ACT Past Papers with Answers

Paper 28 · ACT December 2017 · Form A10 · Math Test

Source question 2. Refer to the source image.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Consider the equation k - _j + 54. For what value of j is the value of k equal to 40 ? DO YOUR FIGURING HERE. 10 98 178 200

Paper 28 · ACT December 2017 · Form A10 · Math Test

Whatis |3-xl whenx=

Paper 28 · ACT December 2017 · Form A10 · Math Test

When Tyiese fell asleep one night, the temperature was 24°F. When Tyrese awoke the next morning, the temperature was 16°F. Letting + denote a rise in temperature and denote a drop in temperature. what was the change in temperature from the time Tyrese fell asleep until the time he awoke? -40°F +8°F

Paper 28 · ACT December 2017 · Form A10 · Math Test

Ming purchased a car that had a purchase price of $5,400, which included all other cost8 and tax. She paid $1,000 as a down payment and got a loan for the rest of the purchase price. Ming paid off the loan by making 28 payments of $200 each, The total of all her payments. including the down payment, was how much more than the car's purchase price?

Paper 28 · ACT December 2017 · Form A10 · Math Test

Shown below is a regular hexagon inscribed in a circle whose radius is 4 inches. What is the perimeter, in inches. of the hexagon? GO ON TO THE NExf PAGE. ACT-A10

Paper 28 · ACT December 2017 · Form A10 · Math Test

Tke floor plan for an L-shaped storage building is shown below with distan¢¢s marked in feet. What is the floor area of the building, in SqU￿e feet? (Note". Walls in this building meet only at right angles.) 22, DO YOUR FIGURING HERE. 190 504 1,496 40, 22, 50,

Paper 28 · ACT December 2017 · Form A10 · Math Test

Quadrila C{5,5), a eral ABCD with vertices A(-2,0), B(0,4), d D(8,2) will be graphed in the standard {x,y) plane below. coordinat Whicb of the following is a type of quadrilateral determined by the￿￿¢ vertices?

Paper 28 · ACT December 2017 · Form A10 · Math Test

Given that f(x) - 3x * 7 and g(x) value of f(g(4)} ? whal is the 19 ACT-A10 16 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

At her hot dog stand, Julie sells hot dogs for $2 each. Purchasing hot dogs and other supplies costs $200 per month. The solution of which of the following inequalities models the numbers of hot dogs, h, Julie can sell per month and make a profit? h-200>0 h-200<0 h+200>0 DO YOUR FIGURING HERE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

In the standard (x,y} coordinate plane, what is the slope oftheline3x+8y-5?

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following (x,y) pairs 18 the solution for the systeni of equations x + 2y = 2 and -2x + y - 16 4

Paper 28 · ACT December 2017 · Form A10 · Math Test

On a map, inch represents 16 actual miles. Two towns that arc 2- inches apart on this map are how many actual miles apait? 11 16 64

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following matrices is equal to 4 16 0-16 ACT-A1Q 17 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

What És the value of tan A in right triangle AABC below? DO YOUR FIGURING HERE. 17 15 17 15 17 15 15 17

Paper 28 · ACT December 2017 · Form A10 · Math Test

Tina runs at a rate of 8 miles per hour. At that rate, how many miles will she run in l? minutes?

Paper 28 · ACT December 2017 · Form A10 · Math Test

A function f(x) is defined as f(x) f(-3) 9 -324 -54 54 108 324 What is

Paper 28 · ACT December 2017 · Form A10 · Math Test

In the figure below, A is on BE and C is on BD. What is the measure of £ABC ? ACT-A10 18 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Marcos programs his calcukator lo evaluate a linear function, but he doesn't say what the function is. When 5 is ent¢red, the calculator displays the Value 2. When J5 is entered, the calLulator displays the value 6. Which of the following expressions explains what the calculator will display when any number, n, is entered? DO YOUR FIGURING HERE. 21

Paper 28 · ACT December 2017 · Form A10 · Math Test

On Friday, the temperature at 8:00 a.m. was 49°F and rose at a const<int rate of -°F per hour until noon. A cold froni passed through at noon, and the temperature Ihen fell at a constant rate of l°F per hour. The temperature first fell below 49°F between: noon and I p.m.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Letter glades in Hugo'8 math class are based on the percent of the total possible points on 4 unit exams (each worth 100 points) and the final exam (worth 200 p'oints) and are assigned according to the chart below. Range Course grade At least 90fo 80Yo-89qo 70Yo-79fo 6010-69￿0 Less than 60Vo The number of points Hugo scored on the unit exam,$ this term were 82. 88, 91. and 83. When course grades were posted, Hugo's course grade was listed as a B. Which of ihe following could NOT have been the number of points he scored on the final exam? ACT-A10 19 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 23-25. Halle is bowling a series of 3 games. She has bowled 2 of 3 games with scores of 148 and 176. The figure below is a top view of the bowling lane. The ditnensions foi the bowling lane are given in the figure. The pin deck is the rectangular area within the bowling lane where the 10 bowling pins are set up. (Note: The figure is not drawn to scale.) 65 feet pin deck 5 feet

Paper 28 · ACT December 2017 · Form A10 · Math Test

The diameter of each pin at its base is 2,25 in. When all of the pins are set lip, which ot the following values is closest to the area, in square inches, that is cov¢red by the bases of the pins? 71

Paper 28 · ACT December 2017 · Form A10 · Math Test

What is the ratio of the total area of the bowling lane to the area of the pin deck?

