ma 223Study Guide and practice questions PDF

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ma 223 test out study guide and practice questions for summer 2021 for all professors and class structures...

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Purdue University Study Guide for MA 22300 for students who plan to obtain credit in MA 22300 by examination. Textbook: Applied Calculus For Business, Economics, and the Social and Life Sciences, Expanded tenth edition. Author:

L. D. Hoffman and G. L. Bradley

Publisher: McGraw Hill, 2010 When you are ready for the examination, obtain the proper form from your academic advisor. Follow the instructions on the form. To prepare for the exam, you are being provided: 1. the assignment sheet 2. the final exam practice problems 3. the final exam formulas The url for the course web page is: http://www.math.purdue.edu/courses/ma22300 The assignment sheet lists the sections of the text that are covered in the course. (A copy of the text is on reserve in the Hicks Undergraduate Library.) The homework problems from the assignment sheet, along with the final exam practice problems, provide good preparation for the exam. The final exam formulas will be provided on the cover of the final exam. A calculator with logarithmic and exponential functions will be needed for the exam. Any brand of one-line calculator may be used. However, no multi-line calculators are allowed. Cell phones may not be used as a calculator.

MA 22300

Assignment Sheet

Text: Applied Calculus by L. D. Hoffman and G. L. Bradley, Expanded tenth edition, McGraw Hill, 2010. Note: Problems in bold are not available in MathZone. You should attempt these problems, in the text, by hand and ask any questions at the next class meeting. Only the problems for Lesson 31 will be worked by hand and submitted for grading. All graphs must be sketched by hand on graph paper. A one-line, scientific calculator with logarithm and exponential functions is required. Graphing calculators or programmable calculators may not be used. Calculators which are capable of numeric or symbolic differentiation and integration are not allowed. Lessons 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Sections 1.1 Appx, 1.1 1.1 1.1, 1.2 1.3 1.4 1.5 1.5, 1.6 1.6, 2.1 2.1 2.2 2.2 2.3 2.3 2.3, 2.4 2.4 2.4 2.5 2.6 2.6 2.6 3.1 3.1 3.2 3.2 3.3 3.3 3.4 3.5 3.5 4.1 4.1, 4.2 4.2 4.4 4.3 4.3

Assignments p10 : 3, 6, 8, 13, 14, 19, 20, 21, 22, 23 p651 : 46, 47, 48, 52, 53, 54∗∗∗ p11 : 62, 66, 68cde, 70 p10 : 25, 26, 27, 28, 40, 42, 49, 50, 73, 74, 75 p10 : 34, 35, 36, 38 p25 : 15, 21, 25, 26, 27 p39 : 2, 4, 9, 11, 17, 18, 22, 28, 32, 41bc, 44bc, 45b p56 : 5, 6, 7, 11, 36, 38, 40, 42 p73 : 1, 2, 3, 5, 6, 13, 15, 17, 19, 20, 23, 24, 40, 42 p74 : 32, 33, 35, 37, 38 p86 : 1, 2, 3, 4, 12, 16 p87 : 26, 27, 35, 37, 38, 39, 41, 42 p112 : 3, 5 p112 : 9, 15, 18, 20, 32, 33, 34, 37, 38 p125 : 1, 6, 7, 9, 11, 14, 18, 21, 24, 25 p125 : 29, 32, 35, 36, 38, 51a, 52, 55, 56, 62 p138 : 1, 2, 3, 5, 8, 9, 11, 12, 13, 17, 18 p139 : 21, 22, 23, 24, 26, 27, 30, 48, 56, 61 p139 : 42, 43, 46, 47 p151 : 3, 4, 5, 9, 11 p152 : 23, 24, 26, 27, 28, 29, 31, 32, 35, 36, 38, 39, 40 p152 : 48, 52, 54, 59, 60, 61, 62, 64, 66, 67 p163 : 2, 3, 6, 7, 8, 12, 13, 15, 18, 19, 24, 25 p175 : 9, 10, 11, 12, 13, 14, 17, 18, 23, 26, 28 p176 : 31, 32, 35, 36, 45, 47, 50, 52 p176 : 41, 42, 43, 44, 46 p204 : 2, 4, 9, 10, 11, 13, 14, 15, 19, 20, 22 p204 : 23, 25, 29, 31, 32, 33, 56, 57, 59bc, 60, 68, 69, 70, 71 (56,57-no graph) p220 : 5, 6, 7, 8, 9, 10, 28, 29, 31, 32, 34 p220 : 1, 2, 3, 47, 48,56, 57, 59ab (56-no graph) p235 : 12, 13, 14, 15, 33, 34, 35, 36 p236 : 17, 19, 24, 27, 29 p254 : 1, 3, 5, 6, 7, 8, 10, 17(min aver cost only), 31abc, 33, 34 p270 : 4, 6, 7, 9, 11, 16, 17, 18 p271 : 19, 21, 23, 25, 36, 37 p303 : 19, 20, 21, 22, 41, 43, 45a, 47ab, 48, 66 p304 : 35bcd, 36cd, 37, 38, 39, 40, 49; p320 : 13, 15, 16, 17 p320 : 24, 27, 32, 33, 35, 36, 45, 50, 53 p350 : 21, 23, 24, 27acd, 28bc, 29bc, 32bc p335 : 2, 4, 5, 7, 8, 9, 10, 12, 13, 15, 16, 18, 19, 20, 26, 34 p336 : 40, 45, 48, 51, 52, 53, 54, 55, 69, 70, 80ab

