7) Find the sum of the first 699 positive even integers. 7)

Transcription

1 Redwood High School. Department of Mathematics Honors Avanced Algebra Prep for FE S. REALLY hard worker's name: SHOW YOUR WORK to obtain full credit MOST PROBLEMS DO NOT HAVE SPACE, WORK ON ADDITIONAL PAPER AND STAPLE IT IN THE BACK for all graphs indicate a) domain, b) vertical asymptote, c) holes, d) y and x intercepts if they exist, and e) end behavior Evaluate the series, if it converges. ) 29 5 i - 3 i= ) Write the quotient in the form a + bi. 2) 9 + 2i 2-7i 2) 3) Find the number of terms of a geometric sequence with the first term, common ratio -3, and last term 8. 3) Find A - if it exists. 4) A = ) 5) How long will it take for $7200 to grow to $23,800 at an interest rate of 4.6% if the interest is compounded continuously? Round the number of years to the nearest hundredth. 5) 6) A man earned $2500 the first year he worked. If he received a raise of $600 at the end of each year, what was his salary during the 5th year? 6) 7) Find the sum of the first 699 positive even integers. 7) Explain how you found out the solution (show your work) 8) There were 3,000 people at a ball game in Los Angeles. The day's receipts were $66,000. How many people paid $ for reserved seats and how many paid $4 for general admission? (4 points) 8) 9) A man earned $2500 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 5th year? 9) 0) The graph of y = ax2 + bx + c goes through the points (, -2), (3, -4), and (-, -8). Find the equation. Show the matrix you are using to solve it 0) ) A brick staircase has a total of 8 steps The bottom step requires 28 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase? )

2 2) Find the sum of the first 422 positive even integers. 2) 3) A deposit of $6000 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = n n =, 2, 3,... Find the balance in the account after 8 years. 3) 4) Let A = and B = Find 4A - 2B. 4) Explain how you found out the solution (show your work) 5) A grain dealer sold to one customer 0 bushels of wheat, 5 of corn, and 3 of rye, for $66.00; to another, 5 of wheat, 3 of corn, and 0 of rye, for $73.40; and to a third, 3 of wheat, 0 of corn, and 5 of rye, for $ What was the price per bushel for corn? 5) 6) Suppose that $8000 is invested at an interest rate of 5.8% per year, compounded continuously. What is the balance after 3 years? 6) 7) An initial investment of $2,000 is appreciated for 8 years in an account that earns 6% interest, compounded quarterly. Find the amount of money in the account at the end of the period. 7) 8) Kimberly invested $6000 in her savings account for 4 years. When she withdrew it, she had $ Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent. 8) 9) Let A = and B = Find 2A + 2B. 9) 20) Find the sum of the first 654 positive even integers. 20) 2) The formula D = 8e -0.04h can be used to find the number of milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. When the number of milligrams reaches 2, the drug is to be given again. What is the time between injections? 2) Explain how you found out the solution (show your work) 22) There were 44,000 people at a ball game in Los Angeles. The day's receipts were $302,000. How many people paid $3 for reserved seats and how many paid $4 for general admission? 22) 2

3 Explain how you found out the solution (show your work) 23) A grain dealer sold to one customer 5 bushels of wheat, 4 of corn, and 3 of rye, for $28.30; to another, 4 of wheat, 3 of corn, and 5 of rye, for $29.0; and to a third, 3 of wheat, 5 of corn, and 4 of rye, for $ What was the price per bushel for corn? (4 points) 23) Solve for y or k, as appropriate. 24) 00e 4k = ) 25) e (ln 0.6)k = ) 26) e x2 e 8x+ = e k 26) 27) e 2k = 25 27) Evaluate the sum ) i 28) i= Evaluate. 29) Find (f + g)(-2) given f(x) = x + and g(x) = x ) 30) Find (f - g)() given f(x) = 5x2-5 and g(x) = x ) 3) Find (g/f)(-2) given f(x) = 4x 2 + 4x + 4 and g(x) = 3x -. 3) Find the composite function for the given functions. 32) f g for f(x) = 2 x - 8 and g(x) = 5 8x 32) 33) f g for f(x) = x + 8 and g(x) = 8x ) 34) g f for f(x) = 4x2 + 4x + 5 and g(x) = 4x ) Evaluate the expression. 35) (g f)(22) when f(x) = x and g(x) = 6x ) 36) (f g)(9) when f(x) = 7x - 9 and g(x) = 5x2 + 7x ) 37) (g f)( ) when f(x) = 9x + 4 and g(x) = -8x2 + 9x ) 3

