ACT Past Papers with Answers

The sum of the measures of the interior angles of a convex polygon with t sides is 180(t 2) degrees. What is the sum of the measures of the interior angles of a convex polygon with 10 sides? 900° ACT-805 14 GO ON TO THE NEXT PAGE.

In the standard (x,y) coordinate plane, point A has coordinates (-8,-3). Point A is translated 8 units to the right and 3 units up, and that image is labeled A,. What are the coordinates of A, ? DO YOUR FIGURING HERE.

096

The expTession io is equivalent to: 24

Source question 8. Refer to the source image.

5 19.5 29.5 39.5 49.5 59.5 69.5 79.5 estimated age (years)

2 x 10 20

What is the Ieast common denominator of the fractions 21, 24 16 112 336 504 ACT-B05 16 GO ON TO THE NEXT PAGE.

In the standard (x,y) coordinate plane, what is the slope of the line through (-7,3) and (2,4) ? DO YOUR FIGURING HERE.

A group of 60 students and 4 sponsors took a field trip to a local museutn. For their first guided tour, students were given a choice of l of 3 art exhibits. Of the 60 students, chose American Folk, chose Western. Each student that expressed a choice chose exactly l exhibit. The remaining students expressed no choice. How many of the students expressed no choice? chose Modern, and

What is the greatest integer solution to 6x- 2 < 11.2 ?

In the figure below, B lies on AC, E lies on DF, AC11 DF, ZXEBF is isosceles with BE- BF, and ZCBF measures 32°. What is the measure of ZBED ? 132° 32°

If x= _l and y = 2, what is the value of 2xy-4xy +8? 13 l9 23 27

Line l is shown in the standard (x,y) coordinate plane below. Alicia drew line p with a slope that is of the slope of line l and with a y-intercept that is 3 times the y-intercept of line l. One of the following equations represents line p. Which one? DO YOUR FIGURING HERE. x+3 -3x.+ I 3x+l

One angle measure and 2 side lengths, in inches,. are given in the right scalene triangle below. In terms of a and b, what is sin g ?

If f(x) - 5x'_ 6x + l and g(x) = 2, which of the following expressions represents (fg)(x) ? 26x' + 33 20x 6x+21 9x +12x- 60x + 46x 12x-I ACT-BOS 19 GO ON TO THE NEXT PAGE.

Megan and Louisa are side-by-side (at point A in the figure shown below) when they begin to run at the same time clockwise (¢) around a small circular track. Megan runs at a rate of 40 seconds per lap, while Louisa runs at a rate of 70 seconds per lap. Which of the following figures best represents Megan's and Louisa's locations 120 seconds after they begin to run? Louisa Louis& Megan +-Megan Louisa Louisa Louisa

The statement 3x - (x + 6) + 8 - 2x + 14 is true for: O only. 4 only. 7 only. all values of x. no values of x. ACT-805 20 GO ON TO THE NEXT PAGE.

The first 7 terms in an arithmetic sequence are listed below. What is the difference between the mean and the median of the 7 terms? DO YOUR FIGURING HERE.

Which of the following expressions represents the sum of 3.8 x 10 and 6.4 x IO, in scientific notation? 10

Lian has 6- yards of ribbon she will use to make bows. She will use yard of ribbon to tnake each bow. After Lian has made all the bows possible with the ribbon. what length of ribbon. in yards, will NOT have been used to make bows? ' 21 32 ACT-B05 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 32-34. Carl purchased a new car. The fuel economy window sticker on the new car contained the information shown below. In this figure, MPG is miles per gallon. EPA .'Fuel EcoDOiny Fuel Economy MPG You save $3,500* 25 in fuel costs ovei. 5 years compared to the average new vehicle. 22 32 combined citylhighway city highw2y *Cost estimates are based on the combined city/highway JVIPG, a certain number of Miles per ye the car is driven, and an average fuel cost of $4.00 per gallon. Annual fuel cost $2,400*.

A certain race car has a maximum speed of 240 Miles per hour. Which of the following is an expression for this maximum speed in feet per second? (Note.. l rnile = 5,280 feet) 240(5,280) 36,000 240(3,600) 5,280 240(5,280) 3,6(K) 60(5,280) 240 240(5,280) 360 DO YOUR FIGURING HERE.

