ACT Past Papers with Answers

Paper 41 · ACT December 2014 · Form 72G · Math Test

For what value(s) of xis (x+ 3)(x- 4) = 0 true?

Paper 41 · ACT December 2014 · Form 72G · Math Test

Which of the following inequalities orders the numbers 1 0.1, 0.04, and 7 from least to greatest? 6 6 1 B. 0.04 < 0.1 < -:: 6 1 C. 0.04 < 一 6 ＜0.1 1 D. -::- 6 < 0.04 < 0.1 1 E. -: 6 < 0.1 < 0.04

Paper 41 · ACT December 2014 · Form 72G · Math Test

Given that 2x+ 1 = 5, what is the value of (x+ 3)3 ? ACT-72(, 14 but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed.

Paper 41 · ACT December 2014 · Form 72G · Math Test

What vector is the result of adding the vectors (1,-2〉, (2,3〉, and (-4,2〉 ? 2 6. What value of x makes �x + 5 = 11 true? 3 3 3

Paper 41 · ACT December 2014 · Form 72G · Math Test

Source question 6. Refer to the source image.

Paper 41 · ACT December 2014 · Form 72G · Math Test

In Summit City, the daily low temperatures, in degrees Fahrenheit (° were - 7, -11,15, 23, 45, 23, and 2. To the nearest 1° F, what was the mean daily low temperature for that week? F F F F

Paper 41 · ACT December 2014 · Form 72G · Math Test

Assume that a, b, and c are real numbers. If a > b, and (a+ c) > (b+ c), then what is true of c ?

Paper 41 · ACT December 2014 · Form 72G · Math Test

What is the slope of the line given by the equation 2x+ 7y = -12 ? 7 2 2 ACT-72G 15 独角兽在这里 2 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 210:i\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

One leg of a right triangle is 4 meters long and the other leg is 8 meters long. The hypotenuse of the triangle is howmanymeters long?

Paper 41 · ACT December 2014 · Form 72G · Math Test

Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, dfeet, the cartwas from a reference point at I-second intervals from t= 0 seconds to t= 5 seconds. t I 0 1812� Which oi the following equations represents this relationship between dand t ?

Paper 41 · ACT December 2014 · Form 72G · Math Test

The ratio of 30 to 24 is the same as the ratio of 40 to whatnumber?

Paper 41 · ACT December 2014 · Form 72G · Math Test

A box contains 3 red, 2 white, and 5 blue beads, each of which is a solid color. Miguel will randomly remove 1 bead from the box, record the color of the bead, and return the bead to the box. Miguel will complete this process 50 times. How many times should Miguel expectto record a bead color thatis NOT white? ACT-72G 16 独角兽在这里 2 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 2101<\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

Whenever 3(a +6b) - c = 0, which of the following expressions is equal to a ? 独角兽在这里 2 DO YOUR FIGURING HERE. 3 3 -2b 3

Paper 41 · ACT December 2014 · Form 72G · Math Test

Given that V2x-9 =1, x =?

Paper 41 · ACT December 2014 · Form 72G · Math Test

A high school ice hockey conference that consists of 10 teams requires that every conference team must playeach of the other conference teams at least once in a season. For n teams in the conference, the number of conference games played in a season must then be 2 at least n - n 2 . What is the minimum number of conference games that must be played in a season for this conference? 5 0 5 0 5 1 4 4 5 9 E G H j k

Paper 41 · ACT December 2014 · Form 72G · Math Test

For an angle with measure ex in a right triangle, ll2 ll2 sin ex=－— and tan ex=一． What is the value of ll3 15 cos ex? 15 A. _11 ＿ 3 15 B. 亩 15 卢 15 D. 三 113 E. � 15 ACT-72G 17 GO ON TO THE NEXT PAGE. 210�T 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

In isosceles triangle b.ABC,吓is congruent to放 and the measure of the vertex angle, LB, is 75° . What is themeasure of LA ? 独角兽在这里 DO YOUR FIGURING HERE. 2

Paper 41 · ACT December 2014 · Form 72G · Math Test

Cowling's rule is a method of calculating a medication dosage for a child by using the child's age and the adult dosage. The rule uses the formula d = a(— t+ 1

Paper 41 · ACT December 2014 · Form 72G · Math Test

Each side of a square is 3 cm long. One vertex of the square is at (4,2) on a square coordinate grid marked in centimeter units. Which of the following points on the grid could be another vertex of the square?

