F F 12:31 9321BA= VPN @ 1 43% K TO O MCV4U-A 2021 9 A 218 1 +6:24 Name: Class: Date: ID: A MCV4U Final Exam 2021 (K: /25)(T: /25)(C: /25)(A: /25) True/False Indicate whether the statement is true or false. 1. An infinite discontinuity means a function is merely a set of scattered points. 2. The quotient rule can be used to differentiate a rational function. 3. The power rule only works with integer exponents. 4. The nth derivative of y = e* will always be e*. 5. Geometric vectors have both magnitude and direction but Cartesian vectors have only magnitude. 6. The dot product of two vectors can only be determined when the vectors are in Cartesian form. Multiple Choice (K: /12) Identify the choice that best completes the statement or answers the question. -1 7. Evaluate the limit: lim - x-2* * - 4x +4' A U B -1 D -00 8. This function: 4 -2 0 ( 1 - A has a jump discontinuity C has a removable discontinuity B has an infinite discontinuity D is continuous D x =6 14. When simplified, 5(u + v) -5(u + v) equals A 10(-u -v) C 10(u + V) BO Duty 2 2020 Leading Wave Nexus Inc. + cLawrence AcademyT5F1213'1 913213 11): A . A ship is sailing at 8 knots (nautical miles per hour) on a heading of300. The wind is blowing at 12 knots from a bearing of 045\". Find the speed (the magnitude ofthe resultant velocity) ofthe ship. A 20 knots C 15.55 knots B 16.05 knots D 12.23 knots . A 10 N force is applied at 45 to the horizontal, Write this force as a Cartesian vector. 10 10 ] _ 2 ' . 2 710 710 ] A [10.10] C [ B [10,0] D 2 2 . A parallelogram is formed by the vectors [1' 2] and [3.41]. Find the area oftlie parallelogram. A 10 square units C 52 5 square units B 710 square units D 11 square units . A line has yintercept 11 and z-intercept 713. Find a vector equation ofthe line. A [X.y.z]:[0,11,0]+r[0_11,13] C [x.y. z] : [0. 0.713] +/[0. 11. 0] B [x.y,z]=[0.11,13]+I[0,11.0] D [x.y.z]=[0,11,0]+1[0,0,713] Matching (K: /3) Match the vector coordinates to each Cartesian vector. @2020 Leading Wave Nexus Inc. cLawrence Academy F F12:32 93218A= VPN @ 1 43% K TO O Name: ID: A Short Answer 22. A football's path is represented by the function h(1) = -4.91 + 10t + 2, where h is its height, in metres, after seconds.. Find the average rate of change of the football's height between 0 s and I s. (A: /3) 23. The demand function for a bottle of hand lotion is p(x) = 0.78 + 0.0003x, where x is the number of bottles sold and p is the price, in dollars. The cost function is C(x) = 480-0.32x + 0.0005x. Find the marginal profit when 700 bottles of hand lotion are sold. (A: /3) 24. For the function f(x) = x - 4x + 6, find the local extrema. Then, classify the local extrema using the second derivative test. (K: /3)(A: /1) 25. Find the equation of the tangent to the curve y = 2 sinx + sin'x at the point where x = ". (A: 12) (T: 12)
