Instructor: Imelda Valencia Course: A3 Honors Pre Calculus

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1 Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus Assignment: Summer Homework for those who will be taking FOCA onl available until Sept Write the epression in the standard form a + b i. ( + i ) (9 3 i ) ( + i ) (9 3 i ) = (Simplif our answer.). Perform the indicated operation and write the result in standard form. 3 3 = (Simplif our answer. Epress comple numbers in terms of i. Tpe an eact answer, using radicals as needed.) 3. Perform the indicated operations and write the result in standard form. 7 7 = (Tpe an eact answer, using radicals as needed. Tpe our answer in the form a + b i.). Use the verte and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's ais of smmetr. Use the graph to determine the domain and range of the function. f() = ( + ) 9 Use the graphing tool to graph the function. Use the verte and one of the intercepts when drawing the graph. The ais of smmetr is. (Tpe an equation. Simplif our answer.) The domain of the function is. (Tpe our answer in interval notation.) The range of the function is. (Tpe our answer in interval notation.) /9

2 5. Use the verte and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's ais of smmetr. Use the parabola to identif the function's domain and range. f() = Use the graphing tool to graph the equation. Use the verte and one of the intercepts when drawing the graph. The equation for the ais of smmetr is. (Tpe an equation.) Use the graph to identif the function's domain. The domain of f is. (Tpe our answer in interval notation.) Use the graph to identif the function's range. The range of f is. (Tpe our answer in interval notation.) Find the zeros for the polnomial function and give the multiplicit for each zero. State whether the graph crosses the ais, or touches the ais and turns around, at each zero. f() = 3( + )( + ) The zeros are. (Use a comma to separate answers as needed.) The multiplicit of is. The multiplicit of is. Does the graph of f() cross or touch the ais and turn around at the intercept,? Cross Touch the ais and turn around Does the graph of f() cross or touch the ais and turn around at the intercept,? Touch the ais and turn around Cross 7. Among all pairs of numbers whose sum is, find a pair whose product is as large as possible. What is the maimum product? The pair of numbers whose sum is and whose product is as large as possible is. (Use a comma to separate answers.) The maimum product is. /9

3 . Divide using snthetic division = + 1 (Simplif our answers. Do not factor.) 1 9. Use transformations of the graph of f() = 5 to graph the function g() given below. Graph and give the equation of the asmptote. Use the graph to determine the domain and range of g(). g() = 5 Graph the function g() = 5 and its asmptote. Graph the asmptote as a dashed line. Use the graphing tool to graph the function. What is the equation of the horizontal asmptote of g() = 5? = What is the domain of g() = 5? (Tpe our answer in interval notation.) What is the range of g() = 5? (Tpe our answer in interval notation.) 3/9

4 10. Begin b graphing f() = log 3. Then use transformations of this graph to graph the given function. What is the vertical asmptote? Use the graphs to determine the given function's domain and range. g() = log ( + ) 3 Graph the function g() = log 3( + ). Graph the asmptote of g() as a dashed line. Use the graphing tool to graph the functions What is the vertical asmptote of g()? = What is the domain of g() = log 3( + )? (Simplif our answer. Tpe our answer in interval notation.) What is the range of g() = log 3( + )? (Simplif our answer. Tpe our answer in interval notation.) 11. Find the domain of the function. f() = log ( + 9) The domain of f is. (Tpe our answer in interval notation.) 1. Find the domain of the following logarithmic function. f() = ln ( ) Which is the correct domain of f() = ln ( )? (,) or (, ) (, ) (, ) or (, ) (, ) 13. Evaluate the epression without using a calculator. log log = 3 /9

