ACT Past Papers with Answers

crosses the x-axis at (3 + If21 , 0). At what other point, if any, does the parabola cross the x-axis? . CanJ]ot be determined from the given informatioll

What is the.peiimeter, in centimeters. of a rectangle with length 10 cm and width 5 cm ? 15 50 . ACT.66C 14 GO ON TO THE NEXT PAGE.

Ifx= wh'at is the value of DO YOUR FIGURING HERE.

+z-30

The 16-member drama club needs to choose a 8tlldent goveinment iepresentative. They decide that the representative, M'ho will be chosen at random, CANNOT be any of the 3 officers of the club. What is the Probability thai Adrian, who is a member of the club but NOT an officei, will be chosen? 16 13 16

For wh.at value of x is the equation 3(x true?

Juanita purchaséd an auiomobile for a total of $14,000. She financed all of -the $14,000 and started loan payrnents of $315 a month for 5 years. At the end of the 5-year persod, how much more than the purchase price will Juanita have paid for her autom'obil¢?

Source question 12. Refer to the source image.

On a real number line, point A is at -5.5 and is

On a map, the lengths of the sides of a triangular parcèl of land ar.e 3, i, .and 7 centimeteTS. The shortest side has an actual letigth of 410 meteis. Which of the following is closest to,the actual length, in meters, of the. longest side? ,17. Nvhat is the slope-intercept fortn of 41 - -4x+3 4x+3

Source question 17. Refer to the source image.

Whatisthevalueof 1-81 17-431 ? -44

You are designing a play mat for toy c￿s. An existing raiIroad track rncets a straight road at an angle of 94° to the road, as shown in the'figure below. Yoll are. adding a new railroad track beyond and parallel to the existiiig track. What is the degree measure of the 'angle bctween the road and the new track, as indicated below? road. eKisting track 94" new track

In right triangle £xABC shoivn below, D is the idpoint of AC.,To the nearest O: I foot, wbat is the length of AD ? ACT-66G 18 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 23-24. When Michelle defiosts frozen hamburger in her family's icroNvave, she enters the hamburger's weight, to the nearest 0.1 pound, and the microwave automatically sets the defTOSt time. Nlichelle defrosts 3 differeut amoullts of fro£en ha￿bUrger ill hèr family's microwave and wonders if there is & relationship between the wei(rhts and corresponding. microwave defrost tirnes. She grapbs the weights and COTIesponding microwave defrost times in the staudard (x,y) coordinate plane, as shown below, and notices a linear relationship between these 3 points. She finds that an equation of the line through these 3 points is y= 420x"+ 10. (2.4, 1,Q18) 1,000 800 600 400 200 (1.5, 640) (0.9, 388)

How many seconds longer is the microwave's defrost time for 2.4 pounds of frozen hafftbuigei than .IoT

AccordiJ]g .to Michelle's equation, about how maAy seconds would it take to defrost 8 ounces of frozen hamburger in her family's microwave? (Note: I pound = 16 ounces) 336 ACT-6BC 19 GO ON TO THE NEXT PAGE.

For all x, (x'+2x+l)(x-l) J + x +3x+l

For ZA in LABC below, which of the following trigolloimetsiL expressions has Vdlue 12 13 cosA cscA secA sinA 5cm 12 ctn

Mark was responsible for buying yo-yos and tops to use 2s prizes for the school carnival. His Teceipt showed that he spent a total of $32.20 and that he bought 60 itetns. Yo-yos cost $0.65 each, and tops cost $0.25 each. How many yo-yos did.mark bu}, to use as prizes for.the school carnival? ' (NoLe". There was no tax charged on the items because tbey. were bought foT a school.) Acf.66C . 20 GO ON TO THE NEXT PAGE.

The operation @ is defined as foIlows': o @ b - where. a and b are real numbers and a * b. What is the l+b'. DO YOUR FIGURING HERE. value of (-2) @ (-6) ? 10

Nam lis plannino to fftake a cake using a recipe that calls for 2- cups of pecans. He. has l- cups of pecans in a canistcr. The amount of pecans in the canister is what fraction of the amount o.f pecans he needs foT the recipe?

As shown below, O is the center of a circle, AB is a dia￿etel of the circl6, C lies on the circle, AC - CB, and OB - 7 cm. What is the area, in square centimeters, of ZL4BC ? 14 98

Which of the ft)Ilowing values of x is in the solutiotL set of the equationx + 5x- 14- 10 ? -24 ACT-66G 21 GO ON TO THE NEXT PAGE.

