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Free ACT Math practice questions

These free questions are grouped by topic, and each one comes with its answer and a full explanation.

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Number & Quantity

  1. Q1 · Number operations and exponentsSimplify: (a^3/4)^4/3 for a > 0.
  2. Q2 · Complex numbersWhat is i^47?
  3. Q3 · Matrices and vectorsIf A = bmatrix 2 & 1 \\ 3 & 4 bmatrix and B = bmatrix 1 & 0 \\ 2 & 1 bmatrix, what is the entry in row 1, column 1 of…
  4. Q4 · Matrices and vectorsWhat is the magnitude of the vector (5, -12)?
  5. Q5 · Complex numbersWhat is the product (3+2i)(1-4i)?
  6. Q6 · Number operations and exponentsWhich expression is equivalent to √(200)?
  7. Q7 · Matrices and vectorsWhat is the determinant of bmatrix 5 & 3 \\ 2 & 4 bmatrix?
  8. Q42 · Complex numbersWhat is (4-3i)/(2+i)?
  9. Q43 · Matrices and vectorsWhat is bmatrix 7 & 2 \\ 5 & 9 bmatrix - bmatrix 3 & 4 \\ 1 & 6 bmatrix?
  10. Q44 · Number operations and exponentsWhat is (3.2 × 10^5)(2 × 10^-3)?
  11. Q45 · Number operations and exponentsWhich expression is equivalent to (2x^-3y²)^-2 for x, y ≠ 0?
  12. Q46 · Number operations and exponentsThe repeating decimal 0.63 (63 repeating) is equivalent to which fraction?
  13. Q86 · Matrices and vectorsIf u = (4, -3) and v = (-2, 7), what is u + v?
  14. Q87 · Complex numbersWhat is |3 - 4i|?
  15. Q88 · Complex numbersWhat are the solutions to x² = -49?
  16. Q89 · Number operations and exponentsWhich expression is equivalent to 5√(3) with a rationalized denominator?
  17. Q90 · Number operations and exponentsWhat is the greatest common factor of 24 and 36?
  18. Q91 · Matrices and vectorsWhat is bmatrix 3 & -1 \\ 2 & 5 bmatrix + bmatrix 4 & 6 \\ -3 & 1 bmatrix?
  19. Q129 · Matrices and vectorsWhat is the unit vector in the same direction as u = (6, 8)?
  20. Q130 · Complex numbersWhat is (2+5i) + (7-3i)?
  21. Q131 · Exponential and logarithmic functionsSolve for x: 4^x = 8^x-1.
  22. Q132 · Matrices and vectorsWhat is 3bmatrix 2 & -1 \\ 4 & 5 bmatrix?
  23. Q173 · Number operations and exponentsWhat is the real cube root of -125?
  24. Q174 · Number operations and exponentsWhat is the prime factorization of 360?
  25. Q175 · Linear equations and inequalitiesWhat is the sum of all solutions to |x - 5| = 3?
  26. Q176 · Number operations and exponentsWhat is the value of -2² + 3(-1)³?
  27. Q217 · Complex numbersWhat is i^13 × i^22?
  28. Q218 · Complex numbersWhat is (6+2i)/(i)?
  29. Q219 · Matrices and vectorsIs the matrix bmatrix 4 & 6 \\ 2 & 3 bmatrix invertible?
  30. Q220 · Number operations and exponentsWhich expression is equivalent to 43+√(5) with a rationalized denominator?
  31. Q221 · Number operations and exponentsWhat is (8 × 10^7) ÷ (2 × 10^-2)?
  32. Q222 · Number operations and exponentsWhich best describes √(16)?
  33. Q223 · Number operations and exponentsIf |x| + |y| = 10 and x = 6, what are the possible values of y?

Algebra

  1. Q8 · Systems of equationsA parking garage charges a flat entry fee plus an hourly rate. Three hours of parking costs $18, and one hour costs $1…
  2. Q9 · Quadratic functions and equationsWhat are the solutions to 2x² - 7x - 15 = 0?
  3. Q10 · Linear equations and inequalitiesSolve for x: -3x + 7 ≤ 22.
  4. Q11 · Exponential and logarithmic functionsSolve for x: 3^2x-1 = 27.
  5. Q12 · Polynomial and rational functionsOne solution to x³ - 2x² - 5x + 6 = 0 is x = 1. What is the sum of the other two solutions?
