ACT Past Papers with Answers

Paper 55 · ACT June 2011 · Form 69F · Math Test

The 1st term in the geometric &equence below is -4. If it can be determined,what is the 6th term? -4,8,-16,32, -64,...

Paper 55 · ACT June 2011 · Form 69F · Math Test

Ifr = 8,b = 3,and g = -5,what does (r + b - g)(b + g) equal?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Every year on Inari's birthday,her uncle gives her $10, plus $2 for each year of her age. How old will Inari be when she receives $34 from her uncle on her birthday? G; 12

Paper 55 · ACT June 2011 · Form 69F · Math Test

For what value ofxis the equation -2x+ 3 = -21 true? DO YOUR FIGURING HERE. ACT-69F 14 GO ON TO THE NEXT PAGE. 2 IO�CT 微信号loviact

Paper 55 · ACT June 2011 · Form 69F · Math Test

What is the mean of the list ofnumbers below? 62, 100, 93, 62, 72, 78, 50, 85, 62, 36 独角兽在这里

Paper 55 · ACT June 2011 · Form 69F · Math Test

Adam is baking a cake for his friend's birthday. The cake requires 1f cups of cocoa, and the frosting 3 _ requires f cup of cocoa. How many cups of cocoa 4 does Adam need?

Paper 55 · ACT June 2011 · Form 69F · Math Test

In a level field, a vertical pole with a height of 6 feet casts a 10-foot shadow. At the same time, a tree growing in this field casts a 90-foot shadow. What is the height, in feet, of the tree?

Paper 55 · ACT June 2011 · Form 69F · Math Test

The total cost of renting a car is $35.00 for each day the car is rented plus·37.5¢ for ·each mile the car is driven. What is the total cost of renting the car for 4 days and driving 300 miles? (Note: No sales tax is involved.) DO YOUR FIGURING HERE. 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

The expression (7c � 2d)(2c + d) is equivalent to: - 2d2 - llcd - 2d2 - llcd + 2d2 + 3cd - 2d2 + 3cd + 2d2 ACT-69F 15 GO ON TO THE NEXT PAGE. 2 lO�CT 微信号 loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

When solved for y, what is 3x+ 5y- 13 =·o ? 3 y= -3x+ 13 5 5 -3x- 8 y= -15x- 65

Paper 55 · ACT June 2011 · Form 69F · Math Test

The speed of one bus exceeds 3 times the speed of another bus by 20 mph. The speed of the slower bus is k mph. Which of the following expressions represents the speed of the faster bus, in miles per hour? k+ 20 3 k- 20 DO YOUR FIGURING HERE. E k+ 20 3k- 20

Paper 55 · ACT June 2011 · Form 69F · Math Test

At 2:00 a.m., the temperature is -15° 3 hours, the temperature decreases 2° F per hour. What is the temperature at5:00 a.m. ? F F F F F

Paper 55 · ACT June 2011 · Form 69F · Math Test

Jing took 6 hours to travel 250 miles by car to Mirror Lake. The graph below shows the distance she traveled versus time. Among the following statements, which one best describes what happened during the interval between 2 hours and 4 hours? 250 200 150 100 . ( s 3 [ 百 ) ． p 3 I 3 A 巴 1 3 3 5 } 1 s I P 。 0 0 5 l 2 3 4 5 time(hours) 6 E G H j k ACT-69F The car traveled at 50 mph. The car traveled 100 miles. The car traveled 200 miles: The car was stopped, and Jing had approximately 150 miles left to travel to Mirror Lake. The car was stopped, and Jing had approximately 100 miles left to travel to Mirror Lake. 16 GO ON TO THE NEXT PAGE. 2 IO�CT 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

A children's wading pool, shown below, is in the shape of a right circular cylinder and has a diameter of6 feet. The pool is filled to auniform depth of 1.5 feet. Which of the following values is closest to the volume of water in the pool, in cubic feet? l . 6 1 (Note: The volume of a right circular cylinder is 1t户h, where r is the radius of the cylinder and h is the height of the cylinder.)

Paper 55 · ACT June 2011 · Form 69F · Math Test

For the function f(x)= Ix I 3 - 1, what is the value of f(-1)? DO YOUR FIGURING HERE.

Paper 55 · ACT June 2011 · Form 69F · Math Test

What is 125% of 332?

