ACT Past Papers with Answers

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the figure below. ZBAC measures 35,. ZABC measures 95°. and points B, C. and D are collinear. What is the measure of ZACD ? 35° 95° 95°

Paper 21 · ACT December 2019 · Form C03 · Math Test

For all nonzero values of x and y. which of ihe following expressions is equivalent io - 3&r'v' 4-ry -31¥'y' -9x'y

Paper 21 · ACT December 2019 · Form C03 · Math Test

At a certain airline company, the cosl to transfer mileage poinls from one person's accounl lo another person's account i,$ $0.75 for every 100 mileage poinls (Tansferred plus a oneiime S20 processing fee. Wbai is the cost to transfer 7.000 mileage points from one account lo another at that airline company. ACT-C 14 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Forx= 155 -84 84 155 what is the value of 4.Y Ilx? DO YOUR FIGURING HERE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Taho earns his regular pay of $1 I per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week. Taho earns i- limes his regular pay. How much does Taho earn in a week in which he works 50 hours.

Paper 21 · ACT December 2019 · Form C03 · Math Test

A science class has 8 juniors and 4 seniors. The ieaLhL T will randomly seleci 2 Siudents, one at a time. to represeni ihe class in a committee at ihe school. Given thai the first student selected is a junior. whal is Ihe probability ihat ihe second studeni selecied will be a senior.

Paper 21 · ACT December 2019 · Form C03 · Math Test

When Tyrone fell asleep one night. the temperature was 24°F. When Tyrone awoke ihe next morning. the lemperaiure was 12°F. Letting + denote a rise in (emperature and - denoie a drop in temperature. what wa5 the change in temperature from ihe time Tyrone fell asleep until ihe time he awoke. -36°F 12°F +6°F +12°F

Paper 21 · ACT December 2019 · Form C03 · Math Test

The iotal cost of renting a car is $35.00 for each day the car is renied plus 42.5¢ for each mile ihe car is driven. ivhat is ihe total c05t of renting the car for 6 days and driving 350 miles? (Note: No sales tax is involved.) ACTU3 15 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the standard (x.y) coordinate plane, what is the slope of the line through (-6.4) and (1,3) 9 DO YOUR FIGURING HERE. I l. One morning at a coffee shop. each cuslomer ordered eiiher decaf or regular coffee, and each ordered it eiiher with milk or without milk. The number of customers who ordered each type of coffee with or withoui milk is listed in the table below. Order Decaf Regular Total Wilh milk Wiihout milk 12 20 16 10 Total 18 l8 36 customer will be randomly selected from all 36 customers for a prize. What is the probability thai the selecled customer will have ordered a regular coffee wiihout milk? 18 13

Paper 21 · ACT December 2019 · Form C03 · Math Test

Source question 11. Refer to the source image.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Which of the following inequalilies describes the solulion sei for 3x- 5 < Ir + l ? x< 6

Paper 21 · ACT December 2019 · Form C03 · Math Test

Which of the following expressions is equivalent to 4{x+2)+3(IK-I)? ACT.WJ 16 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

What is 4% of 1.36 x 104 ? 340 544

Paper 21 · ACT December 2019 · Form C03 · Math Test

What is the least common denominator of the fractions

Paper 21 · ACT December 2019 · Form C03 · Math Test

The point (3.27) is labeled on the graph of f(x) = x in the siandard (x.y) coordinate plane below. The graph of f(x) will be translated 3 coordinate unils to ihe left. Which of the following poinls will be on (he image of the graph after the translation? 30 (3,27) 20 10 10

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the standard (x,v) coordinate plane. what is the rnidpoint of the line segmenl that has endpoinis (-6.9) and (2,5) ? (-2. 7)

Paper 21 · ACT December 2019 · Form C03 · Math Test

What value of x satisfies the equation x+2 ACT£03 17 GO ON TO THE NEXT PAGE. Use the following information to answer questions 19-21 . DO YOUR FIGURING HERE. A large theater complex surveyed 5.000 adults. The results of the survey are shown in the tables below. Age groups 21-30 3140 41-50 51 or older Number

