ACT Past Papers with Answers

Paper 60 · ACT December 2009 · Form 68A · Math Test

Source question 2. Refer to the source image.

Paper 60 · ACT December 2009 · Form 68A · Math Test

978 GO ON TO THE NEXT PAGE. ACT-68A 2>. A supermarket soup can display consists of 5 levels of stacked cans. The fiirure below shows an overhead view of the top level of cans (circles shaded and with solid bordtrs) and the level of cans below it (circles with dashed borders). IEL the display, each level has 4 more cans than the level above it. How ￿allY cans are in the display. DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

What is 150Yo of 50 ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

A box contains seveial tnarbles. Bill draws a ￿arbIe at random from the box, notes that it is blue, and places the marble back in the box. Then Aiko draws a marble at ralldom from the box, notes that her marble is blue, and places it back in the box. Which of the followino is necessanly true? colors. DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

A 21-foot-long board is cut into 3 pieces such that the first piece is twice as long as the second piece and the second piece is twice as long as the third piece. How many feet in length is the longest of tbe 3 pieces? (Note.. Ignore the width of the saw cuts.)

Paper 60 · ACT December 2009 · Form 68A · Math Test

What is the perimeter, in centimeters. of a rectangle with length 8 cm and width 3 cm ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

In the figure below, AE and BD intersect at C. What is the measure of ZE ? 60° 80° Iio. H_ 40" AGT-68A GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

The diagonal BD divides qlladrilateral ABCD into a Tight,triantsle and an equilateral tTiangle, as sbown below. The given dimensions are ill centl￿eterS. How many centirneters loncy is AD ? DO YOUR FIGURING HERE. 10 14 .28 C 6 D

Paper 60 · ACT December 2009 · Form 68A · Math Test

The Circul￿ face of a fair spinnei has a red section, a blue section, and 2 yellow sections, as showIi below. After being spun, the arrow of the spinner is equally likely to be poillting to any l of the 4 sections. What is the probability that, after the arrow has been spun, the section the arrow is pointing to is yellow? blue yellow ye]low

Paper 60 · ACT December 2009 · Form 68A · Math Test

Let a square represent the value of x and a circle represent l. Which of the following expiessions accurately reprèsents 2{3x + 5) ? QE]O,00000 . 00000 E]ll 000 . Ell]D"OOOO E]0 + 00000 . Dt]El+OOOOO . 000 0000

Paper 60 · ACT December 2009 · Form 68A · Math Test

Ivhat is the slope-intercept forn] of 5x - y - 9 = 0 ? -5x*9 5x+9 ACT-68A 16 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

The points S(4,10)' and T(6.-2) lie in the standard (x,y) coordinate plane. What is the ￿ldpoint of ST ? DO YOUR FIGURING HEAE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

Kerry ordered a pizza: one half was topped with peppeTOni for her brother Joel, and the other half was topped with extra cheese for herself. KeLTy ate all of the half of the pizza with extra cheese. Joel ate the half of the pizza with pepperoni. What fraction of the whole pizza did Joel eat? 10

Paper 60 · ACT December 2009 · Form 68A · Math Test

Given that a = andb- what is the value of

Paper 60 · ACT December 2009 · Form 68A · Math Test

Guban weDt shopping at a department store that was having a stoiewide sale where every itern was IOYO off its marked pIice, including atready discounted items. Guban found a sweater with an original price of $30.00 marked with a discounted price of 15fo off its original pIice. There was a 6% sales tax on the final price of all items. How much did Guban pay for the sweater? ACT-B8A 17 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

In the figure below. p￿a1]e] lines I , I , and 13 jlltersect transversal t. What is the value of a + b + c + d ? DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

Max bought several bags of organic lawn fertilizer, and each bag covers 5,000 square feet of lawn. He is fertilizing a lawn that is 50 feet wide. He POUTS I bag into the fertilizer spreader and begins fertilizing. BefoTe he needs to refill the spreadei, Max can fertilize a rectangle that is the width of the lawn and is how many feet long. 50 100 IL 5,050

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the following variable expressions would represent the area of a rectancvle if its length is represented by x + 2 and its width is represented by

Paper 60 · ACT December 2009 · Form 68A · Math Test

A forniula oftcn uscd to find the dollar value of an investment is A = P(I' + r) , wheie A is the dollat value after t yeais, P is the initial arnount invested, and r is the thnual intcrcst rate eKpressed as a decimal. According to this fonnula, which of the following is closest to the dollar value of $1,000 invested for 2 years at a 5 fo annual interest rate? ACT.6BA 18 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

A moiorist traveled at an aver&cre speed of 50 miles per hour and arrived at his destination in exactly 20 Minutes. Which of the following is clc)sest to the nutDber of miles he traveled? DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

Inez has 20 statnps. Some of the stanips are 40¢ stamps and the other.s are 25¢ Sta￿ps. The value of the 20 stamps is $6.95. How many 40¢ stamps does Inez have?