4 Write the equation of the graph after the indicated transformation(s). 38) The graph of y = x3 is shifted 7.0 units to the right and then vertically shrunk by a factor of ) The graph of y = x is vertically stretched by a factor of.6. This graph is then reflected across the x-axis. Finally, the graph is shifted 0.2 units downward. 38) 39) 40) The graph of y = x is shifted 2 units to the left. Then the graph is shifted 8 units upward. 40) 4) The graph of y = 3 x is shifted 4. units to the left. This graph is then vertically stretched by a factor of 2.5. Finally, the graph is reflected across the x-axis. 4) Begin by graphing the standard absolute value function f(x) = x. Then use transformations of this graph to graph the given function. 42) h(x) = - x ) 43) h(x) = 2 x ) Use the graph of y = f(x) to graph the given function g. 44) g(x) = -f(x) 44) Begin by graphing the standard square root function f(x) = function. 45) g(x) = x. Then use transformations of this graph to graph the given 2 x ) 46) g(x) = 2 2x 46) 47) g(x) = - x ) 48) h(x) = -x ) 4

5 49) g(x) = 2 x ) Write the expression in the standard form a + bi. 50) (3 + 7i)(3-7i) 50) 5) (4 + 5i) 2 5) 52) 2i 5 - i 7 52) 53) i 53) Use the vertex and intercepts to sketch the graph of the quadratic function. 54) f(x) = 8 - x 2 + 2x 54) 55) f(x) = 3x x ) 5

6 56) f(x) = - (x - ) 2 56) Solve the equation. 57) 3 (4x - ) = 57) 58) 3 5 2x - = 75 58) Solve the system by graphing. 59) -2x + 3y = 8 4x + 2y = 28 6

7 60) -2x + 4y = 30 2x + 3y = 26 6) k= 7 9 k 6) Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 62) ln (x - 6) + ln (x + ) = ln (x - 5) 62) 63) log 3 (x + 6) + log 3 (x - 6) - log 3 x = 2 63) 64) ln (x - ) - ln (x + 5) = ln (x - 5) - ln (x + 5) 64) Use the given data to find the equation of the regression line. 65) x y ) Solve the quadratic equation by any method. 66) x(x - 2) = 80 66) Write the equation as f(x) = a(x - h) 2 + k. Identify the vertex. 67) f(x) = x 2 + 6x ) Find the sum of the series. 68) (-) n 7 n=0 9 n 68) Round your answer to three decimals. 69) How long will it take for an investment to double in value if it earns 2.25% compounded continuously? 69) 7

8 Solve the system of equations. Explain how you found out the solution 70) -3x - y + 4z = 5 7x + 5y + 7z = 52-8x - 6y + z = -5 70) Solve the system of equations. Explain how you found out the solution 7) 9x - y + 5z = 4 3x + 2y - 8z = -3 8x - 7y + z = -25 7) Solve the equation. 72) 5 2x + 5 (x + ) - 24 = 0 72) Find the required part of the geometric sequence. 73) Find the first term of a geometric sequence with the sixth term 3,22 and common ratio of ) 74) Find the first term of a geometric sequence with seventh term 2. and common ratio of ) Write the geometric series in summation notation. 75) ) ) j 76) j=300 77) n=0 5 3 n 77) Find the indicated part of the arithmetic sequence. 78) Find the common difference of the sequence in which the first term is and the 8th term is ) 79) ) Find the inverse of the matrix, by hand (no calculator) 80) A = ) Find the inverse of the matrix, by hand (no calculator) 8) A = ) 8

9 82) i= i - 82) Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes. 83) 2y - 0 = 5x Find the present value required to achieve the amount A when compounded at a rate of r for t years. Round to the nearest cent. 84) A = $25,000, t =, r = 5% compounded semiannually 84) 85) 2 (5-3x) = 6 85) Solve by completing the square. 86) y2 = - 3y ) Solve the equation. 87) ln x + 2 = 4 87) 88) 325 3x + 4 = 625 2x 88) 89) 4 7-3x = 6 89) 90) 2 + log 3 (2x + 5) - log 3 x = 4 90) 9) log6 (x 2 - x) = 9) Solve the system by addition. (4 points) Classify athe system as inconsistent, consistent dependent or independent 92) 3x 2 - y 3 = -8 92) 3x 4 + 2y 9 = -9 9