5 1. Evaluate the following epression without using a calculator. log 1 log 1 = (Tpe an integer or a fraction.) 15. Evaluate the epression without using a calculator. log log log log = 1. Evaluate the following epression without using a calculator. 3 log log 3 9 = 17. Evaluate the epression without using a calculator. log log 17 = 1. Use the compound interest formulas A = P 1 + r nt and A = Pe rt to solve the problem given. Round answers to the n nearest cent. Find the accumulated value of an investment of $10,000 for ears at an interest rate of.5% if the mone is a. compounded semiannuall; b. compounded quarterl; c. compounded monthl d. compounded continuousl. a. What is the accumulated value if the mone is compounded semiannuall? $ (Round our answer to the nearest cent.) b.what is the accumulated value if the mone is compounded quarterl? $ (Round our answer to the nearest cent.) c. What is the accumulated value if the mone is compounded monthl? $ (Round our answer to the nearest cent.) d. What is the accumulated value if the mone is compounded continuousl? $ (Round our answer to the nearest cent.) 19. Solve the eponential equation b epressing each side as a power of the same base and then equating eponents. = 5 The solution set is. 5/9

6 0. Solve for. 3 7 = 9 The solution set is. 1. Solve the eponential equation b epressing each side as a power of the same base and then equating eponents. 3 = 1 The solution set is. (Simplif our answer.). Solve the following eponential equation b epressing each side as a power of the same base and then equating eponents. 1 9 = 3 The solution set is. 3. Solve the following eponential equation b epressing each side as a power of the same base and then equating eponents. + 5 = 3 The solution set is.. Solve the following eponential equation b epressing each side as a power of the same base and then equating eponents. + 1 e = e The solution set is. 5. Solve the following eponential equation. Epress the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. = 9 What is the solution in terms of natural logarithms? The solution set is. (Use a comma to separate answers as needed. Simplif our answer. Use integers or fractions for an numbers in the epression.) What is the decimal approimation for the solution? The solution set is. (Use a comma to separate answers as needed. Round to two decimal places as needed.) /9

7 . Solve the eponential equation. Epress the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 7 e = 3 What is the solution in terms of natural logarithms? The solution set is. (Use a comma to separate answers as needed. Simplif our answer. Use integers or fractions for an numbers in the epression.) What is the decimal approimation for the solution? The solution set is. (Use a comma to separate answers as needed. Round to two decimal places as needed.) 7. Solve the following eponential equation b taking the natural logarithm on both sides. Epress the solution in terms of natural logarithms. Then, use a calculator to obtain a decimal approimation for the solution. 7 e = 5 What is the solution in terms of natural logarithms? The solution set is. (Use a comma to separate answers as needed. Simplif our answer. Use integers or fractions for an numbers in the epression.) What is the decimal approimation for the solution? The solution set is. (Use a comma to separate answers as needed. Round to two decimal places as needed.). Solve the eponential equation. Epress the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approimation for the solution. ( 3) 7 = 335 What is the solution in terms of natural logarithms? The solution set is. (Use a comma to separate answers as needed. Simplif our answer. Use integers or fractions for an numbers in the epression.) What is the decimal approimation for the solution? The solution set is. (Use a comma to separate answers as needed. Round to two decimal places as needed.) 9. Solve the logarithmic equation. Be sure to reject an value of that is not in the domain of the original logarithmic epressions. Give the eact answer. log ( + ) = log + log Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 7/9

8 30. Solve the logarithmic equation. Be sure to reject an value of that is not in the domain of the original logarithmic epressions. Give the eact answer. log ( 3) = log ( + ) + log 9 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 31. Solve the logarithmic equation. Be sure to reject as a solution an value that is not in the domain of the original logarithmic epressions. log = log 3 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Tpe an eact answer in simplified form. Use a comma to separate answers as needed.) B. There is no solution. 3. Solve the logarithmic equation. Be sure to reject an value of that is not in the domain of the original logarithmic epressions. Give the eact answer. log ( + 1) log = log (3 + ) Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 33. Solve the logarithmic equation. Be sure to reject an value of that is not in the domain of the original logarithmic epressions. Give the eact answer. log log 5 = log 05 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 3. Solve the logarithmic equation. Be sure to reject an value of that is not in the domain of the original logarithmic epressions. Give the eact answer. log + log ( + ) = log 3 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution set is. (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. /9

