Deck 1: Fundamental Concepts of Algebra

Question 1

The two given numbers are coordinates of points and , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. , is at least

A)
B)
C)
D)
E)

Answer 1

Question 2

Factor the polynomial.

A)(3y ³ - 7x) (3y ³ - 7x)
B)(3y ³ - 7x) (3y ³ + 7x)
C)(9y ³ - 7x) (9y ³ + 7x)
D)(9y ³ - 7x)²
E)(3y ³ + 7x)²

Answer 2

(3y ³ - 7x) (3y ³ + 7x)

Question 3

Express as a polynomial.

A)8x ³ + 120x ² y + 200xy ² + 2,000y ³
B)8x ³ + 600x ² y + 120xy ² + 1,000y ³
C)8x ³ + 40x ² y + 200xy ² + 1,000y ³
D)8x ³ + 40x ² y + 600xy ² + 400y ³
E)8x ³ + 120x ² y + 600xy ² + 1,000y ³

Answer 3

8x ³ + 120x ² y + 600xy ² + 1,000y ³

Question 4

Express as a polynomial.

A)3x ⁴ - 9x ⁵ - 12x ³ + 3x ⁶ + 9x ² + 12x - 36
B)3x ⁶ - 9x ⁵ - 12x ⁴ + 9x ³ - 33x ² + 12x - 36
C)3x ⁴ - 9x ³ - 12x ⁵ + 39x ⁶ + 9x ² + 12x - 36
D)3x ⁶ - 9x ⁵ - 12x ⁴ + 33x ³ + 9x ² + 12x - 36
E)3x ⁶ - 9x ⁵ - 12x ⁴ + 39x ³ + 9x ² + 12x - 36

Question 5

Rewrite the expression using a radical.

A)
B)
C)
D)
E)

Question 6

Factor the polynomial.

A)3x ³ y ² (6x ² + y)
B)6x ³ y ² (x ² + y ³ )
C)6x ³ y ² (x ² + y)
D)18x ³ y ² (3x ² + y ² )
E)6x ³ y ² (3x ² + y)

Question 7

Simplify the expression.

A)
B)
C)
D)
E)

Question 8

Express as a polynomial.

A)28x ³ + 24x ² + 28x - 45
B)28x ³ + 125x ² + 63x - 45
C)125x ³ - 28x ² + 28x - 45
D)28x ³ + 24x ² + 63x - 45
E)125x ³ - 24x ² + 28x - 45

Question 9

Simplify the expression:

A)
B)
C)
D)
E)

Question 10

Approximate the real-number expression to four decimal places.

A)15.1613
B)-15.0613
C)15.0613
D)-15.1613
E)-16.0613

Question 11

Factor the polynomial.

A)p(h + t)
B)3(h + pt)
C)p(h + 3t)
D)p(3h + t)
E)3p(h + t)

Question 12

Express the following statement as an inequality. a is not less than 2

A)
B)
C)
D)
E)

Question 13

Replace the symbol "?" to make the resulting statement true for all real numbers : q, b, and c, whenever the expressions are defined.

A)
B)

Question 14

Approximate the real-number expression to four decimal places.

A)0.1703
B)8.1664
C)-1.1680
D)1.2937
E)3.7809

Question 15

In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in two light years.

A)
B)
C)
D)
E)

Question 16

Simplify the expression.

A)
B)
C)
D)
E)

Question 17

Simplify the expression.

A)
B)
C)
D)
E)

Question 18

Write the expression as a simplified rational number.

A)
B)
C)
D)
E)

Question 19

Approximate the real-number expression to four decimal places.

A)18.3355
B)18.2965
C)18.2955
D)17.2855
E)20.3255

Question 20

Simplify the expression.

A)
B)
C)
D)
E)

Question 21

Express as a polynomial.

A)42x ³ - 9x ² + 28x - 8
B)9x ³ + 33x ² + 45x - 8
C)9x ³ + 42x ² + 45x - 8
D)42x ³ - 33x ² + 28x - 8
E)9x ³ + 33x ² + 28x - 8

Question 22

Rationalize the denominator. HINT: Multiply numerator and denominator by

A)
B)
C)
D)
E)

Question 23

Approximate the real-number expression to four decimal places.

