ACT Past Papers with Answers

Paper 87 · ACT 2000 · Form 57B · Math Test

A bag contains 4 red jelly beans, 5 green jelly beans, and 3 white jelly beans. If a jelly bean is selected at random from the bag, what is the probability that the jelly bean selected is green?

Paper 87 · ACT 2000 · Form 57B · Math Test

The balance in Joan’s savings account tripled during the year. Joan then withdrew $500, and the resulting balance was $100. What was the balance in the account before it tripled? _ _ 5 7 5 __ 12 5 __ 23 _ _ 1 5 1 __ 12 6 4 2 –2 –4 –6 – –4 – 6 2 2 4 6 A B C D E x y

Paper 87 · ACT 2000 · Form 57B · Math Test

For what value of x is the equation 2(x – 6) + x = 18 true?

Paper 87 · ACT 2000 · Form 57B · Math Test

An earring manufacturing company has fixed costs of $10,000 per month and production costs of $0.60 for each pair of earrings it makes. If the company pro- duces x pairs of earrings in a month, which of the fol- lowing expressions represents the total of the company’s monthly costs?

Paper 87 · ACT 2000 · Form 57B · Math Test

Anton went to Mexico during summer vacation with his Spanish class. He recorded the number of pesos he spent each day in a table, as shown below. What was the mean number of pesos he spent per day? July 1 2 3 4 5 Pesos spent 250 100 150 100 400

 114

Paper 87 · ACT 2000 · Form 57B · Math Test

In !RST, shown below, RS __ _ ≅ RT __ _ , and the measure of ∠R is 40°. What is the measure of ∠S ?

Paper 87 · ACT 2000 · Form 57B · Math Test

In the formula d = rt, d represents distance in miles, r represents average speed in miles per hour, and t represents time in hours. What is an automobile’s average speed, in miles per hour, if it travels 60 miles in 1 hours?

Paper 87 · ACT 2000 · Form 57B · Math Test

⎪3 – 2⎪ – ⎪1 – 4⎪ = ?

Paper 87 · ACT 2000 · Form 57B · Math Test

If c, d, and f are nonzero real numbers and cd = f, which of the following equations for c must always be true? f _ _ d d _ _ f 1 _ _ 2 R T S GO ON TO THE NEXT PAGE. ACT-57B-PRACTICE 2 2 11. A cookie recipe calls for cup sugar to make 24 two-inch cookies. According to this recipe, how many cups of sugar should be used to make 60 two-inch cookies?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 11. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

In the figure below, B is on DE ___ and DE ___ ! AC ___ . Which of the following angle congruences must hold?

Paper 87 · ACT 2000 · Form 57B · Math Test

For what value of a is x = 3 a solution to the equation x + 3 = ax + 9 ?

Paper 87 · ACT 2000 · Form 57B · Math Test

Quadrilateral ABCD has vertices (–2,–1), (4,–3), (5,2), and (–1,3) in the standard (x,y) coordinate plane. Suppose ABCD is translated 2 units to the left and 1 unit down, forming quadrilateral A′B′C′D′. Which of the following shows the coordinates of the vertices of A′B′C′D′ ? E B 1 2 3 4 C A D 1 _ _ 6 2 _ _ 3 1 _ _ 5 5 _ _ 9 2 _ _ 3

 GO ON TO THE NEXT PAGE. ACT-57B-PRACTICE 2 2 15. In the figure below, F and E are points on GD __ _ _ . What is the ratio of the area of square ABEF to the area of parallelogram ACDG ?

Paper 87 · ACT 2000 · Form 57B · Math Test

000 + 15.000(10)

Paper 87 · ACT 2000 · Form 57B · Math Test

When a = b and c = d, which of the following equa- tions must be true?

Paper 87 · ACT 2000 · Form 57B · Math Test

The scales on both axes of the standard (x,y) coordi- nate plane below are the same. Of the following, which is the best estimate for the slope of AB __ _ ?

Paper 87 · ACT 2000 · Form 57B · Math Test

A road map is drawn to scale so that 1.5 inches represents 90 miles. How many miles does 1.6 inches represent? O x y A B 1 _ _ 4 1 _ _ 4 3 _ _ 4 G A D B C F E 2 in 5 in 2 2 19. In the standard (x,y) coordinate plane shown below, what is the distance in the x direction, in units, from point A to point B ?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 19. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

Which of the following is NOT a solution of (x – 3)(x – 1)(x + 3)(x + 7) = 0 ?

Paper 87 · ACT 2000 · Form 57B · Math Test

Which of the following shows the solution set for the inequality 5x – 1 ≥ 9 ?

Paper 87 · ACT 2000 · Form 57B · Math Test

If a = 10, then which of the following represents 8,003 ? 2 0 –2 2 0 2 0 2 0 8 _ 5 x x x 0 x –2 –2 –2 –2 x O y x A(–4,2) B(1,–1) 115



Paper 87 · ACT 2000 · Form 57B · Math Test

Whal is the value ot b in the solution to the syslem of equatioii% below?