Paper 60 · ACT December 2009 · Form 68A · Math Test

A line in the standard (x,y} coordinate plane has equation 3x - y = 6. What is the slope of this line?

Paper 60 · ACT December 2009 · Form 68A · Math Test

The right triangle shown below has a hypotenuse of 4 inches. The Kneasure of the angle indicat£d is 6°. Which of the following is closest to the length, ill inches, of the side opposite the 6° angle? 4 inches (Note: sin 6° 0.1045 sin 84°_ 0.9945 cos 6° _ 0.9945 cos 84° . 0.1045 tan 6° 0.1051 tan 84° _ 9.5 l44)

Paper 60 · ACT December 2009 · Form 68A · Math Test

Source question 25. Refer to the source image.

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the folIowing could be the value of Nf for some illteger c ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

The height of a trianole is 6 cm longer than the base from which the height is measured. If the area of the triangle is 80 square ceDtimeters, what is the height, in celltimeters?

Paper 60 · ACT December 2009 · Form 68A · Math Test

For real numbers x and y such that x - y < O, which of the folloiving must be trne? x<-y ACT-68A 20 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

In the standard (x,y) COOTdinate plane, a triangLe has vertices (-3.-3), (-4,2), and (-I,l), What will be the coordinates of thc vertices after the triangle is shifted down 2 units? DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

When solved for k, -6 + 7k > 3 - 8k is equivalent to which of the following inequalities?

Paper 60 · ACT December 2009 · Form 68A · Math Test

In the figure below, LkA.BC is equilatcral. Points D. E, and F are the midpoints of the sides of 2L4BC. Points G, H, and I are the midpoints of the sides of LYDEF. A side of gXABC is how tnany times as long as & side of GHI? . 16

Paper 60 · ACT December 2009 · Form 68A · Math Test

What fraction of 2- is I l ? 18 21 GO ON TO THE NEXT PAGE. ACT48A

Paper 60 · ACT December 2009 · Form 68A · Math Test

A greenhouse contained both 6-lllch-high (Feraniuffls and 3-inch-high geraniums. The 6-inch-high geraAlUIllS were taken out of the greenhouse in early spring and grew at a rate of l inch per week. The 3-inch-high geraniums remained ill the CTreenhollse and grew at a rate of l- inchts per week. After the 6-inch-higb geraniums were taken outside, in how ￿anY weeks 4• were both groups of geraniums the same height? DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

(x, 4x'+5x)-(x'_ 3x +2x+6

Paper 60 · ACT December 2009 · Form 68A · Math Test

A rigbt triangle is shown in the figure below. Which of the following eKpressions oives G ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

In IXABC below, AB - AC and L4 measures 50°. What is the measure of ZB ? DO YOUR FIGURING HERE. 50°

Paper 60 · ACT December 2009 · Form 68A · Math Test

The square below has an ￿ea of 64 square centin]eters. The circle inscribed in the square is tangent to the sqllare at A, B, C, and D. What is the area, in square centimeters, of the circle? A: 4

Paper 60 · ACT December 2009 · Form 68A · Math Test

TILe 2 functions f(x) and g(x) arc defined such that x+8 and g(x) - k + 6x + 2. What is the value of f (g(-2)) ? 53 ACT.e8A. .23 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

On a m&p of Blueville in the standard (x,y) coordinate plane, wbere I coordinate unit repiesentg I block. the middle school is at (-8,3) and the high school is at (4,-2). What is th6 Straight-line distance, in blocks, between the hicyh school and the middle school? DO YOUR FIGURING HERE. 13 17

Paper 60 · ACT December 2009 · Form 68A · Math Test

What is the. perimeter, in centimet'ers, of the isosceles trapezoid shown below? 4cm 12 CUL 14cm