***These problems are only available on the course web page.

MA 22300 FORMULA SHEET Volume & Surface Area Right Circular Cylinder

SA =

V = πr2 h ! 2πr2 + 2πrh πr2 + 2πrh

Sphere V = 34πr3 SA = 4πr2 Interest Formulas B(t) = P (1 + kr )kt B(t) = P e rt

MA 22300

Final Exam Practice Problems

Formulas which are provided on the final exam are at the end of this practice final. 1. Find the slope of the line containing the points (−2, 4) and (6, −3). A. 4 B. − 87 C. 41 D. − 87 E. − 21 2. Suppose 280 tons of corn were harvested in 5 days and 940 tons in 20 days. If the relationship between tons T and days d is linear, express T as a function of d. A. T (d) = 5d + 280 B. T (d) = −44d + 500 C. T (d) = 44d + 60 D. T (d) = 60d + 44 E. T (d) = 44d − 60 3. When 30 orange trees are planted per acre each tree yields 150 oranges For each additional tree per acre, the yield decreases by 3 oranges per tree. Express the total yield of oranges per acre, Y , as a function of the number of trees planted per acre, x, if x ≥ 30. A. Y = 4500 + 60x − 3x2 B. Y = 13 x + 80 C. Y = 150x − 3x2 D. Y = 240x − 3x2 E. Y = 900 + 3x − 60x2 4. A manufacturer can sell dining-room tables for $70 apiece. The manufacturer’s total cost consists of a fixed overhead of $8000 plus production costs of $30 per table. How many tables must the manufacturer sell to break even? A. 80 B. 267 C. 200 D. 20 E. 136 √ 5. If f (x) = x +√1 and g(x) =√x2 + 7 then (f (g(−1)) = A. 0 B. 3 C. 7 D. 7 E. 8 + 1 f (x + h) − f (x) 2 = then h x 2 2 2 2 2 2 C. E. − D. − − A. − 2 B. x x(x + h) x(x + h) x+h x (x + h)2

6. If f (x) =

1 is: 7. The domain of f (x) = √ 3 x−1 A. x < 1 or x > 1 B. x > 1 C. x > 0 D. x < 0 or x > 0 E. −1 < x < 1 x2 + 4x − 5 = x→1 x2 − 1 A. ∞ B. 0 C. 3 D. −3 E. 5

