Precalculus Spring Final Review Name Solve the equation on the interval 0 θ < ". ) sin θ + sin θ = 0 A) 0, ", " 3, 5" 3 B) 0, ", 3" C) 0, ", " 3, " 3 D) 0, ", " 3, 5" 3 SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Use a calculator to solve the equation on the interval 0 < ". Round the answer to one decimal place if necessar. ) 7 cos - e =, > 0 Use the information given about the angle θ, 0 θ ", to find the eact value of the indicated trigonometric function. 3) cos θ = 5, 3" θ " Find cos θ. A) - 5 C) - 3 B) 5 D) 3 Epress the sum or difference as a product of sines and/or cosines. ) sin(θ) - sin(6θ) A) sin(5θ) cos θ B) cos(θ) cos(5θ) C) - sin θ cos(5θ) D) - sin θ SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Use a calculator to solve the equation on the interval 0 < ". Round the answer to one decimal place if necessar. 5) - 3 cos = 0 Solve the equation on the interval 0 θ < ". 6) cos θ + = 0 A) C) " 3, 5" 3 ", 3" B) D) 3" " 3, " 3 7) If sin θ =, θ in quadrant II, find the eact value of cos θ + " 6 A) - 3 5 + 8 C) 3 + 5 8 B) D) Solve the equation on the interval 0 θ < ". 3-5 8 5-3 6 8) 3 sin(θ) = 3 A) ", " 6, " 3, 7", 7" 6, 3", 5" 3, 9" B) {0} C) ", 5" D) 0, ", "
SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Establish the identit. sin α + sin β 9) = sin α sin β csc α + csc β Use the information given about the angle θ, 0 θ ", to find the eact value of the indicated trigonometric function. 3) cos(θ) =, 0 < θ < " A) 8 - B) Find sin θ. - 6 C) 6 D) ) You are fling a kite and want to know its angle of elevation. The string on the kite is 3 meters long and the kite is level with the top of a building that ou know is 8 meters high. Use an inverse trigonometric function to find the angle of elevation of the kite. Round to two decimal places. Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve an triangle(s) that results. ) A = 30, a =, b = A) B = 60, C = 60, c = 36. B) B = 90, C = 60, c = 36. C) B = 60, C = 90, c = 36. D) no triangle Use a calculator to solve the equation on the interval 0 < ". Round the answer to one decimal place if necessar. ) 6-5 sin = 5) Find the area of the Bermuda Triangle if the sides of the triangle have the approimate lengths 8 miles, 93 miles, and 30 miles. A) 5,99 mi B) 9,03 mi C) 387,30 mi D),58,58 mi Use the Half-angle Formulas to find the eact value of the trigonometric function. ) sin 7" 8 A) C) - - B) - D) - - - 3 6) A plane takes off from an airport on the bearing S9 W. It continues for 0 minutes then changes to bearing S5 W and flies for hours 0 minutes on this course then lands at a second airport. If the plane' s speed is 0 mph, how far from the first airport is the second airport? Round our answer correct to the nearest mile. A) mi B) mi C) mi D) mi
Solve the triangle. 7) a = 8, c = 6, B = 90 A) b =, A = 36.9, C = 53. B) b =, A = 53., C = 36.9 C) b =, A = 53., C = 36.9 D) b = 9, A = 36.9, C = 53. Solve the triangle. ) a = 50, b =, C = 5 A) c = 57.88, A = 57.5, B = 7.5 B) c = 60.78, A = 53.5, B =.5 C) c = 5.98, A = 55.5, B = 9.5 D) no triangle 8) a = 6, b = 8, C = 70 A) c =, A = 56.9, B = 53. B) c = 6.3, A = 8.6, B = 8. C) c = 9, A = 5.8, B = 57. D) c = 8., A = 3.5, B = 66.5 3) A painter needs to cover a triangular region 6 meters b 66 meters b 75 meters. A can of paint covers 70 square meters. How man cans will be needed? A) 8 cans B) 3 cans C) cans D) 37 cans Find the area of the triangle. If necessar, round the answer to two decimal places. 