HiSET Math Practice Test Welcome to your HiSET Math Practice Test 1. HiSET Math: Algebra Concepts For which value of \( k \) does the equation \( x^2 + kx + 9 = 0 \) have one real solution? 0 6 9 18 None 2. HiSET Math: Algebra Concepts If \( f(x) = 3x^3 - 2x^2 + x - 5 \), what is the coefficient of the \( x^2 \) term in \( f(x + 1) \)? -2 -4 1 5 None 3. HiSET Math: Algebra Concepts What is the solution to the system of equations \( 2x + 3y = 5 \) and \( 4x - y = 3 \)? \( (1, 1) \) \( (2, -1) \) \( (1, -1) \) \( (2, 1) \) None 4. HiSET Math: Algebra Concepts What is the degree of the polynomial \( 7x^4 - 3x^3 + 2x^2 - x + 5 \)? 1 2 3 4 None 5. HiSET Math: Algebra Concepts What is the axis of symmetry for the parabola given by \( y = -3x^2 + 12x - 7 \)? \( x = 2 \) \( x = -2 \) \( x = 3 \) \( x = -3 \) None 6. HiSET Math: Algebra Concepts If \( i^2 = -1 \), what is \( (3 + 4i)(2 - i) \)? \( 10 + 5i \) \( 11 + 5i \) \( 6 + 11i \) \( 6 - 11i \) None 7. HiSET Math: Algebra Concepts What is the standard form of the equation of the line passing through the points (1, 2) and (3, -2)? \( 2x + y = 5 \) \( x - 2y = -3 \) \( 2x - y = 3 \) \( x + 2y = 3 \) None 8. HiSET Math: Algebra Concepts Solve for \( x \) in the equation \( \frac{1}{x} + \frac{1}{x + 2} = \frac{1}{2} \). \( x = 2 \) \( x = 3 \) \( x = 4 \) \( x = -4 \) None 9. HiSET Math: Algebra Concepts Given the function \( f(x) = \frac{4x}{x^2 - 9} \), for which values of \( x \) is \( f(x) \) undefined? \( x = 3 \) and \( x = -3 \) \( x = 0 \) \( x = 9 \) \( x = \pm\sqrt{9} \) None 10. HiSET Math: Algebra Concepts What is the solution set for the inequality \( 3(x - 2) > 2x + 1 \)? \( x > 5 \) \( x < 5 \) \( x > 3 \) \( x < 3 \) None 11. HiSET Math: Algebra Concepts If the function \( g(x) \) is defined as \( g(x) = 2x^3 - 5x^2 + x - 1 \), then what is the value of \( g(-2) \)? -23 5 -5 23 None 12. HiSET Math: Algebra Concepts The quadratic equation \( 2x^2 - x - 1 = 0 \) has roots \( \alpha \) and \( \beta \). What is \( \alpha\beta + \alpha + \beta \)? 0 -1 1 2 None 13. HiSET Math: Algebra Concepts What are the x-intercepts of the function \( f(x) = x^2 - 4x + 3 \)? \( x = 1 \) and \( x = 3 \) \( x = 0 \) and \( x = 3 \) \( x = 1 \) and \( x = -3 \) \( x = -1 \) and \( x = 3 \) None 14. HiSET Math: Numbers and Operations If \( \frac{2}{3} \) of a number is 12, what is \( \frac{4}{5} \) of the same number? \( \frac{80}{3} \) 10 \( \frac{96}{5} \) 16 None 15. HiSET Math: Numbers and Operations What is the sum of the prime factors of 210? 15 16 17 18 None 16. HiSET Math: Numbers and Operations If \( 5^x = 125 \), what is the value of \( 5^{x+2} \)? 625 3125 1250 2500 None 17. HiSET Math: Numbers and Operations If the average of four consecutive even numbers is 17, what is the largest number? 18 20 22 24 None 18. HiSET Math: Numbers and Operations What is the least common multiple (LCM) of 18 and 24? 72 144 36 48 None 19. HiSET Math: Numbers and Operations If \( \frac{1}{x} + \frac{1}{y} = \frac{1}{8} \) and \( x = 16 \), what is the value of \( y \)? 16 24 32 48 None 20. HiSET Math: Numbers and Operations What is the result when the least common denominator of \( \frac{1}{6} \) and \( \frac{1}{8} \) is used to express these fractions? \( \frac{4}{24} \) and \( \frac{3}{24} \) \( \frac{4}{48} \) and \( \frac{6}{48} \) \( \frac{2}{24} \) and \( \frac{3}{24} \) \( \frac{4}{12} \) and \( \frac{3}{12} \) None 21. HiSET Math: Numbers and Operations Which of the following is a cube root of 216? 