Paper 21 · ACT December 2019 · Form C03 · Math Test

Based on the survey resulis, whal was ihe average number of moviegoers for each of the 4 categories? 610

Paper 21 · ACT December 2019 · Form C03 · Math Test

Suppose all the adults surveyed happened to altend I movie each in one particular week. The total amount spent on tickets by those Surveyed in (hal week was $44.000.00. How many adults attended matinees (hat week? 500 ACT-C03 18 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

One of the following circle graphs represenls the proportion by age group of the adulis surveyed. Which one? DO YOUR FIGURING HERE. 31-40

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the figure shown below. all angles are right angles. and ihe side lengihil given are in centimeters. What is the area. in square cenlimelers, of the figure. 42 99 13

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the figure below. E is on CA. and ihe measures of ZBED and ZAEB are 90° and 145° respeclively. If li can be deterniined, what is the measure of 2CED ? 145° ACT<I)3 19 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the standard (x,v) coordinate plane, the graph of the function y - 5 sin(x) - 7 undergoes a single translaiion such that the equation of ils image is y = 5 sin{.r) - 14. Which of ihe following describes this translaiion? DO YOUR FIGURING HERE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

What is the value of 25

Paper 21 · ACT December 2019 · Form C03 · Math Test

A righi triangle 15 shown in the figure below. Whal is the value of sin e ? 12in 13 12 12 13 13 12 13 13in

Paper 21 · ACT December 2019 · Form C03 · Math Test

A 6-inch-by-6-inch square grid shown below is divided into 36 squares. each wilh a side lengih of l inch. Each vertex of ihe 2 shaded iriangles lies al an intersection of 2 grid lines. What fractional part of ihe 6-inch-by-6-inch square is shaded?

Paper 21 · ACT December 2019 · Form C03 · Math Test

All the values in the equalion below are exaci. Whai value of c makes the equation true? (4.25 x 10 2¢+4 )(6 x IO')- 255 ACT.CO3 20 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Whicb of the following inequalities is irue for all positive integers m DO YOUR FIGURING HERE. m<m+l

Paper 21 · ACT December 2019 · Form C03 · Math Test

A formula for ihe volume. V, of a right circular cylinder is V= Irr h, where r is the radius and h is ihe heighi. The cylindrical lank shown below has radius 5 meters and heighi 3 meters and is filled with water. Given that the weighi of I cubic meter of water is approximately 2,205 pvund5, Ihc weighi. in pounds. of the water in the tank is: more than I.0￿,000.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Graphed in Ihe standard (.r.i') coordinate plane below 15 a right triangle with vertices (0,0). (-40.0). and (0.30). What is ihe len8ih, in coordinate units. of ihe hypotenuse of the triangle? (0.30) (40,0) (0.0)

Paper 21 · ACT December 2019 · Form C03 · Math Test

Every graph in one of the following categories has a vertical line of symmelry regardless of how il is oriented in the standard (x,),) coordinate plane. Which one? ACTU3 21 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

ID the standard (x,y) coordinate plane, Ihe graph of y=30(x+17) 42 is a parabola. What are the coordinates of the vertex of the parabola? DO YOUR FIGURING HERE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

One side of square ABCD has a length of 15 mcter5. A certain rectangle whose area is equal io the area of ABCD has a widih of 10 meters. Whal is ihe length. in meters. of the rectangle.

Paper 21 · ACT December 2019 · Form C03 · Math Test

The average weight of 10 boys is 77.0 pounds. If the youngest boy is excluded, the average weight of ihe 9 remaining boys is 78.0 pounds. What is ihe weighi, in pounds, of the youngest boy.

