ACT Past Papers with Answers

Paper 10

ACT December 2022

Form F07 · Math Test · 60 questions

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Carnell is paid a regular hourly wage of $13.50 per hour for working up to and including 40 hours in 1 week. For each additional hour he works in a week, Carnell is paid twice his regular hourly wage. Carnell worked 48 hours this week. What is his pay for this week? (Note: Amounts are before taxes and benefits are deducted.)

A$0,594.00B$0,648.00C$0,756.00D$0,864.00E$1,296.00

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Paper 10 · ACT December 2022 · Form F07 · Math Test

In the standard (x,y) coordinate plane, what is the slope of the line with the equation y − 2 = (x + 3) ?

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AChoice F — see source imageBChoice G — see source imageC−2D1E3

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Sofia earned scores of 85, 86, 87, and 82 points on 4 math tests. What score must Sofia earn on the 5th math test for the average of the 5 tests to be exactly 3 points higher than the average of the first 4 tests? 1 _ _ 2 1 _ _ 2 3 _ _ 2 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

A070B082C085D088E100

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The parallelogram below has consecutive angles with measures x° and 28°. What is the value of x ?

A112B118C124D146E152

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Two side lengths of the right triangle shown below are given in inches. How many inches long is the hypotenuse?

A√•• 22B√•• 55C√•• 73D0011E0073

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Using only Step 1 followed by Step 2 below, Amir correctly solved a linear equation. Step 1: Subtract 16 from both sides of the equation. Step 2: Multiply both sides of the resulting equation by 5. One of the following equations is the equation that Amir solved. Which one? x° 28° ? 8 3 1 _ _ 5 1 _ _ 5 1 _ _ 5 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-F07 2 2

An − 16 = 14Bn − 14 = 16Cn + 16 = 14D5n − 16 = 14E5n + 14 = 16

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Paper 10 · ACT December 2022 · Form F07 · Math Test

All the kindergarten students at Cannon Elementary School are in exactly 1 of 3 classes. The 1st class has 10 boys and 15 girls, the 2nd class has 9 boys and 17 girls, and the 3rd class has 11 boys and 12 girls. All the kindergarten students at Cannon Elementary School are gathered in the gym for an assembly where 1 kindergarten student is randomly selected to win a prize. What is the probability that the selected student will be a boy?

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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 10 · ACT December 2022 · Form F07 · Math Test

Jamal purchased a car that had a purchase price of $6,400, which included all other costs and tax. He paid $1,500 as a down payment and got a loan for the rest of the purchase price. Jamal paid off the loan by making 36 payments of $200 each. The total of all his payments, including the down payment, was how much more than the car’s purchase price?

A$0,800B$2,300C$4,900D$7,200E$8,700

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the solution of the equation 8(x + 2) = 4x − 2(x − 3) ?

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A−B−C−DChoice D — see source imageEChoice E — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The expression (2x)3 (3x)2 is equivalent to: 1 _ _ 2 15 __ _ 22 15 __ _ 37 22 __ _ 37 19 __ _ 51 5 _ _ 3 5 _ _ 6 11 __ _ 3 1 _ _ 6 2 _ _ 3 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-F07 2 2

A36x5B36x7C72x5D72x6E72x7

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Paper 10 · ACT December 2022 · Form F07 · Math Test

3a − 4(2b − 5a) + 7(3a + 2b) is equivalent to:

A04a + 3bB04a + 6bC04a + 7bD44a − 0bE44a + 6b

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A square and a rectangle have the same area. The length of the rectangle is 45 centimeters, and the width of the rectangle is 5 centimeters. What is the length, in centimeters, of a side of the square?

A010B015C025D100E225

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Square ABEF and parallelogram ACDG are shown in the figure below. Points E and F are on DG ___ _ , B is on AC ___ , and the lengths given are in inches. What is the ratio of the area of ABEF to the area of ACDG ?

A1:8B1:16C3:8D8:1E8:3

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A 2-liter bottle of Fizzo contains approximately

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the smallest integer greater than √•• 77 ?

A05B08C09D11E39

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A wheelchair ramp will be constructed for a public library. The ramp will extend 20 inches horizontally for every 1 inch of rise vertically. The rise of the ramp will be 30 inches. Which of the following values is closest to the length, in feet, the ramp will extend horizontally?

A03B10C18D36E50

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Padma’s teacher asked her to subtract 3 from a certain number and then divide the result by 9. Instead, Padma subtracted 9 and divided the result by 3, getting an answer of 43. What would her answer have been had she worked the problem as her teacher asked?

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A015B034C138DChoice D — see source imageEChoice E — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

On the local car dealer’s lot, there are only 26 cars with a sunroof and only 18 cars with cruise control. The number of cars on the lot with both a sunroof and cruise control must be: 40 __ _ 9 43 __ _ 3 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-F07 2 2

Aexactly 44.Bexactly 8.Cat least 8.Dno more than 8.Eno more than 18.

