ACT Past Papers with Answers

Paper 13

ACT April 2022

Form Z08 · Math Test · 60 questions

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

On Monday, Elsa put $40 in her empty lockbox. Each following Monday, Elsa will deposit $18 to her lockbox. Which of the following expressions gives the number of dollars in Elsa’s lockbox after Elsa’s deposit w weeks from now?

A40 + 18wB40 − 18wC40w + 18D40w − 18E(40 + 18)w

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Raheem made a down payment of $250.00 at a local store for an HDTV that cost $880.00 with tax included. He arranged to make 8 equal monthly payments to the store to finish paying for the HDTV. Given that he paid no additional fees, how much was Raheem’s monthly payment?

A$078.75B$080.00C$110.00D$140.00E$141.25

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is 25% of 50% of 80 ?

A05B10C20D40E60

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In scientific notation, 0.00041 = ? DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

A4.1 × 10−5B4.1 × 10−4C4.1 × 10−3D4.1 × 103E4.1 × 104

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the value of 5xy2 when x = −2 and y = −4 ?

A,−320B,−160C, 160D, 320E1,600

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the value of ⎪−8⎪ − ⎪7 − 33⎪ ?

A−34B−18C18D34E48

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Given that a3 ak = a9 for all real numbers a, what is the value of k ?

A02B03C06D12E27

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the least common multiple of 20, 30, and 130 ?

A000,60B000,78C00,180D00,780E78,000

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

If f(x) = 2x2 + 6x − 7, then f(−3) = ?

A−37B0−7C07D11E29

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the figure below, BE ↔ and CF ↔ intersect at point A. Points G and D are in the interiors of angles ∠BAF and ∠CAE, respectively. Some angle measures are given. What is the measure of ∠BAG ? B C D E F G A 56° 32° 64° DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A56°B60°C84°D90°E96°

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Salma attended a concert on Friday. She arrived at the concert hall at 5:46 p.m. and left the concert hall at 11:27 p.m. How long was Salma at the concert hall?

A5 hours 19 minutesB5 hours 41 minutesC6 hours 19 minutesD6 hours 21 minutesE6 hours 41 minutes

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Given that x ≤ 3 and x + y ≥ 5, what is the LEAST value that y can have?

A−8B−2C0D2E8

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the figure below, parallel lines l and m are intersected by transversal n, forming the numbered angles. Which of the following congruence statements is NOT necessarily true?

A∠1 ≅ ∠5B∠2 ≅ ∠8C∠3 ≅ ∠5D∠4 ≅ ∠7E∠6 ≅ ∠8

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the largest possible product for 2 even integers whose sum is 50 ?

A096B100C184D400E624

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The blood types of 150 people are determined for a study. The results show that 62 people have Type O blood, 67 have Type A blood, 15 have Type B blood, and the others have Type AB blood. If 1 person from this study is randomly selected, what is the probability that this person has either Type O or Type AB blood? 2 3 6 7 1 4 5 8 n l m 1 _ _ 3 11 __ _ 25 14 __ _ 25 31 __ _ 75 34 __ _ 75 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

Source page for act-april-2022-form-z08-math-015

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

If x + y = 26 and x − y = 14, then y = ?

A06B07C12D20E40

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The chart below shows the possible combinations of numbers that can land faceup when 2 numbered cubes are rolled at the same time. Each combination is equally likely. What is the probability of rolling the numbered cubes so that the sum of the numbers that land faceup is 8 or greater?

Source page for act-april-2022-form-z08-math-017

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageE0

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The graph of the function y = √••••••• −log10 x is shown in the standard (x,y) coordinate plane below. The function is defined for values of x strictly between which of the following pairs of numbers? 1 2 3 4 5 6 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) 5 __ _ 12 5 __ _ 18 5 __ _ 36 13 __ _ 18 y 1 1 x O DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A−10 and 0−1B0−1 and 0 0C0 0 and 0 1D0 1 and 010E10 and 100

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

To increase the mean of 7 numbers by 3, by how much would the sum of the 7 numbers have to increase?

