ACT Past Papers with Answers

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The vertices of a Tectangle are (-L,-2), (4,-2). (4,3), and (-1,3). When the rectangle is graphed in the standard (x,y) coordinate plane below, what percent of the total area of the rectangle lies in Quadrant III ? DO YOUR FIGURING HERE. 8¥0

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A bag contains 10 pieces of flavored candy: 4 lemon, 3 strawberry, 2 grape, and I cherry. One piece of candy will be randomly picked from the bag. What is the probability the candy picked is NOT grape flavored? GO ON TO THE NEXT PAGE. The ONLY Official Prep Guide from the Makers of the ACT 55 OVIACT loviact The Official ACT Prep Guide When points A and B(-3,4) are graphed in the standard (x,y) coorth'nate plane below. the midpoint of AB will be (1,2). What will be the coordinates of point A ? DO YOUR FIGURING HERE. -*--*..*-.+-.+-. -*--*--+--+---F-.

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Which of the following equations gives the relationship between the Price in dollars, c, and the number of candies, n, in a box of candies at Cartie's Chocolate Shop.

Which of the following is a solution to the equation /-36x-O? DO YOUR FIGURING HERE.

In the figure below, vertices D and F of ADEF lie on CG, the measure of ZCDE is 148°, and the measure of ZEFG is 140°. What is the ￿easure of ZDEF ? 148° 140° 108°

The function f is defined as f(x) - _4x f(-4) ? -320 -192 16 192 320 4/. What is

Which of the following (x.y) pairs is the solution for the system of equations x + 2y - 4 and -2x + y = 7 ?

Which of the following is a value of x that satisfies log.36=2? GO ON TO THE NEKf PAGE. 58 The ONLY Official Prep Guide from the Makers of the ACT, OVIACT loviact Taking and Scoring Your First ACT PracticeTest

A 5-inch-by-7-inch photograph was cut to fit exactly into a 4-inch-by-6-inch frame. What is the area, in square inches, of the part of the photograph that was cut off? DO YOUR FIGURING HERE.

If x and y are positive integers such that the greatest common factor of x y and Jy is 45, then which of the following could y equal?

One caution sign flashes every 4 seconds. and another caution sign flashes every 10 seconds. At a certain instant. the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same GO ON TO THE NEXT PAGE. The ONLY Off icial Prep Guide from Ihe Makers of the ACT 59 OVIACT loviact The Official ACT Prep Guide

For all nonzero values of a ahd b, the value 'of which of the following expressions is always negative? DO YOUR FIGURING HERE. lal + Ibl

Graphed in the same standard (x,y) coordinate plane are a circle and a par&bola. The circle has radius 3 and center (0,0). The parabola has vertex (-3,-2), has a vertical axis of symmety, and passes through (-2,-1). The circle and the parabola intersect at how many points?

Which of the following inequalities is equivalent to -2x-6y>2y-4? x<-4y+2 x>-4y+2 x< 2y+2 x< 4y+2 x> 4y+2 GO ON TO THE NEXT PAGE. 60 The ONLY Official Prep Gulde from the Makers of the ACT .OVIACT loviact Taking and Scoring Your First ACT PracticeTest

For an angle with measure (X in a right triangle, sin (x- 40 and tan CK - What is the value of DO YOUR FIGURING HERE. 41 cos(z? 41 41 1,519 3,281

The perimeter of rectangle ABCD is 96 cm. The Tatio of the side lengths AB:BC is 3.5. What is the length, in centimeters, of AB ?

For AABC shown below, base AC has a length of 16 inches and altitude BD has a length of 8 inches. The area of a certain square is equal to the area of LABC. What is the length, in inches, of a side of the square? 16in GO ON TO THE NEXT PAGE. The ONLY Official Prep Guide from the Makers of Ihe ACT 61 ...OVIACT loviact The Official ACT Prep Guide DO YOUR FIGURING HERE. Use the following information to answer questions 33-36. In the figure shown below, ABCD is a rectangle, EFGH is a square. and CD is the diameter of a semicircle. Point K is the midpoint of CD. Point J is the midpoint of both AB and EF. Points E and F lie on AB. The 3 given lengths are in meters. 10 E J F 12

What is the lcngtb, in meters, of JD ? 13

What is the length, in meteis, of arc CD ?

The figuTe will be placed in the standard (x,y) coordinate plane so that K is at the origin, AB is parallel to the x-axis, and I meter equals I COOTdinate unit. Which of the following values could be tbe y-coordinate of H ? GO ON TO THE NEXT PAGE. 62 The ONLY Official Pr8p Guide from the Makers of the ACT .OVIACT loviact Taking and Scoring Your First ACT Practlce Test

What is the length, in coordinate units, of the ￿tItude from C to AB in ￿ABc shown in the standard (x,y) coordinate plane below? DO YOUR FIGURING HERE. C(2,4) A(I,l) B(7,1)

At a local post office, on average, 3 customers are in line when the post office closes each day. The probability, P, that exactly n customers are in line when the post office closes can be modeled by the equation P - Given that e

What is the amplitude of the function f(x) CO8(3x + Ic) ?