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the followillg equatioDs, when graphed in the sLandard {x,y) coordinate plane, would cross the x-axis atx-2andatx-

Paper 60 · ACT December 2009 · Form 68A · Math Test

A rectangular roolll is 13 feet long, 10 feet wide, and 9 feet high. Not accountincT for doors and windows, what is the surface area, in square feet, of the 4 walls, ceiling, and floor of the TOQIll? 337 414 544 674

Paper 60 · ACT December 2009 · Form 68A · Math Test

The average of Pam's 8 test scores is 77 points. Pam takes a 9th test and earns a score of 95 points. If all 9 tests are equally weighted, Iwhat is Pam's new average? ACT-68A 24 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 44-46. The points A(4,7), B(3,12), C(7,7), and D(7,14) are shown in the standard (x,y) coordinate plane below. D(7,14} B(3,12) A(4,7) C(7:7)

Paper 60 · ACT December 2009 · Form 68A · Math Test

What is the slope of BD ? li 13

Paper 60 · ACT December 2009 · Form 68A · Math Test

What is the c.osine of the smallest angle in right triangle knICD ? 58 10 58 58 10

Paper 60 · ACT December 2009 · Form 68A · Math Test

How many distinct lines are there that each contain at least 2 of the 4 given points? 25 GO ON TO THE NEXT PAGE. AGf.68A

Paper 60 · ACT December 2009 · Form 68A · Math Test

If x is any positive inteoer, then the sum of 6x and I Ix ig always divisible by which of the followiog. DO YOUR FIGURING HERE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

For what value of a would the following system of equations have infinitely many solutions? 2y=6 4y=3a

Paper 60 · ACT December 2009 · Form 68A · Math Test

A fan has 5 identical blades that are equally spaced around the cellter of the fan, as shown below. What is the measure of the angle of rotation that would move Blade M clockwise ( C ) to the position of Blade N ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

Cans A and B are both right circular cylinders. The ra(lius of the base of Can A is 4 tiffles the iadius of the base of Can B, and the height of Can A is 5 times the .height of Can B. The volume of Can A is how many times the volume of Can B ? (Note: V cylinder oh) 80

Paper 60 · ACT December 2009 · Form 68A · Math Test

5

Paper 60 · ACT December 2009 · Form 68A · Math Test

A box contains 100 cardboard circles. Written on each circle is one of the following nurnbers, with llo numbers repeated. <1 . fvf2 , Nf3 ,

Paper 60 · ACT December 2009 · Form 68A · Math Test

By the law of cosines, u 2bc cos L4 for a triangle with sides of lengths a, b, and c oppositè ZA, ZB, and ZC: Iespectively. A boat travels 25 miles due east, makes a 40° turn toward the north. and then trav¢ls 30 miles, as shown below. To the nearest mile, what is the straight-line distance between the boat's starting position and its ending positioll? (Note: cos 40° 0.766, cos(180 - a) = _cos (x) ending position positioil 25

Paper 60 · ACT December 2009 · Form 68A · Math Test

The function f(x) is defined below. What is the value of f(-l) ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the foll'owing equations given in factored form has roots at - i)-o 27 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 56-58. The table below shows an electric utility co]npany'g old and new rates. In the table, kwh stands foi kilowatt-houi, a standard u￿t for measuring electrical eDergy. Runion Electric Association Rates Old rate New rate Monthly service charge $7.00 $11.00 Energy-use charge . first 1,500 kwh kwh over 1,500

Paper 60 · ACT December 2009 · Form 68A · Math Test

Source question 56. Refer to the source image.

Paper 60 · ACT December 2009 · Form 68A · Math Test

By about what percent did the monthly service charge incTease from the old rate to the new rate? 4Yo ACT-68A 28 GO ON TO THE NEXT PAGE.

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the lollowinoT is the graph of the function that gives the percent of increase for electric bills calculated under the new iates compared to the bills calculated under the old rates? DO YOUR FIGURING HERE. ¢30 io io kwh kwh 10 kwh kwh 10 kwh

Paper 60 · ACT December 2009 · Form 68A · Math Test

Which of the following equations describes a line that is perpcndicular to a line with equation 5x- 6y = 30 ?

Paper 60 · ACT December 2009 · Form 68A · Math Test

In a regular pentagon, all 5 interior angles are congruent. What is the measure of each interior angle of a regular pclltagon? 36° 108° END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. AGT-68A 29