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.

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

- 1/6
- 1/3
- 1
- 2
- 3 1/6

The lengths of the triangle shown below are rounded to the nearest 0.1 cm. What is the area, to the nearest 1 cm^{2}, 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.)

- 4
- 5
- 8
- 10
- 14

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 ?

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?

- 0
- 3/4
- 4/3
- 3
- 4

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

F. 1/6

G. 3/2

H. 3

J. 4

K. 6

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?

- 65π/9
- 65π/18
- 130π/9
- 845π/18
- 1690π/9

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 ?

- y = nx
^{2}+ 1 - y = 1/n x
^{2}+ 1 - y = x
^{2}+ n - y = -nx
^{2}+ 1 - y = -1/n x
^{2}+ 1

Four matrices are given below.

Which of the following matrix products is undefined?

- WX
- WY
- YZ
- XW
- XZ

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

- 4x
^{3}- 3x - 4x
^{3}- 3 - 4x
^{4}- 9x^{2} - 4x
^{4}- 3^{x} - 4x
^{4}- 3

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 7/8
- 3 1/4
- 3 1/2
- 3 3/4
- 4

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?

- 1/5
- 5/9
- 5/11
- 9/25
- 11/25

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?

- 3
- 9
- 16
- 21
- 26

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?

- 16
- 15
- 9
- 8
- 3

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?

- 0
- 1
- 8
- 9
- 17

During a snowstorm, the relationship between the depth of accumulated snow, y inches, and the elapsed time, x hours, was modeled by the equation 2x - 5y = -5. One of the following graphs in the standard (x, y) coordinate plane models the equation for positive values of x and y. Which one?

The table below gives experimental data values for variables x and y. Theory predicts that y varies directly with x. Based on the experimental data, which of the following values is closest to the constant of variation?

(Note: The variable y varies directly with the variable x provided that y = kx for some nonzero constant k, called the constant of variation.)

- -2.61
- 0.05
- 3.61
- 15.90
- 20.00

Temperatures measured in degrees Fahrenheit (F) are related to temperatures measured in degrees Celsius (C) by the formula F = 9C/5 + 32. There is 1 value of x for which x degrees Fahrenheit equals x degrees Celsius. What is that value?

- -72
- -40
- -32
- 0
- 32

In the complex numbers, where i^{2} = -1,

1/(1 + i) · (1 - i)/(1 - i) = ?

- i - 1
- 1 + i
- 1 - i
- (1 - i)/2
- (1 + i)/2

For 20 quiz scores in a typing class, the table below gives the frequency of the scores in each score interval. Which score interval contains the median of the scores?

- 96-100
- 91-95
- 86-90
- 81-85
- 76-80

License plates on cars in a certain state consist of 3 letters taken from the 26 letters, A through Z, followed by 3 digits taken from the 10 digits, 0 through 9. Which of the following expressions gives the number of distinct license plates that are possible given that repetition of both letters and digits is allowed?

- 10
^{3}· 26^{3} - (10 + 26)
^{3} - 2(26!)
^{3}(10!)^{3} - (3 + 3)
^{26 + 10} - (26! · 10!)
^{3}+ (26! · 10!)^{3}

What is the amplitude of the function f(x) = 1/2 cos(3x + π) ?

- 1/3
- 1/2
- 3/2
- 2
- 3

At a local post office, on average, 3 customers are in line when the post office closes each day. The probability, P, that exactly n customers are in line when the post office closes can be modeled by the equation P = (3^{n}e^{-3})/n!. Given that e^{-3} ≈ 0.05, which of the following values is closest to the probability that exactly 2 customers are in line when the post office closes?

- 0.08
- 0.11
- 0.15
- 0.23
- 0.45

What is the length, in coordinate units, of the altitude from C to AB in ΔABC shown in the standard (x,y) coordinate plane below?

- 3
- 5
- 6
- 10
- 13

In the figure shown below, ABCD is a rectangle, EFGH is a square, and CD is the diameter of a semicircle. Point K is the midpoint of CD. Point J is the midpoint of both AB and

EF. Points E and F lie on AB. The 3 given lengths are in meters.

For ΔABC shown below, base AC has a length of 16 inches and altitude BD has a length of 8 inches. The area of a certain square is equal to the area of ΔABC. What is the length, in inches, of a side of the square?

- 6
- 8
- 12
- 16
- 32

The perimeter of rectangle ABCD is 96 cm. The ratio of the side lengths AB:BC is 3:5. What is the length, in centimeters, of AB?

- 6
- 18
- 30
- 36
- 60

For an angle with measure α in a right triangle, sin α = 40/41 and tan α = 40/9. What is the value of cos α ?

- 9/41
- 41/9
- 9/40
- 9/√1,519
- 9/√3,281

Which of the following inequalities is equivalent to -2x - 6y > 2y - 4 ?

- x < -4y + 2
- x > -4y + 2
- x < 2y + 2
- x < 4y + 2
- x > 4y + 2

40% of 250 is equal to 60% of what number?

- 150
- 160
- 166 2/3
- 270
- 375

Graphed in the same standard (x,y) coordinate plane are a circle and a parabola. The circle has radius 3 and center (0,0). The parabola has vertex (-3,-2), has a vertical axis of symmetry, and passes through (-2,-1). The circle and the parabola intersect at how many points?

- 0
- 1
- 2
- 3
- 4

For all nonzero values of a and b, the value of which of the following expressions is always negative?

- a - b
- -a - b
- |a| + |b|
- |a| - |b|
- -|a| - |b|

One caution sign flashes every 4 seconds, and another caution sign flashes every 10 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time?

- 6
- 7
- 14
- 20
- 40

To test a new medicine, each of 300 volunteers was assigned a distinct number from 1 to 300. Next, a calculator was used to simulate drawing 150 balls from among 300 congruent balls. The balls were numbered the same way as the volunteers so that 150 volunteers to receive the new medication would be chosen without bias. The other volunteers received a placebo. Weeks later, the 2 groups were compared. Which of the following phrases best describes the company’s testing?

- Randomized census
- Randomized experiment
- Nonrandomized experiment
- Randomized sample survey
- Nonrandomized sample survey

If x and y are positive integers such that the greatest common factor of x^{2}y^{2} and xy^{3} is 45, then which of the following could y equal?

- 45
- 15
- 9
- 5
- 3

A line contains the points A, B, C, and D. Point B is between points A and C. Point D is between points C and B. Which of the following inequalities must be true about the lengths of these segments?

- BC < AB
- BD < AB
- BD < CD
- CD < AB
- CD < BC

A 5-inch-by-7-inch photograph was cut to fit exactly into a 4-inch-by-6-inch frame. What is the area, in square inches, of the part of the photograph that was cut off?

- 2
- 10
- 11
- 12
- 24

Which of the following is a value of x that satisfies log_{x} 36 = 2 ?

- 4
- 6
- 8
- 16
- 18

Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 4 and -2x + y = 7 ?

- (-2, 3)
- (-1, 2.5)
- (1, 1.5)
- (2, 1)
- (4, 0)

The function f is defined as f(x) = -4x^{3} - 4x^{2}. What is f(-4) ?

- -320
- -192
- 16
- 192
- 320

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