PreACT Domain 2: Math Welcome to your PreACT Domain 2: Math 1. PreACT: Math A sphere has a volume of \( 288\pi \) cubic centimeters. What is the radius of the sphere? 6 cm 8 cm 4 cm 3 cm None 2. PreACT: Math In a sequence, each term after the first is 3 more than the previous term. If the first term is 2, what is the 100th term? 302 299 298 301 None 3. PreACT: Math What is the sum of all the integer values of \( x \) that satisfy the inequality \( |x-5| \leq 3 \)? 18 21 15 12 None 4. PreACT: Math If \( \tan(\theta) = 1 \), and \( \theta \) is an angle in the first quadrant, what is \( \theta \) in radians? \( \frac{\pi}{4} \) \( \frac{\pi}{3} \) \( \frac{\pi}{6} \) \( \frac{\pi}{2} \) None 5. PreACT: Math The sum of the interior angles of a polygon is 1800 degrees. How many sides does the polygon have? 12 10 13 11 None 6. PreACT: Math A quadratic function \( f(x) = ax^2 + bx + c \) has a maximum value of 25 at \( x = -3 \). If \( a = -2 \), what is \( c \)? 49 41 53 45 None 7. PreACT: Math If \( \log_2(8) = x \), what is the value of \( x \)? 2 4 3 1 None 8. PreACT: Math Two trains are moving towards each other at speeds of 60 km/hr and 80 km/hr respectively. They begin at a distance of 210 km apart. After how many hours will they meet? 1.5 1.75 2 2.5 None 9. PreACT: Math If the sum of a number and its reciprocal is 5, what is the product of the number and its reciprocal? 1 25 5 4 None 10. PreACT: Math A train travels 360 km in 3 hours. For the next 2 hours, it travels 260 km. What is the average speed for the entire journey? 100 km/hr 124 km/hr 130 km/hr 140 km/hr None 11. PreACT: Math If \( 4^x = 64 \), what is the value of \( x \)? 3 2.5 4 1.5 None 12. PreACT: Math The equation \( \frac{1}{x} + \frac{1}{y} = \frac{1}{6} \) has a solution where \( x = 9 \). What is \( y \)? 18 9 12 24 None 13. PreACT: Math What is the coefficient of \( x \) in the expansion of \( (3x-2)^4 \)? -96 -108 108 96 None 14. PreACT: Math A clock shows the time as 3:15. What is the angle between the hour and minute hands? 7.5 degrees 97.5 degrees 82.5 degrees 52.5 degrees None 15. PreACT: Math What is the result of \( i^{22} \)? 1 -1 i #NAME? None 16. PreACT: Math If \( 3x + 4y = 12 \) and \( x = 2 \), what is \( y \)? 1.5 2 1 0.5 None 17. PreACT: Math What is the value of \( x \) if \( 5x - 2 = 3x + 6 \)? 4 3 2 1 None 18. PreACT: Math If \( 2^x = 32 \), what is \( x \)? 6 5 4 3 None 19. PreACT: Math The sum of the ages of three siblings is 42 years. If the youngest is 4 years younger than the middle, and the middle is 6 years younger than the oldest, what is the age of the middle sibling? 12 years 14 years 16 years 18 years None 20. PreACT: Math An arithmetic sequence starts with an initial term of 5 and a common difference of 3. What is the 50th term of the sequence? 149 152 147 155 None 21. PreACT: Math If \(x\) and \(y\) are real numbers such that \(x^2 + y^2 = 10\) and \(xy = 4\), what is \( (x + y)^2 \)? 18 20 22 24 None 22. PreACT: Math A circle has a radius of 10 cm. What is its circumference? \(20\pi\) cm \(40\pi\) cm \(30\pi\) cm \(10\pi\) cm None 23. PreACT: Math What is the value of \(x\) in the equation \(\sqrt{x+6} = x - 6\)? 10 9 8 7 None 24. PreACT: Math If \(3x + 5y = 15\) and \(5x + 3y = 5\), what is \(x\)? 3 2 5 4 None 25. PreACT: Math The sequence defined by \(a_n = 3n - 2\) starts with \(a_1 = 1\). What is \(a_5\)? 13 14 15 16 None 26. PreACT: Math A circle has a radius of \( r \) and a circumference of \( 8\pi \). What is the area of the circle? \( 16\pi \) \( 64\pi \) \( 32\pi \) \( 4\pi \) None 27. PreACT: Math The function \( f(x) = |x-3| + |x+4| \) achieves its minimum value at \( x = \)? \(-0.5\) 0.5 -1 1 None 28. PreACT: Math What is the greatest common divisor (GCD) of 36 and 54? 18 36 9 6 None 29. PreACT: Math If \( \log_b(8) = 3 \), what is \( b \)? 2 3 4 8 None 30. PreACT: Math The sum of two numbers is 18 and their product is 80. What is the sum of the reciprocals of these two numbers? \( \frac{9}{40} \) \( \frac{1}{9} \) \( \frac{2}{9} \) \( \frac{1}{10} \) None 31. PreACT: Math A cylindrical can's height is 10 cm and its volume is \( 314 \text{ cm}^3 \). What is the radius of the can's base? 5 cm 7 cm 2 cm 3 cm None 32. PreACT: Math In a triangle, the measures of the three angles are \( x \), \( x + 10^\circ \), and \( x - 10^\circ \). What is the measure of the largest angle? \( 80^\circ \) \( 70^\circ \) \( 90^\circ \) \( 60^\circ \) None 33. PreACT: Math What is the value of \( x \) in the equation \( \sqrt{x+6} = x - 6 \)? 10 9 8 7 None 34. PreACT: Math How many distinct integer solutions does the equation \( \sin(x) = 0.5 \) have within one complete cycle \( [0, 2\pi] \)? 1 2 3 4 None 35. PreACT: Math The sum of the interior angles of a polygon is 1800 degrees. How many sides does the polygon have? 12 10 13 11 None 36. PreACT: Math A clock shows the time as 3:15. What is the angle between the hour and minute hands? 7.5 degrees 97.5 degrees 82.5 degrees 52.5 degrees None 1 out of 36 Time is Up! Time's up