Paper 41 · ACT December 2014 · Form 72G · Math Test

The Ferris wheel at a state fair has a radius of 60 feet, rotates at a constant speed, and completes 1 rotation in 4 minutes. How many degrees does the Ferris wheel rotate in 30 seconds? ACT-72G 18 GO ON TO THE NEXT PAGE. 210}\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

At Gussie's Pizzeria, Odetta spends $8.75 (before tax) on the purchase of 2 appetizers and 3 slices of pizza. The price of each slice of pizza is p dollars. The price of each appetizer is twice the price of a slice of pizza. Which of the following systems of equations, when solved, gives the price, a dollars, of an appetizer and the price, p dollars, of a slice of pizza at Gussie's? a =2p 3a =2p 3p =2a p = 2a a = 2p 独角兽在这里 2 DO YOUR FIGURING HERE.

Paper 41 · ACT December 2014 · Form 72G · Math Test

The perimeter of a parallelogram is 76 inches, and the length of 1 side is 10 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

Paper 41 · ACT December 2014 · Form 72G · Math Test

， where d is the child's dosage in milligrams, a is the adult dosage in milligrams, and t is the child's age in years. Dato is taking a 150-milligram dosage of medication that has an adult dosage of 300 milligrams. According to this rule, which of the following values is closest to Dato's age in years?

Paper 41 · ACT December 2014 · Form 72G · Math Test

Suppose 1 cast member will be picked at random from the 20 cast members who sold tickets to receive a prize. What is the probability of picking a cast member who sold more than30 tickets? A 1 5 B 1 4 19 D 2 17 E 4 5 ACT-72G 20 独角兽在这里 2 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 210:]\_CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

For which night was the total amount collected for the tickets greater, and by how many dollars was it greater?

Paper 41 · ACT December 2014 · Form 72G · Math Test

How many seats are in the 8th row of the auditorium? 独角兽在这里 2 DO YOUR FIGURING HERE.

Paper 41 · ACT December 2014 · Form 72G · Math Test

In rectangle ABDE shown below, C lies on即and F lies on吓such that rectangles ABCF and CDEF are similar (ABCF - CDEF), the length of顽is 4 cm, and the length of积is 8 cm. What is the area, in square centimeters, of ABDE ? 2 8 0 2 8 3 3 4 4 4 E G H j k ， B 4 A 8 C D F

Paper 41 · ACT December 2014 · Form 72G · Math Test

Points A, B, C, and D lie on the real number line as shown below. The coordinate of B is 0,亢is 15 units long,即is 20 units long, and AD is 32 units long. What is the coordinate of C ? A B C D

Paper 41 · ACT December 2014 · Form 72G · Math Test

In a certain country, last year's population was estimated to be 3.6 x 106 people, and last year's public debt was estimated to be 1.8 x 109 dollars. Based on these estimates, what was last year's public debt per person in this country? ACT-72G 21 GO ON TO THE NEXT PAGE. 210ACT 微信号 loviact 独角兽在这里 DO YOUR FIGURING HERE. 2 Use the following information to answer questions 31-34. A landscaper will install a triangular garden near the intersection of 2 streets. In the plan of the garden shown below, the angle nearest the intersection is a right angle. The landscaper has purchased the following materials for the garden: 1 bag of fertilizer at a price of $15.50, 50plants at a price of $0.70each, and 3 bags of mulch at a price of $4.00 each. An 8% sales tax was added to the total price of these materials. The landscaper will also install a water sprinkler that will be located an equal distance from the 3 vertices of the garden. ArborDr. .- sidewalk . k S 兰 入 。

Paper 41 · ACT December 2014 · Form 72G · Math Test

The landscaper calculated the area of the garden before purchasing the fertilizer, plants, and mulch. What is the area, in square feet, ofthe garden?

Paper 41 · ACT December 2014 · Form 72G · Math Test

What was the total cost, including sales tax, of the fertilizer, plants, and mulch that the landscaper purchased?