9) A = 83, b = 9, c = 6 A) 7.0 B) 53.60 C) 6.80 D) 3.9 0) A surveor standing 68 meters from the base of a building measures the angle to the top of the building and finds it to be 36. The surveor then measures the angle to the top of the radio tower on the building and finds that it is 50. How tall is the radio tower? A). m B).3 m C) 6.95 m D) 3.63 m Find the area of the triangle. If necessar, round the answer to two decimal places. ) a =, b =, c = 6 A) 8.33 B) 8.33 C) 90.33 D) 87.33 Solve the triangle. 5) b = 5, c = 6, A = 70 A) a = 7.36, B = 7.6, C = 6. B) a = 6.36, B = 6., C = 7.6 C) a = 6.36, B = 7.6, C = 6. D) a = 5.36, B = 6., C = 7.6 Find the area of the triangle. If necessar, round the answer to two decimal places. ) a =, b = 3, c = 6 A) 39.69 B) 8.99 C) 580.0 D) 77.99 Find the eact value of the epression. Do not use a calculator. 6) tan 75 - cos 5 cos 75 A) - B) 0 C) D) 3
Solve the triangle. 7) B =, C = 50, a = 5 A) A = 0, b = 5., c = B) A = 0, b =, c =. C) A = 0, b =, c =. D) A = 0, b =., c = Graph the hperbola. 30) - 5 = 5 Find a rectangular equation for the plane curve defined b the parametric equations. 8) = 6 sin t, = 6 cos t; 0 t " A) + = 36; for in -6 6 B) = - 9; for in - C) = a - = 36; for in - < < D) - = 36; for in - < < SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Graph the equation. 9) ( + ) 6 + ( - ) 5 = - -5 5-5 -5 5-5 3) An arch in the form of a semiellipse is 5 ft wide at the base and has a height of 0 ft. How wide is the arch at a height of ft above the base? A) 7.7 ft B).6 ft C) 35.5 ft D) 0.8 ft Find the verte, focus, and directri of the parabola with the given equation. 3) ( + ) = 0( - ) A) verte: (-, ) focus: (, ) directri: = -6 B) verte: (-, ) focus: (3, ) directri: = -7 C) verte: (, -) focus: (-3, -) directri: = 7 D) verte: (, -) focus: (7, -) directri: = -3
33) An eperimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadwa, just touching it there, and up again to the top of a second tower. The towers are both inches tall and stand 0 inches apart. At some point along the road from the lowest point of the cable, the cable is 0.6 inches above the roadwa. Find the distance between that point and the base of the nearest tower. A) 7.8 in. B) in. C). in. D) 8. in. Name the conic. 35) SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Graph the curve defined b the given parametric equations. 3) = t +, = 3t - ; 0 t 3 8 6 A) circle B) parabola C) hperbola D) ellipse 36) The roof of a building is in the shape of the hperbola - = 5, where and are in meters. Refer to the figure and determine the height h of the outside walls. -8-6 - - 6 8 - - -6-8 a = b = 7 m A). m B) -5 m C) 3 m D) 7 m Find the equation of the parabola described. 37) Directri the line = 3; verte at (0, 0) A) = - B) = 3 C) = - D) = - 5
Find the center, foci, and vertices of the ellipse. 38) 9 + - 7 + 35 = 0 A) ( - ) + 9 = center: (, 0); foci: (, ), (, - ); vertices:(, 3), (, -3) B) 6 + ( - 3) = center: (3, 0); foci: (3, 5), (3, - ); vertices:(3, ), (3, -) C) ( - 3) + 6 = center: (3, 0); foci: (3, 5), (3, - 5); vertices:(3, ), (3, -) D) 9 + ( - ) = center: (, 0); foci: (, ), (, - ); vertices:(, 3), (, -3) Find a rectangular equation for the plane curve defined b the parametric equations. 39) = t 3 +, = t 3 - ; - t A) = 3 ; for in -3 B) = - ; for in -7 9 C) = - - ; for in -7 9 D) = - ; for in - Find the foci and vertices of the ellipse. 0) 8 + 9 = 3969 A) foci at (0, - ) and (0, ) vertices at (0, -9), (0, 9) B) foci at (0, 9) and (7, 0) vertices at (0, 8) and (9, 0) C) foci at (-, 0) and (, 0) vertices at (-9, 0), (9, 0) D) foci at (0, -9) and (0, 9) vertices at (0, -8), (0, 8) Find the center, transverse ais, vertices, foci, and asmptotes of the hperbola. ) 6-36 = 576 A) center at (0, 0) transverse ais is -ais vertices: (0, -6), (0, 6) foci: (- 3, 0), ( 3, 0) asmptotes of = - 3 and = 3 B) center at (0, 0) transverse ais is -ais vertices: (-6, 0), (6, 0) foci: (-, 0), (, 0) asmptotes of = - 3 and = 3 C) center at (0, 0) transverse ais is -ais vertices: (-, 0), (, 0) foci: (- 3, 0), ( 3, 0) asmptotes of = - 3 and = 3 D) center at (0, 0) transverse ais is -ais vertices at (0, -6) and (0, 6) foci at (0, - 3) and (0, 3) asmptotes of = - 3 and = 3 Find the equation of the parabola described. ) Verte at (, -7); focus at (8, -7) A) ( + ) = ( - 7) B) ( + 7) = 6( - ) C) ( + ) = -( - 7) D) ( + 7) = -6( - ) 6
SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Graph the hperbola. 3) 9-36 = Solve the sstem of equations b elimination. 6) 3-5 = - 6 + 8 = - A) =, = 0; (, 0) B) = -, = 0; (-, 0) C) = 0, = ; (0, ) D) = 0, = -; (0, -) 5-5 5-5 7) 7 - = 5 + = 9 Solve the sstem of equations using matrices (row operations). If the sstem has no solution, sa that it is inconsistent. ) + + z - w = 6 - + 3z + w = - + - z - w = -3 - - + z + 3w = A) =, = -3, z = -5, w = ; (, -3, -5, ) B) =, = - 3, z = - 5, w = ;, - 3, - 5, C) = -, = 3, z = 5, w = - ; A) = 6, = ; 6, B) = 8, = ; 8, C) = -8, = - ; -8, - D) = -6, = - ; -6, - SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Graph the solution set of the sstem of inequalities or indicate that the sstem has no solution. 8) + 9-5 + - 5 -, 3, 5, - D) = -, = 3, z = 5, w = -; (-, 3, 5, -) Find the value of the determinant. 5) 8 0 0 6 8 8 5 5 A) 9 B) -87 C) -9 D) 8 - -5 5-5 - 7
Compute the product. 9) - 3 0-6 6-3 A) 3 6-7 -0 0 8 C) 0-6 8-8 B) not defined D) 3-7 0 6-0 8 SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Perform the row operation(s) on the given augmented matri. 50) (a) R = r + r (b) R3 = -r + r3 (c) R3 = 5r + r3-3 -5 - -5 5-5 6 Graph the solution set of the sstem of inequalities or indicate that the sstem has no solution. 5) + 0 + > 8 6 Set up the linear programming problem. 5) An office manager is buing used filing cabinets. Small file cabinets cost $5 each and large file cabinets cost $9 each, and the manager cannot spend more than $75 on file cabinets. A small cabinet takes up 6 square feet of floor space and a large cabinet takes up 9 square feet, and the office has no more than 8 square feet of floor space available for file cabinets. The manager must bu at least 6 file cabinets in order to get free deliver. Let = the number of small file cabinets bought and = the number of large file cabinets bought. Write a sstem of inequalities that describes these constraints. A) 5 + 9 75 6 + 9 8 6 C) 5 + 9 75 6 + 9 8 + 6 B) 5 + 9 75 6 + 9 8 + 6 D) 5 + 9 75 9 + 6 8 6 SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Graph the solution set of the sstem of inequalities or indicate that the sstem has no solution. 53) + 3 - - -8-6 - - 6 8 - - -6-8 - - Show that the matri has no inverse. 5) 0 8-3 - - 7 8
Write the partial fraction decomposition of the rational epression. + 55) ( - )( + + ) A) B) C) D) - - + + + + - + - + + + - + - + + - + - + + - Use a graphing utilit to find the inverse, if it eists, of the matri. Round answers to two decimal places. 56) -6 3 8 5-5 3 5 A) -0.0 0.0 0.0 0.0-0.03 0.0 0.0 0.0 0.0 B) -0.0 0.03 0.0 0.0-0.0 0.0 0.0 0.0 0.00 C) -0.0 0.03 0.0 0.0-0.03 0.0 0.0 0.0 0.0 D) -0.0 0.03 0.0 0.0-0.0 0.0 0.0 0.0 0.0 Solve the sstem of equations using matrices (row operations). If the sstem has no solution, sa that it is inconsistent. - - + 7z = 39 57) -9-6z = -5 7 + z = 63 A) =, = 8, z = 7; (, 8, 7) B) =, = 7, z = 8; (, 7, 8) C) inconsistent D) = -, = 8, z = ; (-, 8, ) Each matri is nonsingular. Find the inverse of the matri. Be sure to check our answer. 58) -6 - - - A) B) - 5 - - 3 5 C) - 5-5 - 3 5 5-3 5 D) 5-5 5-3 5-5 59) The diagonal of the floor of a rectangular office cubicle is ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessar. A) width = 9.7 ft, length =. ft B) width = 3.9 ft, length = 9.7 ft C) width = ft, length = 9 ft D) width = ft, length = ft Solve the sstem of equations b substitution. 60) + = -8 5 = -0 A) = -, = ; (-, ) B) = -, = 0; (-, 0) C) = -, = -; (-, -) D) =, = -; (, -) 9
