EAST LOS ANGELES COLLEGE NAME: MATHEMATICS FINAL EXAM SAMPLE INSTRUCTOR: ANNE SISWANTO; TIME: 10 MINUTES -------------------------------------------------------------------------------------------------------------------------- DIRECTION: Graphing calculators are not allowed. Please write our work on the test paper for full credit. The sample test is longer than the actual final. For the polnomial, one zero is given. Find all others. 1) ( POINTS) P() = 3 - - 11 + ; Objective: (3.3) Find Other Zeros Given One Zero Find all rational zeros and factor f(). ) f() = 3 - + 3 + Objective: (3.3) Find All Rational Zeros and Factor 3) f() = 3 + - 9 - Objective: (3.3) Find All Rational Zeros and Factor Graph the function. ) = - 1 3 ( - ) 3 Solve the problem. Round to the nearest tenth unless indicated otherwise. ) The volume of a gas varies inversel as the pressure and directl as the temperature (in degrees Kelvin). If a certain gas occupies a volume of. liters at a temperature of 30 K and a pressure of 0 newtons per square centimeter, find the volume when the temperature is K and the pressure is 30 newtons per square centimeter. Objective: (3.) Solve Apps: Joint Variation ) At a fied temperature, the resistance R of a wire varies directl as the length l and inversel as the square of its diameter d. If the resistance is 0.7 ohm when the diameter is 1 mm and the length is 0 cm, what is the resistance when the diameter is mm and the length is 090 cm? Objective: (3.) Solve Apps: Joint Variation Objective: (.7) Graph Function Using Shifts/Reflections/Stretches 7) f() = -( + ) - Objective: (.7) Graph Function Using Shifts/Reflections/Stretches Math Final Eam Sample 1 A. Siswanto
The figure below shows the graph of a function = f(). Use this graph to solve the problem. ) State the transformations and sketch the graph of = -f()+. 9) State the transformations and sketch the graph of = f(-)-. (-, ) (, ) (, -3) Objective: (.) Sketch Shift/Reflection/Stretch from Graph Objective: (.) Sketch Shift/Reflection/Stretch from Graph If f is one-to-one, find an equation for its inverse. ) f() = 7 - Objective: (.1) Find Equation of Inverse Function 11) f() = + 9, -9 Objective: (.1) Find Equation of Inverse Function 1) f() = 9 + Objective: (.1) Find Equation of Inverse Function Solve the equation and epress the solution in eact form. 13) log = log + log ( + ) Objective: (.) Solve Logarithmic Equation (Eact Solution) I Math Final Eam Sample A. Siswanto
1) log ( + 3) = 1 - log Objective: (.) Solve Logarithmic Equation (Eact Solution) I 1) log ( + ) - log ( - ) = log Objective: (.) Solve Logarithmic Equation (Eact Solution) I 1) ln + ln 9 = ln Objective: (.) Solve Logarithmic Equation (Eact Solution) I Solve the equation. If necessar, round to the nearest thousandth. 17) + = 3 Objective: (.) Solve Eponential Equation (Approimate Solution) 1) 3+7 = 7 Objective: (.) Solve Eponential Equation (Approimate Solution) 19) e - 3 = Objective: (.) Solve Eponential Equation (Approimate Solution) 0) ( - 1) = Objective: (.) Solve Eponential Equation (Approimate Solution) Find the center and radius of the circle. 1) + + + + 9 = 0 Objective: (.1) Find Center and Radius of Circle From Equation Graph the polnomial function. Factor first if the epression is not in factored form. ) LABEL POINTS ON THE GRAPH f() = 3 + + 9 + a. <> List all possible rational zeros and find all real zeros b. <1> Find the -intercept c. <1> Draw the end behavior d. <3> Use enough points to plot the graph. - - - - Objective: (3.) Graph Polnomial Function Using Factored Form Solve the problem. 3) How long must $0 be in a bank at % compounded annuall to become $ 79.11? (Round to the nearest ear.) Objective: (.) Solve Apps: Compound Interest ) What is the rate on an investment that doubles $01 in 9 ears? Assume interest is compounded quarterl. Objective: (.) Solve Apps: Compound Interest ) Assume the cost of a car is $7,000. With continuous compounding in effect, find the number of ears it would take to double the cost of the car at an annual inflation rate of 9.%. Round the answer to the nearest hundreth. Objective: (.) Solve Apps: Economics Math Final Eam Sample 3 A. Siswanto