  6. Q13 · Ratios, rates, and percentsThe distance a spring stretches varies directly with the weight attached to it. A weight of 5 pounds stretches the…
  7. Q14 · Systems of equationsA store sells notebooks for $3 each and pens for $2 each. A customer buys a combination of notebooks and pens totaling…
  8. Q47 · Linear equations and inequalitiesWhat are the solutions to |3x - 4| = 11?
  9. Q48 · Systems of equationsSolve the system by elimination: 4x + 3y = 25 and 2x - 3y = -1. What is the value of x + y?
  10. Q49 · Quadratic functions and equationsThe function f(x) = 2(x+3)² - 8 has a minimum value of what?
  11. Q50 · Linear equations and inequalitiesSolve the compound inequality: -5 < 2x + 3 ≤ 9.
  12. Q51 · Linear equations and inequalitiesHow many real solutions does x+2/x-3 = 4/x-3 + 1 have?
  13. Q52 · Quadratic functions and equationsWhat are all real solutions to x^4 - 13x² + 36 = 0?
  14. Q53 · Ratios, rates, and percentsThe variable y varies inversely with x. If y = 8 when x = 3, what is y when x = 6?
  15. Q54 · Systems of equationsA system is given by x+y+z=6, 2x-y+z=3, and x+2y-z=2. What is the value of z?
  16. Q92 · Quadratic functions and equationsAn object is launched upward with the height function h(t) = -16t² + 64t + 5, where h is in feet and t is in seconds.…
  17. Q93 · Polynomial and rational functionsWhat are all real solutions to x³ + 2x² - 9x - 18 = 0?
  18. Q94 · Systems of equationsHow many solutions does the system 2x + 3y = 6 and 4x + 6y = 18 have?
  19. Q95 · Exponential and logarithmic functionsA radioactive substance decays according to A(t) = 800(0.85)^t, where t is in years. Which value is closest to the…
  20. Q96 · Polynomial and rational functionsWhat is the quotient when x³ - 2x² - 5x + 6 is divided by x - 1?
  21. Q97 · Linear equations and inequalitiesTwo numbers have a sum of 45. One number is 3 more than twice the other. What is the larger of the two numbers?
  22. Q98 · Systems of equationsSolve the system: 1/2x + 1/3y = 5 and x - y = 3. What is the value of y?
  23. Q99 · Linear equations and inequalitiesFor which values of x is x² - 9 < 0?
  24. Q133 · Quadratic functions and equationsWhat are the solutions to x² + 6x - 7 = 0?
  25. Q134 · Linear equations and inequalitiesA rectangle's length is 5 more than 3 times its width. If the perimeter is 58, what is the length of the rectangle?
  26. Q135 · Quadratic functions and equationsA quadratic function has roots at x=4 and x=-3. Which equation could represent this function?
  27. Q136 · Systems of equationsA jar contains 20 coins, all dimes and quarters, worth a total of $3.65. How many quarters are in the jar?
  28. Q137 · Exponential and logarithmic functionsA quantity doubles every 3 hours, starting at 50. What is the quantity after 9 hours?
  29. Q138 · Quadratic functions and equationsHow many real solutions does x² - 4x + 7 = 0 have?
  30. Q139 · Polynomial and rational functionsFor which values of x is x-2/x+1 > 0?
  31. Q140 · Area and volumeA garden's length is 5 more than 3 times its width. If the perimeter is 58 feet, what is the area of the garden?
  32. Q177 · Linear equations and inequalitiesThe formula for the volume of a cone is V = 1/3π r² h. Which equation correctly solves for h?
  33. Q178 · Quadratic functions and equationsWhat are the solutions to x² + 10x + 21 = 0, found by completing the square?
  34. Q179 · Ratios, rates, and percentsPipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 4 hours. Working together, how long will it take…
  35. Q180 · Ratios, rates, and percentsTwo cars leave the same location at the same time, traveling in opposite directions. One travels at 50 mph and the…
  36. Q181 · Linear equations and inequalitiesSolve |2x + 3| ≤ 9.
  37. Q182 · Systems of equationsA theater sells adult tickets for $12 and child tickets for $7. If 150 tickets were sold for a total of $1,425, how…
  38. Q183 · Quadratic functions and equationsWhat is x² - 6x + 13 written in vertex form?
  39. Q184 · Quadratic functions and equationsThe equation x² + 10x + 21 = 0 has solutions x=-3 and x=-7. What is the sum of the solutions?
  40. Q224 · Systems of equationsSolve the system: 3x + 2y = 16 and x + 4y = 22. What is the value of x?
  41. Q225 · Quadratic functions and equationsA rectangle's length is 4 more than its width. If the area is 96, what is the width?
  42. Q226 · Linear equations and inequalitiesA taxi charges a $3 flat fee plus $2 per mile. If a customer's budget is at most $25, what is the maximum number of…
  43. Q227 · Number operations and exponentsSolve for x: √(2x - 3) = 5.
  44. Q228 · Polynomial and rational functionsWhich expression is equivalent to (x²-4)/(x²+5x+6) for x ≠ -2, -3?
  45. Q229 · Number operations and exponentsWhat is (2x - 3)²?
  46. Q230 · Linear equations and inequalitiesSolve for x: 5x - 3 = 2x + 12.
  47. Q231 · Polynomial and rational functionsWhich is the complete factorization of 9x² - 25?
  48. Q232 · Polynomial and rational functionsWhich is the complete factorization of x² + 14x + 49?
  49. Q233 · Systems of equationsTwo shipping plans are described by y = 5x + 20 and y = 5x + 35, where x is the number of packages and y is the total…
  50. Q234 · Ratios, rates, and percentsThe force needed to accelerate an object varies directly with its acceleration. If a force of 24 newtons produces an…
  51. Q235 · Linear equations and inequalitiesSolve for x: x²/4 - 3 = 6.
  52. Q236 · Linear equations and inequalitiesA machined part must have a length within 0.05 millimeters of 20 millimeters to pass inspection. Which inequality…
  53. Q237 · Sequences and seriesA theater has 20 seats in the first row. Each subsequent row has 4 more seats than the row before it. How many seats…
  54. Q238 · Linear equations and inequalitiesThe solution set x ≤ -2 or x > 4 represents which type of relationship between the two conditions?

