Deck 2: Review and Applications of Algebra

Question 1

The following algebraic expression can be classified as:

A) monomial
B) binomial
C) trinomial
D) multinomial
E) All choices are incorrect

Answer 1

binomial

Question 2

Simplify and collect like terms: 9x - [4y - 3(x - y)]

A) 12 x + 7y
B) 6x - 7y
C) 6x + 7y
D) 12x - 7y
E) 9x - 7y

Answer 2

12x - 7y

Question 3

Simplify the following: (2x³)⁵

A) 10x¹⁵
B) 32x⁸
C) 32x¹⁵
D) 2x¹⁵
E) 2x⁸

Answer 3

32x¹⁵

Question 4

Simplify and collect like terms:

A) 4x + 2y
B) 4xy - 2y
C) 4xy + 2y²
D) 4x - 2y
E) 4xy - 2y²

Question 5

2(b - 2) - (b - 2) =

A) b + 6
B) 3b - 2
C) 3b + 2
D) b - 2
E) b - 6

Question 6

Simplify and collect like terms: 4x + 5 - 2.1(x - 7)x8

A) -1.6x - 14.075
B) -1.6x - 15.325
C) 2.6x + 15.325
D) 2.6x - 14.075
E) -1.6x + 15.325

Question 7

Simplify and collect like terms: 3(x - 2y)(2x + y)

A) 6x² - 6xy - 6y²
B) 6x² + 10xy - 6y²
C) 6x² - 9xy - 6y²
D) 6x² - 9xy + 6y²
E) 6x² + 10xy + 6y²

Question 8

Simplify the following: (x⁵)⁴

A) x⁹
B) x²⁰
C) x
D) x^-1
E) x⁰

Question 9

Simplify the following: b⁸ / b²

A) b⁴
B) b¹⁰
C) b¹⁶
D) b^-6
E) b⁶

Question 10

Simplify the following: (a²) (a^-6) (a³)

A) a¹¹
B) a
C) a^-36
D) a^-1
E) a^-5

Question 11

Simplify:

A) -2a + 13
B) -2a - 1
C) -2a + 7
D) 2a + 7
E) 2a - 1

Question 12

Simplify the following: y⁸ / y⁵

A) y¹³
B) y³
C) y^-40
D) y⁴⁰
E) y^-13

Question 13

Simplify the following: a² x a⁶ x a

A) a⁸
B) a⁷
C) a⁹
D) a¹²
E) a¹³

Question 14

The following numerical coefficient(s) of , is/are:

A) -4,2
B) 3,4
C) 2
D) 3,-4,2
E) 3,-4

Question 15

Simplify the following:

A) x^-1
B) x⁶
C) x^-2
D) x⁷
E) x²

Question 16

Simplify and collect like terms: -a + (2b - c) - (a -b +c)

A) -2a + 3b - 2c
B) -2a + b - 2c
C) 3b - 2c
D) -2a + 3b
E) -2a + 2b - 2c

Question 17

The following algebraic expression , can be classified as:

A) monomial
B) binomial
C) trinomial
D) multinomial
E) All choices are incorrect

Question 18

Evaluate: L(1 - d₁)(1 - d₂) for L = $1000, d₁ = 0.30, and d₂ = 0.20.

A) $440.00
B) $500.00
C) $1785.71
D) $560.00
E) $600.00

Question 19

Simplify and collect like terms:

A) 2y² - 3x²y + 5y³
B) 2xy - 3x²y + 5y³
C) 2y - 3x²y + 5y
D) 2y - 3x² + 5y
E) 2y - 3x²y + 5y³

Question 20

Simplify and collect like terms: 1 - (3x - xy + y) - (-x + y - 5xy)

A) 1 - 2x - 2y - 6xy
B) 1 - 2x - 2y + 6xy
C) 1 - 4x - 2y + 6xy
D) 1 - 2x - 2y + 4xy
E) 1 - 4x - 2y - 6xy

Question 21

Simplify the following:

A)
B)
C)
D)
E)

Question 22

Evaluate the following:

A) 14,857.17
B) 487.56
C) 3714.29
D) 60.945
E) 11.04

Question 23

Evaluate: -4(r - t) - (2r - 4t) for r = 1/2 and t = 1/4.

