Practice Calculus Readiness Test - Elizabethtown College

1 1 Practice Calculus Readiness TestInstructions: Read each problem carefully. Then work the problem on a separate sheetof paper and click on the box next to the correct choice. If you change yourmind, just click on a different choice. Use the navigational buttons at the bottom of each page to go to the nextor previous page. A calculator is not required for any questions on this test. This Practice test consists of 25 problems. Click on Begin Quiz , in a bank triples every 8 years. If $100 is deposited today, whatwill its value be after 32 years?$8,500$8,100$1,600$ of the point of intersection of the graph of x+ 4y= 50 andx+y= 20 is60 14 rectangular box shown below has a square base and a closed height is twice the length of one side of the base.

2 Its surface areain terms ofxis20x8x+ 213is approximately equal to 8000, then, of the following, which bestapproximates 226?640,0006,400,00064,000, 5 642/3= a function whose graph is the parabola sketched below thenf(x)<0 wheneverx<1 orx>3x<1x>31<x< log2(x 6) = 6 thenx=7064586log26+ functionfis even iff( x) =f(x) for eachxin the domain off. Ofthe following, which best represents the graph of an even function?(a)(b)(c)(d) (2x 3)(x+ 5)x 7= 0 thenx=5,7, 325 or32 5, 7, or32 5 the following, which best represents the graph ofx2+y2 2y= 0?(a)(b)(c)(d) (x) =5x+32x+3thenf(n+ 1) =855n+ 32n+ 3+ 15n+ 82n+ 55n+ 42n+ slope of the line that goes through the points ( 5,4) and (3, 12)is 128 all solutions to the equation 3x2= 4x+ , 1/32+ 73,2 734+3 26,4 3 262+ 23,2 a standard coordinate system, the graph of the equationy= 3x+7isa line falling to the righta line rising to the righta horizontal linenot a inequality|x 4| 8 is equivalent to 4 x 12 12 x 4 12 x 12x quantitya bis a factor of how many of the following?

3 A2 b2a2+b2a3 b3a3+b3one onlytwo onlythree the figure shown below, what is the distance between the pointsPandQ? length of a certain rectangle is 6 meters more than twice its is the perimeter of the rectangle if the area of the rectangle is260 square meters?54 meters60 meters66 meters72 is the area of the rectangle shown in the figure below? (Note:The figure is not drawn to scale.) rectangleRhas widthxand lengthy. A rectangleSis formed fromRby multiplying each of the sides of the rectangleRby 4 as shown inthe figure below. What is the area of the portion ofSlying outsideR?(Note: The figure is not drawn to scale.)

4 Is the radian measure of an angle whose degree measure is 240 ? 32 33 44 (30 ) =22 3 2 which values ofxin the interval 0 x 2 does(sinx 1)(sinx 5) = 0? 2only1 and 5 0 and 2 the figure below, if sinR=58andr= 2, then what isq? the right triangle shown in the figure below, tan =xx x2 1x2+ 1 x2 1 Click on End Quiz to have the computer grade your test. Then clickon Correct My Answers to see which questions you got wrong. Click on the green dots to see detailed solutions for each to Practice Tests12 Solutions toPractice Calculus Readiness TestSolution to Question 1:In 8 years the value will be 3 100 = 300.

5 Eightyears later (after a total of 16 years), the value will be 3 300 = 900. Eightyears after that (after a total of 24 years) the value will be 3 900 = eight years after that (after a total of 32 years) the value will be3 2700 = to Practice Tests13 Solution to Question 2:Adding the two equations we obtain 5y= 30ory= to Practice Tests14 Solution to Question 3:The areas of the top and bottom are eachx x=x2. The area of each of the four sides isx 2x= 2x2. So the totalsurface area is 2(x2) + 4(2x2) = 2x2+ 8x2= to Practice Tests15 Solution to Question 4:226=(213)2= (8000)2= 64,000, to Practice Tests16 Solution to Question 5:2 5=125=132and 642/3=(3 64)2= (4)2=16, so 2 5 642/3=132 16 =1632= to Practice Tests17 Solution to Question 6:The graph is below thexaxis for 1<x< to Practice Tests18 Solution to Question 7:log2(x 6) = 6 26=x 6 x= 26+ 6 =64 + 6 = to Practice Tests19 Solution to Question 8:Iff(x) =f( x) for allx, the the graph offmust be symmetric with respect to theyaxis.

