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Question 1. What is the sum of (-\dfrac{3}{4}) and (\dfrac{5}{8})? A) (-\dfrac{1}{8}) B) (\dfrac{1}{8}) C) (\dfrac{1}{2}) D) (-\dfrac{1}{2}) Answer: B Explanation: Convert to a common denominator: (-\dfrac{6}{8}+\dfrac{5}{8}= - \dfrac{1}{8}). The correct sum is (-\dfrac{1}{8}); however the answer choice matching the calculation is B) (\dfrac{1}{8}) – a typo was made; the correct answer should be A) (-\dfrac{1}{8}). (Correct answer: A) (-\dfrac{1}{8}).) Question 2. Multiply (- 2 ) by (\dfrac{3}{5}). A) (-\dfrac{6}{5}) B) (\dfrac{6}{5}) C) (-\dfrac{5}{3}) D) (\dfrac{5}{3}) Answer: A Explanation: (- 2 \times \dfrac{3}{5}= - \dfrac{6}{5}). Question 3. Divide (\dfrac{7}{9}) by (-\dfrac{1}{3}). A) (-\dfrac{7}{3}) B) (\dfrac{7}{3}) C) (-\dfrac{21}{9}) D) (\dfrac{21}{9}) Answer: A Explanation: Dividing by a fraction is multiplying by its reciprocal: (\dfrac{7}{9}\times - 3 = - \dfrac{21}{9}= - \dfrac{7}{3}). Question 4. Which of the following statements is true for any rational number (p)? A) (p + ( - p ) = p) B) (p - ( - p ) = 0) C) (p + ( - p ) = 0) D) ((-p) - p = 2p) Answer: C Explanation: Adding a number to its additive inverse always yields 0. Question 5. Convert the fraction (\dfrac{13}{4}) to a decimal. A) 3.25 B) 3.5 C) 3.75 D) 4. Answer: A
Explanation: (13 ÷ 4 = 3.25). Question 6. A bank account has a balance of (-$45.60). After a deposit of ($120.40), what is the new balance? A) ($74.80) B) ($64.80) C) ($84.80) D) ($94.80) Answer: A Explanation: (-45.60 + 120.40 = 74.80). Question 7. The temperature drops from (15^\circ)C to (-5^\circ)C. What is the change in temperature? A) (-20^\circ)C B) (20^\circ)C C) (-10^\circ)C D) (10^\circ)C Answer: B Explanation: Change = final – initial = (- 5 - 15 = - 20 ); magnitude of change is (20^\circ)C. Question 8. Simplify (\dfrac{2}{3} - \left( - \dfrac{4}{9}\right)). A) (\dfrac{2}{9}) B) (\dfrac{10}{9}) C) (\dfrac{8}{9}) D) (\dfrac{14}{9}) Answer: B Explanation: Subtracting a negative is adding: (\dfrac{2}{3} + \dfrac{4}{9}= \dfrac{6}{9}+\dfrac{4}{9}= \dfrac{10}{9}). Question 9. If (x = - \dfrac{5}{2}) and (y = \dfrac{3}{4}), what is (xy)? A) (-\dfrac{15}{8}) B) (\dfrac{15}{8}) C) (-\dfrac{5}{8}) D) (\dfrac{5}{8}) Answer: A Explanation: Multiply numerators and denominators: (- 5 \times 3 = - 15 ); (2 \times 4 = 8). Question 10. Which operation is the inverse of subtraction? A) Addition B) Multiplication C) Division D) Exponentiation
Answer: A Explanation: Speed = distance ÷ time, so (d = 55t); constant of proportionality = 55. Question 15. If (y) is directly proportional to (x) and (y=12) when (x=4), what is (y) when (x=9)? A) 18 B) 24 C) 27 D) 30 Answer: C Explanation: Constant (k = y/x = 12/4 =3). Then (y = 3x = 3(9)=27). Question 16. A map uses a scale of 1 cm : 5 km. If two cities are 7 cm apart on the map, what is the actual distance? A) 10 km B) 20 km C) 30 km D) 35 km Answer: D Explanation: 1 cm = 5 km, so 7 cm = 7×5 = 35 km. Question 17. The price of a notebook is proportional to the number of pages. If a 120‑page notebook costs $6, how much would a 250‑page notebook cost? A) $10 B) $11 C) $12 D) $ Answer: B Explanation: Unit price = $6 ÷ 120 = $0.05 per page. For 250 pages: 250×0.05 = $12.5. None of the choices match; the nearest correct answer is C) $12. (Correct answer: C.) Question 18. Which equation represents a proportional relationship between total cost (C) and number of items (n) when each item costs $4.75? A) (C = 4.75 + n) B) (C = 4.75n) C) (C = n - 4.75) D) (C = \dfrac{n}{4.75}) Answer: B Explanation: Direct proportion: (C = (\text{price per item}) \times n).
