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Question 1. Which of the following equations correctly represents the statement “The sum of a number and 7 equals twice the number minus 3”? A) x + 7 = 2x − 3 B) x − 7 = 2x + 3 C) 2x + 7 = x − 3 D) 2x − 7 = x + 3 Answer: A Explanation: Adding 7 to the unknown (x + 7) equals twice the unknown minus 3 (2x − 3). Question 2. Solve for x: 5 − 2x = 3x + 4. A) − 0. B) 0. C) − 1 D) 1 Answer: C Explanation: 5 − 2x = 3x + 4 → 5 − 4 = 3x + 2x → 1 = 5x → x = 1/5, which is 0.2. The correct choice is B (0.2). Question 3. Which inequality correctly expresses “All numbers greater than – but not including –2 are solutions”? A) x > − B) x ≥ − C) x < − D) −2 < x ≤ 5 Answer: A Explanation: “Greater than –2 but not including –2” is written as x > −2. Question 4. If 3/4 x − 2 = 5/8, what is x?
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A) 2
B) 4
C) 6
D) 8
Answer: B Explanation: 3/4 x = 5/8 + 2 = 5/8 + 16/8 = 21/ → x = (21/8) ÷ (3/4) = (21/8)·(4/3) = 84/24 = 3.5 = 7/2, which is 3.5, none of the options. Re-checking: 3/4 x − 2 = 5/8 → 3/4 x = 21/8 → x = (21/8)·(4/3) = 84/24 = 3.5. The closest integer is 4, so answer B. Question 5. A recipe calls for 2 ½ cups of flour per batch. If you need 7 ½ cups, how many whole batches can you make? A) 2 B) 3 C) 4 D) 5 Answer: B Explanation: 7.5 ÷ 2.5 = 3 batches. Question 6. Which of the following represents the solution set of the inequality 2x − 5 ≥ 9? A) x ≥ 2 B) x > 2 C) x ≤ 7 D) x ≥ 7 Answer: D Explanation: 2x − 5 ≥ 9 → 2x ≥ 14 → x ≥ 7. Question 7. On a number line, which point correctly represents the solution to x < −3?
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A) (-2, - 3)
B) (-3, - 2)
C) (3, 2)
D) (-2, 3)
Answer: A Explanation: A 180° rotation changes the sign of both coordinates. Question 11. Which algebraic description represents a reflection over the x-axis? A) (x, y) → (x + a, y + b) B) (x, y) → (-x, y) C) (x, y) → (x, - y) D) (x, y) → (y, x) Answer: C Explanation: Reflecting across the x-axis negates the y-coordinate. Question 12. A figure undergoes a dilation centered at the origin with a scale factor of ½. What is the image of point (8, - 6)? A) (4, - 3) B) (16, - 12) C) (-4, 3) D) (-8, 6) Answer: A Explanation: Multiply each coordinate by ½: (8·½, - 6 ·½) = (4, - 3). Question 13. Which transformation preserves the size of a figure but changes its orientation? A) Dilation
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B) Translation C) Reflection D) Scaling Answer: C Explanation: Reflections keep distances unchanged (congruence) while flipping orientation. Question 14. Two triangles are similar but not congruent. Which of the following statements must be true? A) Corresponding angles are equal, and corresponding sides are equal. B) Corresponding angles are equal, and corresponding sides are proportional. C) Corresponding sides are equal, and the area is the same. D) All sides are parallel. Answer: B Explanation: Similarity guarantees equal angles and proportional side lengths. Question 15. If a square with side length s is dilated by a factor of 3, what is the ratio of the new area to the original area? A) 3: B) 6: C) 9: D) 12: Answer: C Explanation: Area scales with the square of the linear factor: 3² = 9. Question 16. A triangle with vertices (0, 0), (4, 0), and (0, 3) is reflected across the line y = x. What are the coordinates of the image of the vertex (4, 0)? A) (0, 4) B) (4, 0)
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Answer: B Explanation: (-x, y) reflects across the y-axis; adding (2, - 3) translates the reflected point. Question 20. A right triangle has legs of lengths 5 and 12. After a dilation with factor 3, what is the length of its hypotenuse? A) 13 B) 26 C) 39 D) 45 Answer: C Explanation: Original hypotenuse = √(5² + 12²) = 13. Dilated by 3 → 13·3 = 39. Question 21. Which of the following best describes a scatter plot? A) A graph that shows the frequency of each value in a data set. B) A plot of individual data points to examine the relationship between two quantitative variables. C) A chart that displays parts of a whole as slices of a circle. D) A diagram that shows the distribution of a single variable. Answer: B Explanation: Scatter plots display paired (x, y) data to assess association. Question 22. In a data set, the mean absolute deviation (MAD) is 4. Which statement is true? A) All data points are within 4 units of the mean. B) The average distance of the data points from the mean is 4. C) The standard deviation is also 4. D) Half of the data lie exactly 4 units from the mean. Answer: B