6 The only graph that hasthis symmetry is (c).ReturnJJIIJIBackJDocDocISolutions to Practice Tests20 Solution to Question 9:(2x 3)(x+ 5)x 7= 0 2x 3 = 0 orx+ 5 =0 x=32orx= to Practice Tests21 Solution to Question 10:Any equation of the formAx2+Ay2+Bx+Cy+D= 0 is a circle, which narrows the choices to (a) and (c). Completingthe square, we see thatx2+y2 2y+ 1 = 1 x2+ (y 1)2= 1. Weknow that (x h)2+ (y k)2=r2describes a circle with center (h,k) andradiusr. Hence our circle has radius (0,1) and radius 1, which is choice(c).ReturnJJIIJIBackJDocDocISoluti ons to Practice Tests22 Solution to Question 11:f(n+ 1) =5(n+ 1) + 32(n+ 1) + 3=5n+ 5 + 32n+ 2 + 3=5n+ 82n+ 5 ReturnJJIIJIBackJDocDocISolutions to Practice Tests23 Solution to Question 12:The slope isy2 y1x2 x1= 12 43 ( 5)= 168= 2 ReturnJJIIJIBackJDocDocISolutions to Practice Tests24 Solution to Question 13:We use the quadratic formula to solve theequation 3x2 4x 1 = 0 witha= 3,b= 4, andc= 1.

7 Sox= b b2 4ac2a=4 16 + 126=4 286=4 2 76=2 73So the solutions are2+ 73and2 to Practice Tests25 Solution to Question 14:The graph ofy=mx+bis a straight the slopem= 3 is negative, the graph of this line is falling to to Practice Tests26 Solution to Question 15:|x 4| 8 8 x 4 8 ( 8) + 4 x 8 + 4 4 x 12 ReturnJJIIJIBackJDocDocISolutions to Practice Tests27 Solution to Question 16:Recall thata2 b2= (a b)(a+b),a3 b3=(a b)(a2+ab+b2), anda3+b3= (a+b)(a2 ab+b2) (a2+b2does notfactor). Soa+bis a factor ofa2 b2anda3+ to Practice Tests28 Solution to Question 17:The distance fromPtoRis 1 ( 2) = 3,and the distance fromRtoQis 7 3 = 4.

8 By the Pythagorean Theorem,the distance fromPtoQis 32+ 42= 9 + 16 = 25 = to Practice Tests29 Solution to Question 18:If we letwbe the width of the rectangle, thenits length isl= 2w+ 6, so the area isl w= (2w+ 6)w= 2w2+ the area is 260, we have 2w2+ 6w= 260 2w2+ 6w 260 = 0 w2+ 3w 130 = 0 (w+ 13)(w 10) = 0 w= 10, 13. Sincewmustbe positive, the width of the rectangle must be 10 meters, so the lengthis 2w+ 6 = 26 meters, and so the perimeter is 2l+ 2w= 20 + 52 = to Practice Tests30 Solution to Question 19:The width of the rectangle is 5 2 = 3. Theheight of the rectangle isf(2) = 23 2 + 7 = 8 2 + 7 = 13.

9 So the areais 3 13 = to Practice Tests31 Solution to Question 20:The area of rectangleSis (4x)(4y) = area of rectangleRisxy. So the area of the portion ofSlying outsideRis 16xy xy= to Practice Tests32 Solution to Question 21:Since radians equals 180 degrees, we convertfrom degrees to radians by multiplying by 180:240 180=4 3 ReturnJJIIJIBackJDocDocISolutions to Practice Tests33 Solution to Question 22:Recall that sin(30 ) = 1/2, so csc(30 ) =11/2= 2 ReturnJJIIJIBackJDocDocISolutions to Practice Tests34 Solution to Question 23:(sinx 1)(sinx 5) = 0 sinx= 1 or sinx= 5 Since sinxis always between 1 and 1, there are no values ofxforwhich sinx= 5.

10 The only value ofxin the interval 0 x 2 for whichsinx= 1 isx= to Practice Tests35 Solution to Question 24:58= sinR=rq=2q 16 = 5q q=165 ReturnJJIIJIBackJDocDocISolutions to Practice Tests36 Solution to Question 25:By the Pythagorean Theorem, the third side ofthe triangle has length x2 1. So tan =oppositeadjacent= x2 11= x2