Math Practice Test Solution Key

Semester 1 Multiple Choice Practice Exam Name: Hour: Pre-Calculus 1. Solve the equation: x³ + 5x² - 6x - 30 = 0 x²(x + 5) - 6(x + 5) = 0 (x + 5)(x² - 6) = 0 x = -5, x = ±√6 A. 5 ± √6 B. -5, 6 C. -5, ±√6 D. -5, ±i√6 2. A ball is thrown straight upward. Use the formula h(t) = -16t² + 32t to find the maximum height reached by the ball. -16t² + 32t = 16 t = 1 A. 16 ft B. 1 ft C. 32 ft D. 2 ft 3. Write a polynomial in standard form with zeros 7 and -2i. (x - 7)(x + 2i)(x - 2i) = (x - 7)(x² + 4) = x³ - 7x² + 4x - 28 A. f(x) = x³ - 7x² + 4x - 28 B. f(x) = x² + 2ix - 7x - 14i C. f(x) = x³ + 7x² + 4x + 28 D. f(x) = x³ - 7x² - 4x + 28 4. Find the sum: 1/(x - 1) + 5/(x + 2) = (x + 2 + 5(x - 1)) / ((x - 1)(x + 2)) = (6x - 3) / ((x - 1)(x + 2)) A. 6/(3x + 1) B. 6/((x - 1)(x + 2)) C. (6x + 9)/((x - 1)(x + 2)) D. (6x - 3)/((x - 1)(x + 2)) 5. Find (f ∘ g)(x) if f(x) = 2x - 6 and g(x) = x² - 1. 2(x² - 1) - 6 = 2x² - 2 - 6 = 2x² - 8 A. 2x² - 8 B. 4x² - 24x + 35 C. 2x³ - 6x² - 2x + 6 D. 2x² - 4 6. The graph of f is given. Identify its domain in interval notation. [Image of a parabola with vertex at (-2, 0)] A. (-∞, ∞) B. (-∞, 2] C. (-∞, 2) D. [0, 4] 7. State the domain for: f(x) = √(x + 1) A. [-1, ∞) B. (-1, ∞) C. (-∞, ∞) D. [0, ∞) 8. Find the inverse of f(x) = 1/2x + 3. x = 1/2y + 3 2x - 6 = y f^-1(x) = 2x - 6 9. Which of the following results in the graph of f(x) = |x| being stretched horizontally by a factor of 2 and reflected over the y-axis? f(x) = |-1/2x| 10. Given the parent function f(x) = √x, state the translations in the graph of f(x) = -√(x + 3). Shift left 3, reflect over x-axis 11. Which statement appears to be FALSE for the graph below? [Image of a graph] The leading coefficient is positive 12. Choose the correct equation for the graph. [Image of a graph] f(x) = (x + 2)(x - 1)²(x - 3) 13. State the asymptotes of y = (2x + 1)/(x - 3). VA: x = 3 HA: y = 2 14. Identify the hole, if it exists, in the graph of f(x) = (x²+4x+3)/(x+1). (x+3)(x+1)/(x+1) = (x+3) Hole at (-1, 2) 15. Given the equation f(x) = log₂(x-3) + 4, which of the following statements is true? The domain is (3, ∞) 16. Identify the expression that is NOT equivalent to log₂20. log₃3²⁰ = 20 17. Solve: (¼)^(x-1) = 8^x 2^(-2x+2) = 2^(3x) -2x + 2 = 3x x = 2/5 18. Solve: 3^x = 7 log₃7 = x x ≈ 1.7712 19. Solve: ln(3-x) = 4 e⁴ = 3-x x = 3-e⁴ ≈ -51.6 20. Solve: log₂x + log₂(x+6) = 4 log₂(x(x+6)) = 4 x(x+6) = 2⁴ x² + 6x - 16 = 0 (x+8)(x-2) = 0 x = -8, 2 21. If $1200 is invested at an interest rate of 7% compounded monthly, determine the balance in the account after 5 years. A = 1200(1+0.07/12)^(12*5) ≈ $1751.20 22. While standing 500 ft from the base of a mountain, you measure the angle of elevation to the top of the mountain to be 35°. How tall is the mountain? tan(35°) = h/500 h = 500 tan(35°) ≈ 350 ft 23. If cosθ = -√3/2 and θ is in Quadrant II, find tanθ. sinθ = √(1 - (-√3/2)²) = 1/2 tanθ = sinθ/cosθ = (1/2)/(-√3/2) = -1/√3 = -√3/3 24. Find the terminal point determined by the angle θ = -4π/3. Answer: C. (-1/2, √3/2) 25. Find the exact value of sin(5π/6). Answer: B. 1/2 26. Write the equation of the sine function with amplitude 3 and period π/2. Answer: C. y = 3sin(4x) 27. State a sine equation that represents the graph below. [Image of a sine graph] Answer: B. y = 2sin(3x) + 1 28. Find tan⁻¹(-√3/3) Answer: A. -π/6 29. Evaluate cot(csc⁻¹(13/5)) Answer: D. 12/5 30. Determine the angular velocity if 32 revolutions are completed in 3 seconds. (in radians/s) Answer: A. 67 rad/s