A03B07C10D21E42

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the standard (x,y) coordinate plane, the line with equation y + 1 = (2x + 8) has a slope of:

Source page for act-april-2022-form-z08-math-020

AChoice F — see source imageBChoice G — see source imageC2D5E6

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

A parallelogram has a perimeter of 88 inches, and 1 of its sides measures 18 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

A18, 18, 34B18, 17, 17C18, 26, 26D18, 35, 35ECannot be determined from the given information

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Five friends play golf at a course that charges both an annual membership fee and a fee to play each round. Each point on the scatterplot below represents the number of rounds each person played during a year and the total fees the golf course charged that person. One of the following values is the fee to play each round. Which one? 3 _ _ 4 3 _ _ 4 3 _ _ 2 1 2 3 20 60 100 140 180 220 260 300 4 5 6 7 total fees (dollars) number of rounds DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A$000.75B$030.00C$053.68D$090.00E$300.00

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Tomás wants to tile a rectangular floor with square tiles that measure 12 inches on a side. The floor measures 10 feet 6 inches long by 8 feet 6 inches wide. If he is able to cut the tiles without waste, what is the minimum whole number of tiles Tomás needs to completely cover the floor?

A080B090C098D099E100

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the standard (x,y) coordinate plane below, nABC is bounded by AB ___ , AC ___ , and the y-axis. Which of the following values is closest to the area, in square coordinate units, of nABC ?

A15.8B31.6C35.0D70.0E79.1

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In right triangle nJKL, the right angle is at K, the length of JK ___ is 10 cm, and sin,L = . What is the value of cos,J ?

Source page for act-april-2022-form-z08-math-025

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

John averages 60 miles per hour (mph) the 6 hours he travels from his house to Ling’s house. On his return trip, John experiences heavy traffic due to construction zones. He averages 36 mph the first 3 hours of his return trip. What is the average speed, in miles per hour, John must drive for the rest of the return trip for a return trip of 7 hours? x y O B(0,6) C(0,−8) A(5,2) 5 __ _ 11 5 __ _ 11 6 __ _ 11 5 ____ _ √•• 96 6 ____ _ √•• 96 5 ______ √••• 146 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-Z08 2 2 At Western High School and Eastern High School, 200 students and 100 students, respectively, were surveyed to determine their fast-food preferences. Each of the 300 students indicated 1 preference among 5 choices, as summarized in the pie charts below. (Note: Each pie chart is made up of sectors that are proportional in size to the percent of students they represent.)

A42B48C54D63E66

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

How many students surveyed at Western High School indicated chicken as their preference?

A12B17C24D36E40

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the measure, to the nearest 1°, of the central angle of the sector that represents the number of students at Western High School who indicated pizza as their preference? Western High School Eastern High School burgers 23% tacos 20% pizza 40% chicken 12% egg rolls 5% pizza 50% burgers 30% tacos 10% chicken 5% egg rolls 5% DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-Z08 2 2 Use the following information to answer questions 27–29.

A040°B080°C108°D120°E144°

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The same survey was taken at Central High School. The percent of students at Eastern High School who indicated chicken as their preference was 1 more than the percent of students at Central High School who indicated chicken as their preference. What percent of students at Central High School indicated chicken as their preference?

A03%B04%C08%D09%E12%

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Jermaine will build a metal wall sculpture that is composed of 3 circles of different sizes, shown below. The smallest circle will have a diameter of 8 inches, and the diameters of the 3 circles will be in the ratio of 1:2:4. To reinforce the sculpture, Jermaine will place a straight metal bar from the center of the smallest circle, through the center of the middle circle, to the center of the largest circle. What will be the length, in inches, of the bar?

A28B36C56D64E72

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Juan will flip a fair 2-sided coin and spin a wheel. The coin has 1 heads side and 1 tails side. The wheel has an equal chance of stopping on any one of its 4 sections: red, blue, yellow, and green. What is the probability that the coin lands tails side up and the wheel stops on the green section? 1 _ _ 2 1 _ _ 8 1 _ _ 6 1 _ _ 3 1 _ _ 2 3 _ _ 4 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

Source page for act-april-2022-form-z08-math-031

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The volume of air, in liters, in the lungs of an average person during normal breathing is a function of time, in seconds. This function is modeled by the sine function graphed in the standard (x,y) coordinate plane below. One of the following values is the period, in seconds, of this function. Which one?

A0.5B2.4C2.5D2.9E5.0

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

If f(x) = 5x and g(x) = −2, then −f_g(x)+ = ?