6 8 9 12 None 22. HiSET Math: Numbers and Operations A number increased by 25\% equals 125. What is the number? 90 100 110 120 None 23. HiSET Math: Numbers and Operations If the reciprocal of a number minus 2 equals the number itself, what is the number? 2 \( \frac{1}{2} \) \( -1 \) \( -\frac{1}{2} \) None 24. HiSET Math: Measurement/Geometry A cone has a radius of 4 cm and a height of 9 cm. What is the volume of the cone? \(48\pi \text{ cm}^3\) \(96\pi \text{ cm}^3\) \(144\pi \text{ cm}^3\) \(36\pi \text{ cm}^3\) None 25. HiSET Math: Measurement/Geometry A cylinder and a cone have the same base radius and height. If the volume of the cylinder is 150 cm\(^3\), what is the volume of the cone? 50 cm\(^3\) 100 cm\(^3\) 200 cm\(^3\) 450 cm\(^3\) None 26. HiSET Math: Measurement/Geometry A rectangular prism has a length of 10 cm, a width of 4 cm, and a height of 5 cm. What is the diagonal length of the prism? 11 cm 13 cm 19 cm 7 cm None 27. HiSET Math: Measurement/Geometry In a circle with a radius of 8 cm, what is the length of an arc subtended by a central angle of 60\(^{\circ}\)? \( \frac{8\pi}{3} \) cm \( \frac{16\pi}{3} \) cm 4\(\pi\) cm 8\(\pi\) cm None 28. HiSET Math: Measurement/Geometry A sphere has a volume of \( \frac{288\pi}{3} \) cm\(^3\). What is the radius of the sphere? 3 cm 6 cm 9 cm 12 cm None 29. HiSET Math: Measurement/Geometry If the area of a circle is 50\(\pi\) cm\(^2\), what is the circumference of the circle? 10\(\pi\) cm 20\(\pi\) cm 25\(\pi\) cm 50\(\pi\) cm None 30. HiSET Math: Measurement/Geometry A trapezoid has bases of 6 cm and 10 cm, and a height of 4 cm. What is its area? 32 cm\(^2\) 64 cm\(^2\) 48 cm\(^2\) 24 cm\(^2\) None 31. HiSET Math: Measurement/Geometry What is the lateral surface area of a right circular cone with a base radius of 3 cm and a slant height of 5 cm? 15\(\pi\) cm\(^2\) 30\(\pi\) cm\(^2\) 45\(\pi\) cm\(^2\) 60\(\pi\) cm\(^2\) None 32. HiSET Math: Measurement/Geometry A regular hexagon is inscribed in a circle with a radius of 8 cm. What is the perimeter of the hexagon? 48 cm 96 cm 24 cm 72 cm None 33. HiSET Math: Measurement/Geometry A pyramid has a square base with sides of length 6 cm and a height of 8 cm. What is the volume of the pyramid? 96 cm\(^3\) 48 cm\(^3\) 144 cm\(^3\) 288 cm\(^3\) None 34. HiSET Math: Data Analysis Probability and Statistics A survey was conducted to determine the favorite type of movie among a group of people. The results were 30% for action, 25% for comedy, 15% for horror, and the rest for drama. What is the probability that a person chosen at random prefers drama? 30% 25% 20% 15% None 35. HiSET Math: Data Analysis Probability and Statistics In a class of 60 students, 30% received an A grade. If three students are selected at random, what is the probability that exactly two of them received an A? 0.324 0.216 0.108 0.432 None 36. HiSET Math: Data Analysis Probability and Statistics A box contains 8 blue, 7 red, and 5 green balls. If two balls are drawn at random, what is the probability that both are green? Jan-95 Feb-57 Jan-38 19-Jan None 37. HiSET Math: Data Analysis Probability and Statistics A dataset has a mean of 50 and a standard deviation of 5. If all the values in the dataset are increased by 5, what is the new standard deviation? 