TEST AND TEST ANSWER KEYS
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1 PART II TEST AND TEST ANSWER KEYS Houghton Mifflin Compan. All rights reserved. Test Bank Chapter P Preparation for Calculus Chapter Limits and Their Properties Chapter Differentiation Chapter Applications of Differentiation Chapter Integration Chapter 5 Logarithmic, Eponential, and Other Transcendental Functions Chapter 6 Differential Equations Chapter 7 Applications of Integration Chapter 8 Integration Techniques, L Hôpital s Rule, and Improper Integrals Chapter 9 Infinite Series Chapter 0 Conics, Parametric Equations, and Polar Coordinates Chapter Vectors and the Geometr of Space Chapter Vector-Valued Functions Chapter Functions of Several Variables Chapter Multiple Integration Chapter 5 Vector Analsis Answer Ke to Chapter Tests Final Eams Answer Ke to Final Eams Gatewa Tests Answer Ke to Gatewa Tests
2 6 Chapter P Preparation for Calculus Test Form A Chapter P Name Class Date Section. Find all intercepts of the graph of (a), 0 (b), 0,, 0, 0, 0,. 0,,, 0. Determine if the graph of is smmetrical with respect to the -ais, the -ais, or the origin. (a) About the -ais (b) About the -ais About the origin All of these. Find all points of intersection of the graphs of 6 and. (a) 0, 6, 0, (b) 0,,, 7 5, 9,, 5,,, 6. Which of the following is a sketch of the graph of the function? (a) (b) 5. Find an equation for the line passing through the point, and perpendicular to the line. (a) (b) Houghton Mifflin Compan. All rights reserved.
3 Chapter P Test Bank 7 6. Find the domain of f(). (a) (b),,,,, 7. Find f for f. (a) (b) 6 8. If f and g, find f g(). (a) (b) 9. If the point, lies on the graph of the equation k, find the value of k. (a) (b) Which of the following equations epresses as a function of? (a) 9 7 (b) Both a and b Neither a nor b (e) 5 7 Houghton Mifflin Compan. All rights reserved.. Given f, find f f. (a) (b) 8. Determine which function is neither even nor odd. (a) f tan (b) f 5 5 f (e) Both a and b f. Find the point that lies on the line determined b the points (, ) and (, ). (a) (0, 0) (b) (5, ) (, 6) (5, 5) (e) (, 0)
4 8 Chapter P Preparation for Calculus. The domain of the function f shown in the figure is. Choose the complete graph of f if f is even. (a) (b) f (e) Describe the transformation needed to sketch the graph of using the graph of (a) Shift f two units to the right. (b) Shift f two units to the left. Shift f two units upward. Shift f two units downward. (e) Reflect f about the -ais. f. 6. Use the vertical line test to determine which of the following graphs represent as a function of. (a) (b) 5 Houghton Mifflin Compan. All rights reserved.
5 Chapter P Test Bank 9 7. Let Find f. < 0 f., 0 (a) (b) 7 Undefined (e) 8. The dollar value of a product in 998 is $0. The value of the product is epected to increase $8 per ear for the net 5 ears. Write a linear equation that gives the dollar value V of the product in terms of the ear t. (Let t 8 represent 998.) (a) V 0 8(t 8) (b) V 8 0t V 0 8t V 8 0(t 8) (e) V 0 8(t 8) 9. During the first and second quarters of the ear, a business had sales of $50,000 and $85,000, respectivel. If the growth of sales follows a linear pattern, what will sales be during the fourth quarter? (a) $0,000 (b) $5,000 $5,000 $55, In order for a compan to realize a profit in the manufacture and sale of a certain item, the revenue, R, for selling items must be greater than the cost, C, of producing items. If R and C 6 050, for what values of will this product return a profit? (a) 55 (b) Houghton Mifflin Compan. All rights reserved.
