Math

ACT Mathematics Test contains 60 multiple-choice questions to be answered in 60 minutes. The ACT Math Test is always the second test. Concepts tested include arithmetic, algebra, coordinate geometry, plane geometry, and trigonometry.

If 5 times a number n is subtracted from 15, the result is negative

If 5 times a number n is subtracted from 15, the result is negative. Which of the following gives the possible value(s) for n ?

  1. 0 only
  2. 3 only
  3. 10 only
  4. All n > 3
  5. All n < 3

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The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day

The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day satisfies the inequality ⎪t - 24⎪ ≤ 30. Which of the following temperatures, in degrees Fahrenheit, is NOT in this range?

  1. -10
  2. -6
  3. -5
  4. 0
  5. 54

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The scatterplot in the standard (x, y) coordinate plane below contains data points

The scatterplot in the standard (x, y) coordinate plane below contains data points showing a strong linear correlation between the variables x and y. Mia drew the line shown to model the data. One of the following equations represents Mia’s line. Which one?

  1. y = -3x + 8
  2. y = -3x + 10
  3. y = -2x + 10
  4. y = 2x + 10
  5. y = 2x + 8

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At a school picnic, 1 junior and 1 senior will be selected to lead the activities

At a school picnic, 1 junior and 1 senior will be selected to lead the activities. If there are 125 juniors and 100 seniors at the picnic, how many different 2-person combinations of 1 junior and 1 senior are possible?

  1. 25
  2. 100
  3. 125
  4. 225
  5. 12,500

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If f(x) = x^2 + x + 5 and g(x) = √x, then what is the value of g(4)/f(1)

If f(x) = x2 + x + 5 and g(x) = √x, then what is the value of g(4)/f(1)?

  1. 2/7
  2. 25/7
  3. 2/25
  4. 2
  5. 4

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The braking distance, y feet, for Damon's car to come to a complete stop is modeled by

The braking distance, y feet, for Damon's car to come to a complete stop is modeled by y = 3(x2 + 10x)/40, where x is the speed of the car in miles per hour. According to this model, which of the following is the maximum speed, in miles per hour, Damon can be driving so that the braking distance is less than or equal to 150 feet?

  1. 10
  2. 30
  3. 40
  4. 50
  5. 60

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A park has the shape and dimensions in blocks given below. A water fountain is located halfway between

A park has the shape and dimensions in blocks given below. A water fountain is located halfway between point B and point D. Which of the following is the location of the water fountain from point A ? (Note: The park’s borders run east-west or north-south.)

  1. 3½ blocks east and 6 blocks north
  2. 5 blocks east and 4½ blocks north
  3. 5 blocks east and 6 blocks north
  4. 8½ blocks east and 4½ blocks north
  5. 9 blocks east and 7½ blocks north

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In the right triangle shown below, which of the following statements is true about ∠A

In the right triangle shown below, which of the following statements is true about ∠A ?

  1. cos A = 12/13
  2. sin A = 12/13
  3. tan A = 12/13
  4. cos A = 13/12
  5. sin A = 13/12

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When graphed in the standard (x, y) coordinate plane

When graphed in the standard (x, y) coordinate plane, which of the following equations does not represent a line?

  1. x = 4
  2. 3y = 6
  3. x - y = 1
  4. y = 3x/4 - 2
  5. x2 + y = 5

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The depth of a pond is 180 cm and is being reduced by 1 cm per week

The depth of a pond is 180 cm and is being reduced by 1 cm per week. The depth of a second pond is 160 cm and is being reduced by 1/2 cm per week. If the depths of both ponds continue to be reduced at these constant rates, in about how many weeks will the ponds have the same depth?

  1. 10
  2. 20
  3. 40
  4. 80
  5. 140

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A machine part is diagrammed in the figure below with the dimensions given in inches

A machine part is diagrammed in the figure below with the dimensions given in inches. If the centers of the circles lie on the same line parallel to the bottom of the part, what is the distance, in inches, between the centers of the 2 holes in the machine part?

  1. 5 3/16
  2. 5 1/16
  3. 5
  4. 4 13/16
  5. 4 3/16

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What is the y-intercept of the line in the standard (x, y) coordinate plane

What is the y-intercept of the line in the standard (x, y) coordinate plane that goes through the points (-3, 6) and (3,2) ?