Paper 41 · ACT December 2014 · Form 72G · Math Test

The plan of the garden will be aligned in the -standard (x,y) coordinate plane so that the right angle is at (0,0) and the other 2 vertices are at (12,0) and (0,-9). What coordinates give the location of the water sprinkler? (3,－彗） (4,-3) (6,-2¾) (6,－彗） ACT-72G 22 GO ON TO THE NEXT PAGE. 2lOVACT 微信号

Paper 41 · ACT December 2014 · Form 72G · Math Test

The landscaper has decided to enclose the garden by installing a decorative fence of uniform height along the garden's perimeter. What is the minimum length, in feet, of fencing required to enclose the garden? loviact 独角兽在这里 DO YOUR FIGURING HERE. 2

Paper 41 · ACT December 2014 · Form 72G · Math Test

Shown below are right triangles LACD and LABE with lengths given in inches. What is the length, in inches, ofAB ? 3 -5 3 l4 4 l5 2 -3 1 -3 5 5 5 6 8 ． A D 15 C B A | 20 1

Paper 41 · ACT December 2014 · Form 72G · Math Test

The circumference of a circle is 50 cm. What is the length, in centimeters, of the diameter of the circle? 25 － 兀 50 － 冗 50 257t 507t

Paper 41 · ACT December 2014 · Form 72G · Math Test

Which of the following values is closest to the distance, in inches, between pointA andpoint B on the ruler shown below? (Note: The ruler shown is NOT actual size.) I 』1 1 IT'|IIIl1|II1|l』1111111』1|I|lfl』l 6 9 一 1 3 -4 6 1 l8 3 一 1 3 -8 2 3 3 3 3 ACT-7怼G 23 GO ON TO THE NEXT PAGE. 210:i\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

If r + 5 = m and r +6 = n, what is the value of n - m ? 独角兽在这里 DO YOUR FIGURING HERE. 2

Paper 41 · ACT December 2014 · Form 72G · Math Test

In the figure below, lines l and m are parallel. Lines a and b intersect l at the same point. What is the value of X? b a (4x+ 6 1 4 8 0 1 1 1 3 A B C D E m

Paper 41 · ACT December 2014 · Form 72G · Math Test

The line y 1 = �x + 3 and the line 2 y = 3x - 12 intersect at (6,6), as shown in the standard (x,y) coordinate plane below. The shaded region is bounded by these 2 lines, the x-axis, and the y-axis. What is the area of the shaded region, in square coordinate units? 8 1 4 7 2 l 2 2 2 4 ． ． ． Fo G H J K

Paper 41 · ACT December 2014 · Form 72G · Math Test

In the figure below, AD, BE, and CF all intersect at point Z. The meas_ures of 2 angles are given. What is the measure of LCZE? 0 0 0 0 0 6 2 4 9 9 7 0 0 1 2 1 l l l . . . . . A B C D E ACT-72G 24 GO ON TO THE NEXT PAGE. 210:i\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

Emma and Kristin each ran 10 laps (4,000 meters) around a 400-meter track without stopping. Emma ran at a constant speed of 250 meters per minute. Kristin ran at a constant speed of 200 meters per minute. Both Emma and Kristin began running at the same instant. How many laps did Kristin have left to run when Emma had completed her run? 2 5

Paper 41 · ACT December 2014 · Form 72G · Math Test

Three linear equations are given below. y= X y= X + l y= -x + l In terms of being parallel, being perpendicular, or intersecting, how are the graphs of these equations related in the standard (x,y) coordinate plane?

Paper 41 · ACT December 2014 · Form 72G · Math Test

For what value of a would the following system of equations have an infinite number of solutions? X - 2y= 8 3x - 6y= 4a

Paper 41 · ACT December 2014 · Form 72G · Math Test

Given that x= 2 when y= 12 for the proportion 王 ＝ 一， k 6 y what is x when y = 8 ? 4 3 ACT-72G 25 独角兽在这里 2 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 210:1\.C_T 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

Two events are independent if the outcome of one event does not affect the outcome of the other event. One of the following statements does NOT describe independentevents. Which one? lands with a 3 faceup. lands heads up. replacing the card, a 4 is drawn. after being rolled a second time, the die lands with a l f?ceup. replacing the card, a 2 is drawn. 独角兽在这里 2 DO YOUR FIGURING HERE.

Paper 41 · ACT December 2014 · Form 72G · Math Test

Which of the following binomials is a factor of 3x2 + 1 lx - 4?