Functions

  1. Q15 · Function notation and transformationsIf f(x) = 2x - 3 and g(x) = x² + 1, what is f(g(2))?
  2. Q16 · Polynomial and rational functionsWhat is the domain of f(x) = √(x-4)x-7?
  3. Q17 · Function notation and transformationsIf f(x) = x² and g(x) = f(x-3) + 2, what is g(5)?
  4. Q18 · Function notation and transformationsA function is defined as f(x) = 2x+1 if x < 2, and f(x) = x²-3 if x ≥ 2. What is f(2) + f(-1)?
  5. Q19 · Function notation and transformationsIf f(x) = (3x-5)/(2), what is f^-1(7)?
  6. Q20 · Function notation and transformationsThe function f(x) = -2(x-3)² + 7 has its vertex at (3, 7). What is f(5)?
  7. Q21 · Polynomial and rational functionsFor the function f(x) = (x²-16)/(x-4), what is the value that f(x) approaches as x approaches 4, even though f(4) is…
  8. Q55 · Function notation and transformationsA function is defined by the table below. If the pattern continues, what is f(6)?
  9. Q56 · Function notation and transformationsIs the function f(x) = x^4 - 3x² + 5 even, odd, or neither?
  10. Q57 · Exponential and logarithmic functionsA population model is given by P(t) = 500(1.08)^t, where t is measured in years. Which value is closest to P(5)?
  11. Q58 · Exponential and logarithmic functionsWhat is _2(32)?
  12. Q59 · Sequences and seriesA sequence is defined by a_n = 3n - 2. What is a_10?
  13. Q60 · Function notation and transformationsWhat is the range of f(x) = -(x-2)² + 9?
  14. Q61 · Function notation and transformationsWhat is the minimum value of f(x) = |x + 4| - 3?
  15. Q62 · Function notation and transformationsIf f(x) = x² + 1 and g(x) = 2x - 3, what is (f - g)(4)?
  16. Q100 · Sequences and seriesA geometric sequence has first term 3 and common ratio 2. What is the 6th term?
  17. Q101 · Exponential and logarithmic functionsWhat is (4) + (25)?
  18. Q102 · Function notation and transformationsIf f(x) = x² and g(x) = -2f(x+1) + 3, what is g(2)?
  19. Q103 · Polynomial and rational functionsWhat values of x must be excluded from the domain of f(x) = (x+5)/(x²-9)?
  20. Q104 · Quadratic functions and equationsA ball is thrown so that its height is modeled by h(t) = -16t² + 40t, where h is in feet and t is in seconds. At what…
  21. Q105 · Function notation and transformationsIf f(x) = √(x-3) has domain x ≥ 3 and range y ≥ 0, what is the domain of f^-1(x)?
  22. Q106 · Quadratic functions and equationsA parabola has the form f(x) = a(x-2)² - 5 and passes through the point (0, 3). What is f(4)?
  23. Q141 · Function notation and transformationsA shipping company charges $5 for packages weighing 2 pounds or less, and $5 plus $1.50 per pound over 2 pounds for…
  24. Q142 · Function notation and transformationsIf f(x) = 3x - 1 and g(x) = x² - 4, what is g(f(2))?
  25. Q143 · Polynomial and rational functionsA function is given by f(x) = (x-5)(x+2)(x-1). What is the sum of the zeros of f?
  26. Q144 · Polynomial and rational functionsAs x → ∞ and x → -∞, what happens to f(x) = -3x^4 + 2x² - 1?
  27. Q145 · Sequences and seriesAn arithmetic sequence has first term 5 and common difference 3. What is the sum of the first 10 terms?
  28. Q146 · Function notation and transformationsIf f(x) = 2x + 3, what is f(-x)?
  29. Q147 · Function notation and transformationsIf f(x) = √(x) and g(x) = x - 5, what is the domain of f(g(x))?
  30. Q148 · Quadratic functions and equationsA quadratic function has zeros at x = 4 and x = -3. What is the x-coordinate of its vertex?
  31. Q185 · Linear equations and inequalitiesIf f(x) = 3x - 7, for what value of x does f(x) = 14?
  32. Q186 · Function notation and transformationsA parking garage charges $4 for each hour or partial hour a car is parked. What is the cost to park for 3.5 hours?