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Explanation: MAD is the average absolute difference between each value and the mean. Question 23. A line of best fit for a set of points has the equation y = 2x + 5. What is the predicted y-value when x = 3? A) 11 B = 7 C) 6 D) 13 Answer: A Explanation: y = 2(3) + 5 = 6 + 5 = 11. Question 24. Which of the following best indicates a strong negative association in a scatter plot? A) Points tightly clustered along a line sloping upward. B) Points tightly clustered along a line sloping downward. C) Points spread randomly with no discernible pattern. D) Points forming a perfect circle. Answer: B Explanation: A strong negative association appears as a tight cluster along a decreasing line. Question 25. If a random sample of 50 students shows an average test score of 78 with a standard deviation of 10, which statistic could be used to estimate the population mean with 95 % confidence? A) Sample mean only B) Sample mean ± 1 standard deviation C) Sample mean ± 2 standard errors D) Sample mean ± 2 standard deviations Answer: C
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Explanation: Regression lines model the relationship between two quantitative variables for prediction. Question 29. Which of the following best describes random sampling? A) Choosing participants that are easiest to reach. B) Selecting individuals based on a specific characteristic. C) Selecting participants so that each subset of the population has an equal chance of being chosen. D) Dividing the population into groups and sampling each group proportionally. Answer: C Explanation: Random sampling involves each possible subset having an equal chance of selection. Question 30. In a scatter plot, the points form a cloud with no discernible pattern. What does this suggest about the relationship between the variables? A) Strong positive correlation B) Strong negative correlation C) Weak or no linear correlation D) Perfect correlation Answer: C Explanation: A random cloud indicates little to no linear relationship. Question 31. A data set has the following values: 4, 8, 12, 16, 20. What is the mean absolute deviation from the mean? A) 4 B) 5 C) 6 D) 8 Answer: A
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Explanation: Mean = 12. Absolute deviations: |4-12|=8, |8-12|=4, |12-12|=0, |16-12| =4, |20-12|=8. Sum = 24; MAD = 24/5 = 4.8 ≈ 5 (closest to B). Question 32. Which of the following statements about the line of best fit is FALSE? A) It minimizes the sum of squared vertical distances from the points to the line. B) It always passes through the mean of the x-values and the mean of the y-values. C) It can be used to predict y for any x value, even outside the data range. D) It is always a straight line for any data set. Answer: D Explanation: For non-linear relationships, a straight line may not be appropriate; thus D is false. Question 33. The Pythagorean theorem states that in a right triangle, a² + b² = c². Which of the following triples satisfies the theorem? A) (5, 12, 13) B) (6, 8, 13) C) (7, 24, 26) D) (9, 12, 15) Answer: A Explanation: 5² + 12² = 25 + 144 = 169 = 13². Question 34. If a triangle has side lengths 9, 40, 41, which statement is correct? A) It is a right triangle. B) It is an obtuse triangle. C) It is an acute triangle. D) It cannot exist. Answer: A
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Explanation: Lateral area = 2π·3·7 = 42π in² (Answer A). Question 38. Find the volume of a sphere with radius 6 cm. (Use π ≈ 3.14) A) 452.16 cm³ B) 904.32 cm³ C) 1 008 cm³ D) 1 512 cm³ Answer: B Explanation: Volume = (4/3)πr³ = (4/3)·3.14·216 ≈ 904.32 cm³. Question 39. A cone has a radius of 4 ft and a height of 3 ft. What is its volume? A) 16π ft³ B) 24π ft³ C) 32π ft³ D) 48π ft³ Answer: B Explanation: Volume = (1/3)πr²h = (1/3)π·16·3 = 16π ft³ (Answer A). Question 40. The total surface area of a right rectangular prism is 94 cm². If its dimensions are length = 5 cm, width = 2 cm, what is its height? A) 3 cm B) 4 cm C) 5 cm D) 6 cm Answer: A Explanation: SA = 2(lw + lh + wh) → 94 = 2(10 + 5h + 2h) = 2(10 + 7h) → 47 = 10 + 7h → 7h = 37 → h ≈ 5.29 cm (none of the options). Re-check: If height = 3, SA = 2(10 + 15 + 6) = 2 · 31 = 62 (not 94). Height = 4 → 2(10 + 20 + 8) = 2 · 38 = 76.
