Math12 Eam (Final) Review Name Do the following as indicated. For the given functions f and g, find the requested function. 1) f() = - 6; g() = 92 Find (f - g)(). 2) f() = 33 + 1; g() = 2-2 Find (f g)(). 3) f() = ; g() = - 1 Find ( f g )(). ) f() = + ; g() = 7 + 6 Find (f + g)(). ) f() = + 9; g() = 8-13 Find (g f)(). 6) f() = 3 + 3; g() = -3 Find (f g)(). 17) log 17 = 1.2 (Round answer to four decimal places.) 18) ln =.7 (Round answer to four decimal places.) 19) ln = 0. (Round answer to four decimal places.) Write the epression as sums or differences of multiples of logarithms. 20) log 3 + 1 21) log 7 Epress as the logarithm of a single epression. Assume that variables represent positive numbers. 22) log 6 ( - ) - log 6 ( - 1) Find the inverse of the one-to-one function. 7) f() = + 9 8) f() = 3 + Graph the function and its inverse on the same set of aes. 9) =log 2 ; = 2 23) (log a t - log a s) + log a u Use a calculator to approimate the logarithm to four decimal places. 2) log 192 2) log 3 π Solve for. ) 27 = 9 26) ln π3 11) 2(3 - ) = 16 27) ln 0.992 12) 23 - = 812 28) log 2 29) log π 1 13) log 3 = 1 1) log 3 = 2 1) log 1 = 16) log = 3.9 (Give eact answer) Solve the equation. Give an approimate solution to four decimal places. 30) 27 = 3.7 31) 3 + 8 = 6 32) e( + 2) = 1
Solve the equation. Give an eact solution. Solve. 33) 3 + 6 = 3) e2 = 7 3) log 7 (2-6) = 1 36) log 3 + log 3 ( - 8) = 2 37) log ( + 2) - log = 2 38) log 2 2 = log 2 (3 + 28) 39) Use the formula R = log a T + B to find the intensit R on the Richter scale, given that amplitude a is 2 micrometers, time T between waves is seconds, and B is 3. Round answer to one decimal place. Write an equation of the circle with the given center and radius. ) (9, -); 11 ) (0, -); 11 Find the center and the radius of the circle. Do not graph. 6) 2 + 2 + + 6 + 23 = 0 7) 2 + 2-1 - + = 0 8) 2 + 2-8 + 2 + 17 = 2 Sketch the graph of the equation. If the graph is a parabola, find its verte. If the graph is a circle, find its center and radius. If it's an ellipse or hperbola, find center and values of a and b. 9) = 2 + + 2 0) = 22-16 + 33 0) The amount of a radioactive substance present, in grams, at time t in months is given b the formula = 7000(2)-0.2t. Find the number of grams present in 2 ears. If necessar, round to three decimal places. 1) Calculate how much mone Lavel has after ears if he originall invested $20 at 6.6% compounded continuousl. Use A = Pert, where A is the final amount, P is the original amount deposited, r is the interest rate, and t is the number of ears. 1) = -( + 2)2 + 3 2) = -22 + 8-13 3) 2 + 2 = 16 ) 2 + ( + 3)2 = 9 ) (- 2)2 + ( - 1)2 = 16 2) The size of the raccoon population at a national park increases at the rate of.9% per ear. If the size of the current population is 117, find how man raccoons there should be in 8 ears. Use = 0 e0.09t and round to the nearest whole number. 3) Find out how long it takes a $2900 investment to earn $00 interest if it is invested at 9% compounded monthl. Round to the nearest tenth of a ear. Use the formula A = P 1 + r nt. n 6) 22 + 2 = 2 7) ( + 1) 2 9 8) ( + 2) 2 9 + ( - 2) 2 - ( + 2) 2 9 9) 162-92 = 1 60) ( - 1) 2 16 - ( + 2) 2 = 1 = 1 = 1 2
