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Computations Ultimate Exam
Question 1. What is the sum of (-7) and (12)? A) (-19) B) (-5) C) (5) D) (19) Answer: C Explanation: (-7+12 = 5). Question 2. Which of the following equals (-4 \times (-3))? A) (-12) B) (12) C) (-7) D) (7) Answer: B Explanation: The product of two negatives is positive; (-4 \times -3 = 12). Question 3. Evaluate (15 - (-9)). A) (-24) B) (-6) C) (6) D) (24) Answer: D Explanation: Subtracting a negative is adding: (15+9=24). Question 4. Which expression correctly represents the order of operations for ((8+2)^2 \div 5)? A) (8+2^2 \div 5) B) ((8+2)^2 \div 5) C) (8+(2^2 \div 5)) D) ((8+2)^{2\div5}) Answer: B Explanation: Parentheses first, then exponent, then division.
Computations Ultimate Exam
Question 5. Using the distributive property, simplify (3(4+5)). A) (12+5) B) (3\cdot4+3\cdot5) C) (7\cdot3) D) (3+4+5) Answer: B Explanation: (3(4+5)=3\cdot4+3\cdot5=12+15=27). Question 6. What is the absolute value of (-13)? A) (-13) B) (0) C) (13) D) (|-13|) Answer: C Explanation: Absolute value is the distance from zero, so (|-13|=13). Question 7. If (a = -2) and (b = 5), what is (a - b)? A) (-7) B) (7) C) (-3) D) (3) Answer: A Explanation: (-2 - 5 = -7). Question 8. Which of the following is undefined? A) (\frac{8}{2}) B) (\frac{-5}{-1}) C) (\frac{0}{5}) D) (\frac{7}{0}) Answer: D
Computations Ultimate Exam
C) (-18)
D) (18)
Answer: B Explanation: Dividing two negatives yields a positive; (-15 ÷ -3 = 5). Question 13. Evaluate (2^3 \times 2^2). A) (2^5) B) (2^6) C) (2^{1}) D) (2^{10}) Answer: A Explanation: When multiplying same bases, add exponents: (3+2=5). Question 14. Which of the following is the correct simplification of ((4 \times
- (4 \times 2)) using the distributive property? A) (4 \times (5+2)) B) ((4+5) \times (4+2)) C) (4 \times 7) D) Both A and C Answer: D Explanation: Both forms are equivalent: (4(5+2)=4\times7=28). Question 15. Find the value of (-(-8) + 3). A) (-5) B) (5) C) (-11) D) (11) Answer: B Explanation: The double negative becomes positive: (-(-8)=8); (8+3=11). Oops answer mismatch. Correct answer is (11). Answer: D Explanation: (-(-8)=8); (8+3=11).
Computations Ultimate Exam
Question 16. Which integer is the additive inverse of (-12)? A) (-12) B) (12) C) (0) D) (24) Answer: B Explanation: The additive inverse of a number (x) is (-x); for (-12) it is (12). Question 17. Compute the expression (6 - [2 - (3 - 5)]). A) (6) B) (8) C) (4) D) (2) Answer: B Explanation: Innermost parentheses: (3-5=-2); then (2-(-2)=4); finally (6- 4=2). Wait oversight: Actually (6 - [2 - (3 - 5)] = 6 - [2 - (-2)] = 6 - [2+2] = 6 - 4 = 2). So answer is D. Answer: D Explanation: Step-by-step evaluation gives (2). Question 18. If (x = -4), what is (|x| + x)? A) (-8) B) (0) C) (8) D) (-4) Answer: B Explanation: (|-4| = 4); (4 + (-4) = 0). Question 19. Which of the following statements is true? A) The product of a positive and a negative integer is positive. B) The sum of two negative integers is positive.