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Paper 10 · ACT December 2022 · Form F07 · Math Test

On her algebra exam, Hannah had to solve the equation x2 + 3x − 8 = 0 for x. Confident that the quadratic formula was the correct method to solve this equation, she started her solution with the equation below. What error, if any, did Hannah make in setting up the equation? x = term −4(1)(8) under the radical. under the radical. denominator. numerator.

AHannah should have used −8 instead of 8 in theBHannah should have used −3 instead of 32CHannah should have used −2 instead of 2 in theDHannah should have used 3 instead of −3 in theEHannah did not make an error.

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Every 10 minutes, Channel 7 begins a 60-second-long commercial. Every 12 minutes, Channel 5 begins a 60-second-long commercial. Each channel began a 60-second-long commercial at the same instant. How many minutes will elapse before both channels next begin a 60-second-long commercial at the same instant?

A22B24C30D44E60

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Paper 10 · ACT December 2022 · Form F07 · Math Test

When Professor Soto began his trip to a mathematics conference, he noticed that the 2 digits of the recorded temperature, in degrees Fahrenheit, had a sum of 8. Later, he noticed that the 2 digits were reversed and that the temperature had warmed 18°F. What was the temperature, in degrees Fahrenheit, at the beginning of his trip?

A17°FB26°FC35°FD53°FE62°F

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Given functions f(x) = 4x + 1 and g(x) = x2 − 2, what is the value of f_g(−3)+ ? −3 ± √•••••••• •• 32 − 4(1)(8) _____________ ___ __ 2(1) DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-F07 2 2 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-F07 2 2 23. In the standard (x,y) coordinate plane, A is located at (4,9). What is the location of the image of A that results from reflecting A over the y-axis?

A−123B0−43C0−31D0 29E1196(−9, 4)7(−4,−9)8(−4, 9)9( 4,−9)10( 9,−4)

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Source question 23. Refer to the source image.

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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 10 · ACT December 2022 · Form F07 · Math Test

For every odd integer x, the expression x2 + x results in:

Aan even integer.Ban odd integer.Ca positive integer.Da negative integer.Ea prime number.

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the least positive number that has a remainder of 5 when divided by 7 and a remainder of 3 when divided by 5 ?

A20B27C33D35E50

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Naomi is going to install baseboard around the perimeter of her room’s rectangular floor, shown below. The floor has dimensions 15 feet by 20 feet. The 2 doorways in her room are each 3 feet wide and do not require baseboard. Assuming an average cost of $0.30 per linear foot requiring baseboard, how much will it cost Naomi to purchase baseboard for her room?

A$10.50B$19.20C$21.00D$88.20E$90.00

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Chou flies directly from New York City to San Francisco. New York City’s time is 3 hours later than San Francisco’s time. Chou left New York City at 7:30 a.m. local time and landed in San Francisco at 11:12 a.m. local time. How long was the trip? baseboard Petsnacks produces and markets food treats and toys for pets. It currently produces 3 different flavored treats for cats and 4 different flavored treats for dogs. One of its cat toys is a spherical catnip ball with an outside diameter of 4 inches. Catnip is an herb that causes a reaction in 80% of all domestic cats. Petsnacks makes a profit of $7.50 on each catnip ball it sells.

A3 hours 42 minutesB4 hours 18 minutesC6 hours 18 minutesD6 hours 42 minutesE7 hours 18 minutes

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Petsnacks is going to test its catnip ball on 200 domestic cats. Which of the following values is equal to the expected number of cats that will NOT have a reaction to the catnip in the toy?

A020B040C080D120E160

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Petsnacks sold 1,500 catnip balls in its 7th month of operation and 1,550 catnip balls in its 8th month. Given that its sales of these toys have followed an arithmetic sequence since the operation began, how much profit, in dollars, did Petsnacks make on the catnip balls in its 3rd month of operation?

A$09,375B$09,750C$10,125D$11,250E$11,625

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Next month at a pet-food trade show, Petsnacks will exhibit 1 box of each flavor of its entire line of pet treats in a row on a shelf. By that time, the company will have added 3 different flavors of gerbil treats to its line of pet treats. Which of the following computations gives the number of additional orders in which Petsnacks will be able to arrange its treats on the shelf with the new line of gerbil treats than without the gerbil treats? 10! ___ _ 3! 10! ____ 3!7! 7! ____ 3!4! 10! ______ 4!3!3! DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-F07 2 2 Use the following information to answer questions 28–30.