Solve the nonlinear sstem of equations for real solutions. 61) = 2 - -2 9 - = 18 Find the indicated term of the sequence. 7) The twent-fourth term of the arithmetic sequence 9, 6, 3,... 62) 63) = - 2-2 = 0 = 2 - = 2-1 7) The fourteenth term of the arithmetic sequence 0, 13, 26,... 76) The fifth term of the geometric sequence 8, 16, 32,... 6) 6) 2 + 2 = 130 2-2 = 32 2 + 2 = 16 2-2 = 16 Solve. 66) The sum of the squares of two numbers is. The sum of the two numbers is 3. Find the two numbers. 67) A rectangular holding pen for sheep is to be designed so that its perimeter is 0 meters and its area is 91 square meters. Find the dimensions of the holding pen. Write the first five terms of the sequence whose general term is given. 68) an = n + 1 2n - 1 69) an = n2 - n Find the indicated term for the sequence whose general term is given. 70) an = 3(2n - 3); a1 77) The sith term of the geometric sequence 1 8, 8, 2 8,... Evaluate the epression. 78) (i + 9) 79) i = 1 i = 1 1 7i Solve the problem. 80) Find the sum of the first eleven terms of the sequence -9, -1, 7, 1,..., 71 where 71 is the eleventh term. 81) Find the sum of the first 70 terms of the arithmetic sequence -20, -11, -2, 7,... 82) If a1 is -13 and d is, find S70. Find the sum of the terms of the infinite geometric sequence. 83) 1, 1, 1 16,... 71) an = (-1) n n + 2 ; a 1 Find a general term an for the sequence whose first four terms are given. 72) 1,, 7,,... 73) 3, 9, 27, 81,... 8), - 2, - 2,... Use Pascal's triangle to epand the binomial. 8) (c + d)6 86) (m - n) 87) (3 + 2) 3
Answer Ke Testname: 12EXAMREVIEWWINTER2011 1) (f - g)() = -92 + - 6 2) (f g)() = 1-63 + 2-2 3) ( f g )() = - 1, where 1 ) 8 + 11 ) 8 + 9-13 6) -273-9 7) f-1() = - 9 8) f-1() = 3-9) 6 inverse -6 function 6-6 ) 2 3 11) 3 12) 20 17 13) 81 1) 9 1) 0 16) 3.9 17) 0.9323 18) 2.0138 19) 0.3297 20) log 3 ( + 1) - log 3 21) log 7 +log - log 22) log 6 - - 1 23) log a tu s 2) 1.117 2) -0.0200 26) 3.32 27) -0.0080 28) 0.307 29) 1.1828 30) 0.2696 31) -6.3691
Answer Ke Testname: 12EXAMREVIEWWINTER2011 32) -0.3906 33) log log 3-6 3) ln 7 2 3) 7, -1 36) 9 37) 1 12 38) 7, - 39) 0) 21.278 1) $1328.17 2) 173 3) 1. ears ) ( - 9)2 + ( + )2 = 121 ) 2 + ( + )2 = 11 6) center (-, -3), radius = 11 7) center (7, 2), radius = 7 8) center (, -1), radius = 9) verte (-1, -) - - 0) verte (, 1) - -
Answer Ke Testname: 12EXAMREVIEWWINTER2011 1) verte (3, - 2) - - 2) verte (2, -) - - 3) center (0, 0); radius = 2 - - ) center (0, -3); radius = 3 - - 6
Answer Ke Testname: 12EXAMREVIEWWINTER2011 ) center (2, 1); radius = - - 6) - - 7) - - 8) - - 7
Answer Ke Testname: 12EXAMREVIEWWINTER2011 9) - - 60) - - 61) (, 18), (, 27) 62) (, 0) 63) (12, ) 6) (9, 7), (-9, 7), (9, -7), (-9, -7) 6) (2, 0), (-2, 0) 66) -3 and 6 67) 7 m b 13 m 68) 2, 1,, 7, 2 3 69) 0, 2, 6, 12, 20 70) 81 71) - 1 17 72) an = 3n - 2 73) an = 3n 7) -60 7) 169 76) 128 77) 312 8 78) 60 79) 2 8 80) 31 81) 20,33 8
Answer Ke Testname: 12EXAMREVIEWWINTER2011 82) 870 83) 3 8) - 2 2 8) c6 + 6cd + 1cd2 + 20c3d3 + 1c2d + 6cd + d6 86) m - mn + m3n2 - m2n3 + mn - n 87) 81 + 2163 + 2162 + 96 + 16 9