10 Solve for the indicated variable. 93) P = 70e 6t, for t 93) 94) ln (x + 3) - ln (y + ) = ln 4, for x 94) 95) ) 96) n=0 5 6 n 96) The function f is one-to-one. Find its inverse. 97) f(x) = 6x 2 + 7, x 0 97) 98) 4 k = 2 k(k - 8) 98) Find the first five terms of the infinite sequence whose nth term is given. 99) an = (-) n - n + 2 2n - 99) Find the first five terms of the infinite sequence whose nth term is given. 00) an = (-) n - n + 3 2n - 00) 0) ) 02) ) 03) ) Find the amount that results from the investment. 04) $480 invested at 5% compounded quarterly after a period of 4 years 04) 05) $,000 invested at 5% compounded annually after a period of 7 years 05) Find the nth term and the indicated term of the arithmetic sequence whose initial term a and common difference d are given. 06) a = 7, d = -7 06) an =? a3 =? 0

11 07) k= 4 9 k 07) ) j 08) j=300 09) Find the common ratio for a geometric sequence with the first term and fifth term 8. 09) Determine whether B is the inverse of A. 0) A = , B = ) ) log 3 (x + 6) + log 3 (x - 6) - log 3 x = 2 ) Solve the problem using a system of three equations in three unknowns, use any system 2) The sum of three numbers is -4. The first, minus the second, plus 2 times the third, is -8. The third, plus 2 times the first, plus the second, is -9. What are the numbers? 2) Use the properties of logarithms to simplify the expression. 3) ln (2x 2-0x) + ln 2x 3) 4) ) 5) Find the common ratio for a geometric sequence with the first term 4 and fifth term 64. 5) 6) log 4 (x + 4) + log 4 (x - 2) = 2 6) Write the first four elements of the sequence. 7) + n n 7) Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. 8) f(x) = 5x 2 + 0x - 2 8) Solve the system of equations by any method. If the system has no solution, say that it is inconsistent. 5x + y = 8 9) 9) 8x + 5y = 6 Solve the matrix equation for X. (by hand) 20) Let A = 0 4 and B = 2 3 ; B - X = 3A )

12 Answer Key Testname: H ADV ALG S FE PREP V2.0. ) Does not converge. 4 2) i 3) 5 4) ) yr 6) $0,900 7) 489,300 8) 6000 paid $ and 25,000 paid $4 9) $800 0) 0 ) 539 bricks 2) 78,506 3) $, ) ) $4.30 6) $ ) $9, ) 3.% 9) ) 428,370 2) hrs 22) 4,000 paid $3 and 30,000 paid $4 23) $ ) ln ) ln 0.5 ln ) x 2 + 8x + 27) ln 5 28) 2,502,500 29) 30) 4 3) ) 6x 5-64x 33) 2 2x - 2

13 Answer Key Testname: H ADV ALG S FE PREP V ) 6x2 + 6x ) 40 36) 37) -8,775 38) f(x) = 0.3(x - 7.0)3 39) f(x) = -.6 x ) f(x) = x ) f(x) = x ) 43) 44) 3

14 Answer Key Testname: H ADV ALG S FE PREP V ) 46) 47) 48) 4

15 Answer Key Testname: H ADV ALG S FE PREP V ) 50) 58 5) i 52) -i 53) i 54) 55) 5

16 Answer Key Testname: H ADV ALG S FE PREP V ) 57) ).5 59) {(3, 8)} 60) {(, 8)} 6) ) 63) {2} 64) ) ^y = x 66) -8, 0 67) f(x) = (x + 3) 2-3; (-3, -3) 68) ) yr 70) {(, 2, 5)} 7) {(, 5, 2)} 72) x = ) ) 6 75) 0.2(0.) i- i= 76) 2,457,650 77) ) -4 79) 3 80)

17 Answer Key Testname: H ADV ALG S FE PREP V2.0. 8) ) ) 6 84) $4, ) 3 86) -3 ± ) {e 8-2} 88) ) {3} 90) 5 7 9) {-2, 3} 92) {(-2, 0)} ln P - ln 70 93) t = 6 94) x = 4y + 95) ) 6 97) f - (x) = 98) -43 x ) 3, - 4 3,, - 6 7, ) 4, - 5 3, 6 5, -, 8 9 0) 2 02) Does not converge 7

18 Answer Key Testname: H ADV ALG S FE PREP V ) ) $ ) $ ) an = 4-7n, a3 = ) ) 7,957,50 09) 3 0) Yes ) {2} 2) -5, 5, -4 3) ln (x - 5) 4) 0.5(0.) i- i= 5) 2 6) {4} 7) 2, 9 4, 64 27, ) f(x) = 5(x + ) 2-7 vertex: (-, -7) 9) x = 2, y = -2; (2, -2) 20) 5-5 X =