A−25B−√• 5C−D02E25

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the circle shown below, C is the center, AB ___ is a diameter, and CD ___ is a radius of length 10 inches that is perpendicular to AB ___ . Which of the following values is closest to the area, in square inches, of the shaded region (the combined area of the semicircle and nBCD) ? y x 5 0 0 10 15 volume (liters) time (seconds) 1 __ _ 25 10 C A B D DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A150B186C207D236E264 2.9 2.4

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

During one of their routines, the Longsboro High School marching band members line up in a succession of L-shaped formations. The first 4 formations, numbers 1 through 4, are shown below, with each dot representing a band member. The pattern demonstrated by the addition of band members in the first 4 formations continues through each successive L-shaped formation in the routine. Which of the following equations gives the relationship between n, the formation number, and b, the number of band members in that formation?

Ab = 0n + 2Bb = 0n + 4Cb = 2n + 3Db = 3n + 2Eb = 5n

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The Better Cellular Company offers customers 2 monthly plans. Plan A costs $40.00 per month plus $0.05 per minute of time used, while Plan B costs $20.00 per month plus $0.10 per minute of time used. What is the least whole number of minutes a customer could use in 1 month to make Plan A less expensive than Plan B for that month?

A050B051C399D400E401

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Which of the following expressions is equivalent to 4 √•••• • 81x16 ?

A3x2B3x4C3x8D9x4E9x8

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

A pyramid has a square base with a side length of 6 feet. The volume of the pyramid is 144 cubic feet. What is the height, in feet, of the pyramid? (Note: The volume of a pyramid with base area B and height h is Bh.) 1 3 2 4 1 _ _ 3 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A08B12C24D48E72

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the value of ?

Source page for act-april-2022-form-z08-math-039

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What are all the real solutions to the equation ⎪1 − 2x⎪ = 3 ?

Ax = −1 onlyBx = −1 and x = −2Cx = −1 and x = 1Dx = −1 and x = 2Ex = 1 and x = 2

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

For what value of a would the following system of equations have an infinite number of solutions? 2x − 3y = 60 4x − 6y = 3a

A02B04C06D12E18

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the equation ax + b = 0, when a, x, and b are integers and x and b are positive, a must be:

Anegative and a factor of b.Bnegative and a multiple of b.Cpositive and a factor of b.Dpositive and a multiple of b.Epositive and equal to b.

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Given the complex numbers 2 − i and 2 + i, which of the following expressions is equal to √••••••••••• (2 − i)(2 + i) ? 1 _____________ 1 1 + _________ 1 1 + _____ 1 + 1 _ _ 3 3 __ _ 10 3 _ _ 7 7 __ _ 11 7 __ _ 10 10 __ _ 3 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A√••••• • 3 + 4iB√••••• • 5 − 4iC√••••• • 5 + 4iD√• 3E√• 5

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Which of the following fractions is closest to 0 ?

Source page for act-april-2022-form-z08-math-044

A−B−CChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

A spin of a certain spinner has 5 possible outcomes. The table below shows the probability of spinning each of the 5 outcomes. The probability of spinning Outcome 4 is a and the probability of spinning Outcome 5 is 2a. What is the value of a ?

A0.06B0.09C0.12D0.18E0.33

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The quadrants of the standard (x,y) coordinate plane are shown below. The vertices of nABC are A(−3,3), B(−3,1), and C(−1,1). The triangle is translated by x′ = x + 5 and y′ = y − 2. The image of (x,y) on nABC is (x′,y′) on nA′B′C′. The vertices of nA′B′C′ lie in which quadrant(s)? 3 __ _ 25 1 _ _ 6 1 _ _ 2 1 _ _ 8 123 _____ 1,000 Outcome 1 2 3 4 5 Probability 0.20 0.38 0.24 a 2a quadrants of the standard (x,y) coordinate plane I II III IV x y O DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

AQuadrant I onlyBQuadrant II onlyCQuadrant III onlyDQuadrants I and IV onlyEQuadrants II and III only

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The figure below shows a map of Jennifer’s neighborhood. Which of the following expressions represents the straight-line distance, in miles, from Jennifer’s home to school? (Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, = = and c2 = a2 + b2 − 2ab cos,∠C.) + 62 − 2(4)(6) cos(25°) + 62 − 2(4)(6) cos(50°) + 62 − 2(4)(6) cos(130°)

Source page for act-april-2022-form-z08-math-047

AChoice A — see source imageBChoice B — see source imageC√•••••••••••••••••••••• 42D√•••••••••••••••••••••• 42E√••••••••••••••••••••••• 42