What are all and only the values of x that are NOT in the domain of the function f(x) = (x-7)(x+2) (x+6)(x-8) -8and6 -6and8 -2and7 -8, -7, 2, and 6 AGT-B05 23 GO ON TO THE NEXT PAGE.

In LDEF. the length of DE is 60 cm, and the length of EF is 6 cm. If it can be determined, what is the length, in centimeters. of DF ? 60 66 96

Let a and b represent real numbers with the property b- I l > O. Which of the following statements about a and b CANNOT be true? b<1 a<landb>O a<landb=

Juwan has 150 cm of wire. For a craft project, he uses all the wire to make I circle with a radius of 5 cm and I square. To the nearest O. I cm, what is the side length of the square?

To the nearest 1 (70, the recycling center's payment to a customer for a bottle is what percent of the resale price of a bottle sold to XYZ Inc. ? 810 5610 80CYo

In I shipment, the recycling center soId a total of 2,700 cans and bottles to XYZ Inc. for $441.00. How many bottles were in the shipment? 1,470 ACT-B05 25 GO ON TO THE NEXT PAGE.

Given constants c, d, m, and n such that x + mx + c has factors of (x + 2) and (x + 4) and x + nx + d has factors of (x + 3) and (x + 7), what is mn ? 16 18 DO YOUR FIGURING HERE.

For every angle O, measured in radians, which of the following is equal to sill(2￿ + O) ? sin(-7t + O) sin(8) sin sin 27[

A small circle and a large circle are tangent at T, as shown in the figure below. The center. O, of the Iarge circle lies on the small circle. The diameter of the large circle is 12 cm. Wh¥lt is the ratio of the area of the small circle to the area of the large ciicle? 12

For all positive values of a and b. which of the following expressions is equal to 2a+b b+2a 2a+b 2ab 4a+b 2ab 2ab 2a+b ACT-B05 26 GO ON TO THE NEXT PAGE.

The vector i represents I mile per hour east, and the vector j represents l rnile per hour north. According to her GPS, at a particular instant, Tia is biking 30° west of north at 16 miles per hour. One of the following vectors represents Tia's velocity, in miles per hour, at that instant. Which one? DO YOUR FIGURING HERE. -81 + 8￿3J 81 + 8￿3J 8j 8W3i + 8j

Let (f. g){x)-￿x+ 1 - 2 and g(x)-x+ l. Which of the following expressions defines (g °f)(x) ?

Consider sets A, B. C, and D such that B is a subset of A, C is a subset of B, and D is a subset of C. Whenever x is an element of B, x must be an element of:

For all positive values of x. which of the following expressions is equivalent to ACT-B05 27 GO ON TO THE NEXT PAGE.

A company sells ice cream in 2-quart containers for $3.00 per container. The company also sells ice cream in 1.5-quart containers for $2.50 per container. What is the ratio of the price per quart for the 2-quart container to the price per quart for the 1.5-quart container? DO YOUR FIGURING HERE. io 10

Each of 100 distinct playing cards is l of 5 solid colors and is numbered with l integer. There are 20 each of blue, red, yellow, green, and orange cards numbered 1-20. One of the 100 cards will be selected at random. What is the probability that the selected card will be blue OR numbered 17 ? 100 17 100 20 100 24 100 25 100

Four golfers will be randomly split into 2 groups of 2 for a tournament. If Jill and Ramona are among the 4, what is the probability that they will be paired together? 12 ACT-BOS 28 GO ON TO THE NEXT PAGE.

Jed is standing 10 meters from a maple tree that is 14 meters from a willow tree, as shown in the figure below, in which the measure of an angle is given. Which of the following equations, when solved for x, gives the distance, x Tneters, between Jed and the willow tree? DO YOUR FIGURING HERE. (Note: For a triangIe with sides of length a, b, and c that are opposite angles ZA, ZB, and 2C, respectively, a +b-2abcos£C.) willow tree 34° 14 maple tree 10 Jed x, + 14, _ 2x(14)(cos 34°) x, + 14, 2(10)(14)(cos 34°) 10, + 14, 2x(14)(cos 34°) 10, + 14, 2(10)(14)(cos 34°)

Suppose the equations (x-4)'+ (y- 3), 4 and (x-4)' (y- 10), 16 are graphed in the same standard (x,y) coordinate plane. How many points of intersection do these graphs share? END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-B05 29