Accuplacer Practice Test: Video 1 Answers (25 Questions) — Questions and Answers
Question 1: Read: 'The author begins each chapter with a question to engage readers.' Why does the author do this?
- To list facts
- To end the book
- To capture readers' interest (Correct answer)
- To confuse readers
Correct answer: To capture readers' interest
Starting with a question is a technique to engage and interest readers.
Question 2: What is the best summary of: 'Exercise improves health, boosts mood, and increases energy'?
- Exercise is difficult
- Exercise is expensive
- Exercise wastes time
- Exercise has many benefits (Correct answer)
Correct answer: Exercise has many benefits
The sentence lists several positive effects, so exercise has many benefits.
Question 3: Read: 'The instructions were so vague that no one knew what to do.' What does 'vague' mean?
- Loud
- Detailed
- Unclear (Correct answer)
- Clear
Correct answer: Unclear
'Vague' means not clearly expressed, which is why no one understood.
Question 4: Read: 'The recipe calls for fresh herbs, but dried ones may be substituted.' What does 'substituted' mean?
- Removed
- Used in place of (Correct answer)
- Cooked
- Bought
Correct answer: Used in place of
'Substituted' means used as a replacement for something else.
Question 5: What is the meaning of the word 'abundant' in 'The garden had an abundant supply of vegetables'?
- Expensive
- Rotten
- Plentiful (Correct answer)
- Scarce
Correct answer: Plentiful
'Abundant' means existing in large quantities, or plentiful.
Question 6: A reader encounters the word 'benevolent' and notices the root 'bene.' This root suggests a meaning related to:
- Good or well (Correct answer)
- Bad or evil
- Time
- Distance
Correct answer: Good or well
The root 'bene' means good, so 'benevolent' means kind or well-meaning.
Question 7: The tone of a passage that uses words like 'wondrous,' 'glorious,' and 'breathtaking' is best described as:
- Mournful
- Indifferent
- Critical
- Enthusiastic (Correct answer)
Correct answer: Enthusiastic
Strongly positive descriptive words create an enthusiastic tone.
Question 8: Which word best completes the sentence: 'Despite the ___ evidence, the jury reached a quick verdict'?
- abundant
- overwhelming
- clear
- scant (Correct answer)
Correct answer: scant
'Despite' signals contrast, so little evidence still led to a quick verdict.
Question 9: A passage states: 'The committee's decision, though widely criticized, ultimately proved prescient.' What does 'prescient' most nearly mean?
- Deeply unpopular
- Showing foresight (Correct answer)
- Hastily made
- Poorly reasoned
Correct answer: Showing foresight
'Prescient' means having foresight or accurately predicting the future.
Question 10: Which detail would best support a main idea that 'exercise improves memory'?
- A history of the Olympic Games
- A recipe for a sports drink
- A study showing runners scored higher on recall tests (Correct answer)
- A list of popular running shoes
Correct answer: A study showing runners scored higher on recall tests
A study linking running to better recall directly supports the claim.
Question 11: What is the y-intercept of the function f(x) = 3x² − 4x + 2?
Correct answer: 2
The y-intercept occurs at x = 0: f(0) = 3(0) − 4(0) + 2 = 2.
Question 12: Which of the following is a zero of f(x) = x³ − x² − 6x?
- x = 4
- x = 3 (Correct answer)
- x = −2
- x = 1
Correct answer: x = 3
Factor: x(x² − x − 6) = x(x − 3)(x + 2), so zeros are x = 0, x = 3, and x = −2.
Question 13: Solve the system: 2x + y = 7 and x − y = 2.
- x = 2, y = 3
- x = 4, y = −1
- x = 3, y = 1 (Correct answer)
- x = 1, y = 5
Correct answer: x = 3, y = 1
Add the two equations to eliminate y: 3x = 9, so x = 3; then y = 7 − 2(3) = 1.
Question 14: What is the domain of f(x) = 1/(x − 4)?
- All real numbers
- x ≠ −4
- x > 4
- x ≠ 4 (Correct answer)
Correct answer: x ≠ 4
The function is undefined when the denominator equals zero, i.e., when x = 4, so the domain is all real numbers except 4.
Question 15: What is the vertex of the parabola y = (x − 3)² + 5?
- (−3, 5)
- (3, −5)
- (−3, −5)
- (3, 5) (Correct answer)
Correct answer: (3, 5)
In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 5).
Question 16: Which of the following is equal to (x+3)(x2+3x−5)?
- x3+6x2+4x−15 (Correct answer)
- 2x3+4x2+x−10
- x3+4x2+6x−15
- x3−6x−4x+15
Correct answer: x3+6x2+4x−15
To expand the expression, use the distributive property (multiply each term in the first parenthesis by each term in the second). Multiply x by (x^2 + 3x - 5) to get x^3 + 3x^2 - 5x. Then, multiply 3 by (x^2 + 3x - 5) to get 3x^2 + 9x - 15. Combine these results: x^3 + 3x^2 - 5x + 3x^2 + 9x - 15. Finally, combine like terms: x^3 + (3x^2 + 3x^2) + (-5x + 9x) - 15, which simplifies to x^3 + 6x^2 + 4x - 15.
