ACT Past Papers with Answers

Paper 48 · ACT April 2013 · Form 71G · Math Test

What value of x makes the equation 4(x-6) 16 true?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Ayita is helping her uncle center a large framed picture on his living room wall. As shown in the figure below, the rectangular wall is 30 feet long, and the rectangular framed picture is 5 feet high and 8 feet long. The left edge of the frame will be x feet from the left edge of the wall, and the right edge of the frame will be x feet from the right edge of the wall. What is the value of x ? F-8-1 30 ACT-71Q 14 GO ON TO THE NEXT PAGE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

The word average indicates arilhmetic mean. l. Harry is paid a regular hourly wage of $12.50 per hour for working up to and including 40 hours in I week. For each additional hour he works in a week, Harry is paid twice his regular hourly wage. Harry worked 46 hours this week. What is his pay for this week? (Note: Amounts are before taxes and benefits are deducted.) DO YOUR FIGURING HERE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

For nonzero values of x and y, which of the following expressions is equivalent to - 24x'¢ 4xy -6x'y -20Iy'

Paper 48 · ACT April 2013 · Form 71G · Math Test

Tristan has 5 pairs of shoes, 6 pairs of pants, and 5 shirts, which can be worn in any combination. He lleeds to choose a clothes combination to wear to the school dance. How many different combinations consisting of l of his 5 pairs of shoes. l of his 6 pairs of pants, and l of his 5 shirts are possible for Tristan to wear to the dance? 11 60

Paper 48 · ACT April 2013 · Form 71G · Math Test

In Arkansas in the twentieth century, the highest Iecorded temperature was 120°F and the lowest recorded temperature was -29°F. This highest recorded temperature was how many degrees Fahrenheit greater than this lowest recorded temperature? 75°F 91°F AGT-71G 15 GO ON TO THE NEXT PAGE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

A new operation, •. is defined on Pciifs of ordered PAirs of integer% as follows: (a,b) • (c.d) dL' + l)d -Ld' What IS Llie Value of (3,1) + (4.5) '? DO YOUR AGURING HERE. 17 17 17

Paper 48 · ACT April 2013 · Form 71G · Math Test

The function y= 2 I. 31 is graphed in the .standard (x,y) cooi'dinate pl￿]e below. One of ihe following graphs in the standard (x,y) conrdinate plane sliows the re.%uli of shifting the fLinction up 4 coordinate unit.s. Which grdph?

Paper 48 · ACT April 2013 · Form 71G · Math Test

5 42 52 27.5 ACT-71G 19 GO ON TO THE NEXT PAGE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

The average of 5numbers is 89. What is the 5th number if the first 4 of the numbers are 78. 92, 96, and94? DO YOUR FIGURING HERE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

A swimming pool in the shape of a right rectangular prism has length 12 feet and width 14 feet. The volume of water in the pool is 2,520 cubic feet. To the nearest foot, what is the depth of the water in the pool?

Paper 48 · ACT April 2013 · Form 71G · Math Test

At Hamburger Heaven, Corissa paid less than $15 for her order of x hamburgers and x bags of french fries. Each hamburger cost h dollars, and each bag of french fries cost f dollars. Which of the following expressions represents the amount of money, in dollars, that Corissa should have received back after she paid for her order with $15 ? (Note: There is no tax on food at Hamburger Heaven.)

Paper 48 · ACT April 2013 · Form 71G · Math Test

| 8(-6) + 3(2) | ? -48 48 IS. A large circle with radius R inches 18 shown in the figure below. 3 small nonoverlapping circles, each with radius r inches, are removed from the large circle. The sbaded region is the area of the large circle remaining after the 3 circle8 were removed. What is the area, in square inches, of the shaded region? ACT-71G 17 GO ON TO THE NEXT PAGE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

Source question 15. Refer to the source image.

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the figure below, lines l and m are parallel, line n is a transversal. and 3 angle measures are given in degrees. What is the value of x - DO YOUR FIGURING HERE. 50° -80 130

Paper 48 · ACT April 2013 · Form 71G · Math Test

Which of the following graphs shows the solution set for the inequality 3x - 5 > 7 ?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Given the function s(t) - 3t -42 what is s(-3) ? 12

Paper 48 · ACT April 2013 · Form 71G · Math Test

A circle with center C is shown below. Points W, X, Y, and Z lie on the circle. The measure of ZWCY is lOO°, the measure of ZXCZ is 80°, and the measure of ZWCZIS 150°. What is the measure of ZXCY ? ACT-71G 18 GO ON TO THE NEXT PAGE DO YOUR FIGURING HERE. Use the following information to answer questions 20-22. The iable below shows the number of pounds of sugar, flour, and butter required to make 500 of each of 3 types of cookies sold at Van Merl's Bakery. Let s repieseni ihe priLe of I pouiid of sugar, f ihe price of I pound of flour, and b the price ot" I pouiid of butler. All prices are in dollars. Pounds of sugar Pounds of flour Pounds of butter Type of cookie Snickerdoodle Chocolate cbip Oatmeal

Paper 48 · ACT April 2013 · Form 71G · Math Test

How many pounds of sugar are required to make 200 chocolate chip cookies?