Solve the sstem of equations using substitution. 6) + = 69 + = 7 A) =, = -5; = 5, = - or (, -5), (5, -) B) =, = 5; = 5, = or (, 5), (5, ) C) = -, = 5; = -5, = or (-, 5), (-5, ) D) = -, = -5; = -5, = - or (-, -5), (-5, -) Epand the epression using the Binomial Theorem. 65) (w - s) 6 A) w 6-8w 5 s + 7w s - w 3 s 3 + 7w s - 8ws 5 + s 6 B) w 6 - s 6 C) w 6-6w 5 s - 30w s + 0w 3 s 3 + 360w s - 70ws 5-70s 6 D) w 6-6w 5 s + 5w s - 0w 3 s 3 + 5w s - 6ws 5 + s 6 Find the maimum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. 6) z = + 7. Find maimum. A) maimum: B) maimum: 37 C) maimum: 8 D) maimum: 30 Find the sum. 63) (-6) + (-) + + 9 +... + 39 A) 60 B) 70 C) 330 D) 65 Use the Binomial Theorem to find the indicated coefficient or term. 6) The coefficient of 8 in the epansion of ( - 3) 7 A) 835 B) 95 C) -95 D) -835 Find the sum of the sequence. 66) k(k - ) k = A) -6 B) -70 C) -80 D) -5 Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 67) a = 8; r = -5 A) a5 = -00; an = 8 (-5) n B) a5 = 5000; an = 8 (-5) n C) a5 = -00; an = 8 (-5) n- D) a5 = 5000; an = 8 (-5) n- Find the indicated term of the arithmetic sequence. 68) The tenth term of the arithmetic sequence -,, 8,... A) 50 B) -6 C) -58 D) 56 Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. 69) a = ; r = 3" A) a5 = + ", an = + 3"(n-) B) a5 = 6", an = 3 n- " C) a5 = 86" 5, an = 3 n " n D) a5 = 6", an = 3 n- " n-
The given pattern continues. Write down the nth term of the sequence {an} suggested b the pattern. 70),, 9, 6, 5,... A) an = C) an = n- 3n - B) an = n D) an = n n- Find the nth term and the indicated term of the arithmetic sequence {an} whose initial term, a, and common difference, d, are given. 7) a = 0; d = 5 an =?; a6 =? A) an = 5 (n + ); a 6 = 8 5 B) an = 5 (n - ); a 6 = 0 C) an = 5 n; a 6 = 5 D) an = 5 (n - ); a 6 = 5 Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. 73) {6 n/ } A) Arithmetic; d = 6 / B) Geometric; r = 6 C) Geometric; r = 6 / D) Neither Find the sum of the sequence. 7) 8 k = A) 3 B) 8 C) D) 88 The sequence is defined recursivel. Write the first four terms. 75) a = 3; an = an- A) a = 8, a = 3, a = 8, a = 56 B) a = 3, a =, a3 = 8, a = 9 C) a = 3, a =, a = 50, a = 9 D) a = 3, a =, a =, a = 9 An arithmetic sequence is given. Find the common difference and write out the first four terms. 7) {sn} = + n 3 A) d = 3 ; s =, s = 7, s 3 =, s = 5 B) d = ; s = 7, s =, s 3= 5, s = 9 C) d = 3 ; s = 7, s =, s 3 = 5, s = 9 D) d = ; s =, s = 7, s 3 =, s = 5 SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. 76) + + 7 +... + (3n - ) = n(6n - 3n - )
Evaluate the factorial epression. 77)!! A) B)! C)! D) Find the nth term and the indicated term of the arithmetic sequence {an} whose initial term, a, and common difference, d, are given. 78) a = 75; d = - an =?; a6 =? A) an = 85 - n; a6 = -5 B) an = 75 - n; a6 = 5 C) an = 75 - n; a6 = -5 D) an = 85 - n; a6 = 5 Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 79) 6th term is -; 5th term is -6 A) a =, d =, an = an- + B) a = -30, d =, an = an- + C) a =, d = -, an = an- - D) a = -, d = -, an = an- - 8) A bag contains 7 red marbles, 3 blue marbles, and green marble. What is the probabilit of choosing a marble that is not blue when one marble is drawn from the bag? 8 A) B) 8 C) 8 D) 3 SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! 