Pre Calculus Spring Final Exam REVIEW

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1 Pre Calculus Spring Final Eam REVIEW Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. ) B = 43 C = 7 b = 4 Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 2) B = 4 a = 4 b = 3 Find the area of the triangle having the given measurements. Round to the nearest square unit. 3) b = 4 in. A = 27 C = 74 Use Heron's formula to find the area of the triangle. Round to the nearest square unit. 4) a = 9 meters, b = 3 meters, c = 6 meters Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. ) B = 63 a = 2 c = 8 Solve the problem. 6) The distance from home plate to dead center field in Sun Devil Stadium is 40 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field? Polar coordinates of a point are given. Find the rectangular coordinates of the point. 7) (-, 20 ) The rectangular coordinates of a point are given. Find the polar coordinates of the point. 8) ( 3, ) Convert the rectangular equation to a polar equation. 9) 2 = 6 Write the comple number in polar form. ) i Find the product of the comple numbers. Leave answer in polar form. ) z = 3(cos 7π 4 + i sin 7π 4 ) z2 = 6(cos 9π 4 + i sin 9π 4 ) Use DeMoivre's Theorem to find the indicated power of the comple number. Write answer in rectangular form. 2) 2 2 (cos 7π 4 + i sin 7π 4 ) Find all the comple roots. Write the answer in the indicated form. 3) The comple square roots of 0(cos 60 + i sin 60 ) (polar form) Find the specified vector or scalar. 4)u = i - 2j, v = 3i + 7j; Find u - v. Use the given vectors to find the specified scalar. )u = -3i - 6j and v = -3i + 7j; Find u v. Find the unit vector having the same direction as v. 6)v = -2i - j Solve the problem. 7) A vendor sells hot dogs and bags of potato chips. A customer bus 3 hot dogs and 4 bags of potato chips for $.2. Another customer bus hot dogs and 3 bags of potato chips for $2.0. Find the cost of each item. 8) One number is less than a second number. Twice the second number is 8 less than 4 times the first. Find the two numbers. Write the form of the partial fraction decomposition of the rational epression. It is not necessar to solve for the constants ) ( + 6)( - )

2 20) 2) 7 - ( + ) 2-2 ( + )( - ) 2 Write the partial fraction decomposition of the rational epression. 22) (- 4)( - ) Graph the solution set of the sstem of inequalities or indicate that the sstem has no solution. 23) > Solve the problem. 2) A steel compan produces two tpes of machine dies, part A and part B. The compan makes a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let = the number of part A produced in a week and = the number of part B produced in a week. Write the objective function that describes the total weekl profit. 26) A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.2 and an ounce of potatoes for $0.02. The dietician is bound b the following constraints. Each ounce of chicken contains 3 grams of protein and 24 grams of carbohdrates. Each ounce of potatoes contains grams of protein and 3 grams of carbohdrates. The minimum dail requirements for the patients under the dietitian's care are 4 grams of protein and 8 grams of carbohdrates. Let = the number of ounces of chicken and = the number of ounces of potatoes purchased per patient. Write a sstem of inequalities that describes these constraints. Graph the inequalit. 24) Write an augmented matri for the sstem of equations. 27) z = 8 + 6z = 7 z = Perform the matri row operation and write the new matri ) R + R Use Gaussian elimination to find the complete solution to the sstem of equations, or state that none eists. 29) + + z = z = z = 4 Perform the indicated matri operations. 30) A = and B = Find A + B. 7 2

3 3) Let C = -3 2 and D = Find C - 2D. Graph the ellipse and locate the foci. 39) = Find the product, AB, if possible. 32) A = , B = ) A = - 3 4, B = Find the inverse of the matri. 34) A = Write the linear sstem as a matri equation in the form AX = B, where A is the coefficient matri and B is the constant matri. 3) = = 60 Evaluate the determinant. 36) Find the standard form of the equation of the ellipse and give the location of its foci. 40) ) Use Cramer's rule to solve the sstem. 38) 2 + = = 4 Graph the ellipse. 4) ( - 2)2 9 + ( - )2 6 = Find the vertices and locate the foci for the hperbola whose equation is given. 42) = 3