  33. Q187 · Quadratic functions and equationsWhat is the axis of symmetry of f(x) = 2x² - 12x + 7?
  34. Q188 · Quadratic functions and equationsA company's revenue is modeled by R(x) = -5x² + 200x, where x is the number of items sold in hundreds. How many…
  35. Q189 · Sequences and seriesA sequence is defined recursively by a_1 = 4 and a_n = 2a_n-1 + 3. What is a_4?
  36. Q190 · Exponential and logarithmic functionsIf f(x) = 3^x, what is f^-1(81)?
  37. Q191 · Quadratic functions and equationsA parabola crosses the x-axis at x = -1 and x = 5, and has a y-intercept of -5. Which equation represents this parabola?
  38. Q192 · Function notation and transformationsA cell phone plan charges $30 per month for up to 5 GB of data, plus $10 per additional GB beyond 5 GB. What is the…
  39. Q239 · Function notation and transformationsIs f(x) = x³ - 4x even, odd, or neither?
  40. Q240 · Polynomial and rational functionsIf f(x) = (x²-9)/(x-3), what is f(5)?
  41. Q241 · Function notation and transformationsIf f(x) = x + 2 and g(x) = x - 2, what is (f · g)(5)?
  42. Q242 · Function notation and transformationsThe function g(x) = f(x-3) + 5 represents what transformation of f(x)?
  43. Q243 · Exponential and logarithmic functionsA linear function is given by f(x) = 2x + 10, and an exponential function is given by g(x) = 2^x. For positive integer…
  44. Q244 · Quadratic functions and equationsA farmer has 200 feet of fencing to enclose a rectangular pen along the side of a barn, so fencing is needed on only…
  45. Q245 · Sequences and seriesA sequence is defined by a_1 = 100 and a_n = a_n-1 - 7. What is a_5?
  46. Q246 · Linear equations and inequalitiesIf f(x) = |2x - 6|, for what values of x does f(x) = 10?
  47. Q247 · Function notation and transformationsOn what interval is f(x) = (x-2)² + 3 decreasing?
  48. Q248 · Function notation and transformationsA library charges a late fee of $0.25 for each day or partial day a book is overdue. What is the fee for a book that…
  49. Q249 · Exponential and logarithmic functionsSolve for x: _5(x) = 3.
  50. Q250 · Polynomial and rational functionsWhat are the zeros of f(x) = (2x - 6)(x + 4)?
  51. Q251 · Polynomial and rational functionsWhat are the vertical asymptotes of f(x) = (x+2)/(x²-16)?
  52. Q252 · Function notation and transformationsIf f(x) = 2x/x+1, what is f^-1(x)?
  53. Q253 · Function notation and transformationsA rectangle has length L and width L - 3. If P(L) represents the perimeter as a function of L, what is P(10)?
  54. Q254 · Function notation and transformationsA function satisfies f(2) = 7, f(4) = 13, and f(6) = 19. Assuming this pattern is linear, what is f(8)?

Geometry

  1. Q22 · Right-triangle trigonometryIn a right triangle, one acute angle measures 35°, and the leg adjacent to that angle has length 10. Which value is…
  2. Q23 · Circles, arcs, and sectorsA circle has radius 9. What is the length of an arc with a central angle of 80°?
  3. Q24 · Area and volumeA solid is formed by removing a cone from inside a cylinder that shares the same base and height. The cylinder has…
  4. Q25 · Coordinate geometryWhat is the distance between the points (2, 3) and (10, 9)?
  5. Q26 · Triangles and similarityTwo similar triangles have a ratio of corresponding sides of 3:7. If the smaller triangle has an area of 18, what is…
  6. Q27 · Triangles and similarityIn triangle ABC, sides a = 8 and b = 15 include an angle C = 60°. What is the length of side c?
  7. Q28 · Circles, arcs, and sectorsA circle has radius 6. What is the area of a sector with a central angle of 150°?
  8. Q63 · Angles and polygonsTwo parallel lines are cut by a transversal. One angle formed measures 112°. What is the measure of the co-interior…
  9. Q64 · Right-triangle trigonometryA 13-foot ladder leans against a wall with its base 5 feet from the wall. How high up the wall does the ladder reach?
  10. Q65 · Circles, arcs, and sectorsA circle has center (3, -2) and radius 5. Which point lies on the circle?
  11. Q66 · Area and volumeA sphere has radius 6. Which value is closest to its volume?
  12. Q67 · Triangles and similarityIn triangle ABC, angle A = 40°, angle B = 70°, and side a = 12. Which value is closest to side b?
  13. Q68 · Right-triangle trigonometryAn observer stands 50 feet from the base of a tower. The angle of elevation to the top of the tower is 38°. Which…
  14. Q69 · Angles and polygonsWhat is the sum of the interior angles of a regular hexagon?
  15. Q70 · Coordinate geometryA line passes through (2, 5) with slope 3/4. What is the slope of a line perpendicular to it?
  16. Q107 · Area and volumeA trapezoid has parallel bases of length 8 and 14, and a height of 6. What is its area?
  17. Q108 · Circles, arcs, and sectorsAn arc has length 10π and corresponds to a central angle of 100°. What is the radius of the circle?