8) How man different -letter words (real or imaginar) can be formed from the letters of the word MISSISSIPPI? Leave our answer in factorial form. Use the information given in the figure. 83) 6 7 3 3 Write out the sum. n 80) 5 k+ k = A) 5 + 5 3 + 5 +... + 5 n B) 5 + 5 + 5 3 +... + 5 n C) 5 + 5 3 + 5 +... + 5 n+ D) 5 + 5 + 5 3 +... + 5 n+ How man are in B but not in A? A) 3 B) 3 C) 8 D) 7 8) In surve of 50 households, 5 responded that the have an HDTV television, 35 responded that the had a multimedia personal computer and 5 responded the had both. How man households had neither an HDTV television nor a multimedia personal computer? A) 5 B) 5 C) 5 D) 35
85) If n(b) =, n(a B) = 3, and n(a B) =, find n(a). A) B) 9 C) D) SHORT ANSWER. Answer the question. SHOW ANY RELEVANT WORK! Construct a probabilit model for the eperiment. 86) Rolling a 6-sided fair die once and tossing a fair coin once. 87) Tossing two fair coins once 88) In a probabilit model, which of the following numbers could be the probabilit of an outcome: 0, 0., -0.0, - 3,, 5,,.5 A) 0, 0.,, B) 0, 0., -0.0, - 3,, C) 0, 0., -0.0,,.5 D) 0.,, 89) The following data represent the marital status of females 8 ears and older in a certain U.S. cit. Marital Status Number (in thousands) Married 306 Widowed 59 Divorced 6 Never married 9 Determine the number of females 8 ears old and older who are married or widowed. A) 306,000 B) 365,000 C) 9,000 D) 370,000 Determine whether the following is a probabilit model. 90) Outcome Probabilit Red -0.0 Blue 0. Green 0.35 White 0. A) Yes B) No 9) Suppose that the sample space is S =,, 3,, 5, 6, 7, 8, 9, and that outcomes are equall likel. Compute the probabilit of the event E =,. A) B) C) 9 D) 5 9) In a surve of 6 hospital patients, 0 said the were satisfied with the nursing care, 9 said the were satisfied with the medical treatment, and 6 said the were satisfied with both. How man patients were satisfied with neither? How man were satisfied with onl the medical treatment? A) 9; 9 B) 3; 3 C) ; 3 D) 3; 9 93) The pscholog lab at a college is staffed b 6 male doctoral students, female doctoral students, male undergraduates, and female undergraduates. If a person is selected at random from the group, find the probabilit that the selected person is an undergraduate or a female. A) 5 3 C) 37 3 B) 3 3 D) 6 3 9) How man -digit numbers can be formed using the digits,, 3,, 5, 6, 7, 8, 9, and 0? No digit can be used more than once. A) 5 B),8,00 C) 3,68,800 D) 90 3
95) A committee is to be formed consisting of 6 men and women. If the committee members are to be chosen from men and 9 women, how man different committees are possible? A) 7560 B) 6 C),886,00 D) 75,58 96) How man 5-card poker hands consisting of three 6's and two cards that are not 6's are possible in a 5-card deck? A) 5 B) 56 C) 65 D) 530 97) A spinner has regions numbered through 8. What is the probabilit that the spinner will stop on an even number or a multiple of 3? A) 5 B) 3 C) 3 D) 98) Given that P(A) = 0.63, P(A B) =.09, and P(A B) = 0., find P(B). A) 0.56 B) 0.6 C) 0.53 D) 0.66 Approimate the area under the curve and above the -ais using n rectangles. Let the height of each rectangle be given b the value of the function at the right side of the rectangle. 99) f() = + + 3 from = - to = ; n = 3 A) B) 3 C) 7 D) 5 Find the numbers at which f is continuous. At which numbers is f discontinuous? 0) f() = - 6 - if 8 if = A) continuous for all real numbers B) continuous for all real numbers ecept = 6 C) continuous for all real numbers ecept = D) continuous for all real numbers ecept =, = 6 Find the limit algebraicall. ) lim -5 9 A) 5 B) -5 C) 0 D) 9 Find the numbers at which f is continuous. At which numbers is f discontinuous? ) f() = + 5 - + A) continuous for all real numbers ecept = -5, = 8, and = 3 B) continuous for all real numbers ecept = 5, = -8, and = -3 C) continuous for all real numbers ecept = 8, = 3 D) continuous for all real numbers ecept = -8, = -3 Determine whether f is continuous at c. 3) f() = - 5-5 ; c = 0 A) continuous B) not continuous ) f() = + ( - )( + 9) ; c = -9 A) not continuous B) continuous
