ACT Past Papers with Answers

Paper 30 · ACT June 2017 · Form 74C · Math Test

A wallet Colltaining 2 five-dollaT bills, 9 ten-dollar bills, and 5 twenty-dollar bills is found and returned to its owner. The wallet's owner will reward the finder with I bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty- dollar bill.: 16 10 16 11

Paper 30 · ACT June 2017 · Form 74C · Math Test

In his costume supplies, Elmo th¢ clown has 4 Dosts, 3 pairs of lips. and 2 wigs. A clown costume consists of I nose, I pair of lips, and I wig. How many different clown costumes can Elmo make? ACT-74C 14 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

The word averag8 indicates arithmetic mean. l. The top surface of a rectanguIar table has an area of 100 square feet and a width Df 5 feet. What is the length, in feet, of the surface? 15 DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

A forn]ula for the volume of a right circular cone is l ffRh, where r is the radius of the base and h is the beight of the gone. Using as an approximate value for ff, which of the following values is closet>t to th¢ volume, in cubic inches. of a cone. with height 28 inches and radius 6 inches? 264 352

Paper 30 · ACT June 2017 · Form 74C · Math Test

In AACD below. B is on AC, E is on AD, the measure of ZCAD is 28°. and AD is perpendicular to both BE and CD. What is the measure of ZCBE ? 28° A￿-74c 15 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is the sum of O.Ix. + 3x + 80 and 0.5x forallx? -Ir+60 DO YOUR FIGURING HERE. -0.4x + 5x + 20

Paper 30 · ACT June 2017 · Form 74C · Math Test

Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at l-second intervals from t= O seconds to t- 5 seconds. Which of the following equations represents this relationship between d and t ? t+15

Paper 30 · ACT June 2017 · Form 74C · Math Test

Dmitry bought a pair of pants at the discounted price of $30. The OTiginal price of the pants was $40. What was the percont of the discount?.

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is tFLe value of1-6 | 17 - 411 ? IL 54

Paper 30 · ACT June 2017 · Form 74C · Math Test

Samantha, Nyla, and Jerry own shares of stock in thc Triumph Hotels company. The shares of stock that they own have a combined value of $6,880. Samantha owns 70 shares, Nyla owns 50 shares. and Jerry owns 40 shares. What is the value of the s￿￿eS Samantha owns? ACT-74G 16 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

A new club wants to attract customers who are at least 18 but less than 30 years of age. One of the number lines below illustrates the range of ages. in years. of the customers the club wants io attract. Which number line is it? DO YOUR FIGURING HERE. 18 30 18 30 18 30 18 30 18 30

Paper 30 · ACT June 2017 · Form 74C · Math Test

In the ligure shown below. E and G lie on AC, D and F lie on AB, DE and FG are parallel 10 BC, and the given lengths &re in feet. What is the length of AC. in feet? 12

Paper 30 · ACT June 2017 · Form 74C · Math Test

Which of the following integers is closest to 50 IS. The ratio of Jane's age to her daughter's age is 9.2. The sum of their ages is 44. How old is Jane? .B. 33 ACT-74C 17 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Source question 15. Refer to the source image.

Paper 30 · ACT June 2017 · Form 74C · Math Test

For the next school year, a college will use ofthe I)0 YOUR FIGURING HERE. money in its operdtillg budget for library books and - of the money Én its operating budget for scholarships. What fraction of the operating budget r¢mains for other uses? 18 18 13 18 27

Paper 30 · ACT June 2017 · Form 74C · Math Test

What value of x mak¢s the proportion below true? 10 35 IO+x 42

Paper 30 · ACT June 2017 · Form 74C · Math Test

The rectangle shown. in the figure below is partitioned into 3 triangles, 2 of which are shaded. What is the totsl area, in square inches. of the 2 shaded regions? loin

Paper 30 · ACT June 2017 · Form 74C · Math Test

Which of the following ordered pairs in the standard (x.y) coordinate plane satisfies the system of inequalities below? x>2 y>0 x+y<5 (2,2) . (4,0) ACT.74C 18 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

The graph .of y - 3 - 5 sin(x- 7t) is shovtr'n the standard (x,y) coordinate plane below. What is the range of y DO YOUR FIGURING HERE. 271 -2£)£ 2 -2<y< 8 3<y< 8

Paper 30 · ACT June 2017 · Form 74C · Math Test

Given functionsf(x) = Ir + l and g(x) - /- 4. what is the value off Ig(~3)) ? 19

Paper 30 · ACT June 2017 · Form 74C · Math Test

A fabric store s611s flannel and calico fabrics. Joan pays $25 for 3 yardg of flannel and 4 yards of calico. Chris pays $1 I for l yard of flannel and 2 yards of calACO. What is the price of l yard of calico?