Paper 87 · ACT 2000 · Form 57B · Math Test

Which ot the followino is an equivalent form of .¥+x(.¥+x)

Paper 87 · ACT 2000 · Form 57B · Math Test

To check the blope of il ramp, a buildino inspector place4 an overlay of the standard (x.)) coordinale plane on the construclion blueprint $0 that the x-axis aligns wilh IhL h()rizontJl ()n the blueprint. The line seomenl rcpresenting the side view of ihe ramp gues through the p()ints (l.-.l) and (14.?). Whai is the %lope of the planned ramp.

Paper 87 · ACT 2000 · Form 57B · Math Test

Due 10 infl¢tli()n, (I C<ir that formerly sold for S15.0(KJ now sell% f(Ir IQY. more. Which of ihe following CiilLul<lti()n% gives the curreni cost, in dollars. of the 15,000+ 10

Paper 87 · ACT 2000 · Form 57B · Math Test

In 3-dimensional %P<ice. Ihe set of all points l? uniis from the urigin is: a LirLIc. a %pherc. ¢1 cylinder. GO ON TO THE NEXT PAGE. ACT-57B-PRACTICE 2 2 33. If !"" 2x – 5 = 1, then x = ?

Paper 87 · ACT 2000 · Form 57B · Math Test

In the regular hexaoon below, I'ertiLe% B, C, (Ind D (ire labeled: OA is perpendicular to CD: A is the midp()iiii ot. CD: (ind O is the midpi)int of BC. Wh<it is Ihe devi'ee measure ot ZAOC ? 2b= 21 a+3b-

Paper 87 · ACT 2000 · Form 57B · Math Test

The numbcr 0.005 is IUO times (Is lar<ye as which ot the follow'ing numbers,.

Paper 87 · ACT 2000 · Form 57B · Math Test

The volume. V, of a sphere is deiermined by the fonnula V = where r is the radius of the .%phere. What is the volume. in cubic Lentiineters, ot- d %phere wilh a diameter 6 cenlimeter% lonu? 15 367[ 72 1447t

Paper 87 · ACT 2000 · Form 57B · Math Test

Which of the following is equal to

Paper 87 · ACT 2000 · Form 57B · Math Test

One neon sion tla.shes every 6 ,%econds. Another neon sign flashes every 8 seconds. If they flash logether and you begin couniing secunds, how mdny seLunds al"IL'r Ihey flash iogeiher will Lhey nexi flash iogether.

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 33. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

A truck sprang a leak at the bottom of its radiator, which held 480 ounces of fluid when it started to leak, and started losing radiator fluid at a constant rate of 4 ounces per minute. Suppose that the radiator continued to leak at this constant rate and that the truck, traveling at 35 miles per hour, could continue traveling at this rate until its radiator was completely empty. In how many miles would the radiator be empty?

Paper 87 · ACT 2000 · Form 57B · Math Test

Each of 3 lines crosses the other 2 lines, as shown below. Which of the following relationships, involving angle measures (in degrees), must be true? I. m∠4 + m∠5 + m∠10 = 180° II. m∠2 + m∠7 + m∠12 = 180° III. m∠2 + m∠7 + m∠10 = 180°

Paper 87 · ACT 2000 · Form 57B · Math Test

How many ordered pairs (x,y) of real numbers will satisfy the equation 2x – 5y = 6 ? 2 p n l 3 1 4 9 7 8 6 5 10 11 12 2 2 37. If Mark works steadily he can complete a task in x hours. What portion of the task remains if he works steadily for y hours, where y is any value less than x ?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 37. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

If a2 – b2 = 81 and a – b = 9, then a = ?

Paper 87 · ACT 2000 · Form 57B · Math Test

For y ≠ 0, is equivalent to:

Paper 87 · ACT 2000 · Form 57B · Math Test

The polygon below was a square with 12-inch sides before a triangle was cut off. What is the perimeter, in inches, of this polygon?

Paper 87 · ACT 2000 · Form 57B · Math Test

A circle in the standard (x,y) coordinate plane has center (2,–3) and radius 4 units. Which of the following equations represents this circle? 9 in 8 in 12 in y8 __ y2 (x – y) _____ x (x – y) _____ y (x – y) _____ (x + y) (y – x) _____ x (x + y) _____ x 117

 118

Paper 87 · ACT 2000 · Form 57B · Math Test

In the figure below, a square is circumscribed about a circle with a 30-inch diameter. Points A, B, C, and D are the midpoints of the square’s sides. What is the total area, in square inches, of the shaded regions?

Paper 87 · ACT 2000 · Form 57B · Math Test

For the triangle shown below, what is the value of tan z ?

