Mixed Deck — All COMPASS Topics Flashcards

What is 40% written as a fraction in lowest terms?

Answer: 2/5

40% = 40/100 = 2/5 after dividing by the GCF of 20.

What is the domain of f(x) = 1/(x − 4)?

Answer: All real numbers except x = 4

The denominator cannot equal zero, so x − 4 ≠ 0, meaning x ≠ 4.

If f(x) = 2x² − 3x + 1, what is f(2)?

Answer: 3

f(2) = 2(4) − 3(2) + 1 = 8 − 6 + 1 = 3.

What is the slope of a horizontal line?

Answer: 0

A horizontal line has no vertical change (rise = 0), so slope = rise/run = 0.

A circle has the equation x² + y² = 25. What is its radius?

Answer: 5

In the standard form x² + y² = r², we have r² = 25, so r = √25 = 5.

Read the following passage and answer the question Technology is rapidly expanding the scope of capabilities for both professional and personal use; such is the case with smart phones. Professionals now have devices available to them capable of digital media, internet access, phone communication, multi-person scheduling and office tools for documents and presentations. Businesspeople that are often mobile may maximize the use of these critical features on smart phones. Individuals who simply enjoy the luxury of multi-function devices often use these devices for frivolous pursuits such as downloading catchy ring tones, instant messaging about the latest gossip and looking up the world record for most cans crushed on one’s head during the Superbowl. This fusion of capabilities and increased availability of such devices could be a sign of a growing blend in society between work and personal life, or individuals could simply be taking a luxurious approach to their connectivity in personal lives. What is the purpose of the conclusion sentence?

Answer: Present two possible explanations for the growing popularity of smart phones was correct.

The conclusion sentence states: 'This fusion of capabilities... could be a sign of a growing blend... or individuals could simply be taking a luxurious approach...' This structure clearly presents two distinct possibilities or interpretations for the observed trends in smartphone popularity. It offers alternative explanations rather than a definitive statement or prediction.

Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. J̲e̲w̲e̲l̲r̲y̲ ̲i̲s̲ ̲a̲n̲ ̲a̲c̲c̲e̲s̲s̲o̲r̲y̲ ̲u̲s̲e̲d̲ ̲b̲y̲ ̲m̲e̲m̲b̲e̲r̲s̲ ̲o̲f̲ ̲a̲l̲l̲ ̲c̲l̲a̲s̲s̲e̲s̲ ̲i̲n̲c̲l̲u̲d̲i̲n̲g̲ ̲w̲a̲t̲c̲h̲e̲s̲, ̲n̲e̲c̲k̲l̲a̲c̲e̲s̲ ̲a̲n̲d̲ ̲e̲a̲r̲r̲i̲n̲g̲s̲.

Answer: Jewelry, including watches, necklaces and earrings, is an accessory used by members of all classes.

The original sentence is grammatically correct as written. The plural subject 'Fraternities' correctly agrees with the plural verb 'are.' Additionally, the infinitive phrases 'to make friends' and 'learn important lessons' maintain proper parallel structure, ensuring the sentence is clear and well-formed.

If 0.05z = 1, then z =

Answer: 20

To solve for z, you need to isolate it by dividing both sides of the equation by 0.05. So, z = 1 / 0.05. Dividing 1 by 0.05 (or 1 by 5/100) gives you 1 * (100/5), which equals 20.

Determine whether the underlined portion of the sentence is correct or whether it needs to be revised. F̲o̲r̲ ̲h̲o̲m̲e̲s̲ ̲i̲n̲ ̲t̲y̲p̲i̲c̲a̲l̲l̲y̲ ̲c̲o̲l̲d̲e̲r̲ ̲g̲e̲o̲g̲r̲a̲p̲h̲i̲c̲ ̲r̲e̲g̲i̲o̲n̲s̲, it is particularly important to have effective and efficient heating systems.

Answer: For homes in typically cold geographic regions

The word 'colder' is a comparative adjective, implying a comparison to something else. However, the sentence describes regions that are inherently cold, not necessarily colder than some other implied region. Using the absolute adjective 'cold' is more appropriate and concise in this context, as 'typically cold' accurately describes the nature of the regions without an unnecessary comparison.

Solve the inequality: 2x − 5 > 9

Answer: x > 7

Add 5: 2x > 14, then divide by 2: x > 7.

A store sells pens at 3 for $1.50. How much do 10 pens cost?

Answer: $5.00

Each pen costs $0.50, so 10 pens cost 10 × $0.50 = $5.00.

