 2c)

A) 9a - 9b + 3c
B) 9a - 11b + 3c
C) 9a - 9b - c
D) 9a - 11b - c

Question 40

Evaluate (2x - 3y)² given x = 3 and y = -1.

A) 81
B) 27
C) 9
D) -9

Question 41

Find the binomial square. (x + 2)²

Question 42

Compute the product. -8x(x² - 5x - 7)

A) -8x³ - 40x² - 56x
B) -8x³ + 40x² + 56x
C) -8x² - 40x - 56
D) -8x² + 40x + 56

Question 43

Find the binomial square. (4x - 3)²

A) 4x² - 12x + 9
B) 16x² - 12x + 9
C) 16x² + 9
D) 16x² - 24x + 9

Question 44

Simplify the expression using the product to a power property. (-10ab⁷)²

A) 100ab¹⁴
B) -100ab¹⁴
C) 100a²b¹⁴
D) -100a²b¹⁴

Question 45

Convert the following number to scientific notation. The diameter of Jupiter is approximately 143,000,000 meters.

A) 1.43 * 10⁷ meters
B) 1.43 * 10⁸ meters
C) 14.3 * 10⁷ meters
D) 14.3 * 10⁸ meters

Question 46

Compute the product. (x + 4)(x - 4)(x + 1)

Question 47

Simplify the expression using the quotient to a power property.

A)
B)
C)
D)

Question 48

Determine the product using the product property. (5p³q⁴)(p²q)

A) 5p⁵q⁵
B) 5p⁶q⁴
C) 5p⁵q⁴
D) 5p⁶q⁵

Question 49

Simplify using the quotient property of exponents. Write the answer using positive exponents only.

Question 50

Subtract d³ + 6d² + 6d + 6 from d⁴ + 9d² + 5d - 9 using a vertical format.

A) d⁴ - d³ + 3d² + 11d - 3
B) d⁴ + d³ + 3d² + 11d - 15
C) d⁴ - d³ + 3d² - d - 15
D) d⁴ + d³ + 3d² - d - 3

Question 51

Use the properties of exponents to simplify the expression. Write the answer using positive exponents only.. -4x⁰ + (-4x)⁰

A) 0
B) -8
C) -2
D) -3

Question 52

Convert the following number to ordinary notation.
The maximum distance from Pluto to the Sun is 7.3 * 10⁷ meters.

Question 53

Use the properties of exponents to simplify the expression. Write the answer using positive exponents only.

Question 54

Find the indicated sum.
(6y² - 4y + 10) + (-3y² - 3y - 8)

Question 55

Write the polynomial in standard form and name the lead coefficient.
-8x² + 3x³ + 1 + (-3x)

Question 56

Simplify the expression using the quotient to a power property.

A)
B)
C)
D)

Question 57

Use the properties of exponents to simplify the expression. Write the answer using positive exponents only..

A)
B)
C)
D) ab⁸c²

Question 58

Compute the product. (3x - 1)(2x + 5)

A) 6x² - 13x - 5
B) 6x² - 17x - 5
C) 6x² + 13x - 5
D) 6x² + 17x - 5

Question 59

Factor out the greatest common factor. -18x⁴ + 10x³ - 12x²

A) -2x²(9x² + 10x - 12)
B) -2x²(9x² - 5x + 6)
C) -18x²(x² + 10x - 12)
D) -18x(x³ + 10x² - 12x)

Question 60

Simplify using the quotient property of exponents. Write the answer using positive exponents only.

Question 61

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 2x + 3

A) (x + 3)(x + 1)
B) (x - 3)(x - 1)
C) (x + 2)(x + 1)
D) prime

Question 62

Factor the trinomial completely. x² - 18x + 80

A) (x + 8)(x + 10)
B) (x - 8)(x + 10)
C) (x + 1)(x + 80)
D) (x - 8)(x - 10)

Question 63

Reduce to lowest terms.

Question 64

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime."
x³ - 4x² - 4x + 16

Question 65

Reduce to lowest terms.

Question 66

Factor the trinomial completely. x² + x - 56

Question 67

Reduce to lowest terms.

A) 1
B) -1
C)
D)

Question 68

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 17x + 70

A) (x - 10)(x - 7)
B) (x + 10)(x + 7)
C) (x + 1)(x + 70)
D) (x + 10)(x - 7)

Question 69

Factor the difference of perfect cubes completely. 27a³ - 1000

A) (3a + 10)(9a² - 100)
B) (3a - 10)(9a² + 100)
C) (3a + 10)(9a² - 30a + 100)
D) (3a - 10)(9a² + 30a + 100)

Question 70

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." 8a³ + 27

A) (2a - 3)(4a + 9)
B) (2a - 3)(4a + 6a + 9)
C) (2a + 3)(4a - 6a + 9)
D) (2a - 3)(4a - 6a + 9)

Question 71

Factor by grouping. x⁵ + 3x³ - 5x² - 15

Question 72

Factor the perfect square trinomial completely. 9x² + 30x + 25

A) (3x + 5)²
B) (3x - 5)(3x + 5)
C) (9x + 5)(x + 5)
D) (3x + 1 )(3x + 25)

Question 73

Factor the trinomial completely. 9x² - 30x + 25

A) (3x - 5)(3x - 5)
B) (3x + 5)(3x + 5)
C) (9x - 5)(x - 5)
D) (3x + 1)(3x + 25)

Question 74

Reduce to lowest terms.

A)
B)
C)
D)

Question 75

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime."
-21x² + 6x + 15x³

Question 76

Factor the trinomial completely. 3x² + 20x + 25

Question 77

Factor out the common binomial factor. 10x(x - 5) - 7(x - 5)

Question 78

Factor the perfect square trinomial completely. x² - 6x + 9

Question 79

Factor using u-substitution. 36 + x⁴ - 13x²

Question 80

Factor the difference of perfect squares completely. 9x² - 16