6 0 Chapter P Preparation for Calculus Test Form B Chapter P Name Class Date Section. Find all intercepts of the graph of (a) (b), 0, 0, 0,., 0,, 0, 0, 0,. Determine if the graph of is smmetrical with respect to the -ais, the -ais, or the origin. (a) About the -ais (b) About the -ais About the origin All of these. Find all points of intersection of the graphs of and. (a) 5,,, (b) 0,, 0, 5,,, 5, 7,,. Which of the following is a sketch of the graph of the function? (a) (b) Houghton Mifflin Compan. All rights reserved.
7 Chapter P Test Bank 5. Find an equation for the line passing through the point, and parallel to the line. (a) (b) 5 6. Find the domain of f. (a) (b),,,, 5, 7. Find f for f. (a) (b) 5 8. If f and g, find f g(). (a) (b) 9. If the point, lies on the graph of the equation k 5, find the value of k. (a) 7 (b) 5 Houghton Mifflin Compan. All rights reserved. 0. In which of the following equations is a function of? (a) 0 (b) 7 7 Both a and b (e) Both a and c. Given f 5, find f f 5. (a) 0 (b). Determine the even function. (a) f sin (b) f f 5 f
8 Chapter P Preparation for Calculus. Find the point that lies on the line determined b the points, and,. (a), (b),, (e), 0, 0. The domain of the function f shown in the figure is. Choose the complete graph of f if f is odd. (a) (b) f (e) Describe the transformation needed to sketch the graph of using the graph of f(). (a) Shift f() two units to the right. (b) Shift f() two units to the left. Shift f() two units upward. Shift f() two units downward. (e) Reflect f() about the -ais. 6. Use the vertical line test to determine which of the following graphs does not represent as a function of. (a) (b) π π Houghton Mifflin Compan. All rights reserved. (e) Both a and d
9 Chapter P Test Bank 7. Let f 5, < Find f.,. (a) (b) (e) 0 8. The dollar value of a product in 998 is $78. The value of the product is epected to decrease $5.75 per ear for the net 5 ears. Write a linear equation that gives the dollar value V of the product in terms of the ear t. (Let t 8 represent 998.) (a) V t (b) V t V t 8 (e) V t 8 V t 8 9. A business had annual retail sales of $,000 in 99 and $,000 in 996. Assuming that the annual increase in sales follows a linear pattern, predict the retail for 00. (a) $56,000 (b) $5,000 $66,000 $98,000 (e) $7, In order for a compan to realize a profit in the manufacture and sale of a certain item, the revenue, R, for selling items must be greater than the cost, C, of producing items. If R and C , for what values of will this product return a profit? (a) 78 (b) 5 85 Houghton Mifflin Compan. All rights reserved.
10 Chapter P Preparation for Calculus Test Form C Chapter P Name Class Date Section A graphing calculator is needed for some problems.. Find the -intercepts for the graph of (a) (b) 0, 0, (e) There are no -intercepts. 0, 0,, 0,, , 0, (, 0,, 0. Choose the complete graph of the equation 0. (a) (b) Identif the tpe(s) of smmetr: 0. (a) About the -ais (b) About the -ais About the origin Both a and b. Find all points of intersection of the graphs of and. (a), 0 and, (b) 5, and,, and 5, 7 5, 7 and, 5 5. A business had annual retail sales of $0,000 in 99 and $,000 in 996. Assuming that the annual increase in sales followed a linear pattern, what were the retail sales in 995? (a) $8,000 (b) $95,000 $88,000 $86,000 Houghton Mifflin Compan. All rights reserved.
11 Chapter P Test Bank 5 6. Find an equation for the horizontal line that passes through the point,. (a) (b) 7. Write an equation satisfied b the graph obtained b shifting 5 three units to the left. (a) 8 (b) 8. Let f and g ). Find the domain of f g. (a) (b) > 0 < > 9. Find the zero(s) of the function f. (a) and (b) Given (a) (b) 5 f 5, find f f. 0 Houghton Mifflin Compan. All rights reserved. f f. Find for f 8. (a) 8 (b) Determine the odd function. (a) f 5 (b) f f 5 f cos. Find the point that does not lie on the line determined b the points 5, and,. (a) 0, (b) 7, 8, 7, (e),
12 6 Chapter P Preparation for Calculus. Find the equation of the line that passes through the point, and is perpendicular to the line that passes through the points 9, 7 and,. (a) 9 7 (b) Let f, < Find f 5.,. (a) 9 (b) 5 (e) 7 6. An open bo is to be made from a rectangular piece of material 9 inches b inches b cutting equal squares from each corner and turning up the sides. Let be the length of each side of the square cut out of each corner. Write the volume V of the bo as a function of. (a) V (b) V 08 V 9 V 9 ( Houghton Mifflin Compan. All rights reserved.