Computations Ultimate Exam
Question 23. Which expression is equivalent to (- (5 - 2))? A) (-5 + 2) B) (-5 - 2) C) (5 - 2) D) (-5 \times 2) Answer: A Explanation: Distribute the negative sign: (-5 + 2). Question 24. If (a = -3) and (b = 4), compute (a^2 + b^2). A) (7) B) (25) C) (-7) D) (-25) Answer: B Explanation: (a^2 = (-3)^2 = 9); (b^2 = 4^2 = 16); sum = 25. Question 25. What is the result of ((-12) + (-7) + 5)? A) (-14) B) (-24) C) (-2) D) (-4) Answer: A Explanation: (-12 + (-7) = -19); (-19 + 5 = -14). Question 26. Which of the following is the correct evaluation of (2 \times (
- 4)^2)? A) (2 \times 7^2 = 98) B) (2 \times 3 + 4^2 = 22) C) ((2 \times 3 + 4)^2 = 100) D) (2^{(3+4)^2} =) huge number Answer: A
Computations Ultimate Exam
Explanation: Parentheses first: (3+4=7); square: (7^2=49); multiply by 2: (98). Question 27. If (x = -5), what is (-x)? A) (-5) B) (5) C) (0) D) (-10) Answer: B Explanation: The negative of a negative is positive. Question 28. Compute ((-3)^2 - 4^2). A) (-7) B) (-1) C) (1) D) (7) Answer: B Explanation: ((-3)^2 = 9); (4^2 = 16); (9-16 = -7). Wait that gives (-7). So answer A. Answer: A Explanation: The correct subtraction yields (-7). Question 29. Which of the following is the additive identity for integers? A) (1) B) (-1) C) (0) D) Any integer Answer: C Explanation: Adding zero leaves any integer unchanged. Question 30. Evaluate (\frac{9}{-3} + (-2)). A) (-5)
Computations Ultimate Exam
B) (\frac{6}{35}) C) (\frac{2}{12}) D) (\frac{7}{15}) Answer: B Explanation: Multiply numerators and denominators: (\frac{2 \times 3}{5 \times 7}= \frac{6}{35}). Question 34. Divide (\frac{4}{9}) by (\frac{2}{3}). A) (\frac{2}{3}) B) (\frac{8}{27}) C) (\frac{6}{8}) D) (\frac{2}{9}) Answer: A Explanation: Dividing by a fraction multiplies by its reciprocal: (\frac{4}{9} times\frac{3}{2}= \frac{12}{18}= \frac{2}{3}). Question 35. Convert the mixed number (3\frac{2}{5}) to an improper fraction. A) (\frac{17}{5}) B) (\frac{13}{5}) C) (\frac{15}{5}) D) (\frac{12}{5}) Answer: A Explanation: (3\frac{2}{5}= \frac{3\times5+2}{5}= \frac{15+2}{5}= frac{17}{5}). Question 36. Which of the following is a proper fraction? A) (\frac{9}{4}) B) (\frac{7}{7}) C) (\frac{3}{8}) D) (\frac{12}{5}) Answer: C Explanation: A proper fraction has numerator less than denominator.
Computations Ultimate Exam
Question 37. Find the least common denominator (LCD) of (\frac{1}{4}) and (\frac{1}{6}). A) 10 B) 12 C) 24 D) 2 Answer: B Explanation: LCD is the smallest common multiple of 4 and 6, which is 12. Question 38. Add (\frac{0.75}{1}) and (\frac{1}{2}). Express the answer as a decimal. A) 1. B) 1. C) 1. D) 0. Answer: A Explanation: (\frac{0.75}{1}=0.75); (\frac{1}{2}=0.5); sum = 1.25. Question 39. Multiply (0.6) by (0.25). A) 0. B) 0. C) 1. D) 0. Answer: B Explanation: (6 \times 25 = 150); place two decimal places → (0.150). Question 40. Divide (4.8) by (0.3). A) 1. B) 16 C) 0. D) 48
Computations Ultimate Exam
B) 14%
C) 0.35%
D) 3.5%
Answer: A Explanation: (\frac{7}{20}=0.35); multiply by 100 → 35%. Question 45. A recipe calls for (\frac{3}{4}) cup of sugar. If you want to make half the recipe, how many cups of sugar are needed? A) (\frac{3}{8}) B) (\frac{1}{2}) C) (\frac{5}{8}) D) (\frac{3}{2}) Answer: A Explanation: Half of (\frac{3}{4}) is (\frac{3}{4}\times\frac{1}{2}= \frac{3} {8}). Question 46. Which of the following fractions is equivalent to the decimal (0.2\overline{7})? A) (\frac{5}{18}) B) (\frac{8}{30}) C) (\frac{5}{9}) D) (\frac{25}{90}) Answer: A Explanation: Let (x=0.2\overline{7}); (100x = 27.\overline{7}); subtract (x): (99x = 27); (x = \frac{27}{99}= \frac{3}{11}). Wait the options don't match. Actually (0.2\overline{7}=0.2777...). Compute fraction: (x=0.2777...); (10x=2.777...); (100x=27.777...); subtract: (90x=25); (x= frac{25}{90}= \frac{5}{18}). So answer A. Question 47. Convert the mixed number (6\frac{3}{10}) to a decimal. A) 6. B) 6. C) 6. D) 6.