Sketch the graph of the rational function. ) LABEL POINTS ON THE GRAPH + f() = - 9 a. <> Find all vertical asmptotes. b. <> Find an horizontal or oblique asmptote. c. <1> Find the -intercept. d. <1> Find the -intercepts. e. <> Eplain whether the graph will intersect its nonvertical asmptote. f. <3> Find enough points in each interval and sketch the graph. - - - - Objective: (3.) Graph Rational Function I Solve the problem. 7) Use the formula P = Iekt. A bacterial culture has an initial population of,000. If its population declines to 000 in hours, what will it be at the end of hours? Objective: (.) Solve Apps: Population Growth/Decline ) In the formula A(t) = A0ekt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined b the nature of the material. A certain radioactive isotope decas at a rate of 0.1% annuall. Determine the half-life of this isotope, to the nearest ear. Objective: (.) Solve Apps: Radioactive Deca/Carbon Dating Solve the sstem using ELIMINATION METHOD. 9) - + 3z = -3 + z = 0 + + z = Objective: (9.1) Solve Sstem of Linear Equations in Three Variables Use the Gauss-Jordan method to solve the sstem of equations. If the sstem has infinitel man solutions, give the solution with arbitrar. 30) 3 + = 0 + = -1 Objective: (.) Use Gauss-Jordan Method (Two Variables) Use the Gauss-Jordan method to solve the sstem of equations. If the sstem has infinitel man solutions, let the last variable be the arbitrar variable. 31) - - 3 - z = -7 + 3-3z = 1 - + + z = 3 Objective: (.) Use Gauss-Jordan Method (Three or Four Variables) 3) - + 9z = 9 - z = 3 + z = 1 Objective: (.) Use Gauss-Jordan Method (Three or Four Variables) Use Cramerʹs rule to solve the sstem of equations. If D = 0, use another method to determine the solution set. 33) - 7 = - = Objective: (.3) Use Cramerʹs Rule to Solve Sstem Use Cramerʹs rule to solve the sstem. 3) - + z = 11 + z = 3 + 3 + z = 1 Objective: (9.3) Use Cramerʹs Rule to Solve 3 3 Sstem Math Final Eam Sample A. Siswanto
Use Cramerʹs rule to solve the sstem of equations. If D = 0, use another method to determine the solution set. 3) + + z = 0 - + z = + + z = Objective: (.3) Use Cramerʹs Rule to Solve 3 3 Sstem Graph the sstem of inequalities. 3) - + 3-3 -1 Graph the conic section. 3) - 1-0 - 1 - = 0 Objective: (.) Graph Conic Section Give the focus, directri, and ais for the parabola. 39) ( - 7) = ( + ) Objective: (.1) Give Focus, Directri, and Ais for Parabola Graph the conic section. 0) + - 1 + + = 0 Objective: (9.) Graph Sstem of Linear Inequalities Solve the nonlinear sstem of equations. 37) + 3 - = -9 - - = Objective: (9.) Solve Nonlinear Sstem of Equations Objective: (.) Graph Conic Section Math Final Eam Sample A. Siswanto
Answer Ke Testname: MFINS 1) 3 + i, 3 - i ),, -1; f() = ( - )( - )( + 1) 3) -3, -, 3; f() = ( + 3)( + )( - 3) ).0 liters ) 0. ohm ) 9) (-, ) (, ) ) f-1() = + 7 7) 11) f-1() = - 9, 0 1) f-1() = + 9 13) 0 1) 1) 9 1) = 1/ ) 17) {.30} 1) {9.07} 19) {1.097} 0) {1.1} 1) (-3, -); r = ) (, 3) - - - - 3) 7 r ) 7.% ) 7.37 ears Math Final Eam Sample A. Siswanto
Answer Ke Testname: MFINS ) 3) 1 - - - - 7) 01 ) r 9) {(0, 3, 0)} 30) {(, 3)} 31) {(3,, 3)} 3) {(,, )} 33) {(-, )} 3) {(0,, 3)} 3) {(, -, -3)} 3) -1 1-1 39) (-7, 7), = -3, = 7 0) - - - - 37) {(-1, -), (1, ), (i, -i), (-i, i)} Math Final Eam Sample 7 A. Siswanto