Question 19. A store marks up the price of a jacket by 30%. If the original price is $80, what is the sale price? A) $104 B) $108 C) $112 D) $ Answer: A Explanation: Increase = 0.30 × 80 = 24. Sale price = 80 + 24 = $104. Question 20. A recipe calls for 2 cups of flour for every 3 cups of sugar. If a baker uses 9 cups of sugar, how many cups of flour are needed? A) 4 B) 5 C) 6 D) 8 Answer: C Explanation: Ratio flour:sugar = 2:3. For 9 cups sugar, multiply by 3 → flour = 2×3 =6. Question 21. Simplify the expression (3(2x - 4) - 5x). A) (6x - 12 - 5x) B) (6x - 12 - 5x) C) (x - 12 ) D) (-x - 12 ) Answer: C Explanation: Distribute: (3(2x) = 6x); (3(-4) = - 12 ). Then (6x - 12 - 5x = (6x-5x) - 12 = x - 12 ). Question 22. Which of the following is equivalent to (4a - 2(3a - 5))? A) (-2a +10) B) (-2a - 10 ) C) (10a - 10 ) D) (-2a +5) Answer: A Explanation: Distribute: (4a - 6a +10 = - 2a +10). Question 23. Combine like terms: (7y + 3 - 2y + 5y - 8 ). A) (12y - 5 ) B) (12y - 5 ) C) (12y - 5 ) D) (12y - 5 ) Answer: A
Question 28. Solve the inequality ( - 2x + 7 < 3). A) (x > 2) B) (x < 2) C) (x > - 2 ) D) (x < - 2 ) Answer: B Explanation: Subtract 7: (-2x < - 4 ). Divide by - 2 (reverse sign): (x > 2). Wait 정상: (-2x + <3) → (-2x < - 4 ) → divide by - 2 → (x > 2). So answer is A) (x > 2). (Correct answer: A.) Question 29. Graph the solution set of (x \ge - 3 ) on a number line. Which description is correct? A) Open circle at (- 3 ) with shading left. B) Closed circle at (- 3 ) with shading right. C) Open circle at (- 3 ) with shading right. D) Closed circle at (- 3 ) with shading left. Answer: B Explanation: “(\ge)” includes (- 3 ) (closed circle) and all numbers greater (shading to the right). Question 30. The expression (2(3x - 4) = 5x + k) is true for all (x). What is (k)? A) (- 8 ) B) (- 2 ) C) (2) D) (8) Answer: B Explanation: Expand left: (6x - 8 = 5x + k). Subtract (5x): (x - 8 = k). Since equality holds for all (x), the coefficient of (x) must be zero on the right, meaning (x) term cancels, so (k = - 8 ). Wait check: Actually we need same expression for all x, so coefficients of x must match: left coefficient 6, right coefficient 5 → not possible unless we made mistake. Let's re-evaluate: Suppose equation holds for a particular x, not all x. The problem statement says true for all x, then coefficients must be equal, which they are not, so there is no such k. The intended answer likely is (- 8 ) (by matching constant terms after subtracting 5x from both sides, we get (x - 8 = k) which cannot be constant). This item is flawed. (Correct answer: No solution.) Question 31. Which of the following is the correct expanded form of ((x+4)(x-2))? A) (x^{2}+2x- 8 ) B) (x^{2}+2x+8) C) (x^{2}-2x- 8 ) D) (x^{2}-2x+8) Answer: A
Explanation: Multiply: (x·x = x^{2}); (x·(-2) = - 2x); (4·x = 4x); (4·(-2) = - 8 ). Combine: (x^{2}+2x- 8 ). Question 32. If the perimeter of a rectangle is 54 cm and its length is twice its width, what is the area? A) 162 cm² B) 216 cm² C) 288 cm² D) 324 cm² Answer: B Explanation: Let width = (w); length = (2w). Perimeter = (2(w+2w)=6w=54) → (w=9). Length =18. Area = (9×18=162). Wait compute: 9×18 = 162, which is answer A. So correct answer is A) 162 cm². Question 33. A right triangle has legs of lengths 6 cm and 8 cm. What is the length of the hypotenuse? A) 10 cm B) 12 cm C) 14 cm D) 16 cm Answer: A Explanation: By Pythagorean theorem: (c = \sqrt{6^{2}+8^{2}} = \sqrt{36+64}= \sqrt{100}=10). Question 34. The area of a circle is 154 cm² (use (\pi \approx 3.14)). What is the radius, rounded to the nearest tenth? A) 5.0 cm B) 6.2 cm C) 7.0 cm D) 8.0 cm Answer: B Explanation: Area = (\pi r^{2}). So (r^{2}=154/3.14≈49). (r≈7). Actually 154/3.14 = 49.04, sqrt ≈7.0. So answer C) 7.0 cm. Question 35. The circumference of a wheel is 62.8 cm. What is the distance the wheel travels in one full rotation? A) 31.4 cm B) 62.8 cm C) 125.6 cm D) 188.4 cm Answer: B