A)14.6629
B)15.7129
C)15.6739
D)17.7029
E)15.6729

Question 24

The two given numbers are coordinates of points and , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. , is at least

A)
B)
C)
D)
E)

Question 25

Rewrite the expression using a radical.

A)
B)
C)
D)
E)

Question 26

Simplify the expression.

A)
B)
C)
D)
E)

Question 27

Approximate the real-number expression to four decimal places.

A)5.4296
B)1.2380
C)5.2886
D)0.1146
E)-3.7264

Question 28

Replace the symbol "?" to make the resulting statement true for all real numbers : l, b, and c, whenever the expressions are defined.

A)
B)

Question 29

Simplify the expression:

A)
B)
C)
D)
E)

Question 30

Express as a polynomial.

A)3x ⁶ - 5x ⁵ - 6x ⁴ + 13x ³ + 5x ² + 6x - 10
B)3x ⁴ - 5x ⁵ - 6x ³ + 3x ⁶ + 5x ² + 6x - 10
C)3x ⁴ - 5x ³ - 6x ⁵ + 13x ⁶ + 5x ² + 6x - 10
D)3x ⁶ - 5x ⁵ - 6x ⁴ + 7x ³ + 5x ² + 6x - 10
E)3x ⁶ - 5x ⁵ - 6x ⁴ + 5x ³ - 7x ² + 6x - 10

Question 31

In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in five light years.

A)
B)
C)
D)
E)

Question 32

Express as a polynomial.

A)729x ³ + 1,701x ² y + 1,323xy ² + 343y ³
B)729x ³ + 1,701x ² y + 441xy ² + 3,087y ³
C)729x ³ + 567x ² y + 441xy ² + 343y ³
D)729x ³ + 1,323x ² y + 1,701xy ² + 343y ³
E)729x ³ + 567x ² y + 1,323xy ² + 3,969y ³

Question 33

Factor the polynomial.

A)4p(k + t)
B)4(k + pt)
C)p(4k + t)
D)p(k + 4t)
E)p(k + t)

Question 34

Rationalize the denominator.

A)
B)
C)
D)
E)

Question 35

Rationalize the numerator.

A)
B)
C)
D)
E)

Question 36

Simplify the expression.

A)
B)
C)
D)
E)

Question 37

Simplify the expression.

A)
B)
C)
D)
E)

Question 38

Express the following statement as an inequality. a is not less than 4

A)
B)
C)
D)
E)

Question 39

Approximate the real-number expression to four decimal places.

A)-370.8916
B)-370.9916
C)370.8916
D)370.9916
E)-371.8916

Question 40

Simplify the expression.

A)
B)
C)
D)
E)

Question 41

Rationalize the denominator.

A)
B)
C)
D)
E)

Question 42

Express the following statement as an inequality. a is not less than 6

A)
B)
C)
D)
E)

Question 43

Factor the polynomial.

A)(8y ² + 5x)²
B)(64y ² - 5x)²
C)(64y ² - 5x) (64y ² + 5x)
D)(8y ² - 5x) (8y ² + 5x)
E)(8y ² - 5x) (8y ² - 5x)

Question 44

Rewrite the expression using a radical.

A)
B)
C)
D)
E)

Question 45

Rationalize the numerator.

A)
B)
C)
D)
E)

Question 46

Simplify the expression.

A)
B)
C)
D)
E)

Question 47

The two given numbers are coordinates of points and , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. , is at least

A)
B)
C)
D)
E)

Question 48

Simplify the expression.

A)
B)
C)
D)
E)

Question 49

In astronomy, distances to stars are measured in light years. One light year is the distance a ray of light travels in one year. If the speed of light is approximately 186,000 miles per second, estimate the number of miles in five light years.

A)
B)
C)
D)
E)

Question 50

Simplify the expression.

A)
B)
C)
D)
E)

Question 51

Simplify the expression.

A)
B)
C)
D)
E)

Question 52

Replace the symbol "?" to make the resulting statement true for all real numbers : p, b, and c, whenever the expressions are defined.

A)
B)

Question 53

Simplify the expression:

A)
B)
C)
D)
E)

Question 54

Approximate the real-number expression to four decimal places.

A)-16.0120
B)-15.0120
C)15.1120
D)15.0120
E)-15.1120

Question 55

Write the expression as a simplified rational number.