4 Find the standard form of the equation of the hperbola satisfing the given conditions. 43) Foci: (0, -8), (0, 8); vertices: (0, -4), (0, 4) 44) Center: (4, 7); Focus: (-3, 7); Verte: (3, 7) Find the location of the center, vertices, and foci for the hperbola described b the equation. 4) ( + 2)2 0 - ( - 2)2 8 = Convert the equation to the standard form for a parabola b completing the square on or as appropriate. 46) = 0 Find the focus and directri of the parabola with the given equation. 47) = 2 Write a formula for the general term (the nth term) of the arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find the indicated term of the sequence. 4) Find a7; 23, 7,,... Find the indicated sum. ) Find the sum of the first 60 terms of the arithmetic sequence -, -9, -27, -3,... Find the standard form of the equation of the ellipse satisfing the given conditions. 6) Endpoints of major ais: (-2, ) and (-2, 7); endpoints of minor ais: (-4, 4) and (0, 4); If the given sequence is a geometric sequence, find the common ratio. 7), -3, 9, -27, 8 Find the verte, focus, and directri of the parabola with the given equation. 48) ( - ) 2 = -4( - 3) Eliminate the parameter. Find a rectangular equation for the plane curve defined b the parametric equations. 49) = t + 4, = t2 0) = 3t, = t + 7 Find a set of parametric equations for the rectangular equation. ) = 2-2 Find the indicated sum. 7 2) i + 9 i=4 Find the common difference. 3) 0, - 3 2, - 3, - 9 2,... 8) 7, 9,, 3 Find the indicated sum. 9) i - 4 i = 7 Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a, and common ratio, r. 60) Find a when a = -3, r = 3. Use the formula for the sum of the first n terms of a geometric sequence to solve. 6) Find the sum of the first 2 terms of the geometric sequence: 2, -6, 8, -4, 62,.... Find the sum of the infinite geometric series. 62) Use the Binomial Theorem to epand the epression and epress the result in simplified form.. 63) (3 - )4 Find the term indicated in the epansion. 64) (4 + 3); th term 4

5 Solve the problem. 6) How man 3-letter codes can be formed using the letters A, B, C, D, and E? No letter can be used more than once. 66) A church has 8 bells in its bell tower. Before each church service 3 bells are rung in sequence. No bell is rung more than once. How man sequences are there? 67) A stack of different cards are shuffled and spread out face down. If 3 cards are turned face up, how man different 3-card combinations are possible? 68) A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or ketchup. How man different hamburgers can be concocted using an 4 of the etras? Use the theoretical probabilit formula to solve the problem. Epress the probabilit as a fraction reduced to lowest terms. 69) A die is rolled. The sample space of equall likel outcomes is {, 2, 3, 4,, 6}. Find the probabilit of getting a 9. Solve the problem. 70) You are dealt one card from a standard 2-card deck. Find the probabilit that ou are not dealt a heart. 7) A single die is rolled twice. The 36 equall-likel outcomes are shown as follows: (, ) (, 2) (, 3) (, 4) (, ) (, 6) (2, ) (2, 2) (2, 3) (2, 4) (2, ) (2, 6) (3, ) (3, 2) (3, 3) (3, 4) (3, ) (3, 6) (4, ) (4, 2) (4, 3) (4, 4) (4, ) (4, 6) (, ) (, 2) (, 3) (, 4) (, ) (, 6) (6, ) (6, 2) (6, 3) (6, 4) (6, ) (6, 6) Find the probabilit of getting a sum of or 6. Solve the problem involving probabilities with independent events. 72) A single die is rolled twice. Find the probabilit of getting a the first time and a 3 the second time.

6 Answer Ke Testname: PRE CALCULUS SPRING FINAL EXAM REVIEW REVISED 20 ) A = 30, a =.3, c = 9.6 2) A = 6, C = 78, c = 4.; A2 = 9, C2 = 20, c2 =.6 3) 4 in. 2 4) 22 square meters ) b =.0, A = 76, C =4 6) feet 7) 2, ) (2, π 6 ) 6 cos θ 9) r = sin2θ ) 20(cos i sin 26.9 ) ) 3 2 (cos 0 + i sin 0) 2) i 3) (cos 30 + i sin 30 ), (cos 2 + i sin 2 ) 4) 8i - 9j ) 27 6)u = i - 3 j 7) $.7 for a hot dog; $.2 for a bag of potato chips 8) 9 and 4 A 9) B - 20) 2) 22) 23) A + + B ( + ) 2 A + + B - + C (- )

7 Answer Ke Testname: PRE CALCULUS SPRING FINAL EXAM REVIEW REVISED 20 24) ) z = ) ) ) ) {(- 3t 2 + 7, t 2, t)} 30) 3) 32) 33) 34) ) ) - 37) ) {(, 2)} =

8 Answer Ke Testname: PRE CALCULUS SPRING FINAL EXAM REVIEW REVISED 20 39) foci at (0, 7) and (0, - 7) ) = - foci at (- 2, 0) and ( 2, 0) 4) ) vertices: (0, -), (0, ) foci: (0, - 2 4), (0, 2 4) 43) = 44) ( - 4) 2 - ( - 7)2 48 = 4) Center at (2, -2); vertices at (2, -2) and (2, 8); foci at (2, -2-8) and (2, ) 46) ( + 3) 2 = -3( - 3) 47) focus: ( 40, 0) directri: = ) verte: (3, ) focus: (2, ) directri: = 4 49) = ) = ) = t; = 2t - 2 8

9 Answer Ke Testname: PRE CALCULUS SPRING FINAL EXAM REVIEW REVISED 20 2) ) ) -73 ) -4,820 6) ( + 2)2 4 + ( - 4)2 9 = 7) -3 8) not a geometric sequence 9) ) -77,47 6) -26,720 62) 26 63) ) 620 6) 60 66) ) 20 68) 3 69) 0 70) 3 4 7) 4 72) 36 9

Precalculus Spring Final Review Name

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.