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AChoice F — see source imageBChoice G — see source imageC(10 − 3)!D10! − 7!E−

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A tree farmer has exactly 3 kinds of trees on his farm: apple, cherry, and evergreen. Of these trees, are apple, are cherry, and 120 trees are evergreen. The farmer has how many trees on his farm?

A203B210C220D400E720

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the median of the list of 10 numbers below? 87, 85, 78, 94, 67, 97, 55, 81, 87, 99

A82B83C85D86E87

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A board 1 inches by 3 inches is 6 feet long. You want to cut as many pieces as possible from the board so that each piece is 1 inches by 3 inches and 6 inches long. Each saw cut wastes inch of the board. How many 6-inch-long pieces will you be able to cut?

A13B12C11D10E09

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The probability that Event A will occur is . The probability that Event B will occur is . Given that Events A and B are mutually exclusive, what is the probability that Event A or Event B will occur? 1 _ _ 2 1 _ _ 3 1 _ _ 2 5 _ _ 8 5 _ _ 8 5 _ _ 8 5 _ _ 8 1 _ _ 8 1 _ _ 8 1 _ _ 4 1 __ _ 32 1 __ _ 12 1 _ _ 8 3 _ _ 8 1 _ _ 2 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-F07 2 2

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the measure, in degrees, of an angle with a measure of radians?

A063°B070°C090°D140°E280°

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Paper 10 · ACT December 2022 · Form F07 · Math Test

As shown below, D is on side CE ___ of rectangle ABCE such that the measure of ∠ADB is 90°. Which of the following angles must be congruent to ∠1 ?

A∠2 onlyB∠4 onlyC∠5 onlyD∠2 and ∠4E∠3 and ∠6

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The area of a circle is 64π square inches. What is the circumference, in inches, of the circle?

A08πB16πC24πD32πE64π

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Paper 10 · ACT December 2022 · Form F07 · Math Test

In the standard (x,y) coordinate plane, points A(2,3), B(4,0), and C(7,b) lie on the same line. What is b ? 7π __ _ 9 1 A B C D E 3 4 5 6 2 21 __ _ 2 9 _ _ 2 1 _ _ 3 19 __ _ 3 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-F07 2 2

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A−B−C−D6EChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

When a ≠ 0, which of the following is equivalent to + ?

Source page for act-december-2022-form-f07-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 10 · ACT December 2022 · Form F07 · Math Test

A jar contains 2 green mints and 3 white mints. If Renée randomly takes 2 mints out of the jar to eat, what is the probability that both of these mints are green?

Source page for act-december-2022-form-f07-math-040

AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The number of decibels, d, produced by an audio source can be modeled by the equation d = 10 log1 2, where I is the sound intensity, in watts per square meter, of the audio source. What is the sound intensity, in watts per square meter, for an audio source that produces 100 decibels? 1 _ _ a 2 _ _ 3 2 __ _ 3a 3 __ _ 3a 3 _____ a + 3 3 + 2a ______ 3a 3 + 2a ______ 3 + a 1 __ _ 10 3 __ _ 10 1 __ _ 20 9 __ _ 20 3 _ _ 5 I ___ __ 10−12 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-F07 2 2

A010−2B01022C01078D014E140

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The diagram below shows the location of Manuel’s boat, which is on a lake and anchored to a stationary buoy at point B. On the shore, Manuel’s house is at point H and his nearest neighbor’s house is at point N, which is 150 meters from H. The measures of 2 angles are given. Which of the following expressions represents the straight-line distance, in meters, from B to N ? (Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, = = .)

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Packmore Box Company manufactures a standard rectangular box a feet by b feet by c feet. A customer ordered a new box with double the volume of the standard box. Which of the following expressions represents the volume, in cubic feet, of the new box? b2 c2

A8abcBa2C2a + b + cD2a + 2b + 2cE2abc

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Paper 10 · ACT December 2022 · Form F07 · Math Test

For her mathematics class, Ms. Wilkerson is preparing a probability experiment using only dried kidney beans, dried pinto beans, and an empty jar. First, she puts 4 kidney beans into the empty jar. How many pinto beans must be added to the jar in order to make the probability of drawing a kidney bean exactly when randomly drawing 1 bean from the jar? 60° 150 m N H B 50° ? sin ∠C ______ _ c sin ∠B ______ _ b sin ∠A ______ _ a 150 sin50° _________ _ sin60° 150 sin50° _________ _ sin70° 150 sin60° _________ _ sin50° 150 sin60° _________ _ sin70° 150 sin70° _________ _ sin50° 1 _ _ 5 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-F07 2 2

A20B16C05D04E01

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A car rental agency has 20 cars. Of those cars, 4 are luxury sedans and all the other cars are midsize sedans. Each luxury sedan rents at a daily rate 50% greater than the daily rate for the midsize sedans. If the luxury sedans rent for $45 per day, what is the average daily rental fee, to the nearest dollar, of all 20 cars at this agency?

