Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 1. Graph the following on the grid provided. a ) (x + 2 ) + (1 - 3)2= 16 5 1-5 5 .... Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 by ( x - 1 ) ( 1 + 2 ) - -1 4 9 5 5 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 4 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment c) 4(x + 3)2+ 16(1-5)2=16 5 1-5 5 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 d) x = -2(y -2)-+3 u -5 5 -5 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 5 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment e) x2 - (1 - 2) =9 5 1-5 5 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 2. Which conic is represented by each equation? Parabola, ellipse, circle, hyperbola a) 6x2 - y2+ 6x - 3=0 a) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) 6x2 + 12 + 6x - 3=0 b) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 c) 6x + y+ 6x - 3=0 c) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 d) 6x- + 6y +6x - 3=0 d) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 3. Determine the radius of the circle 16x2 + 16y2 = 64. 3. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 6 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 4. Determine the length of the major axis of the ellipse + = 1. 64 81 4. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 5. Determine the coordinates of the vertices for the hyperbola: x2 - y = -36 5. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 6. Determine the distance between the vertices of: (x - 7)2 (1 + 3)2 = 1 64 25 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 7. Determine the slopes of the asymptotes of the following hyperbola. x 2 (y - 6) -1 49 81 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 7 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 8. Determine the equation of the asymptotes and the length of the transverse axis of the following hyperbola. A grid is provided for rough work. (x - 3)2 (1 + 1)2 =-1 36 4 equation of asymptotes Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary = length of transverse axis Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 9. Find the equation of the rectangular hyperbola with vertices (-3, -4), (5, -4). A grid is provided for rough work 9. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 8 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 10. If an ellipse has vertices at (-3, -6), (9, -6) and minor axis of length 8. Determine the equation of the ellipse. A grid is provided for rough work. X unit 10. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary = 11. Write the equation of the hyperbola with vertices on the x-axis and centre at (0, 0) . Transverse axis of length 6 and asymptotes with equations y = 12x. A grid is provided for rough work. 11. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 9 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 12. A parabola has vertex (3, -1), a horizontal axis of symmetry and passes through the point (-3, 5). Determine the equation of the parabola. A grid is provided for rough work. X 12. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 13. Determine the equation of a circle with centre (-3, 2) that passes through the point (1, -6) . 13. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 10 of 14Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 14. Determine the equation of the conic graphed below. un 14. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 15. Change the following equation to Standard Form. 4x - y - 24x - 4y + 16 = 0 15. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 11 of 14Mathematics Fro-Calculus 12 Unit 9 Self-Assessment 16. Change the following equation to Standard Form. 3):2 + y + 36): + 112 = 0 16. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Procient = 4 17. What conditions must be true for C in the equation x2 + Cy2 = 36 for an ellipse to have a vertical major axis ? Exemplar}.r =5 l'i'. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Procient = 4 Exemplar}.I =5 18. What conditions must be true for 2 + Cy2 + D): + By = D , so that the conic section is a parabola with vertex (0, D} and horizontal axis of synnnen'y? 18. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Procient = 4 Exemplar}.I =5 Page 12 of 14 Mathematics Pre-Calculus 12 Unit 9 Self-Assessment 19. How would you cut a doubled napped cone with a plane to produce the following. a) a circle Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) an ellipse Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 c) a hyperbola Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 d) a parabola Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 13 of 14Mathematics Pre-Calculus 12 Unit 10 Self-Assessment 1. Which of the following sequences is NOT an arithmetic sequence and EXPLAIN how you knew? A. 6, 2, 1o, 18,... B. 1, 2, 4, s, 16,... C. 1,1, ll, 2, 2 2 D. 5, 10, 15, 20, 1. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 2. Determine the indicated term of the arithmetic sequence. 9, 5, 1, 3, . . .; 34 2) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 3. Given the arithmetic sequence 38, 47, 56, 65, . . . 3) determine the general term In . a) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) determine the 25m term. 13) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =5 Page 4of16 Mathematics Pro-Calculus 12 Unit 10 Self-Assessment 4. Given the arithmetic sequence 19, ll, 3, . . . . , 477 . Determine the number of terms in the sequence. 4) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =! 5. Determine the rst term for the arithmetic sequence given the following values. :27 = 3?, d = 3 5) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Exemplary =! 6. What position is the given term (nd It) for the given arithmetic sequence. 1 2 t 220; 5, 5, 4, . .. \" 3 3 6) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =! Page50f16 Mathematics Pro-Calculus 12 Unit 10 Self-Assessment 3'. Determine the indicated term for an arithmetic sequence given two terms of the sequence. r 218,: 4 16 = 54;determ1ne r10 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 8. The unit measure for atmospheric pressure is kPa (Kilo-Pascals). At sea level the standard atmospheric pressure is 101.3 kPa. For every 1000 feet increase in altitude, atmospheric pressure decreases by 1.8 kPa. What is the atmospheric pressure at 50, 000 feet? 3) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =5 9. Determine the indicated value of the following: 10+ 12+ 14+....(324) 9) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =5 Page60f16 Mathematics Pre-Calculus 12 Unit 10 Self-Assessment 10. Determine the sum of the following arithmetic series: 9 + 3 + (-3)+....+ (-123) 10) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 11. Determine the common difference, d for the arithmetic series given the following values. S1 = 682 and a = 17 11) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 12. Determine n for the arithmetic series given the following values, n is equal for both S,, and t. S = 561, t = 71 and a = 31 12) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 7 of 16Mathematics Pre-Calculus 12 Unit 10 Self-Assessment l3. Determine the indicated sum for the arithmetic series given the following the values. a=8, rl6=68, S12 =? 13) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 14. When an object is dropped from rest it falls about 5 min the rst second, 15 m in the second, second, 25 m in the third second, and so on. If a rock is dropped from a hot air balloon and takes 16 seconds to hit the ground, how high above the ground is the balloon? 14) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 15. Determine the sum of all the multiples of 4 between 1 and 999. 15) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 ' Proficient = 4 Exemplary =5 Pageaof 16 Mathematics Pre-Caleulus 12 All answers rounded to 2 decimal places unless otherwise stated. 17. Given the geometric sequence 16, 8, 4, a) determine the general term r\" . Unit 10 Self-Assessment 3) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) determine the 13\"1 term. 13) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page90f16 Mathematics Pre-Calculus 12 Unit 10 Self-Assessment 18. Given the geometric sequence: 16, 32, 64, ...., 16 384 a) determine the number of terms in the sequence. a) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) which term in the sequence is 2048. b) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 19. Given a geometric sequence with t5 = 162 and to = -4374, determine the first 3 terms of the sequence. 19. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 10 of 1620. The first three terms of a geometric sequence are x, x + 5 and x + 9. Determine the numerical value of the first three terms 20. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 21. If the sum of the first 9 terms of a geometric series is 98 410 and the common ratio is 3, determine the value of the first term. 21. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 11 of 16Mathematics Pro-Calculus 12 U nit 1D Self-Assessment 22. Find the common ratio for each of the following geometric series. Determine whether a sum to innity exists. Find the sum where it exists. a) 9 + 3 + 1.... r : S : Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 l b) '3' l + ..... "f r : S : Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 e) 4+69+.... r : 3 2 Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 12 of16 Mathematics Pro-Calculus 12 Unit 10 Self-Assessment . . . . . 5 . . 4 23. The sum of an mnlte geometric series 1s a and the common ratlo 15 . Find the rst term. 23. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 24. A hard rubber ball is dropped from a moving van with a height of 5 metres. The ball rises to 80% of the previous height after each bounce. a) determine the total vertical distance the ball has traveled when it strikes the ground the eighth time. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b) estimate the total vertical distance the ball travels before it comes to rest. b) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 | Developing = 3 ' Proficient = 4 Exemplary =5 Page 13 of16 Mathematics Pre-Calculus 12 Unit 10 Self-Assessment 25. For what values of x for the geometric series have a sum to infinity? 1 + 3x + 9x2 + 27x+ .... 25. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 26. State the number of terms in each series. 33 a) 2a-3 a = 17 a) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 b + 12 b) _ 3n - 7 k=b b) Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 14 of 16Mathematics Pro-Calculus 12 Unit 10 Self-Assessment 12 l k_l 2?. Evaluate: Z 243[] k=2 3 27. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 :0 1 k 28. Evaluate: Z 75 k=1 6 28. Self Assessment No Attempt = 0 Beginning = 1 Emerging = 2 Developing = 3 Proficient = 4 Exemplary =5 Page 15 of16