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The graph below shows the function f(x) = in the standard (x,y) coordinate plane. Which of the following is an equation of the horizontal asymptote of f(x) ? Jennifer’s home school 6 miles 50° 4 miles sin ∠C ______ _ c sin ∠B ______ _ b sin ∠A ______ _ a 4 sin(130°) __________ sin(25°) 6 sin(130°) __________ sin(25°) 2x − 5 _____ _ 7x + 5 O y x −1 −2 −3 1 3 −3 −2 −1 2 1 3 2 4 2 _ _ 7 2 _ _ 7 5 _ _ 7 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-Z08 2 2 In the ellipse shown below, AC ___ is the major axis with length 16 feet, BD ___ is the minor axis with length 12 feet, and E is the center. Point F lies on side BC ___ of the inscribed rhombus ABCD.

Ax = −1Bx =Cy = −1Dy =Ey =

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

For any ellipse, the area is πab, where a and b are half the lengths of the major and minor axes, respectively. What is the area, in square feet, of the shaded region (the region outside the rhombus and inside the ellipse)?

A012π − 24B012π − 48C048π − 48D048π − 96E192π − 96

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Which of the following expressions gives the measure of ∠EBC ? 1 2 1 2 1 2 1 2 1 2

Asin−1Bsin−1Ctan−1Dtan−1Ecos−1

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

The eccentricity, e, of an ellipse is a measure of the flatness of the ellipse. The eccentricity of a circle is 0. The value of e is given by the ratio , where a and b are half the lengths of the major and minor axes, respectively. Which of the following intervals contains the value of e for this ellipse? 8 F C D A B E 6 3 _ _ 5 3 _ _ 4 3 _ _ 4 4 _ _ 3 4 _ _ 5 √••••• • a2 − b2 ________ _ a DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-Z08 2 2 Use the following information to answer questions 49–51.

A0.0 < e < 0.2B0.2 < e < 0.4C0.4 < e < 0.6D0.6 < e < 0.8E0.8 < e < 1.0

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Given the recursive formula below, which of the following equations is a correct explicit formula for the sequence? 0 a1 = 10 an + 1 = 2an ) )

Aan = 08 + 2nBan = 09 + 0nCan = 09 + 2nDan = 10(2nEan = 10(2n − 1

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

A toddler has 2 sets of blocks. The blocks within each set are equal-sized cubes. The blocks within one set are smaller than the blocks within the other set. The edge length of each smaller block is the edge length of each larger block. How many of the smaller blocks must be stacked together to create an arrangement with the same volume as 1 larger block?

A8B6C4D3E2

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

What is the determinant of the matrix 3 4?

A−40B0−6C040D104E160

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

A different whole number from 1 through 150 will be painted on each of the 150 parking spaces in a new parking lot. Each number will be painted using a minimum number of digits. For example, for space 15, 2 digits, 1 and 5, will be painted, and for the first 15 spaces, a total of 21 digits will be painted. In total, how many digits will be painted for all 150 parking spaces? 1 _ _ 2 8 12 10 20 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-Z08 2 2

A150B287C337D339E342

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

How many seating arrangements are possible for 5 people to sit in the 5 seats of a car if 1 person sits in each seat and only 3 of the 5 people can sit in the driver’s seat?

A010B012C024D072E120

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Let x be an odd integer greater than 1, and let b = x − 1. The equation logb,a = x is true. Which of the following phrases describes every value of a ?

AOdd onlyBOdd or 0 onlyC0 onlyDOdd and 0 onlyEEven and nonzero only

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Quadrilateral ABCD in the standard (x,y) coordinate plane has these 4 vertices: A(0,6), B(−1,1), C(3,1), and D(3,6). Which of the following categories most precisely describes this quadrilateral?

AA parallelogramBA rhombusCAn isosceles trapezoidDA quadrilateral that is not a trapezoidEA nonisosceles trapezoid

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

In the polynomial expansion of (x + y)5 , what is the coefficient of the x2 y3 term?

A01B04C06D10E15

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Paper 13 · ACT April 2022 · Form Z08 · Math Test

Meg has a bucket of plastic balls. Exactly 20% of these balls are yellow, and the rest are white. Some of the balls have a star on them. Exactly 6% of the balls are yellow and have a star on them. Meg will randomly draw 1 ball from the bucket. If the drawn ball is yellow, what is the probability that it will have a star on it? DO YOUR FIGURING HERE. 29 ACT-Z08 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

A0.012B0.030C0.120D0.260E0.300

Form Z08 · Math Test · 60 questions

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