Paper 41 · ACT December 2014 · Form 72G · Math Test

The figure below shows a lighthouse keeper looking down at a rowboat on the sea through a navigational instrument. The instrument is 60 feet above sea level and indicates an angle of depression of 53° to the rowboat. Which of the following is closest to the horizontal distance, in feet, between the navigational instrument and the rowboat? (Note: sin 53° ""0.80, cos 53° "'0.60, tan 53° ""1.33) 36 45 48 53 80 ． ． ． E G H j k

Paper 41 · ACT December 2014 · Form 72G · Math Test

Each of 20 students in a class took a test and received a whole number score. The median of the scores was 87. None of the students received a score of 87, and 30% of the students received scores of 90 or above. How many students received scores of 88 or 89 ? ACT-72G 26 GO ON TO THE NEXT PAGE. 210:l\.CT 微信号loviact

Paper 41 · ACT December 2014 · Form 72G · Math Test

The radius and height of the right circular cylinder shown below are given in centimeters. Which of the following is closest to the volume, in cubic centimeters, of the cylinder? 0 0 0 0 0 2 1 0 4 0 2 3 7 5 2 ， ＇ l 2 ． ． ． E G H j k 独角兽在这里 2 DO YOUR FIGURING HERE. 7 51. What value of x satisfies the equation below? log16 x = 3 . 4 l 1 D. 8

Paper 41 · ACT December 2014 · Form 72G · Math Test

Source question 51. Refer to the source image.

Paper 41 · ACT December 2014 · Form 72G · Math Test

Let x be a negative odd integer. The expression xl is a positive even integer whenever y is any member of which of the following sets?

Paper 41 · ACT December 2014 · Form 72G · Math Test

Point /(3,4) is shown in the standard (x,y) coordinate plane below. Point / is reflected across the line x = 7 and, after the reflection, is labeled J. What are the coordinates of J ? y 、 丿 ） ） ） ） 4 1 0 4 4 l ' , ' ， ＇ l 3 3 0 1 - 1 l ( （ （ （ （ ． ． ． A B C D E • /(3,4) 。 X ACT-72G 27 GO ON TO THE NEXT PAGE. 2lOVACT 微信号loviact 独角兽在这里 2

Paper 41 · ACT December 2014 · Form 72G · Math Test

The angle measures of D.CDE are shown below. Point B of D.ABC lies on酰and point C lies on症 What is the value of cos(a + P) ? v (Note: cos30° =—) 2 E DO YOUR FIGURING HERE. 。 1 - 2 迈 ＿2 迈 2 D l A

Paper 41 · ACT December 2014 · Form 72G · Math Test

The determinant of any 2 x 2 matrix [� :] is ad - be. Cd The determinant of [( x; 3)（ x 2 2)] is equal to 0. What are all possible valuesofx ? A B C D E -5 and 4 -4 and 5 -3 and 2 -1 and 9 －湿and湿

Paper 41 · ACT December 2014 · Form 72G · Math Test

Which of the following inequalities is equivalent to (lxl+ 1) 2 $;4? E G H j k -3$x$1 一3$x$3 -2 $X $ 2 -v了<x5迈 -l$x$l

Paper 41 · ACT December 2014 · Form 72G · Math Test

Given that 2 sin a=2 and 2 cos(f - b) = 2, which of the following could be a value, in radians, of a + b? 。 兀 ＿ 2 2 冗 兀 2 ACT-72G 28 GO ON TO THE NEXT PAGE. 210}\_CT 微信号

Paper 41 · ACT December 2014 · Form 72G · Math Test

One of the following equations determines the graph in the standard (x,y) coordinate plane below. Which one? y loviact 独角兽在这里 DO YOUR FIGURING HERE. 2 -4 -2 -2 。 2 4 6 8 X 三十三＝ l 25 . 9 (x- 3) 2 (y+4) 2 ＋ ＝ 25 . 9 1 (x- 3) 2 (y-4) 2 ＋ 9 . 25 = 1 (x+ 3) 2 , (y+4)2 25 . 9 = 1 (x+ 3)2 , (y+4) 2 ＋ 9 . 25 = 1

Paper 41 · ACT December 2014 · Form 72G · Math Test

Cubes each having a side length of 0.5 cm are put together to form a rectangular solid with 8 layers. Each laye.r has 6 cubes. What is the volume, in cubic ce-ntimeters, ofthe rectangular solid? ·

Paper 41 · ACT December 2014 · Form 72G · Math Test

Consider the 2 functionsf(x) = 2x + 5 andg(x) = 3x + b, where b is a real number. Iff(g(x)) =g(f(x)), then b = ? 。 10 - 3 5 0 l Any real number END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURNTO THE PREVIOUS TEST. ACT-72G 29