MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:


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1 MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an attempt to educate prospective CLC students and interested faculty regarding what kinds of questions to epect on the College Board Educational Testing Service s ACCUPLACER adaptive placement eam. It also educates any interested party regarding the mathematics skills, illustrated by typical eamples, which MUST be known to reach the level of placement desired. [This eam does not measure how many mathematics courses the test taker has completed. This test measures what the test taker actually knows and can demonstrate on the day of the eam. (i.e. No partial credit is awarded)]. PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 45: First, any student intending to place into Calculus and Analytic Geometry I via the Math Placement Eam must be proficient with the types of algebra eercises illustrated as eamples for entry into college algebra MTH / precalculus MTH 44. In addition to the above mentioned algebra skills, a student desiring to place into Calculus and Analytic Geometry I must know the following skills and concepts and be proficient with them. This eam is unforgiving of errors made in haste or through lack of concentration. When an error is made the eam scores it as wrong and does not know the eaminee may have know how to do a particular eercise, but made a minor error. The eam is not timed. Scratch paper and a Casio 00 scientific calculator are provided to assist the eaminee with calculations. Students should make as certain as they can that each of their choices is correct. Finally, the eam is multiple choice and presented in a computer format. NOTE: The eamples provided are not intended to be a complete list of problem types. The eamples are simply illustrations of problem types. Review materials are available at the Math Center. (847)
2 . The student needs to be completely proficient with all aspect of linear functions. In particular, concepts involving slope, yintercept, parallelism, and perpendicularity must be mastered. a) What is the equation of the linear function with slope / and yintercept of 6? y 6 b) Write the equation of two lines one of which is perpendicular to and the other which is parallel to the line with intercept and yintercept of. y y c) Write in the form, y = m + b, the equation of the line which passes through the point A:(, ) and B:(/7, /). 9 y The student must know how to perform horizontal and vertical translations of elementary functions. For eample consider the function defined by y = f(). What is the relationship of the graph of (y k) = f(h) to the graph of y = f() when a) h = 7 and k = b) h =  and k =.5 right 7 up left up.5 Note: Some of the elementary functions referred to in item # just above could be:,,, e, sin( ), cos( ), log 0 ( ), a b c. The student must be proficient with the determination of implicit real valued domains of functions defined by equations. For what values of will f() be a real number in the following? a) 0 b) or
3 c) 6 d) > 0, 8 7 = 5 or The student must be able to complete the square and manipulate and interpret results. Complete the square on the quadratic function defined by Now compare its graph with the graph of. y ( 7) The curve is concave down, verte at (7,) and is slightly shrunk from. 5. The student must be proficient with logarithmic and eponential functions and epressions. a) What is the inverse function of log (5)? f ( ) 5 b) What is the corresponding eponential form of log 5? 5 c) If log 7, then log? The student must be able to graph functions of the form Acos( B C) k or Asin( B C) k Graph the following on the interval from π to π. a) cos( ). 5 b) sin()
4 7. The student must know all of the fundamental trigonometric identities. In particular: opposite a) the right triangle identities like sin( ) = hypotenuse etc. b) the reciprocal identities like sec( ) = etc. cos c) the Pythagorean Identities like sin cos etc. 8. The student must know right trigonometry and be able to apply it to practical applications. a) A tower 00feet tall is located at the top of a hill. At a point 500 feet down the hill the angle between the surface of the hill and the line of sight to the top of the tower is 0 degrees. Find the inclination of the hill to a horizontal plane b) Two men stand 00 feet apart with a flagpole with a flagpole situated on the line between them. If the angles of elevation from the men to the top of the flagpole are 0 degrees and 5 degrees respectively, how tall is the pole and how far is each man from it? Flag pole = 5.6 ft tall; Man= 89.4ft away; Other man 0.6ft away 9. The student must be able to write functions representing geometric shapes and various physical phenomena. a) If the perimeter of the following figure is 0, what is the value of? It may be assumed that the dished out portion is a semicircle. y 0 y
5 b) Epress the area of the following figure as a function of. A rectangle topped by a tangent circle with a diameter equal to the rectangle s width. The length of the rectangle is triple that of its width. A A 4 0. The student will be epected to solve nonlinear systems of equations. Solve the following systems of equations. a) y 7 y ,, b) y 7 y 9 9,4 9,4 9. The student will be epected to solve trigonometric equations. Solve the following trigonometric equations for all (, ) a) sin = cos b) sin sin 0 c) =, 4 4 5,, 6 6 sin( ) 5,,, ,, The student must be familiar with some of the basic theorems regarding polynomials of degree n in. 4 a) Any rational zero of 5 7 must look like what?,,, 5 5
6 b) If + i is a zero of 4 0 then what are all the other zeros? i, c) If i is a zero of a nd degree polynomial in, then what could this particular polynomial be? f 6. The student must be proficient with the arithmetic of comple numbers. Recall that i. a) Simplify i 5i b) Simplify ( + 4i)( i) i 0 + 0i The student must know the algebraic and graphical relationship between a function and its inverse function when such an inverse eists. a) If f ) log, then f ()? ( 9 b) If 5, then f =? 7 5. The student must be familiar with an able to apply the Binomial Theorem. What is the 9 th term of ( 6) 5?
7 6. The student must be familiar with the domain, range and graphs of the si Inverse Trigonometric Functions. a) Sketch the graph of cos ( ) on its domain. b) Evaluate sin and arctan c.) Solve for : cos () cos 4 7. The student must be familiar with and be able to solve logarithmic and eponential equations. Solve the following equations. a) log 5( 6) log 5 0 = ln( 6 7) b) 4 = ln()
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