Question 17: −2⁄3 + 1⁄6 ⋅ (−2) = ____
- -1 (Correct answer)
- -1⁄3
- 2⁄3
- 1
Correct answer: -1
Following the order of operations (PEMDAS/BODMAS), first perform the multiplication: (1/6) * (-2) = -2/6, which simplifies to -1/3. Now the expression is -2/3 + (-1/3). Adding these fractions with a common denominator gives -3/3, which simplifies to -1.
Question 18: (-3)(2+6)⁄4 - 2 =
Correct answer: -8
Following the order of operations (PEMDAS/BODMAS), first solve the expression inside the parentheses: 2 + 6 = 8. Next, perform the multiplication in the numerator: (-3)(8) = -24. Then, divide by 4: -24 / 4 = -6. Finally, subtract 2 from the result: -6 - 2 = -8.
Question 19: x = 3 and x = -3 are both solutions to which of the following equations?
- x2+3x−9 = 0
- x2-9 = 0 (Correct answer)
- x2+9 = 0
- x−3 = 0
Correct answer: x2-9 = 0
To find the correct equation, substitute x=3 and x=-3 into each option. For option D, x² - 9 = 0, substituting x=3 gives 3² - 9 = 9 - 9 = 0, which is true. Substituting x=-3 gives (-3)² - 9 = 9 - 9 = 0, which is also true. This equation represents the difference of squares, (x-3)(x+3)=0, whose roots are indeed 3 and -3.
Question 20: Solve the following system of equations for (x,y), 3x+4y = 25, x−2y = 5
- (3, 1)
- (2, 5)
- (4, 3)
- (7, 1) (Correct answer)
Correct answer: (7, 1)
Using the elimination method, multiply the second equation (x - 2y = 5) by 2 to get 2x - 4y = 10. Now add this new equation to the first equation (3x + 4y = 25): (3x + 4y) + (2x - 4y) = 25 + 10, which simplifies to 5x = 35. Dividing by 5 gives x = 7. Substitute x = 7 into the second original equation: 7 - 2y = 5. Subtract 7 from both sides: -2y = -2. Dividing by -2 gives y = 1. Thus, the solution is (7, 1).
Question 21: What percentage of 128 is 96?
- 80%
- 75% (Correct answer)
- 65%
- 70%
Correct answer: 75%
To find what percentage of 128 is 96, divide the part (96) by the whole (128) and then multiply by 100%. The fraction 96/128 simplifies to 3/4 by dividing both numerator and denominator by their greatest common divisor, 32. Converting 3/4 to a decimal gives 0.75, and multiplying by 100% yields 75%. Thus, 96 is 75% of 128.
Question 22: Which of the following is the greatest?
- 0.65
- 0.62
- 0.67 (Correct answer)
- 0.668
Correct answer: 0.67
To compare decimals, align them by their decimal points and compare the digits from left to right. For 0.62, 0.65, 0.67, and 0.668, all start with '0.6'. Comparing the next digit, we have 2, 5, 7, and 6. Since 7 is the largest of these digits, 0.67 is the greatest number among the choices.
Question 23: If 2 1⁄4 + x = 5 1⁄8, then which of the following is true of x?
- It is greater than 1 and less than 2.
- It is greater than 2 and less than 3. (Correct answer)
- It is less than 1.
- It is greater than 5.
Correct answer: It is greater than 2 and less than 3.
To solve for x, first convert the mixed numbers to improper fractions: 2 1/4 = 9/4 and 5 1/8 = 41/8. The equation becomes 9/4 + x = 41/8. To isolate x, subtract 9/4 from both sides: x = 41/8 - 9/4. Find a common denominator for the subtraction, which is 8, so 9/4 becomes 18/8. Then, x = 41/8 - 18/8 = 23/8. Converting 23/8 back to a mixed number gives 2 7/8, which is greater than 2 and less than 3.
Question 24: 6⁄7 + 5⁄4 =
- 21⁄28
- 46⁄7
- 2 1⁄2
- 59⁄28 (Correct answer)
Correct answer: 59⁄28
To add fractions with different denominators, first find a common denominator. For 6/7 and 5/4, the least common multiple of 7 and 4 is 28. Convert the fractions: 6/7 becomes 24/28 (multiply numerator and denominator by 4), and 5/4 becomes 35/28 (multiply numerator and denominator by 7). Now, add the new fractions: 24/28 + 35/28 = 59/28. This is an improper fraction and can be left as such or converted to a mixed number (2 3/28).
Question 25: 75 is 60% of what number?
- 125 (Correct answer)
- 135
- 145
- 115
Correct answer: 125
This problem can be set up as an equation: 75 = 0.60 * x, where x is the unknown number. To solve for x, divide 75 by 0.60. Performing the division, 75 / 0.60 equals 125.