Paper 48 · ACT April 2013 · Form 71G · Math Test

The bakery has 27 pounds of sugar, 24 pounds of flour, and 20pounds of butter in stock. What is the maximum number of oatmeal cookies the bakery can make from the ingredients in stock?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Which of the following expressions gives the price of the sugar, flour, and butter required to make 500 snickerdoodle cookies and 500 chocolate chip cookies? 13

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the (a,b) solution to the system of equations below, DO YOUR FIGURING HERE. 5a-3 2a+3b=5 19 15 25 21 25 18

Paper 48 · ACT April 2013 · Form 71G · Math Test

Send It Out mails advertisements for businesses. Two types of machines-stuffing machines and postage machines-are used to process envelopes. Each stuffing machine processes envelopes at the rate of 150 envelopes per minute, and each postage machine processes envelopes at the rate of 4 envelopes per second. Send It Out is currently using 24 stuffing machines. How many postage machines should be used so that the stuffing machines and the postage machines process the same number of envelopes in I minute ?

Paper 48 · ACT April 2013 · Form 71G · Math Test

What is the result of the subtraction problem below? (7x' +5) {-4x' + 6x + 3) 3k+6x+2 3k-6x+2 6x+2

Paper 48 · ACT April 2013 · Form 71G · Math Test

For what real number value of a is the equation x. true?

Paper 48 · ACT April 2013 · Form 71G · Math Test

The number 0.003 is 100 times what number? ACT-71G 20 GO ON TO THE NEXT PAGE DO YOUR FIGURING HERE. Use the following information to answer questions 28-30. Each of the 200 people in a random sample of the 2,500 people at the mall today was asked which. if any, of the following types of pets he or she owns: bird, cat, dog. or fish. All 200 people answered the question. The answers were tallied, aiid the exact percents of peop.le who own the pets are shown in the diagram below. cai 510 Iolo dog 15Yo fish 45fo loo OQ/o bird 5%

Paper 48 · ACT April 2013 · Form 71G · Math Test

Because this was a random sample, the percents in the sample are the most likely estimates for the corresponding percents among all the people at the mall today. What estimate does this give for the number of people at the tnall today who Owll dogs but none of the other 3 types of pets?

Paper 48 · ACT April 2013 · Form 71G · Math Test

What percent of the people in the random sample own exactly I type of the 4 types of pets?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Suppose 25 additional people at Tandom weIe asked the question, with the following answers: 15 own fish only, 5 own a cat and a dog only, and 5 own a cat, a dog. and a bird only. Among all 225 people asked, what fraction own fish but none of the other 3 types of pets ? 105 225 105 215 105 200 115 225 115 200 ACT.71G 21 GO ON TO THE NEXT PAGE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

Triangle AABC and collinear points A, C, and D are shown in the figure below. The measure of ZA is 43°, the measure of ZBCA is (4y)°, and the measure of £BCD is (Ily).. What is the measure of ZB ? DO YOUR FIGURING HERE. 43° 12° {4y)° (Ily).

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the standard (x,y) coordinate plane, what are the coordinates of the center of the circle with equation If5)'+(y-l)'_l? (-W5, (-f5. -I,-C5)

Paper 48 · ACT April 2013 · Form 71G · Math Test

Anoki wants to determine the height of a vertical lighthouse, shown below. He measures the angle of elevation to the top of the lighthouse at a point 103 feet along level ground from ihe centei. of the base of the lighttiouse. The angle of elevalion is 31° Which of the following expressions gives the best approximation of the height of the lighthouse. in feet? 11 31° 103 cos 31° 103 tan 31° 103

Paper 48 · ACT April 2013 · Form 71G · Math Test

When graphed in the standard (x,y) coordinate plane. the graph of one of the following linear equations is a line parallel to the x-axis. Which one? 4y ACT-71G GO ON TO THE NEXT PAGI

Paper 48 · ACT April 2013 · Form 71G · Math Test

Lei Ir + 3y= L2 be an eqiiaiion of line l in the standard (.I,y) coordinate plane. Line p has a slope thai is 2 times Lhe slope of l aiid has a y-intercept tliat i,s 3 less than Ihe ):_intcrcepi of l. Line p has which of the followin¥LV eqiialions? DO YOUR FIGURING HERE. 10

Paper 48 · ACT April 2013 · Form 71G · Math Test

The graph of y tan x is shown in the standard (x,y) coordinate plane below. What is the period of tan x ? 32[ I 27[ I

Paper 48 · ACT April 2013 · Form 71G · Math Test

In a certain rectangle, the ratio of the lengths of 2 adjacent sides is 5 to 2. If ihe area of the rectangle is 90 square inche8, what is the length. in inches. of the longer side?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Josey rode her bicycle 4 km at a constant speed, beginning and ending at her home. A graph. with distance traveled plotted along the y-axis and elapsed time during the ride pIotted along the x-axis. was con.structed for the values of y from O kin through 4 km. The shape ol the graph can best be described as a: circle. vertlcal line segment. ACT-71G 23 GO ON TO THE NEXT PAGE. www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

What is the area. in square inches, of the figure below? DO YOUR FIGURING HERE. 16 16 16

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the standard (x,y) coordinate plane. P(-3,-1) will be reflected over the y-axis. What will be the coordinates of the image of P ?