Which equation represents a line parallel to y = 2x + 1?

Answer: y = 2x − 5

Parallel lines have equal slopes; the original slope is 2, so y = 2x − 5 is parallel.

Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Even though I have seen the movie countless times, I still l̲a̲u̲g̲h̲e̲d̲ ̲w̲h̲e̲n̲ ̲t̲h̲e̲ ̲s̲h̲e̲r̲i̲f̲f̲ ̲t̲h̲r̲o̲w̲s̲ ̲h̲i̲s̲ ̲m̲u̲g̲.

Answer: laugh when the sheriff throws his mug.

The phrase 'Even though I have seen the movie countless times' indicates a recurring action or a present state of familiarity. Therefore, the main clause should use the present tense ('I still laugh') to reflect the ongoing nature of the reaction. The present tense 'throws' for the sheriff's action is also appropriate for describing a recurring event within the movie.

Eddie is 7 years older than Brian. If Brian is x years old, then how old was Eddie 11 years ago?

Answer: x-4

We can model this by getting Eddie’s age now and then figuring out how old he was 11 years ago. Right now, he is x+7 . Eleven years ago, Eddie was x + 7 -11 = x - 4 years old. This is answer B. a. The correct calculation should be x+ 7 (to get Eddie’s age now) - 11 , which is x - 4 . b. Correct c. This is an incorrect calculation of Eddie’s present age. d. This response does not relate their ages properly. e. This also does not express their age relationship properly.

(x+3)(x+5) = A. x2+16x +8 B. x2+16x+15 C. x2+8x+15 D. x2+8x+8

Answer: C

Use the FOIL method (First, Outside, Inside, Last) to solve. X2 +3x +5x + 3x5

Which sentence correctly uses the word 'despite'?

Answer: Despite the rain, she went out.

'Despite' is followed directly by a noun or noun phrase, never 'of' or a clause with a subject and verb.

Evaluate: −4 + (−6) − (−3)

Answer: −7

−4 + (−6) − (−3) = −4 − 6 + 3 = −7.

Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Concerns about global warming have grown into actual efforts sanctioned by non-governmental organizations and governments that not only work to u̲n̲d̲e̲r̲s̲t̲a̲n̲d̲ ̲g̲l̲o̲b̲a̲l̲ ̲w̲a̲r̲m̲i̲n̲g̲ ̲a̲n̲d̲ ̲a̲l̲s̲o̲ ̲t̲o̲ ̲p̲r̲e̲v̲e̲n̲t̲ ̲i̲t̲.

Answer: understand global warming but also to prevent its growth.

The correlative conjunction 'not only... but also' is required for proper grammatical structure when presenting two parallel ideas. Additionally, 'prevent its growth' is more specific and accurate than 'prevent it,' as the efforts are aimed at preventing the *increase* or *worsening* of global warming, not its complete eradication. The possessive 'its' is correctly used here.

Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Since the work force is becoming increasingly competitive in light of technological advances and outsourcing, t̲h̲e̲r̲e̲f̲o̲r̲e̲, ̲i̲t̲ ̲i̲s̲ ̲e̲v̲e̲n̲ ̲m̲o̲r̲e̲ ̲b̲a̲s̲i̲c̲ ̲f̲o̲r̲ ̲s̲t̲u̲d̲e̲n̲t̲s̲ ̲t̲o̲ ̲c̲o̲m̲p̲l̲e̲t̲e̲ ̲h̲i̲g̲h̲ ̲s̲c̲h̲o̲o̲l̲ ̲a̲n̲d̲ ̲a̲t̲t̲a̲i̲n̲ ̲a̲t̲ ̲l̲e̲a̲s̲t̲ ̲a̲ ̲b̲a̲c̲h̲e̲l̲o̲r̲’s̲ ̲d̲e̲g̲r̲e̲e̲.

Answer: it is even more basic for students to complete high school and attain at least a bachelor’s degree.

The original sentence incorrectly uses 'therefore' after an introductory clause beginning with 'Since.' 'Since' already establishes a cause-and-effect relationship, making 'therefore' redundant and grammatically incorrect in this context. Option E correctly removes the unnecessary 'therefore,' allowing the main clause to logically follow the introductory 'Since' clause without repetition or grammatical error.

What are the solutions to x² + 4x + 4 = 0?

Answer: x = −2 (double root)

x² + 4x + 4 = (x + 2)² = 0, so x = −2 is a repeated root.