ACT Past Papers with Answers

Tyrone wants ic score 80% or better on today's 40-point biology test. What is lhe least number of points that Tyrone must score to achieve 80% ?

(?￿ - 3)(3x- 4) is equivalent to: l?J_7

The word average indicates arithmetic mean. l. What is the value of the expression (x whenx-4andy= 2y)(x + 2y) DO YOUR FIGURING HERE. C, 14

A recipe for 150 ser.vings requires 4.5 liters of sauce. About how maJJy liteis of sauce are required: for 80 seivings? DO YOUR FIGURING HERE.

Pei bought a 36-inch-long candle. It bwns at a steady rate of 0.48 inches every hour. Which of the following is a relationship between the length., I, in inches, of the candle and Lhe t1￿c, t, in hours, th6 calldle ha5 burned? 1- 35.52t

Jn AABC below, AB - BC, alld ZABC measures 70°. Mlhat is the measure of ZBAC ?. 70° 50° 70°

You have 4 rectangular Tegions fhat you want to cover with cedar chips. .Olle region is 2 feet by 8 feet. anotheI is I fool by 4 feet. another is 2 feet by 20 feet" ' and the last one is I foot by 5 fcct. If a bag of cedar chips covers 10 square feet, how many bags of cedar bips wi]1 you need?

3, 8, 5 3 3 2 1 10, 8, 5.. 3 . 0.37 1 2 3 3, 5, 8, 10,

A point with COOTdinates (a,b) is plotte& in the stan- dard (x,y) coordin&te plane as shown below. The point is then reflected across the y-axis. Which of the fol- lowing are the coordinates for the point after the reflection. .(ffjb)

What quantity must be added to 41 + x - 5 to obtain x +5x+l? 5x +6x+6 5x +6x-4 -3x +6x+6 -3r+4x+6

What is the solution of the equation '12x.- _8(10 - x) ? DO YOUR FIGURING HERE. -20 13 13 li

In the figure below: ABCD is 2 SOU2re with side length 10 centirneters. The rnidpoint of AB is E. What is the arca, In %qu.are centimetcrs, of the shaded region? 25 SO￿5 75

What Is the solutioll to the following'systcin of cqua- tions? x+2y-12 15

If f (x) = 2x arid g(x) = <. what isf I g(3)) ? AGf.60E 17 . GO ON TO THE NEKf PAGE.

A dinncr combination at Nassif's Family Restaurant contains exactly l appetizer, I main course, and I dessert. How many different dinneT combinations are possible when choosing fro￿ 5 appetizers. 4 nlxin couises, and 5.desserts? DO YOUR FIGURING HERE. 14 40 45

Which of the folloivitig is equivalent to the inequality -5+m<_4+2m? m>_9

Which of the following lists orders

Which of the following is equivalent to (3x )- ? 9è 9£ -6 ACT.60E 18 GO ON TO THE NEXT PAGE.

If A- 10 3*C what is logio A ? IO, + lo, +C 2>. What is the solution set of the equation 4x

Source question 25. Refer to the source image.

The given"dimensions of the Tight triangle shown below are in inches.. What is the Icngth, in inchcs, of the hypotcnuse of the triangle? ACT.80E 19 GO ON TO THE NEXT PAGE.

Pilar obtained estirrtates for cleaning her furna¢¢ from .DO YOUR FIGURING HERE. •1 2 heatiJJg companies. Lehrnan Heating, s estimaie was $30 for a service call pluR $22 per bouI for cleaning the furnace. A-l Heating, s estilljate was $35 for a ser- vice call plus $20 per bouT for cl¢aning the furnace. If the estimates werc the same in both the total amount and the llumber of hours for cleaning Pilat's furnace, how many bours foi cleaning the furnace wcrc Teflected in the ettiinates?

In the st2nd2rd (x,y) coordinate planc. what is the slope of the line that passcs through tbe poinls (-3,5) and {7,3) ? -29. If 4 is the first term and 256 is tbc fourth term of a geometric progrcssion, which of thc following. is the second term?

Source question 29. Refer to the source image.

The legs of the rigbt triangle below are doubled in length to bscome the legs of a new rigbt triaDgle. What is the Jength, in feet, of the longest side of tbc new triangle?

If 3x + a = 9. then, in terms of a, x= DO YOUR FIGURING HERE. 9+a

As part of one day's tiaining workollt, 5 me]nbers of a track tearn ran for exactly 3 minutes each. The 5 runners ian the 5 distances given below, in miles. Which dis- tance co￿eSpondS to tbe fastest speed? 11 16

Which of tbe following is.an equation for the line passing through (0,0) aud (4,3) in the standard (J.y) . coordiDate plane? x+ y=

Points P, Q, R, and S lie on a lijje in the order given. Point R is the midpoint.of QS, PR is 5 cm long, and PS is 7 cm long. How many c¢ntimct¢rs long is QS ?