Find the limit algebraicall. 5) lim 0 + A) 0 B) - C) Does not eist D) Find the one-sided limit. ) lim (3"/) - sin A) B) Find the limit as approaches c of the average rate of change of the function from c to. 6) c = 3; f() = 3 + 39 A) 8 B) 90 C) 30 D) 57 Find the derivative of the function at the given value of. 7) f() = 3 + ; = - A) B) 6 C) D) - C) D) 0 Find the limit algebraicall. 3) lim ( - 5) 0 A) 5 B) 0 C) -5 D) does not eist Determine whether f is continuous at c. ) f() = 8-3 + - 6; c = A) not continuous B) continuous Find the limit algebraicall. 8) lim ( - 5)( + 5) 0 A) 5 B) 0 C) -5 D) does not eist Determine whether f is continuous at c. 9) f() = - - 3 ; c = 0 A) not continuous B) continuous Find the limit algebraicall. ) lim 6tan 0 8 A) 0 B) 3 C) Does not eist D) Find the limit algebraicall. 5) lim - (3 - + 3) /3 A) -5 B) 5 C) -5 D) 5 Determine whether f is continuous at c. 6) f() = - + 9 ; c = A) not continuous B) continuous 7) The volume of a right clindrical cone of height 6 cm and radius r cm is V(r) = "r cubic centimeters (cm 3 ). Find the instantaneous rate of change of the volume with respect to the radius r when r = cm. A) 6" cm 3 /cm B) " cm 3 /cm C) 3" cm 3 /cm D) 6 cm 3 /cm ) lim 6 + 6 ( - 6) A) 0 B) -6 C) Does not eist D) 6 Find the derivative of the function at the given value of using a graphing utilit. If necessar, round to four decimal places. 8) f() = sin(3); = 7 A) -5856.565 B) -.5007 C) -.6656 D) 5856.565 5
Answer Ke Testname: SPRINGFINALREVIEW ) B Objective: (7.3) Solve Trigonometric Equations Quadratic in Form ) Objective: (7.3) Solve Trigonometric Equations Using a Graphing Utilit 3) C Objective: (7.6) Use Half-angle Formulas to Find Eact Values ) C Objective: (7.7) Epress Sums as Products 5) 0.9 Objective: (7.3) Solve Trigonometric Equations Using a Graphing Utilit 6) D Objective: (7.3) Solve Equations Involving a Single Trigonometric Function 7) A Objective: (7.5) Use Sum and Difference Formulas to Find Eact Values 8) A Objective: (7.3) Solve Equations Involving a Single Trigonometric Function 9) sin α + sin β csc α + csc β = sin α + sin β = sin α + sin β Objective: (7.) Establish Identities sin α + sin β sin β + sin α sin α sin β = (sin α + sin β) ) 0.63 Objective: (7.3) Solve Equations Involving a Single Trigonometric Function ). Objective: (7.3) Solve Trigonometric Equations Using a Graphing Utilit ) B Objective: (7.6) Use Half-angle Formulas to Find Eact Values 3) C Objective: (7.6) Use Half-angle Formulas to Find Eact Values ) B Objective: (8.) Solve SSA Triangles 5) C Objective: (8.) Find the Area of SSS Triangles 6) C Objective: (8.3) Solve Applied Problems 7) C Objective: (8.3) Solve SAS Triangles 8) D Objective: (8.3) Solve SAS Triangles 9) C Objective: (8.) Find the Area of SAS Triangles 0) D Objective: (8.) Solve Applied Problems ) D Objective: (8.) Find the Area of SSS Triangles ) C Objective: (8.3) Solve SAS Triangles 6 sin α sin β = sin α sin β sin β + sin α