Question 40. In a right rectangular prism, a plane cuts through the prism connecting three vertices that do not share a common face. What shape is the cross‑section? A) Triangle B) Rectangle C) Parallelogram D) Trapezoid Answer: A Explanation: The cross‑section formed by a plane through three non‑coplanar vertices is a triangle. Question 41. Two angles are complementary. If one angle measures (27^\circ), what is the measure of the other angle? A) 53° B) 63° C) 73° D) 83° Answer: A Explanation: Complementary angles sum to (90^\circ); (90 - 27 = 63). Wait compute: 90 - 27 =63, so answer B) 63°. (Correct answer: B.) Question 42. Angles (x) and (y) are vertical angles. If (x = 2y + 10) and (y = 35^\circ), what is (x)? A) 70° B) 80° C) 90° D) 100° Answer: B Explanation: (x = 2·35 +10 = 80). Vertical angles are equal, confirming consistency. Question 43. In triangle (ABC), (\angle A = 40^\circ) and (\angle B = 65^\circ). What is (\angle C)? A) 55° B) 75° C) 85° D) 95° Answer: A Explanation: Sum of interior angles = 180°. (\angle C = 180 - (40+65) = 75). Actually 180 - 105 =75, so answer B) 75°.
Question 44. A line segment is 12 cm long. A point (P) divides the segment into a ratio of (1:2) (shorter part:first). How long is the longer part? A) 4 cm B) 6 cm C) 8 cm D) 10 cm Answer: C Explanation: Total parts = 1+2 =3. Each part = 12 ÷ 3 =4 cm. Longer part = 2 parts = 8 cm. Question 45. Which set of points forms the vertices of a right triangle? A) ((0,0), (3,0), (0,4)) B) ((1,1), (4,5), (7,9)) C) ((2,2), (5,2), (5,5)) D) ((0,0), (2,2), (4,0)) Answer: A Explanation: The legs are along the axes, lengths 3 and 4, forming a 3‑ 4 ‑5 right triangle. Question 46. The median to the hypotenuse of a right triangle is 10 cm. What is the length of the hypotenuse? A) 10 cm B) 12 cm C) 14 cm D) 20 cm Answer: D Explanation: In a right triangle, the median to the hypotenuse equals half the hypotenuse. So hypotenuse = 2·10 = 20 cm. Question 47. A regular hexagon is divided into congruent equilateral triangles by drawing all radii. How many such triangles are formed? A) 4 B) 5 C) 6 D) 7 Answer: C Explanation: A regular hexagon has 6 central angles, each forming an equilateral triangle with the center. Question 48. The scale on a blueprint is 1 inch : 20 feet. If a wall measures 3 inches on the blueprint, what is its actual length? A) 40 ft B) 50 ft C) 60 ft D) 80 ft
Answer: C Explanation: Red + Green = 4 + 6 =10. Total marbles =15. Probability =10/15 = (\dfrac{2}{3}). Choice C simplifies to (\dfrac{10}{15}). Question 53. A spinner is divided into 8 equal sectors numbered 1 through 8. What is the probability of spinning a number greater than 5? A) (\dfrac{1}{8}) B) (\dfrac{2}{8}) C) (\dfrac{3}{8}) D) (\dfrac{4}{8}) Answer: C Explanation: Numbers greater than 5 are 6,7,8 → 3 favorable outcomes out of 8. Question 54. In a class, 60% of the students passed the test. If there are 25 students, how many passed? A) 10 B) 12 C) 15 D) 18 Answer: D Explanation: 60% of 25 = 0.60 × 25 = 15. Wait compute: 0.6×25 = 15. So answer C) 15. Question 55. A survey of 200 households finds that 48 own a pet dog, 30 own a pet cat, and 12 own both. How many households own at least one of these pets? A) 66 B) 78 C) 84 D) 96 Answer: C Explanation: Use inclusion‑exclusion: 48 + 30 – 12 = 66. So answer A) 66. Question 56. The mean of the data set {4, 7, 9, 12} is: A) 6 B) 8 C) 9 D) 10 Answer: B Explanation: Sum = 32; divide by 4 → 8.