5 10 50 55 None 38. HiSET Math: Data Analysis Probability and Statistics The interquartile range of a dataset is 15. If the lower quartile is 20, what is the minimum possible value of the upper quartile? 35 40 45 50 None 39. HiSET Math: Data Analysis Probability and Statistics A fair die is rolled three times. What is the probability of rolling a six all three times? 18-Jan Jan-36 1/216 6-Jan None 40. HiSET Math: Data Analysis Probability and Statistics A set of data is normally distributed with a mean of 100 and a standard deviation of 15. What percentage of the data lies within one standard deviation of the mean? 68% 95% 99.70% 50% None 41. HiSET Math: Data Analysis Probability and Statistics In a certain town, the probability that it will rain on any given day is 0.3. What is the probability that it will rain on exactly two out of five consecutive days? 0.1323 0.3087 0.528 0.1848 None 42. HiSET Math: Data Analysis Probability and Statistics A student must choose 3 courses from a list of 5. How many different combinations of courses can the student choose? 10 20 30 60 None 43. HiSET Math: Data Analysis Probability and Statistics A bag contains 4 red, 5 blue, and 6 green marbles. What is the probability of drawing two blue marbles in a row without replacement? 7-Jan 21-Feb 21-Jan 21-Apr None 44. HiSET Math: Algebra Concepts If \( f(x) = 2x^2 - 4x + 3 \) and \( g(x) = x - 5 \), what is \( f(g(3)) \)? 10 -1 8 5 None 45. HiSET Math: Algebra Concepts What are the solutions to the equation \( 3x^2 - 7x - 6 = 0 \)? \( x = 3, x = -2/3 \) \( x = 2, x = -3/2 \) \( x = -2, x = 3/3 \) \( x = -3, x = 2 \) None 46. HiSET Math: Algebra Concepts If \( h(x) = x^3 - 4x \), find \( h(-2) \). 0 4 8 -12 None 47. HiSET Math: Algebra Concepts Solve for \( x \): \( \frac{1}{2}(6x - 4) = 4x + 6 \). \( x = -5 \) \( x = 5 \) \( x = 10 \) \( x = -10 \) None 48. HiSET Math: Algebra Concepts What is the vertex of the parabola defined by \( y = 2x^2 - 8x + 3 \)? (2, -5) (-2, 3) (2, -1) (4, -5) None 49. HiSET Math: Algebra Concepts If the roots of the equation \( x^2 - px + 16 = 0 \) are real and equal, what is the value of \( p \)? 8 4 16 32 None 50. HiSET Math: Algebra Concepts Simplify the expression: \( (3x - 4)(2x + 5) \). \( 6x^2 + 7x - 20 \) \( 6x^2 - 7x + 20 \) \( 6x^2 + 15x - 8x - 20 \) \( 6x^2 + x - 20 \) None 51. HiSET Math: Algebra Concepts What is the inverse function of \( f(x) = \frac{2x - 3}{5} \)? \( f^{-1}(x) = \frac{5x + 3}{2} \) \( f^{-1}(x) = \frac{5x - 3}{2} \) \( f^{-1}(x) = \frac{2x + 3}{5} \) \( f^{-1}(x) = \frac{5x - 3}{2} \) None 52. HiSET Math: Algebra Concepts What is the remainder when \( 2x^3 - 3x^2 + 4x - 5 \) is divided by \( x - 2 \)? 3 7 11 -1 None 53. HiSET Math: Algebra Concepts If \( a(x) = x^2 + x - 6 \) and \( b(x) = x - 2 \), what is \( a(x) \div b(x) \)? \( x + 3 \) \( x - 3 \) \( x + 2 \) \( x - 2 \) None 54. HiSET Math: Algebra Concepts Solve for \( y \) in the equation \( 2y - 3x = 6 \). \( y = \frac{3}{2}x + 3 \) \( y = \frac{3}{2}x - 3 \) \( y = \frac{3}{2}x + 6 \) \( y = \frac{3}{2}x - 6 \) None 55. HiSET Math: Algebra Concepts Evaluate \( 4x^2 - 9 \) when \( x = 3 \). 18 27 36 45 None 1 out of 55 Time is Up! Time's up