Paper 28 · ACT December 2017 · Form A10 · Math Test

What score will Hdlle need to earn in her 3rd game to have an average 8coI'e of 179 tor (he 3 games? 172

Paper 28 · ACT December 2017 · Form A10 · Math Test

The area ot a rectangle is 300 square meter.g, and its length is 3 times its width. How many meters wide is thc rectangle? 10 ACT-A10 20 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

A parallejogram has a perimeter of 96 inches, and l of its sides measures 16 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides? DO YOUR FIGURING HERE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Elmhurst Street is a two-way street. In each direction, it has one 12-foot-wide lane for caT traffic, one 6-foot- wide bike lane, and one 8-foot-wide parking lane, How many feet wide is Elmhurst Street? H, 52 IL 80

Paper 28 · ACT December 2017 · Form A10 · Math Test

At Central High Schi)01, 4 out of every 10 students ride the bus to and fr05n school, and 3 out of every 8 who ride the bus are freshmen. If there are 2,5(M) students at Central, how many of the students are freshmen who ride the bus?

Paper 28 · ACT December 2017 · Form A10 · Math Test

If 90°<e< 180° andsin g= 20 29 ,thencosO- 29 20 20 21 21 29 29 21 29 20

Paper 28 · ACT December 2017 · Form A10 · Math Test

Given f(x) - x+l for whichf(t) = t ? what is(are) the real value(s) of t l only 2 only -2 and l only l and 2 only l and 2 only GO ON TO THE NEXT PAGE. ACT-AIO 21 DO YOUR FIGURING HERE. Use Ihe following information to answer questions 32-35. In the figure below, a highway rest area (at D) and radar stations (at A and B) lie on a level east-west line" A is 9,000 feet due west of D. An airplane (at C) is shown directly above the rest area, flying due west at a constant speed of 300 feet per second and at a constant altitude of 12,000 feet. The airplane is Iocat¢d at a straight-line distance of 15,000 feet from the radar station at A and 13,000 fect from the radar station at B. Is,￿0 13,000 9,000

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following values is closest to the distance, in feet, between the 2 radar stations? 5,000

Paper 28 · ACT December 2017 · Form A10 · Math Test

Let A, C, and D lie in the standard (x,y) coordinate pIane such that A is at (0,0) and D is al (9,000, 0). Which of the following equations represents the Jine along which the airplane is flying. 15,000

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following values is closest to the number of seconds it will take for the airplanc to fly from C to the point directly above the radar station at A ? ACT-A10 22 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

When collsidering the changing triangle formed by A, B, and the moving airplane (C), which of the angles below incr¢ases in measure as thc airplane flies due west beyond the point directly above A ? I. ZA II. ZB III. zc DO YOUR FIGURING HERE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Troy made a rectangular poster that is 4 feel long and 2 feet wide. The poster is too large to fit in the available display space, so Troy is going to make a new poster that will have an area that is 50go of the area of the original poster. The Jength of Troy's new postcr will be the Icngth of the original poster. How many feet wide will the new poster be?

Paper 28 · ACT December 2017 · Form A10 · Math Test

What is the solution Set of the equalion x+6-2(x+3)- D, {3}

Paper 28 · ACT December 2017 · Form A10 · Math Test

St¢vc plans to use 28 feet of fencing to enclose a region of his yard for a pen for his pet rabbit. What is the area, in square feet, of the largest rectangular region Stev¢ can enclose? 40 49 23 GO ON TO THE NEXT PAGE. ACT-AIO

Paper 28 · ACT December 2017 · Form A10 · Math Test

There are exactly 5 people in a bookstore at 12:00 p.m. Each person earns an annual income that is between $30,000 and $35,000. No one enters or leaves the bookstore until 12.15 p.m., when a professional athlete with an annual income of more than $1,000,000 enters the bookstore and joins the other 5 people. The mean, tnedian, range, and standard deviation of the annual incomes of ibe 5 people in the bookstOTe at 12:00 p.m. are calculated and compared to the same 4 statistics of the annual incomes of the 6 people in the bookstore at 12:15 p.m. If it can be determined, which of the 4 statistics changed the least? DO YOUR FIGURING HERE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Ana and Amy started a landscaping job together. When Ana stopped, she had completed of the job. When Amy stopped, she had completed of the job. Then Ruben Completed the rest of the job in 2 hours. Assume that Ana, Amy, and Ruben all worked at the same rate. Which of the following values is closest to the number of hours it would have taken l of them to complete the entire job alone?