  1. 0
  2. 2
  3. 4
  4. 6
  5. 8

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Ken baked, frosted, and decorated a rectangular cake for the last Math Club meeting

Ken baked, frosted, and decorated a rectangular cake for the last Math Club meeting. The cake was 3 inches high, 12 inches wide, and 16 inches long. He centered the cake on a piece of cardboard whose rectangular top surface had been covered with aluminum foil, as shown in the figure below.

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If 12x = -8(10 - x), then x = ?

If 12x = -8(10 - x), then x = ?

  1. 20
  2. 8
  3. 7 3/11
  4. 6 2/13
  5. -20

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Points B and C lie on AD as shown below. The length of AD is 30 units

Points B and C lie on AD as shown below. The length of AD is 30 units; AC is 16 units long; and BD is 20 units long. How many units long, if it can be determined, is BC?

  1. 4
  2. 6
  3. 10
  4. 14
  5. Cannot be determined from the given information 

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In the figure below, G is the center of the circle, LK is a diameter

In the figure below, G is the center of the circle, LK is a diameter, H lies on the circle, J lies outside the circle on LK, and JM is tangent to the circle at M. Which of the following angles or minor arcs has the greatest degree measure?

  1. arc LM
  2. arc MK
  3. ∠JMG
  4. ∠LHK
  5. ∠MJL

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What are the values for x that satisfy the equation (x + a)(x + b) = 0

What are the values for x that satisfy the equation (x + a)(x + b) = 0 ?

  1. -a and -b
  2. -a and b
  3. -ab
  4. a and -b
  5. a and b

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Absolute Valve: ⎪3(-2) + 4⎪ = ?

⎪3(-2) + 4⎪ = ?

  1. -2
  2. 2
  3. 5
  4. 9
  5. 10

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In the figure below, ΔABC and ΔDEF are similar triangles

In the figure below, ΔABC and ΔDEF are similar triangles with the given side lengths in meters. What is the perimeter, in meters, of ΔDEF ?

  1. 3
  2. 8
  3. 11
  4. 12
  5. 13

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The figure below shows quadrilateral ABCD. What is the measure of ∠C

The figure below shows quadrilateral ABCD. What is the measure of ∠C ?

  1. 120°
  2. 115°
  3. 105°
  4. 100°
  5. 80°

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Mele earned scores of 75, 70, 92, 95, and 97 points

Mele earned scores of 75, 70, 92, 95, and 97 points (a total of 429 points) on the first 5 tests in Economics II. Solving which of the following equations for s gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests?

  1. 429/5 + s = 85
  2. 429/6 + s = 85
  3. (s + 429)/5 = 85
  4. (s + 429)/6 = 85
  5. (s + 429)/6 = 85/100

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The 13-member math club needs to choose a student government representative

The 13-member math club needs to choose a student government representative. They decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Samara, who is a member of the club but NOT an officer, will be chosen?

  1. 0
  2. 1/13
  3. 1/10
  4. 3/13
  5. 1/3

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A museum offers a 2-hour guided group tour

A museum offers a 2-hour guided group tour. For groups with fewer than 25 people the cost is $9.25 per person; for groups with 25 people or more the cost is $8.50 per person. The 27 people in the 9:00 a.m. tour group each paid $9.25 in advance. What is the total refund that the museum owes the 9:00 a.m. group?

  1. $12.50
  2. $13.00
  3. $18.75
  4. $20.25
  5. $25.00

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The cost of a gym membership is a onetime fee of $140

The cost of a gym membership is a onetime fee of $140, plus a monthly fee of $40. Brendan wrote a $500 check to pay his gym membership for a certain number of months, including the onetime fee. How many months of membership did he pay for?

  1. 3
  2. 4
  3. 9
  4. 12
  5. 13

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A restaurant occupying the top floor of a skyscraper rotates

A restaurant occupying the top floor of a skyscraper rotates as diners enjoy the view. Ling and Sarah notice that they began their meal at 7:00 p.m. looking due north. At 7:45 p.m. they had rotated 180° to a view that was due south. At this rate, how many degrees will the restaurant rotate in 1 hour?

  1. 90°
  2. 180°
  3. 240°
  4. 270°
  5. 400°

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The probability distribution of the discrete random variable X

The probability distribution of the discrete random variable X is shown in the table below. What is the expected value of X ?

  1. 1/6
  2. 1/3
  3. 1
  4. 2
  5. 3 1/6

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The lengths of the triangle are rounded to the nearest 0.1 cm

The lengths of the triangle shown below are rounded to the nearest 0.1 cm. What is the area, to the nearest 1 cm2, of this triangle?

