an ACT workbook for the classroom - LSU Math

1 An ACT workbook for the classroombyJeremy AikinandMatt BennettThis product was made possible by the National Science Foundation GK-12 Fellows Program at Louisiana State University, the Louisiana EducationQuality Support Fund, and the Gordon A. Cain Center at Louisiana is a registered trademark of ACT, Inc., which was not involved in the produc-tion of, and does not endorse, this note to the 4 successis a collection of worksheets intended to offer high school students,who have completed algebra and geometry, steady practice on problems similar to thoseencountered on the math portion of the ACT. Each worksheet has 3 problems and thestudents should be given exactly 3 minutes time to work them out.

2 These worksheetscan be used as a daily warm-up routine for the first five or so minutes of class time. Itis important for the teacher to spend a few minutes going over the answers and possiblestrategies for solving the problems after the students complete each worksheet. We rec-ommend that the teacher collects and grades each worksheet, keeping track of the totalnumber of problems each student gets correct throughout the year. It may even be usefulto design a game to go with these worksheets in order to hold the students interest andmotivate them to do their best while competing with their of the following is equivalent to(z)(z)(z)(z)(z)(z)for allz? + rectangle is3times as long as it is wide.

3 If the width of the rectangle is2inches,what is the rectangle s area in square inches? 10 3=? , 5, of the following is divisible by3with no remainder? , , , , , concentration of a substance in a solution is2 10 5milligrams per many milligrams are in3 108milliliters? 10 10 one leg of a right triangle is6centimeters long, and the other leg is8centimeterslong, how long is the triangle s hypotenuse? jar contains 16 gum balls: 5 are yellow, 8 are red, and 3 are blue. Two gum ballsare selected at random from the jar one at a time. If the first gum ball is red, whatis the probability that the second gum ball will also be red? you have in30minutes, what was your average speed, in milesper hour?

4 Any real numbers such that0<m<1<n, which of the followingmustbe true of the value ofmn? <mn< <mn< <mn< <mn< < many solutions are there to the equation2x2 8=0? 1, theny=? + + graphed in the(x,y)coordinate plane, at what point do the linesx y=12andy=2intersect?A.(10,2)B.(2,14)C.(2,12)D.(14,2)E.(12,2) circle with center( 5,1)is tangent to they-axis in the standard(x,y)coordinateplane. What is the radius of this circle? of the following completely describes the solution set for2(x+1) =2x+2? real numbers are solutions are no solutions allx>0,2x2+3x+1x+1simplifies + (x+1) +1D.(2x+1)(x+1) + Janet is2years older than her brother, Tim, and Andrew is5years older thanJanet, and the sum of all3of their ages is42, then how old is Tim?

5 , thenx=? made$121this week for working22hours. How much will she make nextweek if she gets paid at the same rate but only works14hours?A.$100B.$77C.$ $114E.$ the value ofA,BandCin the following fraction are all doubled, how does thevalue of the fraction change?A DC by the by of the following fractions is the equivalent 34=?A. 98E. is the next term in the following sequence?1,23,49,827, isx12divided byx14? 10 10 10 10 average of three numbers isx. If the first number isyand the second numberisz, what is the third number? y y 3y +y+ +y+ two cowboys leave a ranch at 9:00 am, how far apart will they be at 11:00 am ifone travels directly north at20mph and the other travels directly west at15mph?

6 Of the following isNOTa rational number?A. 3B. 4C. a circle has diameter4, what is its area? a circle has circumference8 , what is its area? rectangular prism has volume128in3. If the length of its base is4inches and itsheight is two times the width of its base, what is its height? is the area of the triangle below? sum of the product of two positive numbers and two times their difference is16. Their difference is3. What are the two numbers? needs to be at the airport in30minutes, but the airport is27miles away. Whatis the minimum speed he must drive in order to get there on time? the standard(x,y)coordinate plane, what is the area of the triangle formed bythe linesy=0,x=0and the line connecting the points(0,3)and(5,0)?

7 The figure below,BD =DCandBCis20units long. IfADis the altitude of4 ABC,what is the area, in square centimeters, of4 ABC? be determined by the given are thex-intercepts in the graph ofy=x2 3x 4? 2C. of the following is equal to 72? is the slope of the line6y=12 3x? 2D. 12E. is the largest possible product for two odd integers whose sum is 28? box of oatmeal contains1712cups of oatmeal. At most, how many people canyou serve from this box of oatmeal if a serving must be at least34cup? is the least value ofysatisfying the equationy2 5=3y 5? 3D. +3y=19and3x+y=5, thenx+y=? positive value ofkwould make the lines below parallel in the standard(x,y)coordinate plane?kx+4y=1516x+ky= , then21y+12=?

8 ,x2+kx 40=0. What is the value ofk? a real number greater than5,000,000, which of the following fractions issmallest in value? + + is the product of the two real solutions to the equationx2=12+4x?A. 12B. integer most nearly approximates( 65)( 35)? 2=4x+3, thenx=? of the following equations describes a line that passes through the originand is parallel to the line3x 2y=10? y= +2y= 3x= 3x= +2x=03.|10 14| |8 3|=? , thenb2=? the weight of a600-pound motorcycle should be supported by the rearwheel, how many pounds should be supported by the rear wheel? is the average arenstudents on a school bus. If, among those students,p%play at leastone sport, which of the following general expressions represents the number ofstudents who playNOsports?

9 (1 p) (1 p). (100 p) authors write a book together and as a group, they get35%of the money fromthe sales of their new book. That35%is split equally among the5authors. If thebook generates$1,500,000in sales, how much does one author receive?A.$450,000B.$525,000C.$125,000D. $105,000E.$90, total surface area of the rectangular box shown below is the sum of the areasof the6sides. What is the box s total surface area, in square inches? inches2 inches5 circular pancake has a radius of118inches. When lying flat on a frying pan, howmuch area does the pancake cover, in square inches? has an area of81in2. How many inches long is diagonalBD? 2 ABCD? area of a trapezoid is12h(b1+b2), wherehis the altitude, andb1andb2are thelengths of the parallel bases.

10 If a trapezoid has an altitude of6inches, an area of48in2, and one base7inches long, what is the length, in inches, of its other base? are shown in inches in the drawing of the rectangle below. What is theshaded area, in square inches? all real numbersx, what is the minimum value of6cos(5x)?A. the angles Xand Yeach measure between90 and180 , and ifsinX= cosY,what is thesumof the measures of the angles Xand Y? television is on sale for$1,200, which is a40%discount of the regular is the regular price of the television?A.$2,200B.$1,900C.$1,800D.$2, 100E.$2, of the following fractions is equivalent helicopters leave the same army base at 2:00 pm. How far apart will they beat 4:00 pm if one flies due north at120mph and the other flies due west at90mph?