Paper 48 · ACT April 2013 · Form 71G · Math Test

One of the following graphs in the standard (x.y) coordinate plane is the graph of y > (u + b for some positive a and negative b. Which graph? ACT-71Q 24 GO ON TO THE NEXT PAGI www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

If 2Y-y .r+y then DO YOUR FIGURING HERE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

Shown below are similar triangle5 ZXABC and ￿DEF with ZA = ID and ZB= ZE. The given lengths are in inches. What is the length, in inches, of EF ?

Paper 48 · ACT April 2013 · Form 71G · Math Test

A person's body mass index, BMI, varies directly as the person's weight in kilograms and inversely as the square of the person's height in meters. If k represenis the constant of variation. which of the following expressions represents the BMI of a person who weighs w kilograms and is h meters tall? kh, ACT-71G 25 GO ON TO THE NEXT PAGE. www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the circle shown below, radius AC is 15 inches long, chord BE 1.8 10 inches long. and AC is perpendicular to BE at D. How many inches long is AD ? DO YOUR FIGURING HERE. 5W5

Paper 48 · ACT April 2013 · Form 71G · Math Test

A pyramid composed of 4 congruent triangular sides and a square base is shown "unfolded" in the standard (x.y) coordinate plane below. Points A, B, and C are vertices of l of the triangular sides. What is the total surface area, in square coordinate units. of the pyramid? C(7,23) A(2,11) B(12,11)

Paper 48 · ACT April 2013 · Form 71G · Math Test

The side length8 of the flat. Irape7.oidal ceiling of a bedroom are given in the figure below. Marie will paint the entire ceiling with I coat of paint. using paint that has a Price of $8 per quart and is sold only by the full quart. Each quart of paint covers an area of 90 square feet with I coat of paint. What is the total price of the paint that Marie needs to buy. 12 feet 16 feet 20 feet 24 feet ACT-71G 26 GO ON TO THE NEXT PAGE www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the figure below. F lies on EG, and the measure of ZE is (3a)° Which of the following inequalities is true? DO YOUR FIGURING HERE. (3a)° O<a< 30

Paper 48 · ACT April 2013 · Form 71G · Math Test

Each contestant at a math competition starts with 30 points. A contestant earns Iopoints for each question answered correctly and loses 5 points for each question answered incorrectly. Sammi answered twice as many questions correctly as incorrectly, finishing with 150 points. How many questions did Sammi answer correctly .

Paper 48 · ACT April 2013 · Form 71G · Math Test

In the standard (x,y) coordinate plane, when a * O and b * O, the graph of f(x)= 2x+b x+a has a horizontal asymptote at:

Paper 48 · ACT April 2013 · Form 71G · Math Test

On the real number line, -0.423 is between (n+l) 100 ICMJ and for some integer n. What is the value of n ? -423 -43 -42 ACT-71G 27 GO ON TO THE NEXT PAGE. www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

Tlie steni-and-leuf plot beloiv shows the iiumber of daily credit card sales at Fancy Fl& brics during a 34-d1c y period. Wliat is the niedian number of daily credii card sales.? DO YOUR FIGURING HERE. Stem Leaf 122468 22335578 001357999 0244556 2667

Paper 48 · ACT April 2013 · Form 71G · Math Test

Angle A has a measure of radians. Angle A and Angle B are coterniinal. Angle B could have which of the following measures? 2. 14°

Paper 48 · ACT April 2013 · Form 71G · Math Test

Which of the following coniplex numbers equals (6- 7i)(ff + 61) 9

Paper 48 · ACT April 2013 · Form 71G · Math Test

If x - 4 is one solution to the equation x then the other solution is: 12=0,

Paper 48 · ACT April 2013 · Form 71G · Math Test

For all x such that tan x * O. the expression is equivalent to which of the following. sinx osx secx'sin.¥ (Note: sec x - tanx= cosx cosx secx secx'tanx ACT.71G GO ON TO THE NEXT PAGI www. actmi. net

Paper 48 · ACT April 2013 · Form 71G · Math Test

All quadrilaterals in one of the following categories have diagonals that are congruent. Which category . . Rectangle (4 right angles) DO YOUR FIGURING HERE.

Paper 48 · ACT April 2013 · Form 71G · Math Test

Three line segments are graphed in the standard (x,y) coordinate plane below. Line segment AB has endpoints A(2,0) and B(4,0). A'ff is the image of AB after a rotation counterclockwise ()) by 120° about the origin, and A'B" is A'B, projected onto the x-axis. What is the length, in coordinate units, of A'B" ?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Consecutive terms of a certain arithmetic sequence have a positive common difference. The sum of the first 3 terms of the sequence is 120. Which of the following values CANNOT be the first term of the arithmetic sequence?

Paper 48 · ACT April 2013 · Form 71G · Math Test

Given f(x)-￿X+2, which of the following expressions is equal to f- (x) for all real numbers x ? x+2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-71G 29 www. actmi. net