ACT Past Papers with Answers

IJ) the figuTe below, ZA ID, ZB ZE, and ABC - ADEF. The tneasure of ZA is 20°. The mea- sure of ZF is 75° What IS thc measure of ZB ? 95°

Shariika has a bag containing 50 pieces of candy: 6 strawbeiiy, 12 orange, 10 lime, alld 22 lemon. If Shanika randomly takes a piece of candy from the bag, what is the.probability that the piece shc takes is strawberry or lime? 50 10 50 l6 50 16 34 60 50 ACT-610 GO ON TO THE NEXT PAGE.

Buyer's Buddy Supcimarket is running a saje on all 4 flavors of 2-liter Zing-N-Zest soft drinks. The sale piice for each 2-liter bottle is $0.59, with a limit of 6 bottles per flavor. At u]ost, how many 2-liter bottles can be Pllrchased for S 12.89. excluding tax?

When3x-12y-6andy- 18 what is the value of x ? 10 ACT-61D. 15 GO ON TO THE NEXT PAGE.

For what valuc of x is 3(x + 5) - 2(1- 6) tiue? 27 H, -11 -21 Acf-610 16 GO ON TO THE NEXT PAGE. IS. Which of the following is equivalent to 25a DO YOUR FIGURING HERE.

Source question 15. Refer to the source image.

Suppose that w, y, aDd z each st2nd for a digit from O through 9 and 5w7 +92y I,z96 What is the value of Ihe product w ' y . z ? 19 252

The figure below shows a circle with a radius.of 5 cm and & chord of tbe circle. The chord is 3 crn from the center of the circle. What is the length, in centimeters, of the chord?

What is the sum of the 2 solutions of the equation x +3x-28=0? -28 ACT-61 D GO ON TO THE NEXT PAGE.

What is the value OF y in thc solution to the following systern of equatious? 2r+y+3-30 x+2y-30

In the right triangle below. the side lcngths givcn are in inches. Which of the following expressions equals the sine of ZR ? 23: A regular pentagon, P , has a perimeter of 25 inches, while another regular pentagon, P , has a pcrimeter that is 15 inches greatci thall the peritneter of P . The length of each side of P2 exceeds the lerAgih of each side of Pi by how many inches? ACT-61 D 18 GO ON TO THE NEXT PAGE.

Source question 23. Refer to the source image.

A certain type of combination lock has 3 dials". the first 2 dials each have settings for all the digits O through 9 and the third has settings foi all the 26 capital letters of the alphab'et. A combinatlou Consists of one settin.g from each of the di21s. (For exarllple, 6-4-P is a combi- nation. ble? How many different combinations are possi- DO YOUR FIGURING HERE. 260 520

ThrotLgh how inally degrees does a wheel Totate in

What is the fourth tcrm in the geometric sequence 36,-12, 4,

r(a ) (a )l is equivalent to- io li 21 24 36

Joe wants to put a border all th¢ way around his bed- room waljs l inch below the ceiling, as shown below. The border is sold only in whole rolls, and each ioll is 5 yards long. Joe's bedroom is rectangulai, 12 feet wide and 14 feet long. What is the trrillimum number of rolls of border Joe must buy. border ACT-61D GO ON TO THE NEXT PAGE.

Suppose that the measure of the larger of 2 suppLen]en- tary angles is 5 times the measure of the smaller angle. What is the tneasure of the larger angle? (Note: In the figure below. ZABD and ZDBC are sup- plernentary. The sum of their measures is 180°.) 30°

In the standard (x,y) coordinate plane, what is the slope of the line with the equation 3x- 2y- 24 ?

The community orchestia will oive 18 performances this season. A season ticket costs $60, and single- performance tickets cost $5 each. Huong purchased a scason ticket. What is the minimum nu.mber of perfor- mances Huoug must attend to save money by buying the season ticket instead of buying single-perfomance tickets for the performances she attends? ACT-61D 20 GO ON TO THE NEXT PAGE.

A line in the standard (x,y) cooiditLate plane passes through the origin and the point (-12,6). An equation of this line is= DO YOUR FIGURING HERE. x+18

Which of the following lists the Tcal v&lues of x that make the expression +1 ulldefined? Q only 3 only 1, 3 only

How many positive prime factors does the number 30 have,?

