Pre-Calculus 11 Mock Final Exam

Name: Class: Date:ID: APre-Calculus 11 Mock Final ExamMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1. Two terms of an arithmetic sequence are t 5 30.6 and t 15 89.6. What is t21?A. t 21 24.7B. t 21 18.8C. t 21 125D. t 21 119.12. Determine t11 of this arithmetic sequence: –20, –35, –50, –65, .A. t 11 80C. t 11 15B. t 11 170D. t 11 203. An arithmetic series has S 21 2793, d 13, and t 21 263; determine the first 3 terms of the series.A. 6 19 32B. 6.5 19.5 32.5 C. 2 15 28D. 3 16 294. 4096 is a term in which geometric sequence?A. 2, 4, 8, 16, .B. 4, 24, 144, 864, .C. 2, 12, 72, 432, .D. 3, 6, 12, 24, .5. In a finite geometric sequence, t 1 5 and t 4 40. If the last term is –640, how many terms are in thesequence?A. 9B. 8C. 10D. 66. A geometric series has t 1 3 and S 6. Determine the common ratio.A. r 0.3C. r 0.5B. r 2D. r 0.257. Determine the common ratio of a geometric series that has these partial sums: S 4 3.5, S 5 3.75,S 6 3.875A. r 1B. r 2C. r 0.5D. r 0.58. Determine the common ratio of this infinite geometric series: 6 24 96 384 Does the series converge or diverge?A. r 4, so the series diverges.C. r 6, so the series diverges.B. r 4, so the series converges.D. None of the above9. For which values of the variable, x, is this radical defined? 22x 4A. x 0B. x òC. x 0D. the radical isnever defined10. Write this radical in simplest form: 5 4131a 11 b 12Then state the values of the variables, a and b, for which the radical is defined.A. 3a 2 b 2 5 17ab 2 ; a ò, b òC. a 2 b 2 5 17ab 2 ; a ò, b 0B. 3a 2 b 2 5 17ab 2 ; a ò, b 0D. a 2 b 2 5 17ab 2 ; a 0, b ò1

Name:11. Simplify this expression:A. 45 3 55ID: A 9 5 35B. 225 3 5C.12. Simplify by adding or subtracting like terms:A. 6w 3 w 3w 2 3 w 3w 2B. 6w 3 w 6w 213. Expand and simplify this expression:A. 3a 2 aB. 3 a 2aB.729w 4 3w 3 w 3 27w 7 3w 2 , w òC. 6w 3 wD. 3w 3 w 3w 22D. 25f 2015. Solve this equation: 3x 30 3x5A. x 2 and x B. x 23A. 45 5 155f 2 g ˆ , f 0, g 0 C. 25f 20 fg 4gfg 4g16. Simplify this expression:D.a ÊÁÁ 3 a 2 ˆ , a 0Ë C.3a 2D.3a 214. Expand and simplify this expression: ÊÁÁ 5ËA. 29fg 20 fgB. 25f 203 9 15 55fg 4gD. x C. x 2532 3 9 72 8 2 3 18 42 72 7 6 2 6 9 14 16 3 72 76217. Solve this equation: 4 2x 2 2 5x 4A. x 4B. x 8C.D. 2 3 18 42 72 762 2 6 9 14 16 3 72 7 6C. x 2D. x 1618. Factor this polynomial expression: 147(2x 5) 2 48(2y 1) 2A. 3(14x 8y 31)(14x 8y 39)C. 2(14x 8y 31)(14x 8y 39)B. 2(14x 8y 31)(14x 8y 39)D. 3(14x 8y 31)(14x 8y 39)19. Factor this polynomial expression: 2(3x 2) 2 9(3x 2) 5A. 3(x 1)(6x 5)B. 2(3x 2)(x 5)C. 2(3x 2)(x 5)D. 3(x 1)(6x 5)20. Solve by factoring: 12x 2 31x 9 01919A. x or x B. x or x 34341919C. x or x D. x or x 343421. Solve this equation: (x 1) 2 7 24A. x 1 17B. x 1 31C. x 1 231D. x 1 17

Name:ID: A22. Solve this quadratic equation: 10x 2 4x 5 0Give the solution to 2 decimal places.A. x 0.93 orB. x 1.87 orC. x 0.53 orx 0.53x 1.07x 0.93D. x 0.73 orx 0.7323. Calculate the value of the discriminant for this equation: 2x 2 4x 1 0A. 8B. 4C. –8D. 2Use the following parabola to answer the next 5 questions.24. State the axis of symmetry.A. x 2B. x 0C. x 4D. x 225. State the domain.A. x 4B. 4 x 0C. x 0D. x ò26. State the range.A. y òB.y 0D. y 4y 227. State the equation of the above parabola.A. y (x 2) 2 4B.y (x 2) 2 428. Determine the roots.A. x 4B. There are no real rootsC.C. y (x 2) 2 4D. y (x 2) 2 4C. x 4 and x 0D. x 4 and x 03

