1021 quiz 1 A Term 2006 answers

1021 quiz 1 A Term 2006 answers - Name: MA 1021 - 2006 A...

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Unformatted text preview: Name: MA 1021 - 2006 A Term Section 10 September 7, 2006 Quiz — Sections 1.1-1.5, 2.1-2.4, 3.1 1. All students taking MA 1021 in A Term 2006 will take a common final exam on Wednesday evening, October 11, 2006, and should have already cleared their calendar for this time. 01‘ FALSE (please circle the correct answer — 2 points) (x+h)-f(x) 2. The slope predictor function is defined as m(x) = f h TRUE 0r(please circle the carrect answer — 2 points) Inn 3. Students taking MA 1021 in A Term 2006 will have unlimited chances to pass the Basic Skills component of the final TRUE or (please circle the correct answer — 2 points) Per szllabus— 3 Clwtnce: 4.‘ The expression lin’l f (x) denotes a one—sided limit — in this case, x—>2 the left hand limit of the function f(x) as x approaches 2 from the left. TRUE or (please circle the correct answer — 2 points) ————— —"— S. x = 3 is a possible solution of the expression: logx 27 = x 1‘ FALSE (please circle the correct answer — 2 points) 6. If = x + 5, g(x) = 2x — 5, and h(x) is the composite of f(x) and g(x) (denoted by h = f o g), then the graph of h(x) is a line with slope 2 passing through the origin. r FALSE (please circle the correct answer — 2 points) 7. The line given by f (x) = 3x + 5 is perpendicular to the line given 1 1 by 8(x)="§x—§ 0r FALSE (please circle the correct answer — 2 points) 8. The equation 362 ~— 2x + y2 + 4y — l 7 = 0 describes a circle whose center is to the right of and below the origin. 01‘ FALSE (please circle the correct answer — 2 points) 9. A ball thrown at an initial velocity of 88 feet/second travels at approximately the speed of sound. TRUE or lease circle the correct answer — 2 points) 8'3 Ff/sec Q: 60 mph 4 speed 0F Sounol 10. If the right-hand limit and the lefi~hand limit of a function both exist at x = a , and they are equal to each other, the function is continuous at that point. TRUE or (please circle the correct answer — 2 points) We aISo require ‘lv exist- and Gianni themhrhi'lb) **** End of T rue/False Questions — Quiz Continues on Next Page **** 11. You are given the function f (x) = x2 — 8x +12 A. What are the two values ofx where f (x) =0? (2 points) B. What is the point where the function crosses the y-axis? (2 points) C. Using the “complete-the-square” approach, find the x-coordinate and y—coordinate of the vertex of this function. Note that the general formula for a parabola is given by y — k = a(x — h)2 (2 points) D. What is the equation of the tangent line at the point found in question [C] above? (2 points) E. Sketch the function. Be sure to label the four points noted in [A], [B], and [C] above. (2 points) [A3 (x—2)(x—e) 2 0 => [:3] 1W0): ll ’X:Z. (IL xcé 12. An open-topped cylindrical can is to be made from cardboard. The can will have a volume of 50 cubic inches. The bottom of the can will be cut from a square piece of cardboard, and so some cardboard will be thrown away (see below). The side of can will be made from a rectangular piece of cardboard, rolled into shape. Express the surface area of the material required to make this can as a function of the radius of the can’s bottom. (10 points) Bottom: It takes this ' 1 13. What is the slope-predictor function for: f (x) = — ? x Use the four step approach described in section 2.1 (and as discussed in class) — do not use derivatives to solve this! (12 points) £00? l'1) ‘* ((7‘) hm : fl WM)” la-‘PO In L ,L I”; X‘HA- x m(x)¢ .__.—-—-—-*-'—"—'_" mo p x x-s-k Min,- Ima sigh)” CHOW“) , w?" In LID,“ 1 “w CX)(X+M) ffi W70 L. . ,— i ._ .fll : \w s" " -'~ h—vo C¥)(xek) x2 14. You are given the following function: f (x) 2 Sketch a graph of the function (10 points) x2—3x—10 x+2 15. Evaluate: 4sin5x lim x—)O 7x Show your work! (5 points) 16. A ball is thrown straight upwards from a point [1 feet above the ground, at an initial velocity of 64 feet per second. 5 seconds later, it hits the ground. Note: The general formula for the height of a thrown object is 1 given by: ya) = -— gtz + v01 + y0 ,' where g denotes the 2 acceleration due to the force of gravity, which is about 32 fl/Secz. a. How fast is the ball moving at its highest point? (3 points) b. How fast is the ball moving when it hits the ground? (3 points) 0. Solve for h (4 points) (CL) :15 Lughey} Pot—ml! HM virtual-7 (\j 2.24.9 (to) V‘H’): Ldrflzl': —-31€+ é‘f 237$): Gm“) ’r 4" '3 "3" a5“ ((3 ya): («ta)C§)1+ (9001+ k a o «Hbo't3'zo—l-iq : 0 ll in»; (0)0 ...
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1021 quiz 1 A Term 2006 answers - Name: MA 1021 - 2006 A...

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