Paper 55 · ACT June 2011 · Form 69F · Math Test

(6a+Sb+4c)-(4a + 4b- 2c)is equivalent to:

Paper 55 · ACT June 2011 · Form 69F · Math Test

In the standard (x,y) coordinate plane, the coordinates of the endpoints of丽are (6,8)and (14,18). What is the x-coordinate of the midpoint of邵？ ACT-69F 17 GO ON TO THE NEXT PAGE. 2 IOACT 微信号loviact 独角兽在这里 DO YOUR FIGURING HERE. 2 Use the following -information to answer questions 20-22. In the figure s�own below, _eac� si_de of squa�e Af!CD_is 6 inches-long. Point Elies inside the square, forming the equilateral triangle 6ECD. B 6 A 6 6 c 6 D

Paper 55 · ACT June 2011 · Form 69F · Math Test

What is the area, in square inches, of square ABCD ?

Paper 55 · ACT June 2011 · Form 69F · Math Test

What is the measure of乙BCE?

Paper 55 · ACT June 2011 · Form 69F · Math Test

The entire figure is placed in the standard (x,y) coordinate plane such that the vertices ofthe square are A(6,6), B(0,6), C(0,0), and D(6,0). The x-coordinate of Eis 3. Which ofthe following is a line of symmetry for the figure?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Beverly is using a punch recipe that calls for 2 parts ginger·ale to 1 part fruit juice by volume. Beverly is planning to make 12 liters of this punch for a party. How many liters of fruit juice does Beverly need in order to make 12 liters of this punch? ACT-69F 18 GO ON TO THE NEXT PAGE. 2 lO�CT 微信号loviact 4c 1 24. What is the solution to the equation 7 - -;;- = －— . 25 5 2 2 独角兽在这里 DO YOUR FIGURING HERE. 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

Source question 24. Refer to the source image.

Paper 55 · ACT June 2011 · Form 69F · Math Test

For the line ·segment below, the ratio of the length of 石to the length of积了is 1:4. If it can be determined, what is the ratio of the length of AB to the length of 亢？ AB C

Paper 55 · ACT June 2011 · Form 69F · Math Test

The line with equation 8x + 3y = 5 is graphed in the standard (x,y) coordinate plane. What is the slope of this line? 3 8 3 8 8

Paper 55 · ACT June 2011 · Form 69F · Math Test

The Kingston High School multimedia room has 108 seats, which· are all arranged in rows. The number of seats in each row is 3 less than the number ofrows. How many rows ofseats are in the multimedia room? 10 28. If 90° < 0 < 180° and sin·e =�.then cos 0 =? 26' 10 26 24 10 ACT七9F 19 GO ON TO THE NEXT PAGE. 2 lOVACT 微信号loviact 独角兽在这里 2 DO YOUR FIGURING HERE. Use the following information to answer questions 29-32. The· table below gives the length and number of nails per pound for all types of nails available at Schulberg 's Hardware. A 2-penny nail, for example, is represented in the "N幻I type" column by the notation "2d." Nails bought at Schulberg's can be bought only in I-pound packages. Each package contains onli 1 type·of nail. Number of Nail (iLn e c n h g e t s h ) nails type per I pound 2d 1.00 876 3d 1.25 568 4d 1.50 316 5d 1.75 271 6d 2.00 181 7d 2.25 161 8d 2.50 106 9d 2.75 96 10d 3.00 69 12d 3.25 64 16d 3.50 49 20d 4.00 31 30d 4.50 24 40d 5.00 18

Paper 55 · ACT June 2011 · Form 69F · Math Test

Source question 28. Refer to the source image.

Paper 55 · ACT June 2011 · Form 69F · Math Test

For nails with lengths between 1.00 and 3.00 inches, which of the following expressions gives the length, in inches, of an n-penny nail?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Hadji bought l package of 4d nails and 2 packages of 5d nails. These were the only nails he bought. What is the total number of nails that Hadji bought?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Ty bought an equal number of 12d, 30d, and 40d nails. What is the minimum number of nails of each size that Ty could have bought? ACT-69F 20 (;O ON TO THE NEXT PAGE. 2 lO�CT 微信号 loviact 独角兽在这里

Paper 55 · ACT June 2011 · Form 69F · Math Test

A salesperson gave Miki the following advice to determine the size of nail to use: The length of a nail �hould be 3. tim<'!s the th_ickness_ of t�e. boar� bein� fastened to a wall. According to this advice, what nail size should Miki use to fasten a 1.5-inch-thickboard to a wall? DO YOUR FIGURING HERE. 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

In the standard (x,y) coordinate plane, the equation of a circle is x2 + y2 = 100. At what 2 points does the circle intersect the y-axis? (0, 10) and (0, -10) (0,· 20) and (0, -20) (0, 50) and (0, -50) (0, 100) and (0, -100) (0, 200) and (0, -200) ． ． ． ． ． A B C D E

Paper 55 · ACT June 2011 · Form 69F · Math Test

(-mp)(mp叩is equivalent to: p 36 p36 p 4o P 37 578 . 35. The fraction — is equivalent to the repeating decimal 999 0．邓．What is the 85th digit to the right of the decimal point?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Source question 35. Refer to the source image.