In the complex numbers, where i 1+1 1+1

Temperatures measured in degrees Fahrenheit (F) are related to temperatures measured in degrees Celsius {Q by the formula F - C + 32. There is I v21u¢ of x for which x degrees Fahrenheit equals x degrees Celsius. What is that value? -40 32 GO ON TO THE NEXT PAGE. 64 The ONLY Official Prep Guide from the Makers of theACT .OVIACT loviact Taklng and Scoring Your First ACT PracticeTest

The table below gives expeTimental data values for variables x and y. Theory predicts that y vaTies directly with x. Based on the experimental data, which of the following values is closest to the constant of variation? {Note: The vaTiable y varies directly with the variable x provided that y= kx for some nonzero constant k, called the constant of variation.) DO YOUR FIGURING HERE.

During a snowstorm, the relationship between the depth of accumulated snow. y inches. and the elapsed time. x hours, was modeled by the equation 2x - sy = One of the following graphs in the standard (x,yj coordinate plane models ihe equation for positive values of x and y. Which one? 1 2 3 4 5 x GO ON TO THE NEXT PAGE. The ONLY Official Prep Guide from the Makers of the ACT 65 .OVIACT loviact The Offlcial ACT Prep Gulde

Diana is baking bread, and the original recipe calls for l- teaspoons of yeast and 2- cups of flour. Diana will use the entir¢ contents of a packet that contains 2- teaspoons of yeast and will use the same ratio of ingTedients called for in the original recipe. How many cups of flour will Diana use? DO YOUR FIGURING HERE.

Four tnatrices are given below. 1 3 7 426 Which of the following matiix products is undefined? GO ON TO THE NEXT PAGE. 66 The ONLY Official Prep Guide from the Makers of the ACT OVIACT loviact Taking and Scoring Your First ACT Practlce Test

The 3parabolas graphed in the standard (x,y) coordinate plane below are from a family of parabolas. A general equation that defines this family of parabolas contains the variable n in addition to x and y. For one of the parabolas shown. n l. for another, and for the third, n - 3. Which of the following could be a general equation that defines this family of parabolas for all n > l ? DO YOUR FIGURING HERE. 13 11 l+n -&+1

After polling a class of 20 music students by a show of hands, you find that S students play the guitar and 9 students play the piano. Given that information, what is the minimum number of students in this music class who play both the guitar and the piano?

A teacher assigns each of her 18 students a different integer from I through 18. The teacher forms pairs of study partners by using the rule that the sum of the pair of numbers is a perfect Squ￿¢. Assuming the 9 pairs of students follow this rnle, the student assigned which number must be paired with the student assigned the number l ? GO ON TO THE NEXT PAGE. Th8 ONLY Offtcial Prep Guide from the Makers of the ACT 67 LOVIACT loviact The Offlclal ACT Prep Gulde

Lucky found $8.25 ill pennies, nickels, dimes, and quarters while walking home from school one week. When she deposited this money in the bank. she noticed that she had twice as many nickels as pennies, I fewer dime than nickels, and I moTe quarter than nickels. How many quarters did Lucky find that week? DO YOUR FIGURING HERE. 2*-1

Given 10 io 19

The table below shows the results of a survey of 250 people who were asked whether they like to read and whether they play a musical instrument. Play a musical instrument Do NOT play a musical instrnment Total Like to read 50 60 110 Do NOT like to read 40 100 140 Total 90 160 250 According to the results, what is the probability that a randomly selected person who was surveyed likes to read, given Lhat the person plays a musical instrument? li li GO ON TO THE NEXT PAGE. 68 The ONLY Official Prep Guide from.the Makers of thè ACT ...OVIACT loviact Taking and Scoring Your First ACT PracticeTest

Mario was riding a bicycle with wheels 26 inches in diameter. During I minute of Mario's ride, the wheels made exactly 200 revolutions. At what average speed. in feet per second, was Mario riding during that minute7 DO YOUR FIGURING HERE. 65 65 18 130 18

Whenever j and k are positive integers such that (<3)'_ 27 , what is the value of -

A finite arithmetic sequence has 7 terms, and the first term is What is th¢ diffeTence between the mean and the median of the 7 ternis? GO ON TO THE NEXT PAGE. The ONLY Official Prep Guide from the Makers of the ACT 69 ..OVIACT loviact The Official ACT Prep Guide.

In the CiTcle'with center D shown below, the length of radills CD is 4 cm, the length of BC is I cm, and BC is perpendicular lo radius AD at B. When ZADC is measured in degrees, which of the following expTessions represents the length, in centimeters, of AC ? DO YOUR FIGURING HERE. 45 sin 45 cos 45 sin 45 cos 45 tan

In scalene triangle ZIGHI shown below, point J lies on side HI, GJ bisects ZHGI such that ZHGJ and ZIGJ each measure g, and the given lengths a, b, c, d, and e are in inches and are distinct. For all possible values of LxGH17 d+e adsÈne b(d + e) sin 20 csin6 bsin28 GO ON TO THE NEXT PAGE. 70 The ONLY offi.cial Prep Guide from the Makers of the ACT ..OVIACT loviact Taking and Scoring Your First ACT PractlceTest

The Probability distribution of the discrete random variable X is shown in the table below. What is the expected value of X ? DO YOUR FIGURING HERE. Probability P(X=x) 12 12 12 END OF TEST 2 STOPI DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. The ONLY Offlcial Prep Guide from the Makers of th8 ACT 71