Paper 87 · ACT 2000 · Form 57B · Math Test

In !ABD below, points D, C, and B are collinear, AD ___ is perpendicular to DB ___ , and AC ___ bisects ∠DAB. If the measure of ∠CBA is 40°, what is the measure of ∠ACB ?

Paper 87 · ACT 2000 · Form 57B · Math Test

You have enough material to build a fence 40 meters long. If you use it all to enclose a square region, how many square meters will you enclose?

Paper 87 · ACT 2000 · Form 57B · Math Test

For what nonzero whole number k does the quadratic equa- tion x2 + k2 x + 2k = 0 have exactly 1 real solution for x ? A D C B z 5 12 13 12 __ 13 13 __ 5 5 __ 13 12 __ 5 5 __ 12 A C B D GO ON TO THE NEXT PAGE. ACT-57B-PRACTICE 2 2 47. For all x > 3, = ?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 47. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

The pattern shown in abbreviated form below is com- posed of squares that are arranged horizontally and surrounded by 4 hexagons. All the squares are con- gruent, and all the hexagons are congruent. How many of these congruent hexagons will there be if the pattern is repeated until there are 20 squares?

Paper 87 · ACT 2000 · Form 57B · Math Test

If the circumference of a circle is π inches, how many inches long is its radius?

Paper 87 · ACT 2000 · Form 57B · Math Test

If the function f satisfies the equation f(x + y) = f(x) + f(y) for every pair of real numbers x and y, what is(are) the possible value(s) of f(0) ? 5 _ _ 2 !" 5 ___ _ 2 5 _ _ 4 4 _ _ 5 2 _ _ 5 5 _ _ 2 1 2 3 20 1 __ 18 1 __ 18 1 ____ _ x + 6 x ____ _ x – 6 –x ____ _ x + 6 3x – x2 __________ _ x2 + 3x – 18

 GO ON TO THE NEXT PAGE. ACT-57B-PRACTICE 2 2 51. The area of the trapezoid below is 16 square inches, the altitude is 2 inches, and the length of one base is 3 inches. What is the length, b, of the other base, in inches?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 51. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

This year, 75% of the graduating class of Harriet Tubman High School had taken at least 8 math courses. Of the remaining class members, 60% had taken 6 or 7 math courses. What percent of the gradu- ating class had taken fewer than 6 math courses?

Paper 87 · ACT 2000 · Form 57B · Math Test

Which of the following shaded regions is the graph in the standard (x,y) coordinate plane of the points that satisfy the inequality ⎪y⎪ ≤ 10 ? 10 –10 –10 10 y x 10 –10 –10 10 y x 10 –10 –10 10 y x 10 –10 –10 10 y x 10 –10 –10 10 y x 2 _ _ 3 2 3 b 2 2 54. A standard sheet of paper (8 inches wide by 11 inches long) is rolled up so that the 2 shorter edges just meet, forming a circular tube (cylinder) 8 inches high. How many inches in circumference is the tube?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 54. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

A baseball team played its first 20 games and won 12 of them. Then, the team went on a losing streak and lost its next 4 games. How many consecutive addi- tional victories does the baseball team need in order to bring its winning percentage back to at least what it was just before this 4-game losing streak?

Paper 87 · ACT 2000 · Form 57B · Math Test

Lines p and q intersect at point (1,3) in the standard (x,y) coordinate plane. Lines p and r intersect at (2,5). Which of the following is an equation for line p ?

Paper 87 · ACT 2000 · Form 57B · Math Test

If sin α = , and α is the measure of an acute angle, then cos α = ? (Note: An acute angle has a degree measure from 0° to 90°.) !" 7 ___ _ 4 !" 3 ___ _ 2 4 _ _ 3 1 _ _ 4 3 _ _ 4 289 ___ 4 11 __ _ 2π 1 _ _ 2 1 _ _ 2 119

 120 2 58. The radio station WEST is erecting a new transmitting tower that is 280 feet tall. A support wire will be attached to the ground at point A and to the tower __ s_ h 250 feet up at point B, as own below. The wire must be at least as long as B. Which of the following __ A _ expresses the length of AB, in feet?

Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 58. Refer to the source image.

Paper 87 · ACT 2000 · Form 57B · Math Test

In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms? 3 , 70 2 , 136 A 70° 250′ B 250 tan70° _____ 250_ _ cos70° _____ 250_ _ sin70° ACT-57B-PRACTICE 2 60. Right triangle !ABC has angle measures α, β, and γ degrees and side lengths a, b, and c inches, as illus- trated below. Which of the following is true about the value of the product tan β tan γ ? information. b2 ___ c_ 2 a4 b __ 2 _ A C B c a b β α γ END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.



Paper 87 · ACT 2000 · Form 57B · Math Test

Source question 60. Refer to the source image.