13 Chapter P Test Bank 7 Test Form D Chapter P Name Class Date Section. Show that is smmetric with respect to the origin.. Find the intercepts:.. Find all points of intersection: and.. Find an equation for the straight line that passes through the point, and is parallel to the line. 5. Find an equation in general form for the straight line that passes through the point, and is perpendicular to the line If f, find: a. f b. f c. f 7. If g, find g g. 8. If f and g 5, find g f(). 9. Find the domain: f. Houghton Mifflin Compan. All rights reserved. 0. Sketch a graph of.. Sketch the graph of the equation In which of the following equations is a function of? a. 7 0 b. 5 9 c. d. e. None of these. Given f 7, find f f. 9
14 8 Chapter P Preparation for Calculus. The domain of the function f shown in the figure is. Complete the graph of f if f is odd. f f 5. Use the graph of to sketch the graph of. 6. Find the slope and -intercept of the line given b the equation Let f, < Evaluate:,. a. f 0 b. f c. f 8. A student working for a telemarket compan gets paid $ per hour plus $.50 for each sale. Let represent the number of sales the student has in an 8-hour da. a. Write a linear equation giving the da s salar S in terms of. b. Use the linear equation to calculate the student s salar on Wednesda if the student makes sales that da. c. Use the linear equation to calculate the number of sales per da the student would have to make in order to earn at least $00 a da. Houghton Mifflin Compan. All rights reserved.
15 Chapter P Test Bank 9 Test Form E Chapter P Name Class Date Section A graphing calculator is needed for some problems.. Given the equation: 6 0. a. Solve for. b. Use a graphing calculator to graph the resulting equations on the same set of aes and sketch the graph.. Create an equation whose graph has intercepts at 5, 0, 0, 0, and 5, 0.. a. Use a graphing calculator to graph the equation. b. Identif the intercepts of the graph. c. Test for smmetr.. Identif the tpe(s) of smmetr: Find all points of intersection of the graphs of 6 and. 6. Sketch the graph of the equation: Let f, < Evaluate:,. a. f b. c. f 0 d. f f Houghton Mifflin Compan. All rights reserved. 8. Let f. a. Use a graphing calculator to graph f. b. Estimate the domain and range from the graph. c. Estimate the coordinates of an intercepts of the graph. d. Find the intercepts analticall. 9. Use a graphing calculator to estimate the zero(s) of f In which of the following is a function of? a. 9 b. 7 c. d. 5 e.. Given f 6, find f 0 f.
16 0 Chapter P Preparation for Calculus. Find g g for g.. Determine whether the function f is even, odd, or neither. Justif our answer.. Use the graph of f shown below to sketch the graph of f. f 5. Find two additional points on the line that passes through the point, 5 and has slope m. 6. Find an equation of the line that passes through the point, and is perpendicular to the line determined b the points 8, 9 and 0, For the functions f and g 5 find g f()., 8. A business had annual retail sales of $,000 in 99 and $86,500 in 996. Assume the annual decrease in sales follows a linear pattern. a. Write a linear equation giving sales S in terms of the ear t where t 0 corresponds to 99. b. Use a graphing calculator to graph the equation. c. Use the graph to estimate the annual retail sales for 998 to two digits of precision (the nearest multiple of $0,000). d. Use the graph to estimate the first ear when there will be no sales. Houghton Mifflin Compan. All rights reserved.
Chapter P: Preparation for Calculus
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