Paper 30 · ACT June 2017 · Form 74C · Math Test

The scores gi3en below were earned by 10 stlldents OD a recent biology test. What is the median score? 71, 94, 86, 77, 88. 94, 88. 80, 78, 94

Paper 30 · ACT June 2017 · Form 74C · Math Test

A parallelogram has a perimeter of 84 inches, and l of its sides rneasures 16 inches. If it can be detern]ined, what are the lengths, in inches, of the other 3 sides? ACT.74C 19 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

In the figure below, all of the small squares are equal In area, and the area of rectangle ABCD is I square unit. Which of the following expressions represents the area, in square unlts, of the shaded region? DO,YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

A bag contains 16 red. marbles. 7 yellow marbles, and 19 green marbles. How many additional red marbles must be added to the 42 marbles atready in the bag so that the probability of randomly drawing a red marble is

Paper 30 · ACT June 2017 · Form 74C · Math Test

For all a > O, which of the following expressions is equal to a ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

Jamie claims, "If a triangle is in Set A, then it is not isosceles., Lat¢r, Jamie discovers that LMNP is a counterexample proving this claim false. Which of the following statements must be true about ￿mNP ? IL It is obtuse and not in Set A. ACT-74C 20 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 29-32. Parallelogram ABCD is grapbed in the standard (x.y) coordinate ￿ane below. Sides AB and CD are each 10 coordinate units long. Sides AD and BC are eacb 5 coordinate ullits long. The distance between AD and BC is 3 coordinate units. B(0.4) C(5,4) A(-I,l) D(4,1)

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is the area, in square coordinate ullits. of ABCD ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is the distance. ill C(￿rdInate units, from B to D ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is the slope of BC ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

Parallelograrn ABCD Will be reflected over the y-axis. What will be the coordinates of the iniage of A ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

Which of the following is equivalent to 8 . 40.5 9 ACT-74C 21 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

A school admissions office accepts 2 out of ever 7applicants. Given that the school accepted 630studeDts, how mally applicants were NOT accepted? 140 180 490 DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

What is the value of log2 sf8 ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

Jie asked 90 students to choose I favorite frnit from 4 options. Jie has begun to represent the results in the circle graph below. Peaches were chosen as the favorite of 15 students. Apples. banallas, and strawlErries werc each chosen as favorites by an equal number of the remaining students. Wbat must be the measure of the Centr￿ angle ia the circle graph for b￿anas? Favorite Fruit peach 15 IL 115°

Paper 30 · ACT June 2017 · Form 74C · Math Test

For all real numbers x such that x * O, li 5x 28 11 5+x 7x+20 5+x 4x+35 ACT-74C 22 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 38-40. The Harrisburg. Recreation Center recently cllanged its bours to open I hour later and close 3 hours later than it had previously. Residents of Harrisburg age 16 or older were given a survey. and 560 residents replied. The survey asked each resident his or her student status O]igh school, college, or nonstudent) and what he or she thought about the change in hours (approve, disapprove, or no opinion). The results are sumnwized in the table below. Studellt status Approve 30 14 85 Disapprove No opinion High school College Nonstudent 11 10 353 47 Total 129 367 64

Paper 30 · ACT June 2017 · Form 74C · Math Test

What fraction of theè3e nonstudent residents replied that they dxsapproved of the change in hours? 45 14 75 353 367 353 485

Paper 30 · ACT June 2017 · Form 74C · Math Test

Suppose a person will be chosen at random from these 560 residents. Which of the following values is closest to the probabi]ity that the person chosen will NOT be a high school student and will NOT have replied with no opinion?

Paper 30 · ACT June 2017 · Form 74C · Math Test

After constructing the tabl¢. it was discovered that the student status of 15 residents who replied that they ap oved had been incorrectly cl&8sified as nonstudents. er correcting the errors, exactly 60% of the college students had replied that they approved. To the nearest 1%, what percent of high school students replKed that they approved? Acf-74C 23 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Set A and Set B each consist of 5 distinct numbers. The 2 sets contsin identical numbers with the exception of the number with the least value in each set. The number with the least value In Set B is greater than the number with the least value in Set A. The value of which of the following measures musi be greater for Set B than. for SetA? DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

For all x such that O < x < 90, which of the following . expressions is NOT equal to sin XO ? sin(?x°) cos(90 - x). os(x - 90)° l (Cos x,)

Paper 30 · ACT June 2017 · Form 74C · Math Test

A 3-inch-tall rectangular box with a square base is collstructed to hold a circular pie that a diameter of 8 inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie?