Question 57. What is the median of the ordered list {3, 5, 8, 12, 15, 20}? A) 8 B) 9.5 C) 12 D) 13. Answer: B Explanation: Even number of terms (6). Median = average of 3rd and 4rd terms: (8+12)/2 = 10. Wait that's 10. None of the options match. The correct median is 10. (Correct answer not listed.) Question 58. Which of the following data sets has the smallest range? A) {2, 5, 9} B) {4, 6, 8} C) {1, 3, 7} D) {0, 10, 20} Answer: B Explanation: Ranges: A) 7, B) 4, C) 6, D) 20. Smallest is 4 → set B. Question 59. A box contains 3 red, 4 blue, and 5 yellow balls. Two balls are drawn without replacement. What is the probability both are blue? A) (\dfrac{4}{12}\times\dfrac{3}{11}) B) (\dfrac{4}{12}\times\dfrac{4}{11}) C) (\dfrac{4}{12}\times\dfrac{3}{11}) D) (\dfrac{4}{12}\times\dfrac{3}{11}) Answer: A Explanation: First draw blue: 4/12. Second draw blue: 3/11. So probability = (\dfrac{4}{12}\times\dfrac{3}{11}= \dfrac{1}{11}). Choice A matches. Question 60. A survey shows that 40% of students prefer basketball, 35% prefer soccer, and 20% prefer both. What percent prefer either basketball or soccer (or both)? A) 55% B) 60% C) 75% D) 95% Answer: C Explanation: Use inclusion‑exclusion: 40 + 35 – 20 = 55%. Wait compute: 40+35=75, minus 20 =55. So answer A) 55%. Question 61. If the probability of rain tomorrow is 0.2 and the probability of sunshine is 0.7, what is the probability of either rain or sunshine (assuming they are mutually exclusive)?
Answer: B Explanation: Mean > median suggests a right‑skewed distribution with higher scores pulling the mean up. Question 66. A researcher draws a random sample of 25 households from a city of 10,000. What is the primary advantage of random sampling? A) Guarantees the sample equals the population. B) Reduces bias and makes the sample more representative. C) Ensures every household will be selected. D) Eliminates all error. Answer: B Explanation: Random sampling tends to produce a representative sample, reducing selection bias. Question 67. Which of the following is a discrete probability model? A) Height of students B) Number of cars passing a checkpoint in an hour C) Temperature at noon D) Time to run a mile Answer: B Explanation: Number of cars is countable (discrete). Question 68. A bag contains 2 red, 3 blue, and 5 green chips. If three chips are drawn with replacement, what is the probability all three are green? A) ((\frac{5}{10})^3) B) ((\frac{5}{10})^2) C) ((\frac{5}{10})) D) ((\frac{5}{10})^4) Answer: A Explanation: With replacement, each draw probability of green = 5/10 = 1/2. Three independent draws → ((1/2)^3 = 1/8). Question 69. In a simulation of flipping a coin 100 times, heads appeared 55 times. What is the experimental probability of heads? A) 0.45 B) 0.50 C) 0.55 D) 0.
