Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra 2 Midterm Review ANSWER KEY Chapter 9 Review: Sequences and Series 1. Arithmetic ( d 0.5 ) 2. Neither 3. Geometric ( r 0.5 ) 4. 4, 1, 2,5 5. 5, 2,1, 4 6. an 12 n 1 40 7. an 4 5 8. an 127 n 1 5 n 1 9. an 6 4 n 1 a10 1,572,864 10. 360 11. huge number: 1,741,425,868 12. 157,305, 453 13. 52, 26 a10 348 14. 2585 a10 7,812,500 15. 364 a10 82 16. 7.5 17. 16,598 Chapter 1 Review: Solving Eqs & Ineqs 1. a) a 6 b) x 2, x 2. a) x 7 (graph below should have open circle) b) 87 2 x 2 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 c) x 7 or x 3 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 3. C 5 4. C F 32 9 5. a. b. c. d. Distributive Property Commutative Property of Multiplication Symmetric Property Inverse Property of Addition 6. 26 9 8 3 y 6 5 4 3 2 1 -9 -8-1 -2-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -3 -4 9 y -5 8 -6 7 -7 6 -8 5 -9 4 3 2 1 -1 -9 -8-2-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -3 -4 -5 -6 -7 -8 -9 1 3 d) x 2 2 7. Given Addition Property Multiplication Property Substitution Property Addition Property Addition Property Division Property Symmetric Property 8. B, C, D, E 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 9 -5 8 -6 7 -7 6 -8 5 -9 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 y y Algebra 2 Midterm Review ANSWER KEY Chapter 2 Review: Linear Functions 2 1. a) y x 4 b) f x 3x 3 2 Slope = Slope = 3 3 y-int: -4 y-int: 0 y c) x 2 Slope: undefined y-int: none y x x d) 2 x 5 y 10 2 Slope: 5 y-int: -2 e) 6 y 3 x 18 1 Slope: 2 y-int: -3 y y x 2. x-intercept: - 4 x y-intercept: 2 3. a) Not a function, x-values repeat b) Function, passes Vertical Line Test 4. a) y y 2 x 3 3 5. y 3x 56 1 x 0.35 4 b) 15 ounces 6. a) y 7. shift left 2, shift up 4 b) y 4 x 15 x 8. a) y x4 b) y 2 x 5 y y x 9. a) g x f x 2 3 Shift left 2, shift down 3 x b) g x f x Reflect in x-axis (or flip graph upside down) y y x 10. a) b) c) d) x Positive y 1.71x 53.57 87.77 3.76 11. a) y .375 x 722.25 b) 31.5 million 12. a) 5,1 3 7 b) , 2, 2 2 13. a) Yes, function; Domain: all real numbers; Range: y 0 b) Yes, function ; Domain: all real numbers; Range: y 0 c) Not a function; Domain: 1 x 3 Range: 0 y 4 Algebra 2 Midterm Review ANSWER KEY Chapter 4 Review: Quadratics 1. a) y x 2 6 x 7 V : 1,3 axis : x 3 x int : 1 and 7 y int : 7 axis : x 1 x int : .22 and 2.22 y int :1 D : x | x D : x | x R : y | 16 y R : y | y 3 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10 -12 -14 -16 -18 y y x x 1 2 3 4 5 6 7 8 9 x 14 x 2 b) 2 2 x 3 3x 4 d) can’t be factored e) c) 9 4 x 3 4 x 3 4x 5 x 9 b) x 4, x 3. a) x 4, x 5 4. 2 V : 3, 16 18 16 14 12 10 8 6 4 2 2. a) b) f x 2 x 1 3 2, 6 1 3 5. y x 2 3x 18 6. y .004 x 2 .352 x .369 7. a) x 1 5 2 b) x 2 c) x 5 38 d) x 3 233 16 d) x 4 i 26 7 8. B 9. a) i b) 1 10. a) 2 5i b) 14 2i 11. a) x 9i 12. 1, 10 and 4,30 13. 7, 6 and 2,12 c) i c) d) 1 1 7 i 4 4 b) x i 26 c) x 2 i 6 14. B and D 15. a) 6.94 seconds b) 236 meters c) 13.9 seconds Algebra 2 Midterm Review ANSWER KEY Chapter 5 Review (Sections 5.1 & 5.2): Polynomial Functions 1. Standard form: 4𝑥 3 + 2𝑥 2 − 3, degree = 3, cubic trinomial 2. Standard form: −𝑥 5 + 9𝑥 2 − 2𝑥 + 8, degree = 5, quantic polynomial of 4 terms 3. Standard form: 2𝑥 4 + 6𝑥 − 2, degree = 4, quartic trinomial 4. Standard form: 24𝑥 2 + 3, degree = 2, quadratic binomial 5. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞. 6. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞. 7. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞. 8. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞. 9. Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞. 10. Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → −∞. 11. zeros: -2, -3 y-int: (0, 6) 12. zeros: 0, 1, -3 y-int: (0,0) End Behavior: Left: As 𝑥 → −∞, 𝑓(𝑥) → ∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞. End Behavior: Left: As 𝑥 → −∞, 𝑓(𝑥) → −∞. Right: As 𝑥 → ∞, 𝑓(𝑥) → ∞. 13. rel. min = (-.27, -3.83), rel. max = (2.49, 27.63), Increasing: (-.27, 2.49), Decreasing: (−∞, −.27) and (2.49, ∞) 14. rel. min = (.12, .94), rel. max = (-2.79, 13.21), Increasing: (−∞, −2.79) and (. 12, ∞), Decreasing: (−2.79, .12) 15. Positive coefficient and odd degree 16. Negative coefficient and odd degree