HSPT Domain 4: Quantitative Skills Welcome to your HSPT Domain 4: Quantitative Skills 1. HSPT: Quantitative Skills If \(x\) and \(y\) are integers that satisfy the equation \(2x^2 - 3xy + y^2 = 30\), what is the value of \(x\) when \(y = 3\)? A. 2 B. 4 C. 5 D. 6 None 2. HSPT: Quantitative Skills A sequence is defined as \(a_n = n^2 + n - 1\). What is the fifth term in this sequence? A. 24 B. 29 C. 30 D. 35 None 3. HSPT: Quantitative Skills What is the sum of the roots of the equation \(x^2 - 6x + 8 = 0\)? A. 2 B. 4 C. 6 D. 8 None 4. HSPT: Quantitative Skills A rectangular prism has a volume of 240 cubic units. If its length is 8 units and its width is 5 units, what is its height? A. 3 units B. 6 units C. 9 units D. 12 units None 5. HSPT: Quantitative Skills What is the least common multiple (LCM) of 18, 24, and 32? A. 288 B. 432 C. 576 D. 864 None 6. HSPT: Quantitative Skills In a geometric sequence, the first term is 3 and the common ratio is 2. What is the 5th term? A. 24 B. 48 C. 96 D. 192 None 7. HSPT: Quantitative Skills If the sum of the interior angles of a polygon is 1260 degrees, how many sides does the polygon have? A. 7 B. 8 C. 9 D. 10 None 8. HSPT: Quantitative Skills What is the value of \(x\) in the equation \(\frac{5x - 15}{10} = 2x - 6\)? A. 3 B. 5 C. 7 D. 9 None 9. HSPT: Quantitative Skills A circle has a circumference of 31.4 units. What is the approximate diameter of the circle? A. 5 units B. 10 units C. 15 units D. 20 units None 10. HSPT: Quantitative Skills If \(3x - 2y = 12\) and \(2x + 3y = -6\), what is the value of \(x\)? A. -2 B. 0 C. 2 D. 4 None 11. HSPT: Quantitative Skills In the expansion of \((x + y)^4\), what is the coefficient of the \(x^2y^2\) term? A. 4 B. 6 C. 12 D. 16 None 12. HSPT: Quantitative Skills A set of numbers has a mean of 10 and a standard deviation of 2. If 14 is added to each number in the set, what is the new standard deviation? A. 2 B. 4 C. 6 D. 8 None 13. HSPT: Quantitative Skills What is the area, in square units, of a triangle with sides of lengths 13 units, 14 units, and 15 units? A. 84 B. 88 C. 90 D. 94 None 14. HSPT: Quantitative Skills If the function \(f(x) = 2x^2 + 3x - 5\) intersects the x-axis at two points, what is the product of these two x-intercepts? A. \(-\frac{5}{2}\) B. \(-\frac{5}{3}\) C. 2.5 D. 3 None 15. HSPT: Quantitative Skills A set contains the numbers \{2, 3, 7, x\}. If the median of the set is 5, what is the value of \(x\)? A. 4 B. 8 C. 9 D. 10 None 16. HSPT: Quantitative Skills A circle is inscribed in a square. If the circumference of the circle is \(8\pi\), what is the area of the square? A. 16 B. 32 C. 64 D. 128 None 17. HSPT: Quantitative Skills If \(3^x = 81\) and \(2^y = 32\), what is the value of \(x + y\)? A. 7 B. 8 C. 9 D. 10 None 18. HSPT: Quantitative Skills The ratio of the lengths of the sides of a rectangle is 3:4, and its perimeter is 70 units. What is the length of the shorter side? A. 9 units B. 10.5 units C. 15 units D. 17.5 units None 19. HSPT: Quantitative Skills A fair die is rolled twice. What is the probability of rolling a sum of 9 on the two rolls? A. \(\frac{1}{9}\) B. \(\frac{4}{36}\) C. \(\frac{1}{6}\) D. \(\frac{1}{4}\) None 20. HSPT: Quantitative Skills A cylinder has a radius of 3 units and a height of 4 units. What is the volume of the cylinder? A. 36\(\pi\) units\(^3\) B. 48\(\pi\) units\(^3\) C. 54\(\pi\) units\(^3\) D. 72\(\pi\) units\(^3\) None 1 out of 20 Time is Up! Time's up
