# 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.

#### 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

#### During a snowstorm, the relationship between the depth of accumulated snow

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

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.)

1. -2.61
2. 0.05
3. 3.61
4. 15.90
5. 20.00

#### Temperatures measured in degrees Fahrenheit (F) are related to

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?

1. -72
2. -40
3. -32
4. 0
5. 32

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

In the complex numbers, where i2 = -1,

1/(1 + i) · (1 - i)/(1 - i) = ?

1. i - 1
2. 1 + i
3. 1 - i
4. (1 - i)/2
5. (1 + i)/2

#### For 20 quiz scores in a typing class, the table below gives the frequency of the scores

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?

1. 96-100
2. 91-95
3. 86-90
4. 81-85
5. 76-80

#### License plates on cars in a certain state consist of 3 letters

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?

1. 103 · 263
2. (10 + 26)3
3. 2(26!)3(10!)3
4. (3 + 3)26 + 10
5. (26! · 10!)3 + (26! · 10!)3

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

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

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

#### At a local post office, on average, 3 customers are in line when the post office closes

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 = (3ne-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?

1. 0.08
2. 0.11
3. 0.15
4. 0.23
5. 0.45

#### What is the length, in coordinate units, of the altitude from C to AB

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?

1. 3
2. 5
3. 6
4. 10
5. 13

#### In the figure shown below, ABCD is a rectangle, EFGH is a square

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

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?

1. 6
2. 8
3. 12
4. 16
5. 32

#### The perimeter of rectangle ABCD is 96 cm

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?

1. 6
2. 18
3. 30
4. 36
5. 60

#### For an angle with measure α in a right triangle, sin α = 40/41

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 ?

1. 9/41
2. 41/9
3. 9/40
4. 9/√1,519
5. 9/√3,281

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

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

1. x < -4y + 2
2. x > -4y + 2
3. x < 2y + 2
4. x < 4y + 2
5. x > 4y + 2

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

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

1. 150
2. 160
3. 166 2/3
4. 270
5. 375

#### Graphed in the same standard (x,y) coordinate plane are a circle and a parabola

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?

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

#### For all nonzero values of a and b, the value of which expressions

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

1. a - b
2. -a - b
3. |a| + |b|
4. |a| - |b|
5. -|a| - |b|

#### One caution sign flashes every 4 seconds, and another caution sign flashes every 10 seconds

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?

1. 6
2. 7
3. 14
4. 20
5. 40

#### To test a new medicine, each of 300 volunteers was assigned

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?

1. Randomized census
2. Randomized experiment
3. Nonrandomized experiment
4. Randomized sample survey
5. Nonrandomized sample survey

#### If x and y are positive integers such that the greatest common factor

If x and y are positive integers such that the greatest common factor of x2y2 and xy3 is 45, then which of the following could y equal?

1. 45
2. 15
3. 9
4. 5
5. 3

#### A line contains the points A, B, C, and D. Point B is between points A and C

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?

1. BC < AB
2. BD < AB
3. BD < CD
4. CD < AB
5. CD < BC

#### A 5-inch-by-7-inch photograph was cut to fit exactly

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?

1. 2
2. 10
3. 11
4. 12
5. 24

#### Which of the following is a value of x that satisfies logx 36 = 2

Which of the following is a value of x that satisfies logx 36 = 2 ?

1. 4
2. 6
3. 8
4. 16
5. 18

#### Which is the solution for the system of equations x + 2y = 4 and -2x + y = 7

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

1. (-2, 3)
2. (-1, 2.5)
3. (1, 1.5)
4. (2, 1)
5. (4, 0)

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

The function f is defined as f(x) = -4x3 - 4x2. What is f(-4) ?

1. -320
2. -192
3. 16
4. 192
5. 320

#### A company ships notepads in rectangular boxes that each have inside dimensions

A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of notepads that will fit in 1 closed box?

1. 10
2. 11
3. 12
4. 22
5. 36

#### Vertices D and F of DEF lie on CG, the measure of ∠CDE is 148°

In the figure below, vertices D and F of DEF lie on CG, the measure of ∠CDE is 148°, and the measure of ∠EFG is 140°. What is the measure of ∠DEF ?