A) 1
B) 5
C) 3
D) -5
E) -1

Question 24

Simplify and collect like terms:

A) -0.7x² - .4x + 1.15
B) 0.7x² - .4x + 1.15
C) -0.7x² - .4x + .35
D) 0.7x² - .4x + .35
E) -0.7x² + .8x + 1.15

Question 25

Evaluate the following:

A) -5.857
B) -10.446
C) 5.857
D) 0.5857
E) 13.485

Question 26

Evaluate the following: 25^3/2

A) 8.6
B) 37.5
C) 125
D) 5
E) 625

Question 27

Simplify the following:

A) a⁰
B) a
C) a^-11
D) a^-5
E) a^-12

Question 28

Evaluate the following: 2.48832^1/5 =

A) 95.396217
B) 0.0104826
C) 1.2
D) 3.0
E) 0.8333333

Question 29

(5x - 2y)(x - 2y) =

A) 5x² - 12xy - 4y²
B) 5x² + 8xy - 4y²
C) 5x² - 12xy + 4y²
D) 5x² - 8xy + 4y²
E) 5x² + 12xy + 4y²

Question 30

Simplify and collect like terms:

A) 2.957x
B) 2.208x
C) 3.057x
D) 2.068x
E) 1.983x

Question 31

Evaluate the following:

A) -9.971
B) -22.579
C) 58.29
D) 9.971
E) 25.743

Question 32

Evaluate the following expression: P(1 + rt), for P = $1575, r = .055,

A) $39.87
B) $1614.87
C) $1973.71
D) $16,128
E) $724.96

Question 33

Simplify and collect like terms:

A) 3.076P
B) 3.018P
C) 2.787P
D) 3.532P
E) 2.956P

Question 34

Evaluate the following: -16^5/4

A) 32
B) 64
C) -64
D) -32
E) 10

Question 35

Evaluate the following: =

A) r⁹t⁴
B) r⁶t⁶
C) r⁶t⁷
D) r⁹t¹¹
E) r⁹t⁹

Question 36

Evaluate the following expression: 3x + 4y -6xy, for x = 2, y = -3

A) 30
B) -42
C) 54
D) -18
E) 24

Question 37

Evaluate the following:

A) 12.006
B) 698.137
C) 1.201
D) 36.006
E) 35.58

Question 38

Simplify the following:

A) 16a¹⁰b⁵
B) 2a¹⁰b⁵
C) 16a³b³
D) 2a⁵b⁵
E) 16a⁵b³

Question 39

Simplify: 8 - (2x + 4y - 3) - (4y + 10)

A) -8y - 2x + 21
B) -8y - 2x + 1
C) -8y - 2x - 2
D) -2x + 1
E) -2x + 21

Question 40

Evaluate the following:

A) 233.95
B) 6.888
C) 0.689
D) 23.395
E) 23.763

Question 41

Solve for the unknown rounded to the nearest dollar.

A) 1,500
B) 2,500
C) 1,750
D) 3,750
E) 875

Question 42

Calculate the result to the nearest cent given n = 3; i = .087 and R = $925

A) $18,716.57
B) $22,512.13
C) $5,341.55
D) $2,354.02
E) $2,158.21

Question 43

Calculate the result to four decimal places given r = 1.3 and t = 2.6

A) 1.0683
B) .0563
C) .0885
D) 1.2573
E) 6.2675

Question 44

Solve for the unknown rounded to the nearest cent.