9 35. Solve the triangle. A = 50, B = 1, a = 7 C = (Do not round until the final answer. Then round to the nearest degree as needed.) b (Do not round until the final answer. Then round to the nearest tenth as needed.) c (Do not round until the final answer. Then round to the nearest tenth as needed.) 3. Two ships leave a harbor at the same time. One ship travels on a bearing S11 W at 11 miles per hour. The other ship travels on a bearing N75 E at 1 miles per hour. How far apart will the ships be after hours? The distance is approimatel miles. (Round to the nearest tenth as needed.) feet The figure shows a 50 foot tower on the side of a hill that forms a angle with the horizontal. Find the length of each of the two gu wires that are anchored 50 feet uphill and downhill from the tower's base and etend to the top of the tower. 50 feet 50 feet Part (a) What is the length of the uphill gu wire? feet (Round to the nearest tenth as needed.) Part (b) What is the length of the downhill gu wire? feet (Round to the nearest tenth as needed.) 3. The rectangular coordinates of a point are given. Find the polar coordinates (r, θ) of this point with θ epressed in radians. Let r > 0 and 0 θ < π. ( 3, ) The polar coordinates are. (Tpe an ordered pair. Tpe eact answers for each coordinate, using π as needed. Use integers or fractions for an numbers in the epression. Simplif our answer.) 39. The rectangular coordinates of a point are given. Find polar coordinates of the point such that r > 0 and 0 θ < π. ( 1,0) The polar coordinates are. (Tpe an ordered pair. Tpe our answer in radians. Tpe an eact answer. Simplif our answer.) 9/9

10 0. Consider the following sstem. + + z = 1 This is Equation 1. 5 = This is Equation. z = 1 This is Equation 3. Equation does not contain the variable (1) To obtain a second equation that does not contain this variable, () (1) z... () add Equations 1 and 3. add Equations and 3. add Equations and Determine if (7,,) is a solution of the sstem. + + z = 11 z = 5 z = Choose the correct answer below. The ordered triple is a solution to the sstem. The ordered triple is not a solution to the sstem.. Determine if the given ordered triple below is a solution of the following sstem. + 3 = = 7z = ( 1, 1, ) Is the ordered triple a solution to the sstem? No Yes 3. Solve the given sstem of equations z = z = 3 7z = Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is,, B. There are infinitel man solutions. C. There is no solution.. (Simplif our answers.) 10/9

11 . Solve the sstem. If there is no solution or if there are infinitel man solutions and the sstem's equations are dependent, so state. + 3z = z = z = 15 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is {(,, )}. (Simplif our answers.) B. There are infinitel man solutions. C. There is no solution. 5. Solve the given sstem of equations z = z = 9 + z = 10 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is,, B. There are infinitel man solutions. C. There is no solution.. (Simplif our answers.). Solve the sstem. If there is no solution or if there are infinitel man solutions and the sstem's equations are dependent, so state. + 3z = 3 + z = 0 z = 1 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is {(,, )}. (Simplif our answers.) B. There are infinitel man solutions. C. There is no solution. 11/9

12 7. Solve the sstem. If there is no solution or if there are infinitel man solutions and the sstem's equations are dependent, so state. 3 + = 3 + z = z = 0 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is {,, }. (Simplif our answers.) B. There are infinitel man solutions. C. There is no solution.. Solve the sstem. 3 = z = 1 + z = 3 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is,, B. There are infinitel man solutions. C. There is no solution.. (Simplif our answers.) 9. Solve the sstem. If there is no solution or if there are infinitel man solutions and the sstem's equations are dependent, so state. 5( + ) + 3z = 1 ( 5 + z) = 3 (1 + ) = 5(z 5) Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is,,. (Simplif our answers.) B. There are infinitel man solutions. C. There is no solution. 50. Find the quadratic function = a + b + c whose graph passes through the given points. ( 3, ), (, 3), ( 1, 0) = 51. Find the quadratic function = a + b + c whose graph passes through the given points. ( 1, 1), ( 1, 7), (, ) = 1/9