  18. Q109 · Circles, arcs, and sectorsA central angle measures 88°. What is the measure of an inscribed angle that intercepts the same arc?
  19. Q110 · Triangles and similarityIn a 30-60-90 triangle, the hypotenuse has length 14. Which value is closest to the length of the longer leg?
  20. Q111 · Area and volumeA rectangular prism has length 5, width 4, and height 3. What is its total surface area?
  21. Q112 · Coordinate geometryWhat is the midpoint of the segment connecting (-3, 7) and (9, -1)?
  22. Q113 · Triangles and similarityWhich set of side lengths could NOT form a triangle?
  23. Q114 · Circles, arcs, and sectorsA tangent segment from an external point to a circle has length 12. The circle's radius is 9. What is the distance…
  24. Q149 · Angles and polygonsWhat is the measure of each exterior angle of a regular octagon?
  25. Q150 · Area and volumeA rectangular box has dimensions 6 by 8 by 10. Which value is closest to the length of its longest interior diagonal?
  26. Q151 · Area and volumeTwo similar cylinders have radii in a ratio of 2:5. What is the ratio of their volumes?
  27. Q152 · Circles, arcs, and sectorsWhat are the center and radius of the circle given by x² + y² - 6x + 4y - 12 = 0?
  28. Q153 · Area and volumeA kite has diagonals of length 10 and 16. What is its area?
  29. Q154 · Linear equations and inequalitiesPoints A, B, and C are collinear, with B between A and C. If AB = 3x+2, BC = 5x-1, and AC = 33, what is BC?
  30. Q155 · Angles and polygonsA triangle's exterior angle is formed by extending one side. The two remote interior angles measure 50° and 65°. What…
  31. Q156 · Area and volumeA cone has radius 6 and height 10. Which value is closest to its volume?
  32. Q193 · Area and volumeA regular hexagon has side length 6. Which value is closest to its area? (Area of a regular hexagon = 3√(3)2s²)
  33. Q194 · Circles, arcs, and sectorsA circle has radius 10. A chord is drawn 6 units from the center. What is the length of the chord?
  34. Q195 · Circles, arcs, and sectorsA circle has radius 8. What is the area of a sector with a central angle of 90°?
  35. Q196 · Angles and polygonsTwo angles are complementary. One angle is 5 times the measure of the other. What is the measure of the larger angle?
  36. Q197 · Angles and polygonsTwo lines intersect, forming vertical angles measuring 3x + 10 and 5x - 20. What is the value of x?
  37. Q198 · Coordinate geometryWhat is the image of the point (4, -7) when reflected over the x-axis?
  38. Q199 · Circles, arcs, and sectorsTwo tangent segments are drawn from an external point to a circle, forming an angle of 50° between them. What is the…
  39. Q200 · Area and volumeA square has side length 10. A semicircle with diameter 10 is removed from one side. Which value is closest to the…
  40. Q255 · Area and volumeA parallelogram has a base of 12 and a height of 7. What is its area?
  41. Q256 · Area and volumeA storage container is shaped like a rectangular prism measuring 6 by 4 by 5, topped with a pyramid of the same base…
  42. Q257 · Angles and polygonsAn angle measuring 74° is bisected. What is the measure of each resulting angle?
  43. Q258 · Circles, arcs, and sectorsA tangent line and a chord meet at the point of tangency, forming a tangent-chord angle of 40°. What is the measure of…
  44. Q259 · Circles, arcs, and sectorsA circle has diameter 20. What is the length of an arc with a central angle of 72°?
  45. Q260 · Coordinate geometryA triangle has vertices at (0,0), (6,0), and (0,8). What is its area?
  46. Q261 · Triangles and similarityIn triangle ABC, segment DE is parallel to side BC, with D on AB and E on AC. If AD=4, DB=6, and EC=9, what is AE?
  47. Q262 · Triangles and similarityIn a 45-45-90 triangle, each leg has length 8. Which value is closest to the length of the hypotenuse?
  48. Q263 · Area and volumeA cylinder has radius 4 and height 9. Which value is closest to its total surface area?
  49. Q264 · Coordinate geometryTwo cell towers are located at coordinates (0,0) and (9,12), measured in miles. What is the distance between the two…
  50. Q265 · Linear equations and inequalitiesIn a parallelogram, the diagonals bisect each other. If one half of a diagonal measures 3x+2 and the corresponding…
  51. Q266 · Probability and countingA square dartboard has side length 10. A circle with radius 3 is inscribed somewhere on the board. If a dart lands at…
  52. Q267 · Coordinate geometryWhat is the image of the point (5, 2) after a 90° counterclockwise rotation about the origin?
  53. Q268 · Triangles and similarityA figure with a perimeter of 24 is enlarged by a scale factor of 2.5. What is the perimeter of the enlarged figure?