A) 108.74
B) 98.44
C) 68.41
D) 15.25
E) 88.67

Question 45

Solve the following to four decimal places

A) 1.0390
B) 0.0678
C) 0.0412
D) 0.0390
E) 0.0098

Question 46

Solve for x: 2x + = x + 10

A)
B)
C)
D)
E)

Question 47

Calculate the final result to two decimal places, where f = $8.25

A) -15.22
B) - 18.22
C) 12.22
D) 15.22
E) 18.22

Question 48

Evaluate the following: =

A) r⁵
B) r^17/12
C) r¹²
D) r²
E) r³⁶

Question 49

Solve for x: 2/3 ( x + 3) = -1/2 (6 x + 20) + 15

A)
B)
C) 1.5
D)
E) 3.875

Question 50

Solve the following to four decimal places

A) 49.5768
B) 45.1526
C) 47.4774
D) 21.6818
E) 32.9871

Question 51

Calculate the result to two decimal places given t = 1.25

A) 4.43
B) 5.27
C) 3.85
D) 4.67
E) 3.10

Question 52

Solve for x and y:
x + y = 40
-x + y = -20

A) x = 30; y = 10
B) x = - 10; y = 30
C) x = - 30; y = - 10
D) x = - 60; y = 20
E) x = - 60; y = - 20

Question 53

Solve for x:

A) 6
B) -6
C) -10
D)
E) 10

Question 54

Solve for the unknown rounded to two decimal places

A) 1,875.13
B) 2,388.44
C) 3,960.51
D) 4,137.68
E) 5,408.77

Question 55

Calculate the final result to two decimal places, where z = .1515

A) .48
B) 2.65
C) 1.48
D) 3.22
E) 5.48

Question 56

(8²)(2^-4)( -2)² =

A) 1024
B) 256
C) 4
D) 48
E) 16

Question 57

Solve for x and y in the following pair of equations:
y = -0.2x + 4.2
X - 0.5y = 10

A) x = 11; y = 2
B) x = 2; y = 11
C) x = 11; y = 6.4
D) x = 6.45; y = 2.9
E) x = 6.4; y = 11

Question 58

Solve for x and y:
2x + 3y = 7
3x - y = 5

A) x = 6; y = 2
B) x = - 2; y = 1
C) x = - 2; y = - 1
D) x = 2; y = 1
E) x = 2; y = - 1

Question 59

Evaluate the following:

A)
B)
C)
D)
E) 1

Question 60

Calculate the final result to two decimal places, where x = $6.80

A) $26.28
B) $27.38
C) $28.48
D) $18.58
E) $30.28

Question 61

If actual sales of $18,000 were 36% of budgeted sales, what were the budgeted sales?

A) $50,000
B) $52,920
C) $25,920
D) $10,080
E) $46,080

Question 62

Bart purchased three-quarters of a 32% interest in a Swiss Chalet franchise for $270,000. What is implied value of the franchise?

A) $115,200
B) $632,800
C) $980,750
D) $1,125,000
E) $1,625,000

Question 63

Anders has $35,000 to invest. He invested part at 5.5% and part at 7%. His investments earned $2,195 total interest for the year. How much did Anders invest at each rate?

A) $17,000; $18,000
B) $18,000; $17,000
C) $20,000; $15,000
D) $15,000; $20,000
E) $10,000; $25,000

Question 64

At a United Way fund raiser, students sold cinnamon buns for $2 each or 3 for $5. They sold 500 all together, and raised $900. How many of the 3 for $5 were sold?

A) 100
B) 200
C) 300
D) 250
E) 150

Question 65

A company laid off 80% of its work force. The number of employees after the layoff is 3,000. How many employees were there before the layoff?

A) 5,400
B) 7,200
C) 3,600
D) 15,000
E) 3,750

Question 66

The commission on a transaction is 3% of the first $100,000 and 2% of the balance. What was the amount of a transaction where the commission charged was $10,100?

A) $225,000
B) $545,000
C) $310,000
D) $355,000
E) $455,000

Question 67

What is the range of y given the domain x = -3 to x = 5 for the equation -3x + y = 15?

A) 0 to 24
B) 6 to 30
C) 24 to 30
D) -6 to -3.3
E) 0 to 30

Question 68

A project manager needs to allocate a staff of 460 employees to a 3-stage project. Stage 2 must have 20% more staff than Stage 1. Stage 3 required 50% more than Stage 2. Determine the number of employees needed for stage 1, 2 and 3 respectively.