(Note: The area of any triangle with sides of length a, b, and c opposite angles of measure A, B, and C, respectively, is given by 1/2 ab sin C.)

  1. 4
  2. 5
  3. 8
  4. 10
  5. 14

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In the circle with center D, the length of radius CD is 4 cm

In the circle with center D shown below, the length of radius CD is 4 cm, the length of BC is 1 cm, and BC is perpendicular to radius AD at B. When ∠ADC is measured in degrees, which of the following expressions represents the length, in centimeters, of arc AC ?

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A finite arithmetic sequence has 7 terms, and the first term is 3/4

A finite arithmetic sequence has 7 terms, and the first term is 3/4. What is the difference between the mean and the median of the 7 terms?

  1. 0
  2. 3/4
  3. 4/3
  4. 3
  5. 4

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Whenever j and k are positive integers such that (√3)^j = 27^k

Whenever j and k are positive integers such that (√3)j = 27k, what is the value of j/k?

F. 1/6
G. 3/2
H. 3
J. 4
K. 6

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Mario was riding a bicycle with wheels 26 inches in diameter

Mario was riding a bicycle with wheels 26 inches in diameter. During 1 minute of Mario's ride, the wheels made exactly 200 revolutions. At what average speed, in feet per second, was Mario riding during that minute?

  1. 65π/9
  2. 65π/18
  3. 130π/9
  4. 845π/18
  5. 1690π/9

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The 3 parabolas graphed in the standard (x,y) coordinate plane

The 3 parabolas graphed in the standard (x,y) coordinate plane below are from a family of parabolas. A general equation that defines this family of parabolas contains the variable n in addition to x and y. For one of the parabolas shown, n = 1; for another, n = 2; and for the third, n = 3. Which of the following could be a general equation that defines this family of parabolas for all n ≥ 1 ?

  1. y = nx2 + 1
  2. y = 1/n x2 + 1
  3. y = x2 + n
  4. y = -nx2 + 1
  5. y = -1/n x2 + 1

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Which of the following matrix products is undefined

Four matrices are given below.

Which of the following matrix products is undefined?

  1. WX
  2. WY
  3. YZ
  4. XW
  5. XZ

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For all nonzero values of x, (12x^6 - 9x^2)/3x^2

For all nonzero values of x, (12x6 - 9x2)/3x2 = ?

  1. 4x3 - 3x
  2. 4x3 - 3
  3. 4x4 - 9x2
  4. 4x4 - 3x
  5. 4x4 - 3

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Diana is baking bread, and the original recipe calls for

Diana is baking bread, and the original recipe calls for 1 1/2 teaspoons of yeast and 2 1/2 cups of flour. Diana will use the entire contents of a packet that contains 2 1/4 teaspoons of yeast and will use the same ratio of ingredients called for in the original recipe. How many cups of flour will Diana use?

  1. 1 7/8
  2. 3 1/4
  3. 3 1/2
  4. 3 3/4
  5. 4

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The table below shows the results of a survey of 250 people

The table below shows the results of a survey of 250 people who were asked whether they like to read and whether they play a musical instrument.

According to the results, what is the probability that a randomly selected person who was surveyed likes to read, given that the person plays a musical instrument?

  1. 1/5
  2. 5/9
  3. 5/11
  4. 9/25
  5. 11/25

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Given 10^(2x-1)/x = 1

Given 10(2x-1)/x = 1, x = ?

  1. -1/2
  2. -1/8
  3. 1/2
  4. 10/19
  5. 1

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Lucky found $8.25 in pennies, nickels, dimes, and quarters

Lucky found $8.25 in pennies, nickels, dimes, and quarters while walking home from school one week. When she deposited this money in the bank, she noticed that she had twice as many nickels as pennies, 1 fewer dime than nickels, and 1 more quarter than nickels. How many quarters did Lucky find that week?

  1. 3
  2. 9
  3. 16
  4. 21
  5. 26

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A teacher assigns each of her 18 students a different integer

A teacher assigns each of her 18 students a different integer from 1 through 18. The teacher forms pairs of study partners by using the rule that the sum of the pair of numbers is a perfect square. Assuming the 9 pairs of students follow this rule, the student assigned which number must be paired with the student assigned the number 1?

  1. 16
  2. 15
  3. 9
  4. 8
  5. 3

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After polling a class of 20 music students by a show of hands

After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano. Given that information, what is the minimum number of students in this music class who play both the guitar and the piano?

  1. 0
  2. 1
  3. 8
  4. 9
  5. 17

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