  54. Q269 · Angles and polygonsWhat is the measure of one interior angle of a regular decagon (10 sides)?

Statistics & Probability

  1. Q29 · Probability and countingA bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If one marble is drawn at random, what is the…
  2. Q30 · Statistics and data analysisThe mean of 6 numbers is 18. If one of the numbers is removed, the mean of the remaining 5 numbers is 20. What was the…
  3. Q31 · Probability and countingTwo fair six-sided dice are rolled. What is the probability that the sum of the two dice is at least 10?
  4. Q32 · Probability and countingIn how many ways can a committee of 3 people be chosen from a group of 8 people?
  5. Q33 · Probability and countingA game costs $5 to play. A player wins $20 with probability 0.15, and otherwise wins nothing. What is the expected net…
  6. Q34 · Statistics and data analysisA distribution has a mean of 70 and a standard deviation of 8. What is the z-score for a value of 82?
  7. Q71 · Probability and countingOf 60 students, 35 play a sport, and 20 of those 35 also play an instrument. If a student who plays a sport is…
  8. Q72 · Statistics and data analysisWhat is the median of the data set 4, 7, 7, 9, 12, 15, 7, 20?
  9. Q73 · Probability and countingIn a race with 5 runners, in how many different ways can 1st, 2nd, and 3rd place be awarded?
  10. Q74 · Probability and countingEvents A and B are independent, with P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?
  11. Q75 · Statistics and data analysisData set A has a standard deviation of 4. Data set B has a standard deviation of 9. Both sets have the same mean.…
  12. Q76 · Statistics and data analysisA box plot shows a first quartile of 15 and a third quartile of 35. What is the interquartile range?
  13. Q77 · Statistics and data analysisA scatterplot has a correlation coefficient of r = -0.85. Which best describes the relationship?
  14. Q115 · Probability and countingThe probability of rain tomorrow is 0.35. What is the probability that it does NOT rain?
  15. Q116 · Probability and countingOf 100 people surveyed, 60 like coffee, 45 like tea, and 25 like both. What is the probability that a randomly…
  16. Q117 · Probability and countingA coin is flipped and a six-sided die is rolled. How many total outcomes are possible?
  17. Q118 · Probability and countingA bag contains 3 red marbles worth 2 points each if drawn, and 7 blue marbles worth 0 points. If one marble is drawn…
  18. Q119 · Statistics and data analysisA student's test score is at the 75th percentile. What does this mean?
  19. Q120 · Statistics and data analysisA researcher wants to know how often adults in a city exercise. She surveys only people leaving a gym. What is the…
  20. Q157 · Probability and countingA bag contains 5 red marbles and 5 blue marbles. A marble is drawn, its color noted, and then replaced before a second…
  21. Q158 · Statistics and data analysisWhat is the range of the data set 2, 5, 6, 8, 9, 11, 45?
  22. Q159 · Statistics and data analysisA frequency table shows the value 1 occurring 5 times, 2 occurring 8 times, 3 occurring 4 times, and 4 occurring 3…
  23. Q160 · Probability and countingA fair coin is flipped 3 times. What is the probability of getting at least one head?
  24. Q161 · Statistics and data analysisA distribution has mean 100 and standard deviation 15. According to the empirical rule, approximately what percent of…
  25. Q162 · Probability and countingA committee of 2 men and 2 women is to be chosen from a group of 5 men and 6 women. How many different committees are…
  26. Q163 · Statistics and data analysisFor the data set 3, 4, 5, 6, 50, how do the mean and median compare?
  27. Q201 · Probability and countingA spinner has 8 equal sections numbered 1 through 8. What is the probability that a spin lands on a multiple of 3?
  28. Q202 · Statistics and data analysisWhat is the population standard deviation of the data set 4, 8, 6, 10, 12? (Round to the nearest hundredth.)
  29. Q203 · Probability and countingOf 50 students, 30 play soccer, 25 play basketball, and 10 play both sports. How many students play neither sport?
  30. Q204 · Probability and countingA bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability…
  31. Q205 · Statistics and data analysisGroup A has a median of 60 and an IQR of 10. Group B has a median of 75 and an IQR of 20. Which group shows more…
  32. Q206 · Statistics and data analysisA line of best fit for a data set is y = 2.5x + 10. Using this model, what value of y is predicted when x = 8?
  33. Q207 · Probability and countingA standard deck of 52 cards is shuffled, and one card is drawn. What is the probability of drawing a face card (jack,…
  34. Q270 · Ratios, rates, and percentsIn a class, 40% of students are male. Of the male students, 25% play chess. What percent of the entire class is male…
  35. Q271 · Probability and countingHow many different ways can 6 numbers be chosen from a set of 49, without regard to order?
  36. Q272 · Statistics and data analysisThe data set 10, 12, 14, 16, 90 includes an outlier. By how much does removing the outlier change the mean?
  37. Q273 · Statistics and data analysisA study finds a strong positive correlation between monthly ice cream sales and the number of drowning incidents. What…
  38. Q274 · Probability and countingEvents A and B are mutually exclusive, with P(A) = 0.3 and P(B) = 0.45. What is P(A or B)?