What is the distance, in coordinate units. between the points (-4,8) and (2,2) in the standard (x,y) coordinate plane? (J:i)' 40 72 104 136 12

.The measures of the interior angles of a trapezoid arc in the ratio of 3..4:5:6. What is tbe measure of the largest interior angle? io. 20° .D. 120° .ly L

Which of the following ratios is equivalent to the ratio of2 to4 ? ACT.610 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 39-41. Ms. Martin uscs a computer program to produce periodic progress reports for the ,1 O students in ber Advanced Math- ematics II class. The ieport crives a student's scores on tests. quizzes, and hO￿ewOrk assignments and the average of all 10 students, scores on each. The progress report shown below Nyas produced near the cnd of the terni for Richard Baldwin. Student. B aLdwin, Richard Possible points Student score Class average Task Homework #l 100 96 Homework #2 100 84 Hornework #3 100 89 Quiz #l 100 85 Quiz #2 100 93 Quiz #13 Quiz #4 100 89 100 Test #l 100 88 Test #2 100 68 Prctest 69 Posttcst 100

The solution of which of the followintr inequalities would tell Richard the minimum score (represented by x) be Deeds to earn ori.Quiz #4 iu ordei to have a quiz . average of at least 90 ? 85+93+89+x >90 (85+93+89) 85+93+89+x >90 85+93+89+x 85+93+89 ACT.610 22 GO ON TO THE NEXT PAGE.

In Nfs, Martin's class, tach student who does not turn in a homework assignment receKves a score of O lor the assignment. Of the 10 students in Ms. Martin's Advanced Mathematics Il class, what is the maximum possible number who did not turn in Homework #l ?

Wbich of the following gives the fractions alld- in order frotn least to greatcst?

What is the midpo3nt of the line segment with end- points (3,6) and (10.-24) in the standard (I,y) coordi- nate plane? 15 J5 13 AGf-&1 D 23 GO ON TO THE NEXT PAGE.

The circle in the figure below has a 12dius of 8.. centi- meters. What is the length, centimeters. of the arc that is inlercepted by a central angle of 600 ? 87[ 60°

If 27-3" 9y-6 and y- 6, then what is the real. number value of x ?

The diagram below sbows a quarter of each of 2 circles both having point C as their center. Point B lies on AC and point D lies on CE. The length of BC is.5 inches and the length of AB is 3 inches. What is the area, in square. inches, of the shaded portion? 25 39 55 ACT-SID 24 GO ON TO THE NEXT PAGE.

From a blimp 1,130 feet above the ground. the angle of depression Lo a marker on the ground is 52°, as. shown in the figure below. MiThich of the following expres- sions gives the distance along the ground, ill feet, from the marker to point P directly below thc blimp. DO YOUR FIGVRING HERE. 52" 1,130 ft 1,130 cos38° tall 38°

Given a real number n such that I. | > n. wbich of the following must be true? n< O

A polynomial function P(x) bas degree n. The graph in the standard (x,y) coordillaLe plaDe of y P(x) contains exactly 3 points on the i-axis. Which of the following could NOT be the value of n DO YOUR FIGURING HERE.

The radius of a right circular conc is doubled and its height is tripled to form a new right circular CODe. What is the ratio of the volume of the original cone to the volutne of the new cone? (Note: V Ttr A foi iadills r.and height h.)

Source question 55. Refer to the source image.

Which of the following integers must be 3 factor of the sum of any 3 consecutive positive 3lltegcrs?

A solid block of wood has 6 iectallgular faces. The length, width, and height of the block are a. b, and, c inches. respectively. Which of the following expres- sions represents the block's surface area, in square inches? D, 2a+2b+2c Acf-61D 26 GO ON TO THE NEXT PAGE.

The quadrants of the st2ndaTd (x,y) coordinate plane are shown in the figurc below. Given that the vertex of Z(x is the origin, the positive x-axis is one side of Z(x, Its other side lies in Quadrant 11, and Sin (X - what is cos 2ix ? DO YOUR FIGURING HERE. quadrants standard (x,y) coordinate plane

For a specific nonzeio value of b, the graph of sin bx in the standard (x,y) coordinate plane inter- sects the x-axis at k values of x in the interval O < x < 27[. At bow many values of x in this interval does thè graph of y - 2 sin bx intersect the x-axis? k+2 vo. Iii Lne siandard (x,)) Coordinate pldne below, tile coor- dinates of D are (d,k), arid the coordLDates of E are (e,k). Whell D is iotated 180° about E: the result is F. In terrns of d, e, and k, what are the coordinates of F ? d,0) d, k) END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT.61D 27

Source question 60. Refer to the source image.