Computations Ultimate Exam
Answer: C Explanation: (\frac{3}{10}=0.3); add to 6 → 6.3. Question 48. Which of the following is a terminating decimal? A) (\frac{1}{3}) B) (\frac{5}{8}) C) (\frac{7}{11}) D) (\frac{2}{7}) Answer: B Explanation: Fractions whose denominator (in lowest terms) has only 2s and 5s produce terminating decimals. Question 49. Find the decimal equivalent of (\frac{13}{40}). A) 0. B) 0. C) 0. D) 0. Answer: A Explanation: (13 ÷ 40 = 0.325). Question 50. Simplify (\frac{2}{3} \times \frac{9}{4}). A) (\frac{3}{2}) B) (\frac{6}{7}) C) (\frac{18}{12}) D) (\frac{5}{6}) Answer: A Explanation: Multiply numerators and denominators: (\frac{2 \times 9}{3 \times 4}= \frac{18}{12}= \frac{3}{2}). Question 51. What is (\frac{5}{12}) expressed as a percent (rounded to the nearest whole percent)? A) 41%
Computations Ultimate Exam
Explanation: Markup: (1.25); discount: (1.25 × 0.90 = 1.125) → 112.5% of original. Question 55. Find the original price if an item sells for $84 after a 20% discount. A) $ B) $ C) $ D) $ Answer: B Explanation: Let original be (x); (x × 0.80 = 84); (x = 84 ÷ 0.8 = 105). Question 56. A car’s value depreciates 15% each year. If the current value is $12,000, what will it be after one year? A) $10, B) $10, C) $11, D) $13, Answer: A Explanation: 15% of 12,000 = 1,800; subtract → 10,200. Question 57. Convert 45 miles per hour to feet per second (1 mile = 5280 ft, 1 hour = 3600 sec). A) 66 ft/s B) 70 ft/s C) 72 ft/s D) 80 ft/s Answer: C Explanation: (45 \times \frac{5280}{3600}=45 \times 1.4667≈66). Wait compute precisely: 5280/3600 = 1.4667; 45×1.4667≈66.0. So answer A. Answer: A Explanation: The conversion yields about 66 ft/s.
Computations Ultimate Exam
Question 58. What is the ratio of 3 centimeters to 0.5 meters, expressed in simplest integer form? A) 3: B) 6: C) 3:0. D) 6: Answer: B Explanation: Convert 0.5 m = 50 cm; ratio 3:50 simplifies dividing by 1? Actually 3:50 cannot simplify. Multiply both sides by 2 to avoid decimal: 6:100 → simplify dividing by 2 → 3:50. None of the options match. Let's re-evaluate: Desired ratio in integer terms: 3 cm to 0.5 m = 3 cm to 50 cm = 3:50 (already simplest). Option not present; maybe they expect 6:100 simplified to 3:50, still not listed. Choose closest: 6:5 is wrong. We'll adjust question. Revised Question 58. What is the ratio of 3 centimeters to 0.5 meters, expressed as a fraction in simplest form? A) (\frac{3}{5}) B) (\frac{3}{50}) C) (\frac{6}{5}) D) (\frac{1}{10}) Answer: B Explanation: 0.5 m = 50 cm, so ratio = (3/50). Question 59. If 5 pencils cost $2.25, what is the unit price per pencil? A) $0. B) $0. C) $0. D) $0. Answer: B Explanation: $2.25 ÷ 5 = $0.45. Wait that's $0.45, option C. Answer: C Explanation: Dividing total cost by quantity gives $0.45 per pencil.
Computations Ultimate Exam
Question 63. If a quantity is reduced by 30% and the result is 70, what was the original quantity? A) 91 B) 100 C) 110 D) 130 Answer: B Explanation: Let original be (x); (0.70x = 70); (x = 100). Question 64. A store offers a 25% discount on an item whose sale price after discount is $120. What was the original price? A) $ B) $ C) $ D) $ Answer: C Explanation: Let original (p); (p × 0.75 = 120); (p = 120 ÷ 0.75 = 160). Question 65. What is 18% of 250? A) 35 B) 40 C) 45 D) 50 Answer: C Explanation: 0.18 × 250 = 45. Question 66. A population grew from 2,400 to 2,880. What is the percent increase? A) 15% B) 20% C) 25%
Computations Ultimate Exam
D) 30%
Answer: B Explanation: Increase = 480; (480 ÷ 2400 = 0.20) → 20%. Question 67. If 3/5 of a number is 27, what is the number? A) 45 B) 50 C) 60 D) 75 Answer: C Explanation: Let (n); (\frac{3}{5}n = 27); (n = 27 × \frac{5}{3}=45). Wait that yields 45 (option A). So answer A. Answer: A Explanation: Solving gives 45. Question 68. A 30% tip on a $45 restaurant bill is: A) $12. B) $13. C) $14. D) $15. Answer: B Explanation: 0.30 × 45 = 13.5. Question 69. Find the percent decrease when a price drops from $80 to $68. A) 12% B) 14% C) 15% D) 20% Answer: A Explanation: Decrease = $12; (12 ÷ 80 = 0.15) → 15% (option C). Actually that is 15%, not 12. So answer C. Answer: C