Answer Ke Testname: SPRINGFINALREVIEW 3) A Objective: (8.) Find the Area of SSS Triangles ) A Objective: (8.) Find the Area of SSS Triangles 5) C Objective: (8.3) Solve SAS Triangles 6) B Objective: (8.) Use the Complementar Angle Theorem 7) B Objective: (8.) Solve SAA or ASA Triangles 8) A Objective: (.7) Find a Rectangular Equation for a Curve Defined Parametricall 9) 5 - -5 5-5 Objective: (.3) Analze Ellipses with Center at (h, k) 30) 5-5 5-5 Objective: (.) Analze Hperbolas with Center at the Origin 3) B Objective: (.3) Solve Applied Problems Involving Ellipses 3) D Objective: (.) Analze Parabolas with Verte at (h, k) 33) B Objective: (.) Solve Applied Problems Involving Parabolas 7
Answer Ke Testname: SPRINGFINALREVIEW 3) Objective: (.7) Graph Parametric Equations Using a Graphing Utilit 35) C Objective: (.) Know the Names of the Conics 36) A Objective: (.) Solve Applied Problems Involving Hperbolas 37) C Objective: (.) Analze Parabolas with Verte at the Origin 38) A Objective: (.3) Analze Ellipses with Center at (h, k) 39) B Objective: (.7) Find a Rectangular Equation for a Curve Defined Parametricall 0) A Objective: (.3) Analze Ellipses with Center at the Origin ) D Objective: (.) Analze Hperbolas with Center at the Origin ) B Objective: (.) Analze Parabolas with Verte at (h, k) 3) 5-5 5-5 Objective: (.) Analze Hperbolas with Center at the Origin ) D Objective: (.) Solve a Sstem of Linear Equations Using Matrices 5) C Objective: (.3) Evaluate 3 b 3 Determinants 6) B Objective: (.) Solve Sstems of Equations b Elimination 8
Answer Ke Testname: SPRINGFINALREVIEW 7) B Objective: (.) Solve Sstems of Equations b Elimination 8) 5 - -5 5-5 - Objective: (.7) Graph a Sstem of Inequalities 9) D Objective: (.) Find the Product of Two Matrices 50) 5) -3-5 0-7 -8 3 0-8 -76 67 Objective: (.) Perform Row Operations on a Matri 8 6 - -8-6 - - 6 8 - - -6-8 - Objective: (.7) Graph a Sstem of Inequalities 5) C Objective: (.8) Set up a Linear Programming Problem 9
Answer Ke Testname: SPRINGFINALREVIEW 53) - 5) - Objective: (.7) Graph a Sstem of Inequalities 0 8-3 - - 7 5 0 0 6 0 0 0 0 0 0 3 56 0 0 0 0 5-3 - - 7 5 0 0 0 0 0 0 0 0 0 0 3 56 Objective: (.) Find the Inverse of a Matri 5 0 7-7 0 0 0-8 - 6 7 0 0 3 0 0 0 5 0 7 0 6 0 0 3 0 0 55) B Objective: (.5) Decompose P/Q, Where Q Has a Nonrepeated Irreducible Quadratic Factor 56) D Objective: (.) Find the Inverse of a Matri 57) A Objective: (.) Solve a Sstem of Linear Equations Using Matrices 58) C Objective: (.) Find the Inverse of a Matri 59) A Objective: (.6) Solve a Sstem of Nonlinear Equations Using Elimination 60) A Objective: (.) Solve Sstems of Equations b Substitution 6) B Objective: (.6) Solve a Sstem of Nonlinear Equations Using Substitution 6) B Objective: (.8) Solve a Linear Programming Problem 63) D Objective: (.) Find the Sum of an Arithmetic Sequence 0
Answer Ke Testname: SPRINGFINALREVIEW 6) C Objective: (.5) Use the Binomial Theorem 65) D Objective: (.5) Use the Binomial Theorem 66) B Objective: (.) Find the Sum of a Sequence Algebraicall and Using a Graphing Utilit 67) D Objective: (.3) Find a Formula for a Geometric Sequence 68) A Objective: (.) Find a Formula for an Arithmetic Sequence 69) D Objective: (.3) Find a Formula for a Geometric Sequence 70) B Objective: (.) Write the First Several Terms of a Sequence 7) B Objective: (.) Find a Formula for an Arithmetic Sequence 7) C Objective: (.) Determine if a Sequence is Arithmetic 73) C Objective: (.3) Determine if a Sequence is Geometric 7) D Objective: (.) Find the Sum of a Sequence Algebraicall and Using a Graphing Utilit 75) B Objective: (.) Write the Terms of a Sequence Defined b a Recursive Formula 76) First we show that the statement is true when n =. For n =, we get = (6-3 - ) =. This is a true statement and Condition I is satisfied. Net, we assume the statement holds for some k. That is, + + 7 +... + (3k - ) = k(6k - 3k - ) is true for some positive integer k. We need to show that the statement holds for k +. That is, we need to show that + + 7 +... + (3(k + ) - ) = (k + )(6(k + ) - 3(k + ) - ). So we assume that + + 7 +... + (3k - ) = k(6k - 3k - ) sides of the equation. + + 7 +... + (3k - ) + (3(k + ) - ) = k(6k - 3k - ) is true and add the net term, (3(k + ) - ), to both + (3(k + ) - ) = k(6k - 3k - ) = k(6k - 3k - ) + (3k + ) + (9k + 6k + )