Paper 55 · ACT June 2011 · Form 69F · Math Test

A jar contains exactly 12 gumballs, each of which is a solid color. There are 5 blue and 7 white gumballs. Chris will draw one gumball at random and then, without replacement, will draw another gumball from the jar at random. Which of the following expressions gives the probability that Chris will draw 2 blue gumballs? 5 - 12 5 - 12 4 - 12 5 - 11 4 - 11 + . . . . 5 - 12 5 - 12 5 - 12 5 - 12 5 - 12 ACT-69F 21 GO ON TO THE NEXT PAGE. 2 IO�T 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

Jonah has 72 solid-colored disks that are either red, blue, or green. He lines them up on the floor and finds that there are 15 more red disks than green and 9 more green disks than blue. How many red disks does he have? DO YOUR FIGURING HERE.

Paper 55 · ACT June 2011 · Form 69F · Math Test

A contractor charges $1.75 per square foot to waterproof the top surface of a wooden deck. What would be the contractor's charge for waterproofing the top surface of the trapezoid-shaped wooden deck shown below? /_ \＼ft 24ft 14 ft

Paper 55 · ACT June 2011 · Form 69F · Math Test

In /:::,OBC shown in the st邱<lard (x,y) coordinate plane below, M is the midpoint of硕N is the midpoint of积，and Q is the midpoint of灰．Which of the following statementsis always true? y · 0(0,0) Q C(w,0) x 沉is -1. 啼is -1. 阮is 1. ACT-69F 22 GO ON TO THE NEXT PAGE. 21o�T 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

The junior class at Silverwood High School'sponsored a costume party. Each student wearing a costume paid $2 admission, and each student NOT wearing a costume paid $5 admission. An amount of $489 was collected from the 150 students who paid admission. How much of the amount was collected from students NOT wearing a costume? DO YOUR FIGURING HERE.

Paper 55 · ACT June 2011 · Form 69F · Math Test

Which of the following complex numbers is a sum of 西and灯？

Paper 55 · ACT June 2011 · Form 69F · Math Test

Point P lies on side双of rectangle ABCD as shown below. The measure of LABP is 67° and the length of 耘is 7.5 inches. Which of the following ex.pre_ssions is the length, ininches, of秤？ D P ? A

Paper 55 · ACT June 2011 · Form 69F · Math Test

For any circle with 2 se.cants drawn from P to the circle, as shown.in the figure below, the lengths of the segments of the secants are determined by a(a + b) =c(c + d). DO YOUR FIGURING HERE. In the figure below, A, B, D, and E are on the circle. Point B is on secant segment AC, and D is on secant segment窃．The lengths of AB, BC, and cJ5are given in meters. What is the length, in meters, of丽？ A 6 7 9 0 2 1 l A B C D E

Paper 55 · ACT June 2011 · Form 69F · Math Test

While lifting weights, a person sits on an incline weight bench and pushes the weights straight up, as shown in the figure below on the left. The weight bench is shown below on the right. The angle between the horizontal seat and the backrest is 110° . What is the measure of the angle between the backrest and the vertical path of the weights?

Paper 55 · ACT June 2011 · Form 69F · Math Test

In the standard (x,y) coordinate蝠 plane, the graph of y =x 2 is shifted 5 units down and 4 units right. Which of the following is an equation of the translated graph? 2 + 5 - 4 ACT-69F 24 GO ON TO THE NEXT PAGE. 2,o�CT 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

When Kaylee kicked.the winning soccer goal, she was 10 yards behind the midfield line and 5 yards from the sideline, as shown in the figure below. To the nearest yard, how far was Kaylee from the center of the goal line when she kicked the winning goal? | l00 yd | DO YOUR FIGURING HERE. 60 I I 勺oal line 1+midfield line d 、 一＿、？ 、..Kaylee 工5yd 10 yd 5 47. A sector of a circle has an area equal to -f,;- -of the area 12 of the circle. What is the measure of the sector's central angle?

Paper 55 · ACT June 2011 · Form 69F · Math Test

Source question 47. Refer to the source image.

