ACT Past Papers with Answers

Paper 86 · ACT January 2001 · Form 56B · Math Test

Disregarding sales tax, how much will you save when you buy an $11 c9mpact disc that is on sale for 25% oft? \

Paper 86 · ACT January 2001 · Form 56B · Math Test

As part of a school project, Akio wants to find the average cost of renting a newly released videotape from video rental stores in his neighborhood. He surveys 4 stores and finds the cost of renting a newly released v,tdeotape from the 4 stores to be $3.50, $3.40, $3.50, and $3.00, respectively. Using this data, what is the average cost of renting a newly released videotape from these 4 stores? E; $3.50

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the figure below， 政了is parallel to历f with X on双？ and Bon厉． AlsoAB三 Jic, and the measure of LXABis 110° . What is the measure of乙ACB? DO YOUR FIGURING HERE. o o o o o 5 0 5 0 0 3 4 5 7 1 1 ． ． ． E G H J K 二 . E ACT-56B-SAMPLE 14 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2 S. Regular hexagon ABCDEF is inscribed in a circle, as shown below. If the length of radius ol5 is 15 centi­ meters, how long is刀l, in centimeters? DO YOUR FIGURING HERE. 6 F c 6. The price of a pumpkin is directly proportional to its weight. If a pumpkin that weighs 15.0 pounds costs $3.25, how much will an 11.4-pound pumpkin cost?

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 5. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 6. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the figure below, D is a point on AB, and CD is perpendicular to戏． Based on this information, which ofthe following is the best conclusion? I . ｀ ＼ A D B

Paper 86 · ACT January 2001 · Form 56B · Math Test

If 3x- 7 = 4x- 16, then x = ? 7 23 _ 7 9

Paper 86 · ACT January 2001 · Form 56B · Math Test

Which of the following is always equal to a(5- a)- 6(a + 4) ? - a- 24 - a + 4 - 24 ACT-5613-SAMPLE 15 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

One marble is drawn at random from a bag containing 3 red, 2 blue, and 4 green marbles. What is the proba­ bility that the marble drawn is NOT blue? DO YOUR FIGURING HERE. ， `.' 2 9 9 24 81

Paper 86 · ACT January 2001 · Form 56B · Math Test

Wanda prngrams her calculator to perform a linear function, but she doesn't tell you what that function is. When n = 6, the value of the function is 2. When n = 12, the value is 4. Which of the following expres­ sions explains what the calculator will display when any number, n, is entered? 3 ｀ 、． ＇ ＼

Paper 86 · ACT January 2001 · Form 56B · Math Test

On the line segment belov.:, the ratio of lengths XY to YZis 1:3. What is the ratid'bf XY to XZ? X y z

Paper 86 · ACT January 2001 · Form 56B · Math Test

If a board 7 feet IO inches long is cut into 2 equal parts, as shown below, what will be the length, to the nearest inch, of each part? |

Paper 86 · ACT January 2001 · Form 56B · Math Test

The speed of one train exceeds twice the speed of another by 30 mph. If r mph is the speed of the slower train, which of the following expresses the speed, in miles per hour, of the faster train? ACT-568-SAMPLE 16 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

The circle shown below has a radius of10 meters, and the length of chord秝is 16 meters. If O marks the center of the circle, what is the length of灰';? DO YOUR FIGURING HERE. A B C D E 2迈 6 12 4V可 36 3 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

What is the value of the expression x" - 2x" + 4x + 4 for X = -2? 1

Paper 86 · ACT January 2001 · Form 56B · Math Test

What is the next term after -+ in the geometric 4 sequence 16 1 , -4, 1,－一 ．？ 4' ＼ ｀ l _ 8 O l - 16 l _ 8 1 - 2 1

Paper 86 · ACT January 2001 · Form 56B · Math Test

On the blueprint for Betty's house, -} inch represents 4 an actual length of 1 foot. What is the area, in square feet, of Betty's rectangular bedroom, which I 2¾ inches by 3 inches on the blueprint? 2 is E G H j k 0 4 0 0 4 3 4 6 2 4 1 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

Ifa > 0 and b < 0, then the sum of a and b: ACT-56B•SAMPLE 17 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 3 1 2O. Ifx+ －＝ — thenx=? 4 28' DO YOUR FIGURING HERE. 14 21 16 7

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 20. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

y.'hat_is the slope of the line given by the equation 3x+5y=-l5? B 5 ． －了 5

Paper 86 · ACT January 2001 · Form 56B · Math Test

T_he、 length of a s记e of a square is represented as (2x- 3) inches. Whi;h of the followmg general expres­ �io!ls :epresents the· area of the sq-uare, in square inches? 2 - 12x+ 6 - 6x+9 - 9

Paper 86 · ACT January 2001 · Form 56B · Math Test

\Yhich of the following is a polynomial factor of x2 -2x - 15?