Answer Ke Testname: SPRINGFINALREVIEW = 6k3-3k - k + 8k + k + = 6k3 + 5k + k + Simplif the epression (k + )(6(k + ) - 3(k + ) - ) to verif: (k + )(6(k + ) - 3(k + ) - ) = (k + )(6(k + k + ) - 3k -3 - ) = (k + )(6k + k + 6-3k - ) = (k + )(6k + 9k + ) = 6k3 + 5k + k + Condition II is satisfied. As a result, the statement is true for all natural numbers n. Objective: (.) Prove Statements Using Mathematical Induction 77) A Objective: (.) Write the First Several Terms of a Sequence 78) D Objective: (.) Find a Formula for an Arithmetic Sequence 79) C Objective: (.) Find a Formula for an Arithmetic Sequence 80) C Objective: (.) Use Summation Notation 8) A Objective: (3.3) Use the Complement Rule to Find Probabilities 8)!!!! Objective: (3.) Solve Counting Problems Using Permutations Involving n Nondistinct Objects 83) C Objective: (3.) Count the Number of Elements in a Set 8) C Objective: (3.) Count the Number of Elements in a Set 85) D Objective: (3.) Count the Number of Elements in a Set 86) S = {H, H, 3H, H, 5H, 6H, T, T, 3T, T, 5T, 6T}; each outcome has a probabilit of Objective: (3.3) Construct Probabilit Models 87) S = {HH, HT, TH, TT}; each outcome has the probabilit of Objective: (3.3) Construct Probabilit Models
Answer Ke Testname: SPRINGFINALREVIEW 88) A Objective: (3.3) Construct Probabilit Models 89) B Objective: (3.) Count the Number of Elements in a Set 90) B Objective: (3.3) Construct Probabilit Models 9) D Objective: (3.3) Compute Probabilities of Equall Likel Outcomes 9) B Objective: (3.) Count the Number of Elements in a Set 93) C Objective: (3.3) Find Probabilities of the Union of Two Events 9) D Objective: (3.) Solve Counting Problems Using Permutations Involving n Distinct Objects 95) A Objective: (3.) Solve Counting Problems Using Combinations 96) A Objective: (3.) Solve Counting Problems Using Combinations 97) B Objective: (3.3) Find Probabilities of the Union of Two Events 98) A Objective: (3.3) Find Probabilities of the Union of Two Events 99) B Objective: (.5) Approimate the Area Under the Graph of a Function 0) A Objective: (.3) Determine Whether a Function Is Continuous ) B Objective: (.) Find the Limit of a Sum, a Difference, and a Product ) C Objective: (.3) Determine Whether a Function Is Continuous 3) A Objective: (.3) Determine Whether a Function Is Continuous ) A Objective: (.3) Determine Whether a Function Is Continuous 5) C Objective: (.) Find the Limit of a Quotient 6) D Objective: (.) Find the Limit of an Average Rate of Change 7) B Objective: (.) Find the Derivative of a Function 8) C Objective: (.) Find the Limit of a Sum, a Difference, and a Product 9) A Objective: (.3) Determine Whether a Function Is Continuous ) B Objective: (.) Find the Limit of a Quotient 3
Answer Ke Testname: SPRINGFINALREVIEW ) C Objective: (.) Find the Limit of a Quotient ) A Objective: (.3) Find the One-sided Limits of a Function 3) C Objective: (.) Find the Limit of a Polnomial ) B Objective: (.3) Determine Whether a Function Is Continuous 5) D Objective: (.) Find the Limit of a Power or a Root 6) B Objective: (.3) Determine Whether a Function Is Continuous 7) A Objective: (.) Find Instantaneous Rates of Change 8) C Objective: (.) Find the Derivative of a Function