8. lim

9. lim e−x = x→∞

A. 0 B. 1 C. −1 D. ∞ E. e 10. Suppose

 2  x −1 if x < 0 x−1 f (x) =  2 x − 3x + 2 if x ≥ 0

Find all values where the function f is discontinuous. A. x = −1 B. x = 0 C. x = 1 D. x = 2 E. f is continuous for all values of x. 11. Find all values of x for which the function f (x) = 2x3 − 3x2 − 12x + 12 is increasing. A. −1 < x < 2 B. x < −1 C. x > 2 D. x < −1 and x > 2 E. x < 2 and x > 2

1

MA 22300

Final Exam Practice Problems

12. The derivative of

x2 + 1 is: x+5

x2 + 10x − 1 3x2 + 10x + 1 2x2 + 10x D. B. 2x C. (x2 + 1)2 (x + 5)2 (x + 5)2 2 −x − 10x + 1 E. (x + 5) 2

A.

13. If y = (3 − x2 )3 then y ′′ = A. −6x(3 − x2 )2 B. 24x2 (3 − x2 ) − 6(3 − x2 )2 C. 6(3 − x2 ) D. 24x2 (3 − x2 ) E. 12x2 − 6(3 − x2 ) 14. The line tangent to the graph of f (x) = x − A.

5 4

B.

3 4

C.

3 2

D. 0 E.

1 at x = 2 has slope: x

1 2

15. Find an equation for the tangent line to the curve x2 y + xy 3 = 2 at the point (1, 1). A. 2x + y = 3 B. 3x + 4y = 7 C. 2x + 3y = 5 D. 5x − 2y = 3 E. 5x + 3y = 8 16. After t years the population of a certain town √ is P (t) = 50 + 5t thousand people. A population P has an associated CO2 level, C(P ) = ( P 2 + 1)/2. After 2 years, the rate at which CO2 level is changing with respect to t will be: √ √ √ √ √ A. 5/(2 5) B. 150/ 3601 C. 30 3601 D. 30/ 3601 E. 50/ 3601 17. If yx2 + y 3 = x − y. Then y ′ = A. 1 − 2xy − 3y 2 B. 1 − 2xy − x2 − 3y 2 C. (1 − 2xy )/(3y 2 + 1) D. (1 − 2xy )/(x2 + 3y 2 + 1) E. (2xy )/(x2 + 3y 2 + 1) 18. If the concentration C(t) of a certain drug remaining in the bloodstream t minutes after it is injected is given by C(t) = t/(5t2 + 125), then the concentration is a maximum when t = A. 25 B. 15 C. 5 D. 10 E. 20 19. If f (x) = 2x4 − 6x2 then which one of the following is true? p A. f has a relative max. at x = ± 3/2 and a relative min. at x = 0. p B. f has a relative max. at x = 0 p and a relative min. at x = ± 3/2. p C. f has a relative max. at x = − p 3/2 and a relative min. at x = p3/2. D. f has a relative max. at x = 3/2 and a relative min. at x = − 3/2. p E. f has no relative max. points, but has relative min. at x = ± 3/2. 8 . Then at x = 2, f has: x A. an inflection point B. a relative maximum C. a vertical tangent D. a discontinuity E. a relative minimum

20. The derivative of a function f is f ′ (x) = x2 −

21. If f (x) = 13 x3 − 9x + 2, then on the closed interval 0 ≤ x ≤ 4, A. f has an absolute max. at x = 3 and an absolute min. at x = 0. B. f has an absolute max. at x = 4 and an absolute min. at x = 3. C. f has an absolute max. at x = 0 and an absolute min. at x = 4. D. f has an absolute max. at x = 0 and an absolute min. at x = 3. E. f has an absolute max. at x = 4 and an absolute min. at x = 0.