Paper 21 · ACT December 2019 · Form C03 · Math Test

The tolal amounl of a certain substance present in laboratory experiment is given by the formula where A is the toial amount of the substance h hours after an initial amount (Ao) of the substance began accumulating. Which of ihe following expressions gives the number of hours it wilR take an initial amount of 10 grams of this substance to accumulate to IW grams? ACT403 22 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

For all values of x greater than 3. which of the following expressions is equivalent to DO YOUR FIGURING HERE. x+3 x+2 x+2 x+3

Paper 21 · ACT December 2019 · Form C03 · Math Test

Shown below, a board 9 feet 4 inches long is cut into 2 equal parts. What is the length. to the nearesi inch. of each part? 9 feel 4 inches

Paper 21 · ACT December 2019 · Form C03 · Math Test

If the po%itive integers x and v are relalively prime (thelr greatest common factor is l) and Ihenx+y= 49

Paper 21 · ACT December 2019 · Form C03 · Math Test

What is the 358ih digit after the decimal point in the repeating decimal 0.3178 9

Paper 21 · ACT December 2019 · Form C03 · Math Test

To promote a new brand of shoe4. a shoe store will run a promotion using a jar containing 3 red balls marked 'IO% off." 2 white balls marked "30% off.. and I green ball marked "60% off." Each customer will randomly select I ball from the jar to determine the discount that the customer will receive on any single pair of Ihe new brand of shoe5. Given ihal the new brand of shoes regularly costs S60 per pair. what is the average discount amounl. in dollars. that the store can expeci to give each customer duc to this promotion. ACT¢03 23 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer queslions 42-44. A 500-5quare-mile national park in Kenya has large and small protected animals. The number of large protected animals at ihe beginning of 2014 is given in ihe table below. Large animal Elephant Rhinoceros Lion Leopard Zebra Giraffe Number 600 100 200 300 400 800 Total Ai the beginning of 2014. the number of all protecled animals in ihe park was 10.000. Zoologisis predict thai for each year from 2015 10 2019, the lolal number of protected animals in the park at the beginning of the year will be 2% more than the number of protected animals in the park al the beginnin8 of the previous year.

Paper 21 · ACT December 2019 · Form C03 · Math Test

At the beginning of 2014, the number of lions in the park was p percent of the lotal number of large animals. Which of the following is closest 10 the value of p

Paper 21 · ACT December 2019 · Form C03 · Math Test

In this park, the average number of gallons of water consumed per day by each elephant. lion, and giraffe is 50, 5, and 10. respectively. Which of the following matrix producls yields the average total number of 8allons of water consumed per day by all the elephants. lions. and giraffes in the park? 50 [6￿ 2(MJ 800 | 10 50 io 21X) 8Th) 150 5 10] 8(Kl 2(K) [50 5 10] 50 8(J) 2(K) 10 ACT£03 24 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Let i be a positive integer less than 6. Based on the zoologists prediction, which of the following expressions represents the number of PToiecled animals in the park i years afier the beginning of 2014 ? 10,000(1 + 0.02), DO YOUR FIGURING HERE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Anela and Jacob plan to attend a concert in Brady. Anela will drive 375 km io Brady at a conslant speed of 75 km/hr. stopping one lime for a 30-minule break. Jrficob will stan 600 km from Brady and will drive at a constant speed of 90 km/hr for 2 hours. He will lake a l-hour break and then drive to Brady at a conslani speed of 70 kmnir. To the nearest O. I hour. Jacob musl leave how much earlier ihan Anela in order for them to arrive in Brady at the sarne time?

Paper 21 · ACT December 2019 · Form C03 · Math Test

Which of ihe followins is equal to allx*Og 3x+5 7x-3 for -2T+I -2x+4

Paper 21 · ACT December 2019 · Form C03 · Math Test

A rectangular siage is 90 feet long and 30 feet wide. What is the area, in square yards, of ihis stage? 30C3 300 675 900 ACT<03 25 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

A rectangle. with its vertex coordinates labeled, is graphed in the standard (.r.)) coordinaie plane below. A laiiice poini is a point wilh coordinates that are both integers. A lattice point inside bui N(yr on the reciangle will be chosen al random. What is the probability that the sum of the x-coordinate and the y-coordinate of the chosen lattice poini will be odd? DO YOUR FIGURING HERE. (0.4)

Paper 21 · ACT December 2019 · Form C03 · Math Test

The nth term of an arftthmeiic progression is given by the forniula a. l )d. where d is the cornmon difference and ai is the first terni. If ihe third ierm of an arithmetic progression is and ihe sixth ierni is what is the s¢venth ierm?

