University:
Carleton College
Course:
MATH 101 | Calculus with Problem Solving
Academic year:

2024
Views:

349

Pages:

5
Author:

5CelestialChronicle

Algebra I CP 1. Which expression is equivalent to (-2)^-2? A. (-2)^(-2 * 2) B. (-2)^(-2 * -1) C. (-1)(-2)^2 D. (-1)(-2)^-2 Answer: B 2. Which expression is equivalent to (4x^6)/(2x^3)? A. 2x B. 8x C. 8x^3 D. 16x^6 Answer: C 3. Which expression is equivalent to (27x^12)/(32y^5)? A. 27x^12 / 32y^5 B. 64y^5 / 27x^12 C. (27/32)x^7y^3 D. (27/32)x^7/y^3 Answer: C 4. Which expression is equivalent to (-5x^-3y^4)^-2? A. -25x^5/y^8 B. 25x^5/y^8 C. -y^8/25x^5 D. x^6/25y^8 Answer: D 5. What rule applies to the table? x | y ---| --- -2 | 1/4 -1 | 1/2 0 | 1 1 | 2 2 | 4 8 | 16 Answer: C. y = 4 * 2^x 6. Rewrite 21^(3/4) without a rational exponent. Answer: ∛(21⁴) 7. What is the degree of -5 + 4x² - 2x + 5x³? Answer: 3 8. Simplify: (6m² - 5m + 4) + (7m² + 2m - 5) = 13m² - 3m - 1 (Combine like terms!) 9. Simplify: (12s² + 8s - 6) - (9s² - 2s + 5) = 12s² + 8s - 6 - 9s² + 2s - 5 = 3s² + 10s - 11 10. Simplify: (x + 3)(x + 10) FOIL! x² + 3x + 10x + 30 = x² + 13x + 30 11. Simplify: (2n + 3)² FOIL! (2n + 3)(2n + 3) = 4n² + 6n + 6n + 9 = 4n² + 12n + 9 12. Factor: x² + 7x + 12 (x + 3)(x + 4) 13. What are the solutions of the equation x² + 30x = 1000? x² + 30x - 1000 = 0 (x + 50)(x - 20) = 0 x = -50 or x = 20 14. Factor: x³ - 7x² - 4x + 28 4 terms, so factor by grouping! x²(x - 7) - 4(x - 7) = (x - 7)(x² - 4) = (x - 7)(x + 2)(x - 2) 15. What is the vertex of the graph of the function y = -2/3x² + 5? Use -b/2a, b = 0, a = -2/3 -0 / 2(-2/3) = 0 Now plug 0 in for x: y = -2/3(0)² + 5 = 5 (0, 5) How would the graph of the function y = x^2 be affected if the function were changed to y = -2x^2 + 3? A. The graph would be reflected, stretched, and shifted up 3 B. The graph would be reflected, stretched, and shifted down 3 C. The graph would be reflected, shrunk, and shifted up 3 D. The graph would be reflected, shrunk, and shifted 1 1. down 3 Answer: A Vertex form: y = a(x - h)^2 + k, vertex is (h, k) 17. What is the vertex of the graph of the function y = 3(x - 4)^2 + 17? A. (-4, 17) B. (-4, -17) C. (4, -17) D. (4, 17) Answer: D 18. What is the axis of symmetry of the function y = -x^2 + 6x - 18? A. x = -3 B. x = 3 C. x = -8 D. x = 8 Answer: B QF: x = (-b ± √(b^2 - 4ac)) / (2a) a = 5, b = 2, c = -3 x = (-2 ± √(4 - 4(5)(-3))) / (2(5)) x = (-2 ± √64) / 10 x = (-2 ± 8) / 10 x = 3/5 and -1 19. Use the quadratic formula to solve: 5x^2 + 2x - 3 = 0. A. 1, 3 B. 3/5, -1 C. 2, 5 D. 6, 1 Answer: B 20. What is the value of the discriminant of the equation 6x^2 - 5x - 3 = 0? A. -47 B. 24 C. 97 D. 115 Answer: C b^2 - 4ac = (-5)^2 - 4(6)(-3) = 25 + 72 = 97 21. How many solutions does 5x^2 - 2x + 3 = 0 have? A. None B. One C. Two D. Three Answer: A Find the discriminant! b^2 - 4ac = (-2)^2 - 4(5)(3) = 4 - 60 = -56 Because we got a negative, no solution. 22. The graph represents what type of function? [Image of a parabola opening downwards] A. absolute value B. exponential C. linear D. quadratic Answer: D woosh graph!