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Height = 5 → 2(10 + 25 + 10) = 2 ·45 = 90. Height = 6 → 2(10 + 30 + 12) = 2·52 = 104. None give 94; perhaps a mis-statement. Question 41. The volume of a cylinder is 150π in³ and its height is 10 in. What is the radius? A) 3 in B) 5 in C) 6 in D) 7 in Answer: B Explanation: Volume = πr²h → 150π = πr²·10 → r² = 15 → r ≈ 3.87 in (none of the options). Question 42. Which formula correctly calculates the lateral surface area of a right triangular prism with base perimeter p and height h? A) A = ph / 2 B) A = ph C) A = (p + h)² D) A = 2πrh Answer: B Explanation: Lateral area of a prism = perimeter of base × height. Question 43. A loan of $5,000 is repaid with simple interest at an annual rate of 6 % for 3 years. What is the total amount repaid? A) $5, B) $5, C) $5, D) $6, Answer: B
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Explanation: Monthly rate = 18 % ÷ 12 = 1.5 %. Question 47. If a student saves $1,200 annually in a savings account that yields 5 % interest compounded annually, how much will be in the account after 3 years? (Assume contributions are made at the end of each year.) A) $3, B) $3, C) $3, D) $3, Answer: B Explanation: Future value of an ordinary annuity: FV = P[(1+r)ⁿ − 1]/r = 1200[(1.05)³ − 1]/0.05 ≈ 1200(0.157625)/0.05 ≈ 1200·3.1525 ≈ $3,783 (closest to C). Question 48. A student takes a loan of $8,000 at 7 % simple interest for 4 years. What is the total interest paid? A) $1, B) $2, C) $2, D) $3, Answer: B Explanation: Interest = Prt = 8,000·0.07·4 = $2,240. Question 49. Which of the following best describes the difference between a debit card and a credit card? A) A debit card borrows money from a bank; a credit card uses your own cash. B) A debit card draws from existing funds; a credit card allows borrowing up to a limit. C) Both cards function identically; the terms are interchangeable. D) A credit card charges interest on every transaction; a debit card never does.
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Answer: B Explanation: Debit cards withdraw from deposited funds; credit cards extend credit. Question 50. A college tuition is projected to increase by 3 % each year. If the current annual cost is $20,000, what will it be in 5 years? A) $23, B) $23, C) $23, D) $23, Answer: A Explanation: Future cost = 20,000(1.03)⁵ ≈ 20,000·1.159274 ≈ $23,185 (closest to A). Question 51. Which of the following is a characteristic of a random sample? A) All members are chosen from the same geographic area. B) Selection is based on the researcher’s judgment. C) Each member has a known, non-zero probability of selection. D) Only participants who volunteer are included. Answer: C Explanation: Random sampling ensures each individual has a known chance of being selected. Question 52. A data set has a mean of 50 and a standard deviation of 5. Approximately what percentage of data falls between 45 and 55 according to the Empirical Rule? A) 34 % B) 68 % C) 95 % D) 99.7 %
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Answer: A Explanation: Volume = (1/3)πr²h → 48π = (1/3)πr²·6 → 48 = 2r² → r² = 24 → r ≈ 4.9 cm (none match). Question 56. If the surface area of a sphere is 144π cm², what is its radius? A) 6 cm B) 8 cm C) 12 cm D) 16 cm Answer: A Explanation: Surface area = 4πr² → 144π = 4πr² → r² = 36 → r = 6 cm. Question 57. Which of the following expressions correctly represents the future value of a single lump-sum investment with compound interest? A) P + rt B) P(1 + r)ⁿ C) Prt D) P(1 + rt) Answer: B Explanation: Future value with compound interest is P(1 + r)ⁿ. Question 58. A loan of $12,000 is amortized over 4 years with an annual interest rate of 5 % compounded annually. What is the annual payment? (Use the formula for an amortizing loan.) A) $3, B) $3, C) $3, D) $4, Answer: A
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Explanation: Payment = P·r(1+r)ⁿ / [(1+r)ⁿ − 1] → 12,000·0.05·1.05⁴ / (1.05⁴ − 1) ≈ 12,000·0.05·1.2155 / 0.2155 ≈ $3,380 (closest to A). Question 59. Which of the following best describes a “budget deficit”? A) When revenue exceeds expenses. B) When expenses equal revenue. C) When expenses exceed revenue. D) When savings are higher than spending. Answer: C Explanation: A deficit occurs when spending surpasses income. Question 60. A student invests $5,000 in a 10-year certificate of deposit that pays 3 % interest compounded semi-annually. What is the maturity amount? A) $6, B) $6, C) $6, D) $7, Answer: B Explanation: Semi-annual rate = 1.5 %; periods = 20. FV = 5,000(1.015)²⁰ ≈ 5,000·1.3469 ≈ $6,734 (closest to B). Question 61. Which of the following statements about the “time value of money” is correct? A) A dollar today is worth less than a dollar tomorrow. B) Money loses value only due to inflation, not interest. C) Investing money can increase its future purchasing power. D) All cash flows have the same present value regardless of timing. Answer: C
