CALCULUS MPT SAMPLE QUESTIONS
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1 CALCULUS MPT SAMPLE QUESTIONS Important Note: Calculators are not permitted wen writing te Mat Placement Test. In order to fully enefit from tese practice prolems, you sould solve tem witout te aid of a calculator. Algera: Polynomials; factoring; rational epressions; radicals; eponents; applications. y y 1. Simplify: y y y. Simplify: 5 5. Simplify: y y 4. Simplify: 1 1 y 5. Simplify: 1 1/ / 1/ 1/ ( 1) ( 1) 6. Rationalize te numerator and simplify: ( ) 7. Te saded corner squares are cut from te rectangle sown and te remaining piece is folded along te dased lines to create an open top o. Epress te volume of te o in terms of
2 Equations and Inequalities Solving equations and inequalities for linear, quadratic, and factored forms; equation of a line; applications. 8. Solve for in eac of te following: (a) () a c a c (c) (d) 9 7 (e) (f) (g) () In slope-intercept form, find te equation of te line wic passes troug te point (, ) and is perpendicular to te line given y y A swimming pool is positioned 10 meters away from a uilding as diagrammed. Te fenced deck around te pool as an area equal to te surface area of te pool. Wat is te widt of te deck around te pool? Deck 0 m 5 m Pool 10 m B U I L D I N G
3 Functions Function definition; domain; range; geometric interpretation; composition; inverse functions; asic uilding-lock functions; piecewise-defined functions; function models. 11. Given f ( ) 5 find: 1 (a) f ( ) () f ( ) (c) f ( ) (d) f ( ) f ( ) 1. Find te domain of 1 f ( ). 1. Epress te area of an equilateral triangle as a function of its side lengt,. 14. Use te grap of te function f to find (a) te domain of f () te range of f (c) f () (d) f (0) (e) f () 15. Te function f is defined elow:, 1 f ( ), 1 4, 4 (a) Find te domain of f. () Find te range of f. (c) Sketc te grap of f. 16. For f ( ) and g ( ) find: (a) g g f (c) Domain of f g and g f f ( ) 17. Find te inverse of te function f ( ) Sketc te grap of te inverse function 1 y f for te function f sown to te rigt.
4 Eponential and Logaritmic Functions Definitions; properties; applications. 19. Sketc te grap of g( ) Epand and simplify: e e 1. Solve for : log 1 log log 1. Find te domain of g ( ) log. 5. Trigonometry Find te inverse of 1 4. Simplify: lne 5. Solve for : e e 4 f : f ( ) e. 6. A company uses an eponential depreciation model for its macinery. kt V ( t) V0e ; V (t) = value at time t A piece of macinery initially valued at $100,000 depreciates to $60,000 after 5 years. Wat is its depreciated value after 10 years? Degree and radian angular measure: rigt triangle trigonometry; definition of te trigonometric functions of any angle; graps; asic identities; applications. 7. In standard position sketc (approimately) te angle wic measures 4 radians. 8. For te diagrammed angle cos sin tan
5 9. Evaluate te following: (a) 90 cos () 0. A television crew is filming a race 10 m from a track s finis line. (a) Wen te camera angle measures 40, ow far is te lead runner from te finis line? () Epress te distance etween te lead runner and te finis line as a function of. 1. If tan( ) and sin( ) 0, (a) In wic quadrant does terminate? () Find te eact values for sin() and cos( ).. Factor and simplify: sin cos sincos. How is te grap of y sin Solve: sin, 0 sin (c) sec 10 m related to te grap of y sin()?
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NAME: Solutions to te in class part. Te grap of a function f is given. Calculus wit Analytic Geometry I Exam, Friday, August 30, 0 SOLUTIONS (a) State te value of f(). (b) Estimate te value of f( ). (c)