Paper 21 · ACT December 2019 · Form C03 · Math Test

The probability of Jamie being chosen to bat first in Ihe lineup for his baseball ieam is What are the odds in favor of Jamie being chosen io bai first? (Note: The odds in favor of an evenl are defined as the ratio of the probability that the eveni will happen to ihe probability that the evenl will Nuf happen.) 10 ACT<03 26 GO ON TO THE NEXT PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

A 120-liter solution thai is 5* salt is mixed with an 80-liter solulion that is 15% salt. The combined solution is what percent salt? DO YOUR FIGURING HERE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

A 50-foot-long rectangular swimming pool with verlical sid¢s is 3 feet deep at ihe shallow end and 10 feel deep al the deep end. The bottom of the pool slopes downward at a constant angle from horizontal along Ihe length of the pool. Which of the following expressions gives (his constant angle? (Note: For tan x if and only if <x< ian 50 tan 13 50 10 lan 50 13 50

Paper 21 · ACT December 2019 · Form C03 · Math Test

A hyperbola that has i'ertices (1,2) and (3,2) and that passe% ihrough ihe origin is shown below in the landard (.r.y) coordinate plane. The hyperbola has which of the following equations. (1,2) (3,2) (x-2)' 3(v-2)' (x-2) Ix+?) 3(}1+2) (x-2)

Paper 21 · ACT December 2019 · Form C03 · Math Test

As shown below. AIIA walked her dog 250 feet due east from ihe enlrance of a dog park (o a trash can and then walked 7(K) feel in a straight line 25° north of east io a bench. Which of the following expressions is equal to the distance. in feet. between the entrance and the bench? DO YOUR FIGURING HERE. 7(KJ ENTRANCE 25° 250 Iij 950 cos 25° 250 cos 25° 250 sin 155° +700 +700 700 + 250 - 2(700)(250) cos 25° 700 + 250 - 2{71K))(250) cos 155°

Paper 21 · ACT December 2019 · Form C03 · Math Test

For real numbers a, b. and c such thai a > b > c and b > O, which of the stal¢ments below i5(are) always III. Ibl > Icl

Paper 21 · ACT December 2019 · Form C03 · Math Test

Kenji and Mary are members of a school committee that will be meeting this afternoon. The 6 members of the commiltee will be seated randomly around a circular table. Whal is the probability that Kenji and Mary will NOT sit next to each oiher at ihe meeting. 88

Paper 21 · ACT December 2019 · Form C03 · Math Test

The digit in the ones place of 2 is 6. What is the digit in the ones place of 290 ? 28 GO ON TO THE NExf PAGE.

Paper 21 · ACT December 2019 · Form C03 · Math Test

Which of the following expressions represents the area, in square coordinate unils, of LRST shown in the standard (x.)) coordinate plane below? DO YOUR FIGURING HERE. S(b.e) R(a.d) T{c,d) (c-a){e-d) c(e-b) e(c-o) ((. d), + (b a)'l((e d), + (b - c),) (e-d) +(b-a) )( (e-d) +(b-c) )

Paper 21 · ACT December 2019 · Form C03 · Math Test

In the complex numbers, where i whal complex number x is a solution lo the equation x(2 + 31 ) = l ? 13 13 13

Paper 21 · ACT December 2019 · Form C03 · Math Test

The rectangular container shown below has a small comparlrnent for water created by a rectangular dividing wall of negligible width. One face of the dividing wall, shown shaded, has an area of 39 square inches. What is the volume. in cubic inches. of the larger compartment? Sin 13in 12in 15 in END OF TEST 2 STOPI DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. 29