MAT 10 Test 2 Review (chapters 6,7,11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multipl both sides of each equation b a common denominator to eliminate the fractions. Then solve the sstem. 1) 7 + 4 = 4 1) 6-2 = 21 (-6, 8) (6, 8) (6, -8) (-6, -8) Solve the problem b writing and solving a suitable sstem of equations. 2) Carole's car averages 12. miles per gallon in cit driving and 2. miles per gallon in highwa driving. If she drove a total of 22. miles on 27 gallons of gas, how man of the gallons were used for cit driving? 17 gallons 10 gallons 12 gallons 22 gallons 2) Write an augmented matri for the sstem of equations. ) 6 + 2 + 2z = 2 4 + 8 + 6z = 80 4-2 + z = 6 2 2 2 6 80 6 8 4 6-2 4 6 4 4 2 2 8-2 80 2 6 6 6 2 2 4 8 6 4-2 6 2 2 2 4 8 6 80 4-2 6 ) Obtain an equivalent sstem b performing the stated elementar operation on the sstem. 4) Replace the third equation b the sum of itself and -1 times the second equation. - 2-7z = 17-8 + 4 + z = -9 + 9 - z = -4-2 - 7z = 17-8 + 4 + z = -9 1 + - 4z = - 2-7z = 17-8 + 4 + z = -9 - + 1 + 2z = -1-2 - 7z = 17 1 + - 4z = + 9 - z = -4-2 - 7z = 17-8 + 4 + z = -9-1 - + 4z = 4) 1
) Replace the fourth equation b the sum of itself and times the second equation ) - 2 + z - 6w = 4 4 - z - 2w = - - 4z + 2w = - -2-4z - 2w = 8-2 + z - 6w = 4 12 - z - 6w = -1-4z + 2w = - -2-4z - 2w = 8-2 + z - 6w = 4 4 - z - 2w = - - 4z + 2w = - 10-7z - 8w = -7-2 + z - 6w = 4 4 - z - 2w = - - 4z + 2w = - -14 + 7z + 4w = 2-2 + z - 6w = 4 4 - z - 2w = - - 4z + 2w = - 12 + z - 8w = -7 The reduced row echelon form of the augmented matri of a sstem of equations is given. Find the solutions of the sstem. 6) 6) 1 0 0 0 0 2 0 1 0 0 0 8 0 0 1 0 0 4 0 0 0 1 0-4 0 0 0 0 0 1 (2, 8, 4, -4, w) for an real number w (2, 8, 4, -4) (2, 8, 4, -4, 1) No solution Solve the sstem of equations. If the sstem is dependent, epress solutions in terms of the parameter z. 7) 2 + - z = 2 - + 2z = 1 7-7 + 4z = 7 7) (2,, 7) (1, 0, 0) No solution 7 + z 7, z, z for an real number z 7 8) - + z = 2 + + z = 4 + - z = 0 (1, 1, 2) No solution (1, 2, 1) (2, 1, 1) 8) 2
Solve the problem b writing and solving a suitable sstem of equations. 9) Julia is preparing a meal b combining three ingredients. One unit of each ingredient provides the following quantities (in grams) of carbohdrates, fat, and protein. 9) Protein(g) Carbohdrates(g) Fat (g) Ingredient A 1 Ingredient B 2 4 2 Ingredient C 4 1 Ideall the meal should contain 26 grams of protein, 4 grams of carbohdrates, and 12 grams of fat. How man units of each ingredient should Julia use? 4 grams of ingredient A, grams of ingredient B, 2 grams of ingredient C 4 grams of ingredient A, 2 grams of ingredient B, grams of ingredient C 2 grams of ingredient A, grams of ingredient B, 4 grams of ingredient C grams of ingredient A, 4 grams of ingredient B, 2 grams of ingredient C Perform the indicated operation where possible. 10) -1-4 -8 1 9 4 8-8 6 - - 0 1-1 -8-6 2 11-4 -9-8 0 8-4 2-10 - 2-9 -8 2 8-4 2-6 17 4-1 8 0-10 -12-14 10-4 1-8 0 10 12 14-10 - 10) Perform the indicated operation. 1 11) Let C = - and D = 2-9 -6-1 -2. Find C - 2D. -6 4-9 6-1 -2 11) Write a matri to displa the information. 12) When the owner of a picture framing store took inventor of her unused frames, she found that she had 0 oak-8", 11 oak-12", 49 oak-18", 6 walnut-8", and 11 walnut-18". Write this information as a 2 matri. 0 6 11 0 49 11 0 11 49 6 0 11 0 11 49 6 0 11 0 11 49 11 0 6 12) Given the matrices A and B, find the matri product AB. 1) A = -2, B = 0-2 4 0 2 6 Find AB. -8 0 0-4 -4-18 0-8 -18-4 -8 0 0 4 8 0 1)