A$27B$33C$38D$42E$56

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Paper 10 · ACT December 2022 · Form F07 · Math Test

A portion of a regular polygon (all sides of equal length and all interior angles of equal measure) with n sides is shown below. The midpoint of BC ___ is M. The distance, in centimeters, from the polygon’s center, R, to the midpoint of a side is the same for all sides. Which of the following is an expression for the area, in square centimeters, of the polygon? + (MR)2

A(BC)(MR)B(CM)(MR)Cn(BC)Dn(BC + BR + CR)E√••••••••••••• (CM)2

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Let a, b, and c be the respective side lengths, in feet, of a triangle. Given that a is 5 and b is 7, which of the following inequalities gives all and only the possible values of c ?

Ac > 02Bc < 12C0 < c < 12D2 < c < 12E5 < c < 07

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Paper 10 · ACT December 2022 · Form F07 · Math Test

For the complex number i, which of the following expressions is equivalent to (x + i)(x − i) ? + 1 − 1 + 2ix + 1 − 2ix + 1 − 2ix − 1 R A B M C D E n _ _ 2 n _ _ 2 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-F07 2 2 The center of the circle shown below is at B, and the length of diameter AD ___ is 12 cm. The measure of DE C is 60°, and the measure of AC C is 70°.

Ax2Bx2Cx2Dx2Ex2

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the measure of major arc ACE C ?

A130°B230°C240°D250°E260°

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Triangle nACD is a right triangle. Which of the following expressions represents the length, in centimeters, of AC ___ ?

A06 sin,35°B06 sin,55°C06 sin,70°D12 sin,35°E12 sin,70°

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Paper 10 · ACT December 2022 · Form F07 · Math Test

If all points on the circle remain fixed in their current positions except E, which moves along the circle counterclockwise ( ) until it reaches A, the length of CE ___ during this movement will: 70° 60° E D B A C DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-F07 2 2 Use the following information to answer questions 49–51. DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-F07 2 2 52. The function f(x) = x3 is defined for all real numbers x. Which of the following expressions represents f −1 (x) ? √• x

Source page for act-december-2022-form-f07-math-051

Aremain unchanged.Bdecrease, then increase.Cdecrease only.Dincrease only.Eincrease, then decrease.637Choice G — see source image8Choice H — see source image9x10− x

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Source question 52. Refer to the source image.

Source page for act-december-2022-form-f07-math-052

AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Given positive integers a and b such that b < a < 14, what is the largest value of a + b that has a factor of 3 ?

A15B18C21D24E27

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Paper 10 · ACT December 2022 · Form F07 · Math Test

At an end-of-school-year party for juniors and seniors only, there are 20 more juniors than seniors. Of the 52 students at the party, 25% have summer jobs. Which of the following is closest to the maximum possible percent of the seniors at the party who have summer jobs?

A25%B36%C44%D81%E97%

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Paper 10 · ACT December 2022 · Form F07 · Math Test

What is the minimum value of 2x − 3y given that x and y satisfy the system of inequalities below? x ≥ −2 y ≤ 3 x − y ≤ 5

A−25B−13C07D17E25

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Paper 10 · ACT December 2022 · Form F07 · Math Test

The ratio of a to b is 5 to 1, and the ratio of b to c is 9 to 1. What is the value of ? 1 ____ 3 √• • x 1 __ _ x3 1 _ _ 3 1 _ _ 3 2a + 3b _______ 4b + 3c 1 _ _ 3 13 __ _ 31 37 __ _ 39 37 __ _ 7

Source page for act-december-2022-form-f07-math-056

A3BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

If t is any real number, which of the following statements must be true? = −t2

A−t < 0B−t < tC−t = tD−t ≤ ⎪−t⎪E(−t)2

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Paper 10 · ACT December 2022 · Form F07 · Math Test

Let a and b be positive real numbers such that log(a) = 3 and log(b) = 2. What is the value of log(a2

A?B7C8D11E12618

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Paper 10 · ACT December 2022 · Form F07 · Math Test

For real numbers a and b on the number line below, where a < b, which of the following values is a possible value for b ?

Source page for act-december-2022-form-f07-math-059

A−2B0CChoice C — see source imageD1EChoice E — see source image

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Paper 10 · ACT December 2022 · Form F07 · Math Test

For all positive values of x, which of the following expressions is equivalent to 2 3 √•• • 2x · 3 √• x ? √••• • 12x √••• • 24x √••• 4x2 √••• 8x2 √•••• 16x2 a b a 3 _ _ 7 9 _ _ 4 DO YOUR FIGURING HERE. 29 ACT-F07 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

A3B3C3D3E3

Form F07 · Math Test · 60 questions

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