13 5. Solve the sstem z z z Select the correct choice below and fill in an answer boes within our choice. = 0 = 9 = 53 1 A. There is one solution. The solution set is,, B. There are infinitel man solutions. C. There is no solution.. (Simplif our answers.) 53. Find the equation of the quadratic function = a + b + c whose graph is shown on the right. Select three points whose coordinates appear to be integers. 1 = (Simplif our answer. Tpe an epression using as the variable.) 5. You throw a ball straight up from a rooftop. The ball misses the rooftop on its wa down and eventuall strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground,, after seconds., seconds after the ball is thrown, ball's height, in feet, above the ground a. Find the quadratic function = a + b + c whose graph passes through the given points. = b. Use the function in part (a) to find the value for when = 5. When = 5, =. 13/9

14 55. The bar graph shows the average annual spending per person on selected items in 010. The combined spending on housing, vehicles/gas, and health care was $ 13,. The difference between spending on housing and spending on vehicles/gas was $ The difference between spending on housing and spending on health care was $ 703. Find the average per person spending on housing, vehicles/gas, and health care in 010. Find the average per person spending on housing in 010. Annual Spending per Person, Adjusted for Inflation Annual spending per person ($) Housing p Vehicles/ gas t 010 Health care v Find the average per person spending on vehicles/gas in 010. Find the average per person spending on health care in On a recent trip to the convenience store, ou picked up gallons of milk, bottles of water, and snack size bags of chips. Your total bill (before ta) was $ 3.0. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $.00 more than a bottle of water, how much does each item cost? How much does a snack size bag of chips cost? $ (Tpe an integer or a decimal.) How much does a bottle of water cost? $ (Tpe an integer or a decimal.) How much does a gallon of milk cost? $ (Tpe an integer or a decimal.) 57. Use a sstem of linear equations in three variables to solve the following problem. A certain brand of razor blade comes in packages of, 1, and blades, costing $, $ 3, and $ per package, respectivel. A store sold 1 packages containing a total of razor blades and took in $ 53. How man packages of each tpe were sold? Write a sstem of linear equations using the given information. Choose correct answer below. A z = z = z = C z = z = z = 1 B z = z = + + z = 53 D z = z = + + z = 1 There were packages of blades, packages of 1 blades, and packages of blades sold. 1/9

15 5. A person invested $ 700 for 1 ear, part at %, part at 11%, and the remainder at 1%. The total annual income from these investments was $ 7. The amount of mone invested at 1% was $ 100 more than the amounts invested at % and 11% combined. Find the amount invested at each rate. The person invested $ at %, $ at 11%, and $ at 1%. 59. Find the values of,, and z in the triangle to the right. (+ ) z ( ) = = z = 0. Using the graph shown, fill in the blank so that the resulting statement is true. The equation of the parabola is of the form. The equation of the parabola is of the form (1) (1) = p. = p. 1. Using the graph shown, fill in the blank so that the resulting statement is true. The equation of the parabola is of the form. ( 5, ) The equation of the parabola is of the form (1) (1) ( + 5) = p( + ). ( 5) = p( ). ( ) = p( + 5). ( + ) = p( + 5). 15/9

16 . Find the focus and directri of the parabola with the given equation. Then graph the parabola. = 0 What is the focus? (Tpe an ordered pair. Simplif our answer.) What is the directri? (Tpe an equation. Simplif our answer.) Choose the correct graph of the parabola. A. B. C. D Find the focus and directri of the parabola with the given equation. Then graph the parabola. = 3 The focus is. (Tpe an ordered pair.) The directri is. (Tpe an equation.) Use the graphing tool to graph the parabola /9

17 . Convert the equation to standard form b completing the square on. Then find the verte, focus, and directri of the parabola. Finall, graph the parabola = 0 The equation in standard form is. What is the location of the verte of the parabola given b the equation? (Tpe an ordered pair.) What is the location of the focus of the parabola? (Tpe an ordered pair.) What is the directri of the parabola? (Tpe an equation.) Use the graphing tool to graph the parabola Graph the ellipse and locate the foci. + = Choose the correct graph below. A. B. C. D Locate the foci. (Tpe ordered pairs. Use a comma to separate answers. Tpe eact answers, using radicals as needed. Simplif our answers.) 17/9