A) Stage 1 = 115; Stage 2 = 138; Stage 3 = 207
B) Stage 1 = 120; Stage 2 = 120; Stage 3 = 320
C) Stage 1 = 320; Stage 2 = 120; Stage 3 = 120
D) Stage 1 = 207; Stage 2 = 115; Stage 3 = 138
E) Stage 1 = 200; Stage 2 = 100; Stage 3 = 60

Question 69

A moving company charges an hourly rate plus a per kilometer rate. Sam paid $128.50 for his rental, having traveled 77Km over a 6 hour period. Taylor paid $205 for her rental, having traveled 140 km over a nine hour period. Determine the hourly rate and per Km rate charged by the rental company.

A) Hourly rate = $20; Km rate = $.25
B) Hourly rate = $18; Km rate = $.50
C) Hourly rate = $15; Km rate = $.50
D) Hourly rate = $12; Km rate = $.75
E) Hourly rate = $15; Km rate = $.75

Question 70

The stock market index decreased this month by one-thirteenth of last month's index. If this month's index is 2,400, what was last month's index?

A) 2,585
B) 2,320
C) 2,483
D) 2,600
E) 2,215

Question 71

Solve for the unknown rounded to two decimal places

A) 17.68
B) 24.67
C) -24.22
D) -65.11
E) -85.28

Question 72

It takes 40 minutes to produce product A and 60 minutes to produce product B. Last week 60 hours were used in manufacturing both products. A total of 140 units were produced. Determine the number of product A and B produced.

A) Product A = 100; Product B = 40
B) Product A = 40; Product B = 100
C) Product A =80; Product B = 60
D) Product A = 70; Product B = 70

Question 73

Ajax Corporation has $48,000 to spend on advertising and is considering radio, television and newspaper ads. For radio ads, Ajax will spend a quarter of what it will spend on newspaper ads. For television ads, it will also spend 70% of what it will spend on radio ads. How much will the company spend on radio, newspaper and television ads respectively?

A) radio = $8,421; newspaper = $33,684; television = $5,985
B) radio = $5,985; newspaper = $33,684; television = $8,421
C) radio = $33,684; newspaper= $5,985; television = $8,421
D) radio = $12,000; newspaper = $24,000; television = $12,000
E) radio = $6,000; newspaper = $30,000; television = $12,000

Question 74

An employee earns $1,562.50 for 55 hours of work during last week. His regular workweek is 40 hours and he gets overtime at time and one-half the regular rate of pay. What is the regular hourly rate of pay?

A) $37.50
B) $28.41
C) $42.61
D) $58.59
E) $25.00

Question 75

Solve for x:

A) 13.9082
B) 13.8996
C) 14.8148
D) 25.0000
E) 225.0000

Question 76

Stavros sells gold and green fabric in his drapery store. He buys the same quantity of both each quarter for $18 per metre for the gold fabric and $20 for the green fabric. His last order totalled $2,290. The supplier has advised Stavros that the gold fabric will increase by 20% and the green fabric by 25%, and his total order for the next quarter will be $2813. How many metres of gold fabric does Stavros order each quarter?

A) 65
B) 56
C) 85
D) 55
E) 25

Question 77

The retail price of a packaged CD is $60.00, which includes a markup of 150% of cost. What is the cost price of the CD?

A) $40
B) $24
C) $36
D) $20
E) $32

Question 78

Sam has $20,000 to invest. He invested part at 5% and part at 6%. His investments earned $1,120 total interest for the year. How much did Sam invest at each rate?

A) $12,000; $8000
B) $10,000; $10,000
C) $6000; $14,000
D) $14,000; $6000
E) $8000; $12,000

Question 79

Tickets for the school play were $3 for students and $5 for all others. The box office sold 750 tickets for a total of $3,200. How many student tickets were sold?

A) 475
B) 275
C) 500
D) 250
E) 300

Question 80

The retail price of a sweater is $161.00, which includes a markup of 40% of cost. What is the cost price of the sweater?

A) $115
B) $70.84
C) $64.40
D) $96.60
E) $100.63