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the equation m= 3 l+q —, q represents a positive integer. As q gets larger and larger without bound, the value of m: 2 ACT-56B-SAMPLE 18 GO ON TO THE NEXT PAGE. T 院 c IA 孛 v eo } 2 微信号 loviact

Paper 86 · ACT January 2001 · Form 56B · Math Test

The book Fahrenheit 451 by Ray Bradbury is about a society in which all books are banned and burned. The title of the book gives the approximate temperature at which paper starts to burn. Since Fahrenheit, F, and Celsius, C, temperatures are related by the formula 5 C =1,(F - 32), which of the following would make an 9 equivalent title for the book?

Paper 86 · ACT January 2001 · Form 56B · Math Test

The length of a rectangle is 6 inches longer than the width. If the perimeter of the rectangle is 48 inches, what is the width, in inches? 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

What are all the solutions for x if 2x" - 3x - 20 =0 ? \ 5 2 5 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

In TereU:s history class, all tests count equally. So far, Terell ha 、 s taken ·2 of the 3 tests in history and earned scores of 93% and 82%, respectively. What is the min­ imum percent Terell needs on the third test to have a test average of at least 85% ? 独角兽在这里

Paper 86 · ACT January 2001 · Form 56B · Math Test

If a, b, and c are positive integers such that ab = x and cb =y, then xy =? 2 DO YOUR FIGURING HERE. 2 ACT-56B-SAMPLE 19 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

What is the area, in square inches, of a circle with a diameter equal to 10 inches? DO YOUR FIGURING HERE.

Paper 86 · ACT January 2001 · Form 56B · Math Test

To get a driver's license, an applicant must pass a written test and a driving test. Past records show that 80% of the applicants pass the written test and 60% of those who have passed the written test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants would you expect to get driver's licenses? 4 32. If sinA = 7, then which of the following could be 5 tanA? F I 4 G 3 4 3

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 32. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

If x is any number other than 4 and 5, · then (4-x)(x-5) (x-4)(x-5) =?

Paper 86 · ACT January 2001 · Form 56B · Math Test

V'SO+ V飞还＝ ？ ACT-568-SAMPLE 20 GO ON TO THE NEXT PAGE. 2 eoVIACT 才立 惶 学 陕 微信号loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

Triangle.6.ABC is similar to.6.DEF. AB is 8 inches long,积 ． is 10 inches long, and AC is 16 inches long. If the longest side of.6.DEFis 40 inches long, what is the perimeter, in inches, of.6.DEF? :C. 90

Paper 86 · ACT January 2001 · Form 56B · Math Test

Sides AB, BC, CD,和d DA of square ABCD have mid­ points L, M, N, and K, as shown below. If 戏IS 6 inches long, what is the area, in square inches, of the shaded region? B K D N M c

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the figure below,了 is a diameter of the circle, B is a point on the circle:',�nd戏三质． What is the degree measure of乙ABC ? DO YOUR FIGURING HERE. B A c

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the standard (x,y) coordinate plane, what are the coordinates of the midpoint of a line segment with endpoints (-1,3)and (2,7)? ACT-566-SAMPLE 21 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

In a downhill ski race, Margo posted a time of 2 min­ utes and 24 seconds for a course 1.2 miles long. About how many miles per hour did she average for the race? DO YOUR FIGURING HERE.

Paper 86 · ACT January 2001 · Form 56B · Math Test

For the 2 functions f(x) and g(x), tables of values are shown below. What is the value of g(f(3))? E G H j k 5 3 1 2 7 - － －

Paper 86 · ACT January 2001 · Form 56B · Math Test

For positive real numbers x, y, and z, which of the ' I 2 5 following expressions'is equivalent to x'y,z0 ? 习了 5 立 儒 严 灼 寸飞亨

Paper 86 · ACT January 2001 · Form 56B · Math Test

A formula for the area of a rhombus is A = � 1 d心， where d1 and d2 are the lengths of the diagonals. Which of the following is an expression for d2 ? ） d 丛 － dl A 一矶 Adl _2 邓 dl ACT-56B-SAMPLE 22 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

The line graphed below shows the predicted gasoline use for a certain car. Which of the following is the closest estimate of this car's predicted rate of gasoline use, in miles per gallon? DO YOUR FIGURING HERE. 20 15 gallons 10 . . . . . A B C D E 8 0 3 5 0 2 3 3 3 4 5 。 100 200 300 400 500 600 700 800 miles

Paper 86 · ACT January 2001 · Form 56B · Math Test

The graph of y � ax2 + bx + c in the standard (x,y) coordinate plane is shown below. y X When y = 0, which of the following best describes the solution set forx ? .