As, sbown in the figllre below, a silo consists of a right circular cylinder with a hemisphere on top. The radius of the cylinder and of ,the herrAisphcre is 10 fcct, and Ihe height of the cylinder is 25 feet. Which of the followin• is closest to the vol.ume, in cubic feet, of the silo? DO YOUR FIGURING HERE. (Note: The volume of a right circular cy.linder is given by 7tRh, where r is the radius and h is the height. The volume of a hemisphere is given by 7tr . where T is the radius.) 10 2,200 8,900 9,900 21,700 25

An isosceLes trapezoid has an area of 35 square feet. a hekght of 5 feet, and one base that is 8 feet long. The other base tnusi be how mally.feet long.

What is the slope of thc line through the points (-4,1) and (-6,-3) in the standard (x,y) coordinate plane?

Points A, B. and C are vertices of an.cquilateral triangle. Points A, B, and.D are collinear pojnts, with B. between A and D.. What is the measure of'ZCBD ? 30° 40° 90° ACT-6ec 22 GO ON TO THE NEXT PAGE.

The decimal representation of Iepeats and can be written as 0,8.i7142857142... What is the 10.oth ditrit to the right of the decimal point in this dccimal representation? DO YOUR FIGURING HERE.

Points A(-3,0). B(0.3), and C(3'0) lie in the standard (x,y) 'cooidinate plane. If ABCD is a square, then what is the length, in coordinate units, of CD ? ,E. 6<2

The giaph of the cqu&tion ry.- 8 is reflected across the x-axis in the standard (x,y) coordinate plane. Which of the following is 2n equation of the reflection?

For the Photo Piints option, at leagt how rllany prints must be sold to cover thc start-up. fee for the fund-raiser?

The graph in the standaid (x,y) coordinate plane below. shows y

In AFGH below, FG is 14 feet long. To the nearest tenth of a foot. how many feet long. is GH ? (Note: The law of sines states that for a triangle with sides of length a, b, and c opposite ZA, £B. and ZC, respectively, sinA sinB sÈllC (Note: sin 45°_ 0.707, sin 63°. x 0.891, sin 72° _ 0.951} 14 45° 72° ACTfj6C 25 GO ON TO THE NEXT PAGE.

Tamas. is 35 feet away from the. 12ase of a vertical flagpole, on level ground: He sees the top of the flagpole at an angle of inclination of 40° About how rnany feet higher than Tam&s's eye level is thè top of the flagpole? cos 40° 35 sin 40° 35

ID the sÉaDdard (x,y) coordinate plane, what aie the coordinates of the centei of the circle whose equation isx 6x+y +4y+12-0? AcT￿sc 26 GO ON TO THE NEXT PAGE.

Stephanie has a iectangular graph -10 inches wide and 8 Incbcs high that she needs to paste into a lab report foi her science class. Stephanie 'will use a photocopy rnachine repeatedly to reduce the size of her graph: With each reduction, the width and height will each be reduced to 80*0 of what they each were. What is the rniniLllUm number of reductions using the photocopy machine that will allow the graph .to fit in a space

If det ad- bc, tben det d-bc -ad+bc "ab-dc -ab+bc

Source question 55. Refer to the source image.

A parabola with vertex (3,7) and axis of symn]étry

Whenx#5 andx*-5, is equivalent to: 25 -G- 8x 25 -IOx 25 IK+12x - AGf-66C 28 GO ON TO THE NEXT PAGE.

An angle with ineasure.l) is shown in the standard. (K.y) coordinate plane below. The angle with measure ty has the po￿tiVe x-kxis as one side and has the portion of ". the line y =. x shown as its othei side. What is the ITalue ofsinty? DO YOVR FIGURING HERE:

The amount of money: A dollar8, in a savings account after t. years is 2iven by A = P + Prt, where P dollars is the amount of money.in the account originally and r is the raté. of slm-ple interest. WhiGh of the following èxpressions gives P in terms o! A. r. and t ? .l+rr l+rt 2rl .60, ConsideI the equation Ifb _ <a - 3<a, where'a and b are positive.real nwiibeis. Nlffiat is.b in terms of a ? END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. AGT.e 29

Source question 60. Refer to the source image.