Name:ID: A29. Determine an equation of a quadratic function with the given characteristics of its graph: coordinates of thevertex: V(4, 4); passes through A(3, 2)A. y 2(x 4) 2 4C. y 3(x 4) 2 4B. y 2(x 4) 2 4D. y 2(x 4) 2 430. Write this equation in standard form: y 3x 2 12x 16A. y 3(x 2) 2 4 B. y (x 2) 2 4C. y 3(x 2) 2 4 D. y 3(x 2) 2 431. Solve this quadratic-quadratic system algebraically.y x 2 4x 23y (x 1) 2 15A. (6, –1) and (1, 14)C. (–1, 1) and (14, 6)D. (1, –1) and (6, 14)B. (–1, –1) and (6, –14)32. What are the coordinates of the point(s) of intersection of the line y 7x 5 and the quadratic functiony x 2 15x 4?A. (9,58) and ( 1, 12)C. (9, 58)and(1,12)B. ( 9,58), and (1, 12)D. (9, 58) and (1, 12)33. Write an inequality to describe this graph.A.y 2(x 1) 2 3B.y 2(x 1) 2 3C.y 2(x 1) 2 3D. y 2(x 1) 2 334. Which inequality below is represented by this number line?A. 4x 2 17x 15 0 B. 4x 2 17x 15 0 C. 4x 2 17x 15 0 D. 4x 2 17x 15 035. Solve the quadratic inequality: 2x 2 3 4x 3A. 3 x 1, x òC. x 1 or x 3, x òB. x 3 or x 1, x òD. 1 x 3, x ò4

Name:ID: A36. The answer to a quadratic inequality is 3 x 5. What is the original inequality?C. (x 3)(x 5) 0A. (x 3)(x 5) 0B. (x 3)(x 5) 0D. (x 3)(x 5) 037. Write an inequality to describe this graph.A.y 3x 238. This is a graph of y A.B.f(x) x 2 2x 4f(x) x 2 4x 3B.y 3x 2C.y 3x 2D. y 3x 21. Determine an equation of the quadratic function y f(x).f(x)C.D.5f(x) x 2 2x 3f(x) x 2 4

Name:ID: A39. This is the graph of the reciprocal of a linear function. Which graph below represents the linear function?A.C.B.D.40. Determine the reference angle for the angle 290 in standard position.A. 290 B. 20 C. 110 D. 70 41. Point P(0, –5) is a terminal point of an angle θ in standard position. Determine the value of tan θ.A. –5B. 0C. 5D. undefined6

Name:ID: A42. Determine the exact value of cos 30 .A.13B.32C.23D.1243. Angle θ is in standard position and its terminal arm lies in Quadrant 4. The sine of its reference angle isDetermine the exact value of cos θ .206A.B.620C.420D.4.620444. Point P(2, 6) is on the terminal arm of an angle θ in standard position. Determine the exact value of sin θ.A.40, or6103B.8, or40410C.6, or40310D.2, or4045. For ABC, determine the measure of A to the nearest degree.A. 144 B. 43 C. 120 7D. 77 110

Name:ID: A46. Determine the length of x, to the nearest tenth of a centimetre.A. 26.6B. 36.5C. 11.247. Determine the measure of x, to the nearest tenth of a degree.A. 25.6 B. 18.1 C. 136.3 D. 71.9 8D. 17.1

Name:ID: A48. What is the length of x, to the nearest tenth of a metre?A. 27.7 mB. 21.8 mC. 26.1 mD. 37.6 m49. While flying, a helicopter pilot spots a water tower that is 7.4 km to the north. At the same time, he sees amonument that is 8.5 km to the south. The tower and the monument are separated by a distance of 11.4 kmalong the flat ground. What is the angle made by the water tower, helicopter, and monument?A. 91 B. 11 50. Solve.55h 14h h 2 h2 h 6 h 3A. h 1 or h 1B. h 1C. 40 D. 48 C. h 1D. h 29

Name:ID: A51. Simplify this rational expression and state the non-permissible values of the variable.m2 162m 6m 8m 4m 4A.; m 4 and m 2C.; m 4 and m 2m 2m 2m 4m 4B.; m 4 and m 2D.; m 4 and m 2m 2m 252. Simplify.p q p qpq pqA.pq, p 0, q 0p qC.B. 1, p 0, q 053. Solve.11 2b b 55 2 15A. x 2D.B. x 5 154p2q2 p2 q2, p 0, q 0pqp 2 q 2 p 2 q 2 2pq, p 0, q 0pqC. x 5 152D. no solution54. Simplify.a3a 1 a 2 144 a 2 10a 243a 2 a, a 120A. 10a 120 2a 1, a 12B. 10 (a 12) 2a 1, a 12, a 12, a 2C.(a 12)(a 12)(a 2)D. 2a 2 35a 12, a 12, a 12, a 2(a 12)(a 12)(a 2)955. Solve this equation: x 3 24204A. x and x 9994B. x and x 209C. x 204and x 99D. no solution56. Identify the vertical asymptotes of the graph of the reciprocal of the quadratic function y x 2 4x 5.A. x 2C. y 1 and y 5B. x 1 and x 5D. no vertical asymptotes10

Name:ID: A57. Solve.d5 22d 8d 9 d 81A. d 1 or a 5B. d 1 or d 9C. d 1 or d 558. Solve.w 51 2w20A. w 10C. w 10 or w 10 D. no solutionB. w 5D. d 1 or d 911. Find the number.332C.or232D. 3 or359. The sum of a number and two times its reciprocal isA. 3 or 2B. –3 or 2360. The sum of a number and its square is13A. or2213B.or 2234C.D.1or 141or 2261. This is the graph of the absolute value of a function f(x). What is an equation for f(x)?A.B.y x 2 10x 21 y x 2 10x 21 C. y x 2 10x 21 D. y x 2 10x 21 11

Name:ID: A62. Which absolute value function is represented by this graph?A.B.y 7x 21 y 7x 2 21 C. y 7x 21 D. y 7x 2 21x 12

Pre-Calculus 11 Mock Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. Two terms of an arithmetic sequence are t5 30.6 and t15 89.6. What is t21? A. t21 24.7 B. t21 18.8 C. t21 125 D. t21 119.1 _ 2. Determine t11 of this arithmetic sequence: –20, –35 .