Messiah College Calculus I Placement Exam Topics and Review

Transcription

1 Messiah College Calculus I Placement Exam Topics and Review The placement exam is designed to test a student s knowledge of material that is essential to the Calculus I course. Students who score less than 60% will be strongly recommended to enroll in MATH 03, a -credit supplementary course to MATH. The placement exam is to be taken via Webassign, without use of a calculator. Although calculators are generally allowed on chapter exams in our calculus courses, the use of a calculator or any computer-based computation is prohibited on the placement exam. Topics covered on the exam, along with several sample questions for each topic, are listed below. The page numbers listed below indicate where the specified topic is found in the course textbook: Calculus, 9th edition by Larson, Hostetler, and Edwards. Links are provided to the Khan Academy for explanations on how to do most of the sample problems. Solutions to problems in the text are listed in the back of the book. Solutions to the example problems given below can be found in the file Calculus Placement Exam Review Key. Section P: Graphs and Models (pp.-7 Exercises,,3,,5,9,,,3,5,7,63,65,69) Also, know the following:. Equations and graphs of parabolas Find the vertex of the parabola y = x x + 3. Where does this parabola intersect the x-axis? y-axis? Find the equation of the parabola shown below.

2 . Quadratic equations and the quadratic formula. Solve the following quadratic equations: i. x + x 3 = 0. ii. 3x x = 3 3. Find solution sets for simultaneous linear equations. Solve the following system of equations: y = x + 3 y = x + 8 Which of the following graphs shows the system of equations its solution? x + y = y 5x 3 and y x = 5. Find solution sets for simultaneous equations in general. ex Solve the following systems of equations: y = 5x + 6 y = x. Find all intersections of the circle x + 0x + y 8y = with the line x + y = 8. Sketch the two curves and label the points of intersection.

3 Section P: Linear Models and Rates of Change (pp. 6-8 Exercises,3,9,5,5,9,33,37,,5,7,53,6,63) Also, know the following:. linear equations including perpendicular and parallel lines. Identify the slope and the intercepts for the equation 3x + y =. Sketch the graph of this equation. Find the equation of the line passing through the point (-,3) and parallel to the line 3x + y =. Find the equation of the line passing through the points (,-) and (,000). Section P3: Functions and Their Graphs (pp. 7-9 Exercises 3,7,9,,7,,3,7,35,37,5) Also, know the following:. Domain of a function: Find the domain of x Functional notation and equations as functions: For the function f ( x) =, find: x 6 a) f(5) b) f(a) c) f(a+3) 3. Use translations and shifting to describe the graphs of functions. f x = x to sketch the following graphs: Use the graph of ( ) a) f(x+) = (x+) b) f(x)+ = x + c) f(x)-3 = x

4 Real Numbers and the Real Line. Know the definition of absolute value and solve equalities and inequalities involving absolute value: x + 5 = 3 Solve the given inequality and shade the portion of the x-axis that corresponds to the solution of 3x + > 5, given the graph of y= 3x+ below. Solve inequalities in general: Solve x + > x Shade the portion of the x-axis that corresponds to the solution of x +, x given the graph of y = x + below. x Solve x + x 0

5 The Cartesian Plane. Distance and midpoint formulas Find the distance between (,3) and (-,). Do the following points form a right triangle: (,0), (,), (-,-5)? Equation of circles and completing the square: Find the radius and center of the circle x x + y + y =. Sketch the graph. Find the equation of the circle shown below. Review of Trigonometric Functions. The amplitude and period of functions of the form y = Asin Bx or y = Acos Bx. Sketch the graph of y = 3sin π x. What is the amplitude and period of this function. Sketch the graph of y = 3+. 5cos x. State the amplitude and period of this function. π If tanθ = 3 and 0 θ, what is θ in radians? 5

6 What are sin θ, cos θ, and s ecθ?. simple trigonometric equations. Solve the following equations: i. sinθ = cosθ. ii. sinθ cos θ =. 5 cosθ. Other Problems. Simplify the following: ( 3y )( y ) ( y ) 3 a b 5a b 3 a b b ( 5 x y )( x 5 y ) 8x 3 6 y 3 6

7 . Perform the indicated operation and simplify: a + a + 5a + 0a + a 6 a a ( 3u )( u ) 7u( u ) ex x 8 3x + + 3x x x 9x 9x 6x x 3x 5x + + 7x + 8x 3 x y y x y x 3. Factor polynomials Factor the following: i. x 6 ii. x 5x 3x 3 iii. 3x 3 + 3x 7x 7 7