1. 072°
2. 098°
3. 100°
4. 108°
5. 116°

#### Which of the following is a solution to the equation x^2 - 36x = 0

Which of the following is a solution to the equation x2 - 36x = 0 ?

1. 72
2. 36
3. 18
4. 6
5. -6

#### Carrie’s Chocolate Shop and Tamika’s Treat Shop both sell candy

Carrie’s Chocolate Shop and Tamika’s Treat Shop both sell candy in boxes. The table below lists the price (the total amount the customer pays) of each box of candy sold at the shops. For each shop, there is a linear relationship between the price of a box of candies and the number of candies in that box. These are the only numbers of candies that can be purchased at the shops.

#### For a math homework assignment, Karla found the area and perimeter

For a math homework assignment, Karla found the area and perimeter of a room of her house. She reported that the area of her rectangular living room is 180 square feet and that the perimeter is 54 feet. When drawing a sketch of her living room the next day, she realized that she had forgotten to write down the dimensions of the room. What are the dimensions of Karla’s living room, in feet?

1. 9 by 20
2. 10 by 18
3. 12 by 15
4. 14 by 13
5. 16 by 11

#### Joseph will have a 200-foot-long fence installed around his yard

Joseph will have a 200-foot-long fence installed around his yard. The A+ Fence Company charges a \$500.00 fee, plus a set amount per foot of fence. The A+ Fence Company has given Joseph an estimate of \$2,200.00 to install the fence around his yard. What is the set amount per foot of fence?

1. \$04.00
2. \$04.80
3. \$08.50
4. \$11.00
5. \$13.50

#### Andrea manages a company that currently has 116 customers

Andrea manages a company that currently has 116 customers, which is 8 more than twice the number of customers the company had 1 year ago. How many customers did the company have 1 year ago?

1. 50
2. 54
3. 62
4. 66
5. 100

#### When points A and B(-3,4) are graphed in the standard (x,y) coordinate plane

When points A and B(-3,4) are graphed in the standard (x,y) coordinate plane below, the midpoint of AB will be (1,2). What will be the coordinates of point A?

1. (-7,6)
2. (-2,1)
3. (-1,3)
4. (-1,8)
5. (5,0)

#### A bag contains 10 pieces of flavored candy

A bag contains 10 pieces of flavored candy: 4 lemon, 3 strawberry, 2 grape, and 1 cherry. One piece of candy will be randomly picked from the bag. What is the probability the candy picked is NOT grape flavored?

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

#### The square root of a certain number is approximately 9.2371

The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers?

1. 3 and 4
2. 4 and 5
3. 9 and 10
4. 18 and 19
5. 81 and 99

#### In 1985, the cost of clothing for a certain family was \$620

In 1985, the cost of clothing for a certain family was \$620. In 1995, 10 years later, the cost of clothing for this family was \$1,000. Assuming the cost increased linearly, what was the cost of this family’s clothing in 1991 ?

1. \$908
2. \$848
3. \$812
4. \$810
5. \$772

#### The vertices of a rectangle are (−1,−2), (4,−2), (4,3), and (−1,3)

The vertices of a rectangle are (−1,−2), (4,−2), (4,3), and (−1,3). When the rectangle is graphed in the standard (x,y) coordinate plane below, what percent of the total area of the rectangle lies in Quadrant III ?

1. 8%
2. 12%
3. 12.5%
4. 32%
5. 48%

#### If x^2 + 4 = 29, then x^2 − 4

If x2 + 4 = 29, then x2 − 4 = ?

1. 5
2. √21
3. 21
4. 25
5. 33

#### Which of the following inequalities orders the numbers 0.2, 0.03, and 1/4 from least to greatest

Which of the following inequalities orders the numbers 0.2, 0.03, and 1/4 from least to greatest?

1. 0.2 < 0.03 < 1/4
2. 0.03 < 0.2 < 1/4
3. 0.03 < 1/4 < 0.2
4. 1/4 < 0.03 < 0.2
5. 1/4 < 0.2 < 0.03