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MA 22300

Final Exam Practice Problems

22. A display case is in the shape of a rectangular box with a square base. Suppose the volume is 21 cubic ft and it costs $1 per square ft. to build the glass top and $0.50 per sq. ft. to build the sides and base. If x is the length of one side of the base, what value should x have to minimize the cost? Round your answer to two decimal places. A. 3.04 ft. B. 2.41 ft. C. 3.74 ft. D. 2.24 ft. E. 3.36 ft. 23. What is the area of the largest rectangle with sides parallel to the axes which can be inscribed in the first quadrant under the parabola y = 4 − x2 ? Round your answer to 2 decimal places. A. 1.15 B. 1.33 C. 3.08 D. 4.00 E. 2.67 24. The radius of a circular oil spill is increasing at the rate of 3 ft/min. How fast is the area increasing when the radius is 4 ft? A. 24πft2 /min B. 48πft2 /min C. 8πft2 /min D. 16π ft2 /min E. 32πft2 /min 25. A manufacturer has been selling lamps at $6 apiece and, at that price, consumers have been buying 3,000 lamps per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in the price, 1000 fewer lamps will be sold each month. The manufacturer can produce the lamps at a cost of $4 per lamp. At what price should the manufacturer sell each lamp to generate the greatest possible profit? A. $6.25 B. $6.50 C. $7.00 D. $7.50 E. $7.75 √ 26. If 18x = 3, then in which of the following intervals does x lie? A. 0 < x < 1 B. −1 < x < 0 C. 1 < x < 2 D. −2 < x < −1 E. 2 < x < 3 27. A population has been growing exponentially. In 1960, it was 50,000 and in 1965, it was 100,000. What was the population in 1970? A. 200,000 B. 150,000 C. 250,000 D. 300,000 E. 225,000 28. The amount of a certain radioactive substance remaining after t years is given by a function of the form Q(t) = Q0 e−0.003t . The half-life of the substance is: A. 53 years B. 0.00435 years C.333 years D. 231 years E. 167 years √ dy = 29. If y = ln 1 − x2 then dx 1 x 2x 1 1 A. √ C. − B. − √ D. E. √ 2 2 2 2 1−x 2(1 − x ) 2 1 − x2 1−x 1−x dy = dx 2 2 2 B. x2 ex −1 C. 2xex −1 D. 2xex E. e2x 2

30. If y = ex then A. ex

2

31. What lump sum of money should be deposited in a money market certificate paying 8.25% interest compounded monthly to amount to $5000 in 10 years? Round your answer to the nearest dollar. A. $2514 B. $4669 C. $2740 D. $2262 E. $2197 32. How quickly will money double if it is invested at a rate of 8 percent compounded continuously? Round your answer to two decimal places. A. 0.87 years B. 25 years C. 5.55 years D. 8.66 years E. 6.33 years 33. Suppose the total cost in dollars of producing q units is C(q) = 2e−q + 3q 2 − 2. Calculate the marginal cost when 5 units have been produced and calculate the actual cost of producing the 6th unit. Round your answer to the nearest cent. 3

MA 22300

Final Exam Practice Problems

A. marginal cost = $29.99, actual cost = $32.99 B. marginal cost = actual cost = $29.99 C. marginal cost = $29.99, actual cost = $36.00 D. marginal cost = $30.01, actual cost = $32.99 E. marginal cost = actual cost = $30.01 34. A cylindrical can with no top has been made from 27π square inches of metal. Express the volume, V , of the can as a function of its radius, r. A. V = 27πr 2 B. V = 2π r (27 − r 2 ) C. V = πr 2 (27 − r 2 − 2r ) D. V = 27π 2 r 2 E. V = 34 πr 2 (27 − r 2 ) 35. For what value of a does the function f (x) = x2 + ax have a relative minimum at x = 1? A. −2 B. 0 C. 2 D. −1 E. 1

Volume & Surface Area Right Circular Cylinder V = πr2 h 2πr 2 + 2πrh SA = πr 2 + 2πrh

FORMULAS

Interest Formulas B(t) = P (1 + rk )kt B(t) = P e rt

Answers 1. B; 2. C; 3. D; 4. C; 5. B; 6. D; 7. A; 8. C; 9. A; 10. B; 11. D; 12. A; 13. B; 14. A; 15. B; 16. B; 17. D; 18. C; 19. B; 20. E; 21. D; 22. B; 23. C; 24. A; 25. B; 26. A; 27 A; 28. D; 29. C; 30. D; 31. E; 32. D; 33. A; 34. B; 35. A;

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