Paper 30 · ACT June 2017 · Form 74C · Math Test

Quadrilateral ABCD is shov/n in the figure below with the lengths of the 4 sides given meters. The measure of £C is 90°. What is tan A ? 12 13 12 13 12 13 12 13 ACT.74C 24 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Given today is Tuesday. what day of the week w&s it 200 days ago? DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

In the figure below, line m is perpendicular to line n. and both lines intersect line q at the same point. The measure of £1 is (3x - 10)°, and the measure of 22 is (2x + 10)°. What is the measure of £3 ?

Paper 30 · ACT June 2017 · Form 74C · Math Test

The greatest common factor of 2 whole numbers is 10. The least common multiple of these same 2 numbers is 120. What ￿e the 2 nujnbers? 6and20 . 30and40

Paper 30 · ACT June 2017 · Form 74C · Math Test

The side lengtbs of a certain triangle are 4, 5. and 7 centimeters. Which of the following descriptions best classifies this triangle? 49: A professional baseball will play I game Saturday and I garne Sunday. A sportswriter eslimates the tearn has a 60% chance of winning on Satllrday but only a 35% chance of winning on Sunday. Using the sportswriter's estimates. what is the probabi]Aty that the t¢am will lose both games? (Note: Neither game can result in a tie.) ACT-74C 25 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Source question 49. Refer to the source image.

Paper 30 · ACT June 2017 · Form 74C · Math Test

The graph offlx) = (he domain of f(x) ? is shown below. What is DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Get-A-Great-Read Books is adding a new phone line. The phone company says that the f￿st 3 digits of thc phone ttumber must be 555. but the remaining 4 digits, where each digit is a digit from O through 9. can be chosen by Get-A-Great-Read Books. How many phone numbers are possible? 5(9,)

Paper 30 · ACT June 2017 · Form 74C · Math Test

In the standard (x,y) coordinate plane. the circle centered at (1,3) that passes through (4,7) is the set of all points that are: endpoints (1,3) and (4.7). equidistant from (1,3) and (4,7). equidistant from the line segment with endpoints (1,3) and (4,7).

Paper 30 · ACT June 2017 · Form 74C · Math Test

Which of the following values is the x-coordinate of the point in the standard (x,y) coordinate plane where the graph of the line y = 7 intersects the graph of the function y = In(x- 2) + 3 ? Acf-74C 26 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Three copy machines-A, B, and C-copy al the same rate and will all be used to make copies of a report. At 8:00 a.m.. all 3 machines begin copying. Machine A breaks down at 10:00 a.m. and is back in service at 1:00 p.m. Machine B breaks down at 12:IX) p.rn. (noon) and begins copying again at 3:00 p.m. All 3 machines finish copying at 5..00 p.m. when the copying of the reportr is complete. One of the following graphs shows the number of copies made. as a function of t. the time at any given point during the copying. Which graph is it? DO YOUR FIGURING HERE. 8:00 12:00 4:00 8:(KJ 12.(I) 4:00 8:00 12:W 4:00 8:1K) I2.￿ 4:IX) 8:00 12:CKJ 4:00

Paper 30 · ACT June 2017 · Form 74C · Math Test

A sporting-goods store sells baseba]I caps for $22 each. At this price, 40 caps are sold per week. For every $1 decrease in price, the store will sell 4 more caps per week. The store will adjust the price to maximize revenue. What will be the tllaximum possible revenue for I week? (Note: The revenue equals the number of caps sold times the price per Cap.) AGT.71C 27 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

Each of the following graphs in th'e standard (x.y) oordxnate plane has the same sC￿e on both axes. One graph is the graph of ax + by < c, where O < a < b < c. Which one is it? DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

The art club designed and ll￿le banners of the school color8, blue and white, for their fund-raiser. Each banner required - yard of blue material and - yard of white materiaL The club originally planned 10 purchase exactly enough material to make 500 banners. but found th¢ material to b¢ cheaper if purchased in full bolts-the blue material in 10-yaTd bolts and the white material in 12-yard bolts. How many extra banners was the club able to make if they purchased enough full bolts to make at le&st 500 banners? 28 GO ON TO THE NEXT PAGE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

For all real numbers x and the imaginary number i. whAch of the following expressAons is equivalent to (x-3i)'? +271 DO YOUR FIGURING HERE.

Paper 30 · ACT June 2017 · Form 74C · Math Test

The graph in the standard (x,y) coordinate plane below is the graph of one of the followin£ functions. Ivhich okne? n(x) = l(x + 6)'(x - 4)

Paper 30 · ACT June 2017 · Form 74C · Math Test

The table below shows the numbers of rows and columns in each of 5 matrices. Matrix Number of rows Number of columns For distinct values of k, m. and n. which of the following matrix products is NOT possible? IL CE END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-74C 29