18 . Graph the ellipse and give the location of its foci. ( 1) ( + 5) + = 1 5 Choose the correct graph below. A. B. C. D Locate the foci. (Tpe ordered pairs. Use a comma to separate answers. Tpe eact answers, using radicals as needed. Simplif our answers.) 7. Use the center, vertices, and asmptotes to graph the hperbola. Locate the foci and find the equations of the asmptotes. ( + 3) ( + 1) = 1 9 Graph the hperbola. Choose the correct graph below. A. B. C. D Determine the location of the foci. (Tpe an ordered pair. Simplif our answer. Tpe an eact answer, using radicals as needed. Use a comma to separate answers as needed.) The equations of the asmptotes are = ±. (Simplif our answer. Tpe our answer in point slope form. Use integers or fractions for an numbers in the equation.) 1/9

19 . Find the verte, focus, and directri of the parabola with the given equation. Then graph the parabola. ( 1) = 1( + 3) The verte of the parabola is. (Tpe an ordered pair.) The focus of the parabola is. (Tpe an ordered pair.) The directri of the parabola is. (Tpe an equation. Simplif our answer.) Use the graphing tool to graph the parabola Give the center and radius of the circle described b the equation and graph the equation. Use the graph to identif the domain and range. ( + ) + ( ) = 9 The center is. (Tpe an ordered pair. Simplif our answer.) The radius is. (Tpe an integer or a simplified fraction.) Graph the circle. Epress the domain of the relation in interval notation Epress the range of the relation in interval notation. 19/9

20 70. Use the center, vertices, and asmptotes to graph the hperbola. Locate the foci and find the equations of the asmptotes. ( ) ( + 3) = Graph the hperbola. Choose the correct graph below. A. B. C. D. Determine the location of the foci. (Tpe an ordered pair. Simplif our answer. Tpe an eact answer, using radicals as needed. Use a comma to separate answers as needed.) The equations of the asmptotes are = ±. (Simplif our answer. Tpe our answer in point slope form. Use integers or fractions for an numbers in the equation.) 0/9

21 i. i i = (, ) [ 9, ) = 1 (, ) [ 11, ) 1/9

22 ., 1 Cross Touch the ais and turn around 7. 11, (, ) (, ) (, ) (, ) 11. ( 9, ) /9

23 1. (,) or (, ) , , , , ln 9 ln. 3/9

24 . 3 ln ln ln ln A. The solution set is.(simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 31. A. The solution set is. (Tpe an eact answer in simplified form. Use a comma to separate answers as needed.) 3. A. The solution set is.(simplif our answer. Use a comma to separate answers as needed.) A. The solution set is 5.(Simplif our answer. Use a comma to separate answers as needed.) 3. A. The solution set is 7.(Simplif our answer. Use a comma to separate answers as needed.) /9

25 3., 5π 39. (1,π) 0. (1) z. () add Equations 1 and The ordered triple is a solution to the sstem.. Yes 3. A. There is one solution. The solution set is 1,, 3. (Simplif our answers.). A. There is one solution. The solution set is {( 1,, 3 )}. (Simplif our answers.) 5. A. There is one solution. The solution set is 1, 1, 1. (Simplif our answers.). A. There is one solution. The solution set is {( 1, 1, 3 )}. (Simplif our answers.) 7. A. There is one solution. The solution set is { 1, 0, }. (Simplif our answers.). A. There is one solution. The solution set is 1, 3,. (Simplif our answers.) 9. A. There is one solution. The solution set is 1 1, 5, 1. (Simplif our answers.) /9

26 5. A. There is one solution. The solution set is,,. (Simplif our answers.) C z = z = z = (1) = p. 1. (1) ( + 5) = p( + ). /9

27 . (5,0) = C (,0) = ( + 1) = 1( + ) ( 1, ) ( 1, 3) = /9

28 D. 11,0,, A , 5, , A , 1, , ( + 3). (1, 3) (1, ) = /9

29 9. (,) [ 5,1] [1,7] 70. D. 5, 3, + 5, ( ) 1 9/9

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