The student tells her p￿t￿er that 2 high schools are to be 2- cm aparl on the map. About how many miles apart are thcse high schools?

A square park mttasures should be the park, s area, in square cenliuieters, on the mile on eacb sidc. What 64 16 ACT.60E 22 GO ON TO THE NEXT PAGE.

A quadrilateral has diagollals that d'o NOT bisect each o.ther. Which of the following types of quadrilatcrals could it b¢? 'B. RectaThgJe DO YOUR FIGURING HERE.

Mary takes 2'Jnedications throughout the day and nighi. One medication is 10 be taken every 6 hours 2nd the other IS to be taken every 4 hours. If Mary begins taking both medications at 7:00 A.M. and takes both medications on schedule, how many hours later will it be when she next takes both medications at ttje same time?

If .1 is a solution of the equation x + hx +'lO = O, what does. h equa17 11 10 . ACT-SOE 23 GO ONTO THE NEXT PAGE.

The 5 con(7ruent circles shown in thc diagram below haie their centers lyino on the same diarneter of the larger circle. Each circle is tangent to 2 other circles. If the area of each sm?11 circle is 4K square units, what is thc area, in square units, of the larger circle? 407[ 20

Which of tbe following is equivalent to O27r ?

" There is a patterll when adding the cubes of the first c consecutive COUDting numbers, as illustrated below. 1'+2'_9-(1+2)' 1 +2'+3' 36-(1+2+3)' Which of the following is an expression for the sum of the cubes of the r￿st c consecutive counting numbers? +c)' +c) +c) AC7-60E 24 GO ON TO THE NEXT PAGE.

The'5 positive integers a, a, a, b, and c have a average of o, What is the value of b+c L3a

Source question 50. Refer to the source image.

tn the figure below. A, B, 2nd C ¥e the midpoints of thc sides of LPQR, and M, N, and O are (he midpoin15 of the sides of AABC. The interiors of APAB, ZXAQC, LSBCR, and "LSMNO shaded. What fIaction of the interior of APQJt is sFiaded? 13 16

The Malcolm X High School Student Council is plan- ning a spring outdoor caTlliv21. In the figure below, tbe locations foi several plaJJn¢d activities are represented as points X, Y, Z, P, and Q on the standard (x,y) coordi- uate plane, where each COOTdinate unit represents l yard. Tbc ticket booth is to be placed exactly midway between X and Z. About how many yards will tbe"ticket booth be from Y ? X(20,100) Y(100,110) P(120,80) z(1 20,40) Q(5Q,20) ACT-60E 26 GO ON TO THE NEXT PAGE. .53. For what value of t does the equation h - 3t - t .havc its rnaximum value for h ? DO YOUR FIGURING HERE. <4. For all x > O, which of the following LS equi¥'alent to x(x+l) 2x+l x{x+l) l¥+1 x(x+l)

Source question 53. Refer to the source image.

Source question 54. Refer to the source image.

The interioI angles of a quadrilateral are in the ratio

The 2 legs of a right triangle Measure 37 inches and 45 inches, respectively. Whal is tbe Cosille of the tri- .angle' s smallest interior angle? 37 45 45 37 .37 37+45 45 37'+45 ACT4OE 27 GO ON TO THE NEXT PAGE. 57, In creating a business plan for a cycle shop that sells both tricjcles an'd bicycles, a business analysi giaphed the inveDiOry constraints set by the shop owner. and then shaded the iÈgion, shown below, wherc all of tbc Gonstiaints w¢rc met. Which of the following state- tncnts dcfines the shaded region? DO YOUR FIGURING HERE. number of bicycles 80 60 40 20 number of 0 20. 40 60 80 iootricycles number of bicycles exceeds 30. of bicyclcs is Icss than the nurnbci of tricycles. number of bicycles is less than 100. 'D. The number of tricycles aDd bicycles together exceeds 100, and the DUtDbcr of bicycles is less Ihan l 00. less than 100, and the number of tricycles exceeds 30.

Source question 57. Refer to the source image.

In trigollomctry, an angle of - sine and cosine as an angle that has wbich of the fol- lowing deLYree meaS￿es? . 77[ radians has the same DO YOUR FIGURING HERE. 30° 60°

Which of the following is an equation of the ciicle with ccnter at (-2,3) and a radius of 5 coordinate units in thc standard (x.y) COOTdinatc plane? x +y +4x-6y- x +y +4x-6y-L2 x +y-4x+6y=12 END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-eOE 29