14) A = 0-2 2 0 4-2 -2 0 7 0-2 4 0-2 7, B = -1 2 0-2 1 Find AB. AB is not defined. 0-6 -4 0-6 14) 1) A = -2 1 0 4-9 -6-6 16-11, B = 0-2 Find AB. AB is not defined. 1) 9-6 -6 16-11 9 0 0 12 4
Graph the feasible region for the sstem of inequalities. 16) + 2 2 + 0 16) - - - - - - - - - -
Find the value(s) of the function on the given feasible region. 17) Find the maimum and minimum of z = 7 + 9. 17) 9, 28 70, 6 42, 4-28, -9 Find the value(s) of the function, subject to the sstem of inequalities. 18) Find the maimum and minimum of Z = + 2 subject to: 0 10, 0, + 2 6. 40, 0 40, 6 10, 6 0, 6 18) Use a calculator to estimate the limit. 19) lim 1 4-1 - 1 4 2 Does not eist 0 19) Use the properties of limits to evaluate the limit if it eists. 20) lim - 2-2 - 1 + 0 Does not eist -8 20) Find the average rate of change for the function over the given interval. 21) = 2 between = 2 and = 8 21) 2 1 7-10 Solve the problem. 22) Compute the instantaneous rate of change of the function at at = a. f() = -2 -, a = -8. 48 47-40 40 22) 6
Find the point from those given that has the given propert. 2) The point where the slope of the tangent is greatest 10 2) -10 10-10 (0,0) (1,-) (-1,1) Find the equation of the tangent line to the curve when has the given value. 24) f() = 4 ; = 24) = 1-16 = 20 + 1 = - 4 2 + 8 = -9-80 Find f'() for the function, then find f'() for the given. 2) g() = +, g'(1) g'() = 2 + ; g'(1) = 8 g'() = + ; g'(1) = 8 g'() = 2 + ; g'(1) = 8 g'() = ; g'(1) = 2) Find the derivative. 26) f() = 24-9 - 7 4 + 2 4 + 2-7 8-272 8-272 - 7 26) 27) f() = ; ( > 0) 4(4 ) - 6-6/ 6 6/ 1-4/ 27) 28) = 2-4 28) ' = 1 + 4 2 ' = 1-4 2 ' = 1 + 4 ' = + 4 2 Find the following. 29) f'(4) if f() = 7-29) - 16-11 16 11 16 16 7
Find the derivative of the function. 0) f() = (2-4 + 2)(2-2 + 4) f'() = 104-6 + 242 + 4-16 f'() = 24-2 + 242 + 4-16 f'() = 24-6 + 242 + 4-16 f'() = 104-2 + 242 + 4-16 0) Use the quotient rule to find the derivative. 1) = - 1 1) ' = -2 + 2 ( - 1)2 ' = -2-2 ( - 1)2 ' = 2 + 2 ( - 1)2 ' = 2-2 ( - 1)2 2) = 2 + 8 + 2) ' = 2 + 8 ' = 2 + 8-2/2 ' = 2 + 8 - ' = 2 + 8 2/2 Find the derivative of the function. ) = 4 + 2 2 ' = 4 + 2 ' = 1 4 + 2 ' = 4 4 + 2 ' = 8 4 + 2 ) Find the derivative. 4) = 4e2 8e2 8e2 8e42 8e 4) Find the derivative of the function. ) = ln 92 2 2 + 9 1 2 + 9 2 18 ) Find the derivative. 6) f() = e ln, > 0 e (ln + ) e ( ln + 1) e ln e 6) 7) f() = ln e 7) 1 e 1 - ln e ln e 1 - ln e 8
8) f() = e + ln 8) e + eln e( + 1) e(1 + 1 ) e + ln 9
Answer Ke Testname: 10TEST2REVIEW 1) C 2) B ) D 4) A ) C 6) D 7) D 8) A 9) A 10) D 11) C 12) C 1) B 14) A 1) B 16) A 17) B 18) B 19) A 20) D 21) B 22) B 2) C 24) C 2) A 26) C 27) D 28) A 29) B 0) A 1) D 2) B ) A 4) D ) C 6) B 7) B 8) B 10