Paper 86 · ACT January 2001 · Form 56B · Math Test

If IyI =)'.+ 6, then y = ? 2 46. What fraction lies exactlyhalfway between -;'- and—? 3 3 4 3 一 5 5 - 6 7 - 12 9 - 16 旦 24 ACT-56B-SAMPLE 23 GO ON TO THE NEXT PAGE. 2 竺吟气 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 46. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

Elliott writes a check for $15. He records the check in his check register, which up to this time has shown the correct balance. When figuring his new balance, he accidentally adds $15 instead of subtracting. The bal­ ance in his check register now shows: DO YOUR FIGURING HERE.

Paper 86 · ACT January 2001 · Form 56B · Math Test

Six plants, each of a different plant type, are to be arranged on a display shelf's 6 spots. If each spot must have a plant, in how many diffeient arrangements can the plants be placed?

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the standard (x,y) coordinate plane, what is the distancebetween the points (3,-4) and (-5,2) ? \、` ｀ •

Paper 86 · ACT January 2001 · Form 56B · Math Test

A formula for the volume, V, of a right circular cylinder is V=1t户h, wher� r is the radius and h is the height. The cylindrical tank shown below has radius 5 meters and height 4 meters and is filled with V:ater. 4 If 1 cubic meter of water weighs approximately 2,205 pounds, then the weight, in pounds, of the water in the tankis:

Paper 86 · ACT January 2001 · Form 56B · Math Test

What are the values of0, between 0° and 360° , when tan0=-l ? and 315° only and 315° only and 225° only and 135° only , 135° , 225° , and 315° ACT-56B-SAMPLE 24 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

Which of the following is an equation of a circle with its center at (3,4) and tangent to the x-axis in the stan­ <lard(x,y) coordinate plane? 2 + (y-4) 2 =16 2 +(y-3) 2 =16 2 + (y-3) 2 = 9 2 +(y-4) 2 = 9 +(y+3) 2 =16

Paper 86 · ACT January 2001 · Form 56B · Math Test

Which of the following best represents the graph of y $ax+b for some positiv�a and negative b? DO YOUR FIGURING HERE. y y x B y ·X C . y X y X 4 、 ＼｀ \ ` X

Paper 86 · ACT January 2001 · Form 56B · Math Test

One of the graphs below is that of y =A sin0 for 0 between O and 6.28 radians, w..here A is a constant. Which graph? E y 3 2 1 1 2 3 - － l y , 4 3 2 1 一了巨X －：归 ·OJ23456x ACT-568-SAMPLE 25 GO ON TO THE NEXT PAGE. 2�叩气 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the figure below, D, E,. and Fare the midpoints of the sides AB, BC, and AC, respectively. If the measure of LBCA is 20° , and the measure of LBAC is 60° , what is the sum of the measures of LDFE and LFED? B DO YOUR FIGURING Hl:RE. 0 0 0 0 0 60 80 00 20 60 l l l . . . . . A B C D E c

Paper 86 · ACT January 2001 · Form 56B · Math Test

A formula for the surface area (A) of the rectangular solidshown below is·A = 2/w + 2lh + 2wh where l rep­ resents length; w, width; and h, height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor? ＼ h w 2 4 6 8 2 1 ． ． ． E G H l k 迈 1 57. If sinx = — and cos x =-�.then sec x =? 2 2' 2 一 迈 ACT-56B-SAMPLE 26 GO ON TO THE NEXT PAGE. 2 eOVIACT 拉 馆 学 院 微信号 loviact 独角兽在这里 2

Paper 86 · ACT January 2001 · Form 56B · Math Test

Source question 57. Refer to the source image.

Paper 86 · ACT January 2001 · Form 56B · Math Test

In a rhombus, all 4 sides are the same length. Rhombus ABCD below has vertices at A(0,0) and C(4,6). What is the slope of diagonal励？ y C(4,6) 2 3 3 亿，0) 2 ► x DO YOUR FIGURING HERE.

Paper 86 · ACT January 2001 · Form 56B · Math Test

Yvette earned a score of 56 on a recent 25-question multiple-choice exam. The scoring for the exam was +6 for each correct answer, -2 for each incorrect answer, and O for each unanswered question. What is the maximum number of questions Yvette could have answered correctly?

Paper 86 · ACT January 2001 · Form 56B · Math Test

In the standard (x,y) coordinate plane, the graphs ofthe 3 equations x - 1 = 0, y + 2 = 0, and x + y = 4 form the boundary of a triangle. What is the area of this triangle,·expressed in square coordinate units? 2 2 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-56B-SAMPLE 27