Paper 28 · ACT December 2017 · Form A10 · Math Test

If o and b are positive real numbers, which of the following is equivalent to {2a-'Ifb)' , 8b' 16b' 16b ACT-A10 24 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

To become a contestant on a quiz show, a person must correctly order 4 rock stars by age, from youngest to oldest. The contestant knows which one is the oldest rock star, but randomly guesses at the order of the other 3 rock stars. What is the probability the contestant will get all 4 in the correct order? DO YOUR FIGURING HERE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following expressions is Gquivalent ro Ir+6 4x+3 4x+6

Paper 28 · ACT December 2017 · Form A10 · Math Test

An automobile license plate number issued by a certain state has 6 character positions. Each of the first 3 position4 contains a single digit from O through 9. Each of the last 3 positiong contsinq l of the 26 letters of the alphabet. Digits and letters of the alphabet can be iepeaÉed on & liccnse plate. How many diff¢rent such license plate numbers can be made? 36 46,656 1,000,000 25 GO ON TO THE NEXT PAGE. ACT-A10

Paper 28 · ACT December 2017 · Form A10 · Math Test

The function y=f(x) is graphed in the standard (x,y) coordinate plane below. DO YOUR FIGURING HERE. The points on the gr&iph of the function y - 3 +f(x - Lan be obtained from th¢ points on y =f(x} by a shift of: l unit to the right and 3 units down.

Paper 28 · ACT December 2017 · Form A10 · Math Test

When log5 whatisA? -32 io 25

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which of the following lists iho.qe integer values of D tor which the fraction lie8 bftween

Paper 28 · ACT December 2017 · Form A10 · Math Test

For all real numbers a, b, and c 8uch that a > b and c < O, which of the following inequalities musi be true? ac>bc a+c<b+c" A¢T.A10 26 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

The triangle shown below has side lengths 37, 38, and 39 inches. Which of the following expressions gives the measure of the Iargest angle of the triangle? (Note: For cvery triangle with sides of length a, b, and c that are opposite ZA, ZB, and £C, respectively* a +b-2abcosC.) DO YOUR FIGURING HERE. 38in 39in 37in cos 37'_ 38 39, 2{38)(39) 39'_ 37, _ 38, 2(37)(38) cos cos '137, 38, 39, + 2(38)(39)1 cos '138, 37, 39, + 2(37)(39)1 cos '139, 37, 38, + 2(37)(38)1

Paper 28 · ACT December 2017 · Form A10 · Math Test

Pete has an average score of exactly x points on 4 equally weighted tests. How many points higher than x must Pete score on th¢ 5th equally weighted test to raise his average score after the 5th test to x + 2 points?

Paper 28 · ACT December 2017 · Form A10 · Math Test

The intersection of lines l and m forms the 4 angles £A, ZB, ZC. and ZD. The measure of IB is 3- times the measure of ZA. Which of the following values is closest to the measure of ZA ?

Paper 28 · ACT December 2017 · Form A10 · Math Test

A sequence is defined for all positive integers by +n+landsi-3.WhatlSS4 18 49 ACT-A1 D 27 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

If a is an integer less than -1, which of the following orders the expressions la I, and from least value to greatest value? DO YOUR FIGURING HERE. < lal

Paper 28 · ACT December 2017 · Form A10 · Math Test

At the school carnival. Ann is playing a game involving a stack of 10 index cards. Each card has a single number written on it: I card has a 1, 2 cards have a 2, 3 cards have a 3, and 4 cards have a 4. Ann will choose I card at random, and she will be awarded the number of points equal to the number written on the card. Let the random variable X represent the number of points Ann receive8 on any I draw. What is the expected value of X ?

Paper 28 · ACT December 2017 · Form A10 · Math Test

Which ot the following is equivalent to the sum of any consecutive odd integeTS. X, y, and z, such that X<y<z? x+y+z

Paper 28 · ACT December 2017 · Form A10 · Math Test

The mean of the set of 5 numbers {42, 3, 11, 27. x} is 24, and the median of the set of 4numbers {53, 8, 29, y} is 38. If it can be determined, which of the following values is equal to x - y -38 10 38 ACT-A10 28 GO ON TO THE NEXT PAGE.

Paper 28 · ACT December 2017 · Form A10 · Math Test

Consider all rectangles such that the reLtangle's length is greater than the rectangle's width and the length and width are whole numbers of inches. Which of the following perimeters, in inches, is NOT possible for such a rectangle with an area of 144 squaTe inches? DO YOUR FIGURING HERE. 58, The equation (x- 7) + (y- 8) 10 is that of a circle that lies in the standard (x,y) coordinate plane. One endpoint of a diameter of the circle has y-coordinate I l. What is the y-coordinale of the other endpoint of that diarneter?

Paper 28 · ACT December 2017 · Form A10 · Math Test

Source question 58. Refer to the source image.

Paper 28 · ACT December 2017 · Form A10 · Math Test

The plans for a diving pool call for a rectangular PTism that has a length of 30 meters: a width of 25 meters, and a depth of 5 meters. If the plans are changed to increase both the length and the width of the pool by IO¥o, what will be the increase, lo the nearest ItTo, in the volume of Ihe pool?

Paper 28 · ACT December 2017 · Form A10 · Math Test

One solution of the equation 4x 2x +x+7=0 is l. Which of the following describes the other 2 801utions? positkve real number. complex number that is not real. END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-AIQ 29