  39. Q275 · Statistics and data analysisA stem-and-leaf plot has the following rows: stem 2 with leaves 1, 5, 8; stem 3 with leaves 0, 2, 2, 9; stem 4 with…
  40. Q276 · Probability and countingA game show wheel has three outcomes: winning $100 with probability 0.1, winning $20 with probability 0.3, and winning…
  41. Q277 · Statistics and data analysisIn a survey of 400 people, 250 said they prefer Product A. What is the sample proportion who prefer Product A?
  42. Q278 · Statistics and data analysisWhat is the range of the data set 5, 7, 9, 11, 50?
  43. Q279 · Statistics and data analysisTeam A has an average score of 82 over 10 games. Team B has an average score of 78 over 15 games. By how much does…
  44. Q280 · Probability and countingA student takes two independent tests. The probability of failing test A is 0.2, and the probability of failing test B…
  45. Q281 · Probability and countingOf 200 people surveyed, 120 own a car, 80 own a bicycle, and 30 own both. If a person who owns a bicycle is selected…

Integrating Essential Skills

  1. Q35 · Ratios, rates, and percentsA jacket originally priced at $80 is marked up 15%, then later marked down 20% from the new price. What is the final…
  2. Q36 · Ratios, rates, and percentsA car travels 250 miles using 10 gallons of gas, then travels 180 miles using 6 gallons. What is the car's combined…
  3. Q37 · Ratios, rates, and percentsAn account earns simple interest at an annual rate of 4%. If $2,000 is deposited and left for 3 years with no…
  4. Q38 · Ratios, rates, and percentsA recipe uses 3/4 cup of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies, at the same…
  5. Q39 · Ratios, rates, and percentsA painter can paint a room alone at a rate of 1/5 of the room per hour. After working alone for 2 hours, a second…
  6. Q40 · Area and volumeA rectangular plot of land measures 24 feet by 18 feet. What is its area in square yards? (1 yard = 3 feet)
  7. Q41 · Statistics and data analysisOne class of 20 students has an average test score of 85. A second class of 30 students has an average score of 90.…
  8. Q78 · Ratios, rates, and percentsAn interest rate rises from 5% to 8%. By how many percentage points did the rate increase, and what is the percent…
  9. Q79 · Ratios, rates, and percentsOn a map, 1 inch represents 25 miles. If two cities are 7.5 inches apart on the map, what is the actual distance…
  10. Q80 · Exponential and logarithmic functions$1,000 is invested at 6% annual interest, compounded annually. Which value is closest to the balance after 2 years?
  11. Q81 · Ratios, rates, and percentsA cyclist rides 60 miles at 30 miles per hour, then rides another 90 miles at 45 miles per hour. What is the cyclist's…
  12. Q82 · Ratios, rates, and percentsAn item originally priced at $50 is discounted 20%, and then 8% sales tax is applied to the discounted price. What is…
  13. Q83 · Ratios, rates, and percentsBrand A sells 24 ounces of juice for $4.32. Brand B sells 30 ounces for $5.70. Which brand has the lower price per…
  14. Q84 · Linear equations and inequalitiesHow many liters of a 40% acid solution must be mixed with 10 liters of a 10% acid solution to create a mixture that is…
  15. Q85 · Ratios, rates, and percentsA recipe requires 2.5 pounds of flour. If flour is sold only in 16-ounce bags, what is the minimum number of bags…
  16. Q121 · Ratios, rates, and percentsA car travels at 72 kilometers per hour. What is this speed in meters per second? (1 km = 1000 m, 1 hour = 3600 seconds)
  17. Q122 · Ratios, rates, and percentsA model building is built at a scale of 1:50. If the model is 8 centimeters tall, how tall is the actual building, in…
  18. Q123 · Ratios, rates, and percentsA restaurant bill is $68. A customer wants to leave an 18% tip. What is the total amount paid, including the tip?
  19. Q124 · Linear equations and inequalitiesA company has fixed costs of $500 and variable costs of $8 per unit produced. Each unit sells for $20. What is the…
  20. Q125 · Ratios, rates, and percentsA 12-pack of soda costs $5.40. A 24-pack costs $9.60. Which pack has the lower price per can, and what is that price?
  21. Q126 · Area and volumeA room measures 15 feet by 12 feet. What is its area in square inches? (1 foot = 12 inches)
  22. Q127 · Ratios, rates, and percentsAn item originally priced at $120 is discounted 25%, and then an additional 10% is taken off the new price. What is…
  23. Q128 · Statistics and data analysisA student's final grade is based 70% on exams (average 82) and 30% on homework (average 95). What is the student's…
  24. Q164 · Ratios, rates, and percentsA metal block has a mass of 540 grams and a volume of 60 cubic centimeters. What is its density, in grams per cubic…
  25. Q165 · Ratios, rates, and percentsA salesperson earns a 6% commission on sales. If total sales for the month are $12,500, what is the commission earned?
  26. Q166 · Ratios, rates, and percentsA flight departs at 2:15 PM and lands 3 hours 40 minutes later. What time does the flight land?