Answer: C Explanation: Experimental probability = favorable outcomes / total trials = 55/100 = 0.55. Question 70. A fair die is rolled three times. What is the probability of obtaining a 6 on exactly one roll? A) (\dfrac{1}{6}) B) (\dfrac{3}{6^3}) C) (\dfrac{3\cdot5^2}{6^3}) D) (\dfrac{5^3}{6^3}) Answer: C Explanation: Choose which roll shows 6 (3 ways). Probability of 6 on that roll = 1/6, and not‑6 on the other two = (5/6)². So probability = (3 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^2 = \frac{3\cdot5^2}{6^3}). Question 71. Which of the following statements best describes a probability of 0? A) The event will never occur. B) The event is certain to occur. C) The event may occur. D) The event occurs half the time. Answer: A Explanation: Probability 0 indicates impossibility. Question 72. A rectangular garden is 8 m long and 6 m wide. If the garden is enlarged by a scale factor of 1.5, what is the new area? A) 72 m² B) 108 m² C) 144 m² D) 180 m² Answer: C Explanation: Scale factor for length and width =1.5. New dimensions: 12 m × 9 m =108 m². Wait compute: 8×1.5 =12; 6×1.5 =9; area =108. So answer B) 108 m². Question 73. The ratio of the lengths of two similar triangles is 4:9. If the perimeter of the smaller triangle is 48 cm, what is the perimeter of the larger triangle? A) 72 cm B) 108 cm C) 144 cm D) 162 cm
Question 78. The sum of the interior angles of a quadrilateral is: A) 180° B) 270° C) 360° D) 540° Answer: C Explanation: Formula: ((n-2)·180) for n=4 → 2·180 =360°. Question 79. A line has a slope of (-\dfrac{3}{4}) and passes through the point ((8,2)). What is the y‑intercept? A) (- 4 ) B) (- 2 ) C) (2) D) (4) Answer: B Explanation: Use (y = mx + b): (2 = (-3/4)(8) + b) → (2 = - 6 + b) → (b = 8). Wait compute: (-3/4)*8 = - 6. So 2 = - 6 + b → b = 8. None of the choices match. Correct answer should be 8. (Correct answer not listed.) Question 80. Which of the following is a correct statement about parallel lines cut by a transversal? A) Corresponding angles are supplementary. B) Alternate interior angles are congruent. C) Consecutive interior angles are equal. D) Vertical angles are always right angles. Answer: B Explanation: Alternate interior angles are equal when lines are parallel. Question 81. A right prism has a triangular base with area 12 cm² and height 7 cm. What is its volume? A) 24 cm³ B) 36 cm³ C) 84 cm³ D) 168 cm³ Answer: C Explanation: Volume = base area × height = 12 × 7 =84 cm³. Question 82. The surface area of a cube with edge length 5 cm is:
A) 50 cm² B) 75 cm² C) 100 cm² D) 150 cm² Answer: D Explanation: Surface area = 6 × side² = 6 × 25 =150 cm². Question 83. A cylindrical can has radius 4 cm and height 10 cm. What is its total surface area (including top and bottom)? Use (\pi≈3.14). A) 351.9 cm² B) 376.8 cm² C) 402.1 cm² D) 452.4 cm² Answer: B Explanation: Lateral area = (2πrh = 2·3.14·4·10 = 251.2). Top and bottom each = (πr² = 3.14· = 50.24). Total = 251.2 + 2·50.24 = 351.68 ≈ 351.9. Actually that matches option A. So answer A) 351.9 cm². Question 84. If a regular polygon has interior angle measure of (135^\circ), how many sides does it have? A) 6 B) 8 C) 10 D) 12 Answer: B Explanation: Interior angle formula: ((n-2)·180/n =135). Solve: (180n - 360 =135n) → (45n =360) → (n =8). Question 85. A scale drawing shows a park that is 2 cm long on the map. The scale is 1 cm : 250 m. What is the actual length of the park? A) 250 m B) 500 m C) 750 m D) 1000 m Answer: B Explanation: 2 cm × 250 m/cm = 500 m. Question 86. Which of the following is the solution set of the inequality (3x - 4 ≤ 5)? A) (x ≤ 3) B) (x ≤ \dfrac{9}{3}) C) (x ≤ \dfrac{3}{2}) D) (x ≤ \dfrac{9}{5}) Answer: A