Paper 55 · ACT June 2011 · Form 69F · Math Test

List B consists of all the integers -in List A below and also 3 integers 12, b, and c, where a� 17, b = c, and b � 42. What'is the median of the integers in List � ? List A: 12, 16, 17, 29, 29, 35, 41, 42, 47, 47, 50

Paper 55 · ACT June 2011 · Form 69F · Math Test

The solution set for the inequality I2x - aI � 3 is {x I 1 � x � 4}. What is the value of a? ACT-69F 25 GO ON TO THE NEXT PAGE. 210ACT 微信号 loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

Which of the following is the least common denominator for the expression below? 1 . 十 1 . 1 17 · 23· 612 . 172 · 23, 17 · 23 3 DO YOUR FIGURING HERE. ·235 • 612

Paper 55 · ACT June 2011 · Form 69F · Math Test

As shqwn in the figure below, the drill holes for Well A and WellB are 300 feet apar� on level ground. Well A is dug straight down and reaches oil at 2,000 feet Well B is dug straight down and reaches oil at 1,500 feet. What is the angle.of elevation from the point where Well A reaches oil to the point where WellB reaches oil? (Note: The figure is NOT drawn to scale.) WellB 300 ＼ 2，。。。 勹 00 乡：：：：:J.f..－一一一一一一一一一一一一一一一： ＇' 书） 一1行）

Paper 55 · ACT June 2011 · Form 69F · Math Test

Tables of values for the 2 functionsfand g are shown below. What is the value of g(f(5))? X f(x) 6 3 1 5 ＿ ＿ 8 6 5 3 6 5 1 3 8 - － ． ． ． E G H L K ACT-69F 26 GO ON TO THE NEXT PAGE. 2 lOVACT 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

In the figure below,凶CD is a right triangle, B lies on 亢，and the measures of乙DAC and LDBC are given. The length of顽is lO yards. What is the approximate length,in yards,of峦？ 7 1 7 7 l 3 4 13 15 24 ． ． ． ． ． A B C D E A B I--lO- － ？ － D c

Paper 55 · ACT June 2011 · Form 69F · Math Test

For positive integers a and b, an operation /J. . ca� be a . b defined by a !J. b == 7 + �. When the sum ofa and b is b . a 5 and the product of a and b is 6, what is the value of a !J. b? F 5 6 H 3 6

Paper 55 · ACT June 2011 · Form 69F · Math Test

Gi b iven the matrix equation shown below, what i� £.. ? a ［罚＋忙］ ＝［订 (Note: Whenever n is a positive integer,the notation n! represents the product of the integers from n to 1. For example, 3! = 3 • 2 • 1.) DO YOUR FIGURING HERE. 4 5 ACT-69F 27__ GO ON TO THE NEXT PAGE. 210ACT 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

Graphed in the standard (x,y) coordinate plane below is the soluti�n set for a system of 3 linear inequalities. For values of x and y that satisfy this system, what is the maximum value of 6x - 2y ? y DO YOUR FIGURING HERE. 2 0 2 4 2 l l l 2 ． ． ． E G H j k X

Paper 55 · ACT June 2011 · Form 69F · Math Test

The square base of a regular pyramid has a side length of 4 inches. Each of the other 4 faces of the pyramid is a triangle with a base of 4 inches and a height of 6 inches. The pyramid has a total surface area of 64 square inches. A second regular pyramid has a square base that is 4 inches by 4 inch�s, but its total surface area is double that of the first pyramid. What is the height, in inches, of each of the triangular faces of the second pyramid?

Paper 55 · ACT June 2011 · Form 69F · Math Test

As shown in the figure below, a triangle bas 2 sides each of length 5 feet and a 3rd side of le11gth x feet. The degree measure of the angle between the 2 sides that are 5 feet long is 0. In terms of x, cos 0 = ? (Note: For any triangle, if a, b, and c are the lengths of the sides opposite乙A,乙B, and LC, respectively, then a2 =炉＋c2 - 2bc cos LA.) 三 X 50 50 50 50 50 ACT-69F . 28 GO ON TO THE NEXT PAGE. 2,o�CT 微信号loviact 独角兽在这里 2

Paper 55 · ACT June 2011 · Form 69F · Math Test

Which of the following diagrams provides information that is sufficient to prove that 6.PQR and 6.STU, shown below, are congruent? p\)：二s R 乙P三乙S p � U LQ立T Q 二 二乙R立U T S R LP LS p � U LR 立T Q T 乙s 归嘉 R LP LS p t> u 卢 Q r 乙s妇画 R 乙p~4S p \:> u 冗垃 Q r二�s两顷 R LP 乙S pv u 陨兰 劝 Q � 称国 T S R

Paper 55 · ACT June 2011 · Form 69F · Math Test

What is the value of c if x + 2 is a factor of 2x3 + 2x2 - 2cx + 4 ? DO YOUR FIGURING HERE. END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. AC下69F 29