  27. Q167 · Ratios, rates, and percentsWhat is 40% of 25% of 800?
  28. Q168 · Ratios, rates, and percentsA train travels at 80 miles per hour for 2.5 hours, then slows to 60 miles per hour for 1.5 hours. What is the total…
  29. Q169 · Ratios, rates, and percentsAn item normally costs $40, but there is a $5 discount per item when buying 3 or more. What is the total cost of…
  30. Q170 · Linear equations and inequalitiesIn 5 years, a person will be twice as old as they were 3 years ago. What is the person's current age?
  31. Q171 · Ratios, rates, and percentsA recipe for 8 servings uses 2 cups of sugar. How much sugar is needed for 20 servings, at the same rate?
  32. Q172 · Ratios, rates, and percentsThe actual length of an object is 50 centimeters, but a student measures it as 47 centimeters. What is the percent…
  33. Q208 · Ratios, rates, and percentsAn employee earns $18 per hour for the first 40 hours worked in a week, and 1.5 times that rate for each hour beyond…
  34. Q209 · Ratios, rates, and percentsIf 1 US dollar is equivalent to 0.92 euros, how many euros is $150 equivalent to?
  35. Q210 · Ratios, rates, and percentsA car's fuel tank holds 14 gallons. If gasoline costs $3.45 per gallon, how much does it cost to fill an empty tank?
  36. Q211 · Ratios, rates, and percentsA recipe calls for flour and sugar in a ratio of 5:2. If 20 cups of flour are used, how many cups of sugar are needed?
  37. Q212 · Ratios, rates, and percentsA $2,000 loan has 5% simple annual interest. What is the total amount owed after 2 years?
  38. Q213 · Ratios, rates, and percentsA runner's pace is 8 minutes per mile. What is this pace in miles per hour?
  39. Q214 · Statistics and data analysisOne class of 15 students has an average score of 80. A second class of 5 students has an average score of 90. What is…
  40. Q215 · Ratios, rates, and percentsA store buys an item for $40 and sells it at a 60% markup. Later, the item is put on sale for 25% off the selling…
  41. Q216 · Ratios, rates, and percentsA swimming pool holds 15,000 gallons of water. If 1 cubic foot equals approximately 7.48 gallons, which value is…
  42. Q282 · Ratios, rates, and percentsA restaurant bill is $60 before tax. An 8% sales tax is applied, and then a 20% tip is added based on the pre-tax…
  43. Q283 · Ratios, rates, and percentsA container holds 15 liters. Approximately how many gallons is this, given that 1 gallon ≈ 3.785 liters?
  44. Q284 · Ratios, rates, and percentsA stock price rose from $40 to $52. What was the percent increase?
  45. Q285 · Probability and countingA weather forecast gives a 30% chance of rain on each of the next two days, with the two days independent of each…
  46. Q286 · Ratios, rates, and percentsOne painter can paint a fence in 8 hours. A second painter works twice as fast as the first. Working together, how…
  47. Q287 · Ratios, rates, and percentsWhich option has the lowest price per ounce: A) 16 oz for $4.00, B) 20 oz for $5.20, or C) 32 oz for $7.68?
  48. Q288 · Ratios, rates, and percents$200 is converted to euros at a rate of 1 USD = 0.92 EUR. A 5% fee is then charged on the converted amount. How many…
  49. Q289 · Ratios, rates, and percentsAn item originally priced at $200 is discounted three separate times, each time by 10% off the current price. What is…
  50. Q290 · Ratios, rates, and percentsA ship travels at 20 knots (nautical miles per hour). Approximately how many regular miles per hour is this, given 1…
  51. Q291 · Statistics and data analysisA student has test scores of 85, 90, and 78 on the first three tests. What score is needed on the fourth test for the…
  52. Q292 · Ratios, rates, and percentsIf 1 US dollar is equivalent to 0.92 euros, approximately how many US dollars is 138 euros equivalent to?
  53. Q293 · Ratios, rates, and percentsA phone costs $600. A store offers a 15% discount, and then charges 8% sales tax on the discounted price. What is the…
  54. Q294 · Ratios, rates, and percentsA paint mixture uses blue and white paint in a ratio of 3:5. How many liters of blue paint are needed to make 40…
  55. Q295 · Ratios, rates, and percentsA 2.5-pound bag of rice costs $4.00. What is the price per ounce? (1 pound = 16 ounces)
  56. Q296 · Ratios, rates, and percents4 workers can complete a job in 10 hours. Working at the same rate per worker, how long would 5 workers take to…
  57. Q297 · Area and volumeA room measures 12 feet by 15 feet. If flooring costs $3.50 per square foot, what is the total cost to floor the room?
  58. Q298 · Function notation and transformationsUsing the formula C = 5/9(F - 32), what is 77°F in degrees Celsius?
  59. Q299 · Linear equations and inequalitiesA company spends $2,000 to set up production, plus $15 per unit produced. Each unit sells for $35. How many units must…
  60. Q300 · Ratios, rates, and percentsA cyclist rides 40 miles in 2 hours, then rides another 45 miles in 1.5 hours. Which value is closest to the cyclist's…