A)
B)
C)
D)
E)

Question 56

Rationalize the denominator. HINT: Multiply numerator and denominator by

A)
B)
C)
D)
E)

Question 57

Factor the polynomial.

A)6x ³ y ³ (3x ⁴ + y)
B)18x ³ y ³ (3x ⁴ + y ² )
C)6x ³ y ³ (x ⁴ + y ⁴ )
D)3x ³ y ³ (6x ⁴ + y)
E)6x ³ y ³ (x ⁴ + y)

Question 58

Simplify the expression.

A)
B)
C)
D)
E)

Question 59

Approximate the real-number expression to four decimal places.

A)8.7110
B)2.6316
C)1.9149
D)0.7915
E)-0.4338

Question 60

Simplify the expression.

A)
B)
C)
D)
E)

Question 61

Rewrite the number without using the absolute value symbol, and simplify the result.

A)105
B)35
C)21
D)-105
E)-35

Question 62

Simplify the expression.

A)
B)
C)
D)
E)

Question 63

Write the expression as a simplified rational number.

A)
B)
C)
D)
E)

Question 64

Rewrite the following expression without using the absolute value symbol, and simplify the result.

A)
B)
C)
D)
E)

Question 65

Express the number in decimal form.

A)0.079
B)0.0000079
C)0.00079
D)0.000079
E)0.0079

Question 66

Replace the symbol "?" to make the resulting statement true for all real numbers : q, b, and c, whenever the expressions are defined.

A)
B)

Question 67

Rationalize the numerator.

A)
B)
C)
D)
E)

Question 68

Factor the polynomial.

A)7x ² y ⁴ (2x ³ + y)
B)7x ² y ⁴ (x ³ + y ⁵ )
C)14x ² y ⁴ (2x ³ + y ² )
D)7x ² y ⁴ (x ³ + y)
E)2x ² y ⁴ (7x ³ + y)

Question 69

Simplify the expression.

A)
B)
C)
D)
E)

Question 70

Factor the polynomial.

A)m(k + t)
B)m(4k + t)
C)4(k + mt)
D)m(k + 4t)
E)4m(k + t)

Question 71

Rationalize the denominator. HINT: Multiply numerator and denominator by

A)
B)
C)
D)
E)

Question 72

Approximate the real-number expression to four decimal places.

A)6.7588
B)4.7298
C)4.7688
D)3.7188
E)4.7288

Question 73

Express as a polynomial.

A)65x ³ - 21x ² + 27x - 20
B)65x ³ - 30x ² + 27x - 20
C)21x ³ + 30x ² + 27x - 20
D)21x ³ + 65x ² + 38x - 20
E)21x ³ + 30x ² + 38x - 20

Question 74

Simplify the expression.

A)
B)
C)
D)
E)

Question 75

Express as a polynomial.

A)8x ³ + 28x ² y + 294xy ² + 196y ³
B)8x ³ + 84x ² y + 294xy ² + 343y ³
C)8x ³ + 28x ² y + 98xy ² + 343y ³
D)8x ³ + 84x ² y + 98xy ² + 686y ³
E)8x ³ + 294x ² y + 84xy ² + 343y ³

Question 76

Express as a polynomial.

A)3x ⁶ - 7x ⁵ - 15x ⁴ + 21x ³ - 26x ² + 45x - 105
B)3x ⁶ - 7x ⁵ - 15x ⁴ + 44x ³ + 21x ² + 45x - 105
C)3x ⁶ - 7x ⁵ - 15x ⁴ + 26x ³ + 21x ² + 45x - 105
D)3x ⁴ - 7x ³ - 15x ⁵ + 44x ⁶ + 21x ² + 45x - 105
E)3x ⁴ - 7x ⁵ - 15x ³ + 3x ⁶ + 7x ² + 45x - 105

Question 77

Approximate the real-number expression to four decimal places :

A)3.6600
B)4.3961
C)1.8961
D)0.7869
E)2.6461

Question 78

Simplify the expression.

A)
B)
C)
D)
E)

Question 79

Factor the polynomial.

A)(4y ² - 5x) (4y ² + 5x)
B)(4y ² + 5x)²
C)(16y ² - 5x)²
D)(4y ² - 5x) (4y ² - 5x)
E)(16y ² - 5x) (16y ² + 5x)

Question 80

Rationalize the denominator.

A)
B)
C)
D)
E)