# 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.

#### 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

#### Which of the following expressions is equivalent to a(4 − a) − 5(a + 7)

Which of the following expressions is equivalent to a(4 − a) − 5(a + 7)?

1. −2a − 35
2. −2a + 07
3. −a2 − a − 35
4. −a2 − a + 7
5. −2a3 − 35

#### Content of ACT Mathematics Test

The ACT Mathematics test questions are drawn from several areas. These content topics represent areas of mathematics commonly taught by the end of grade 11 that are important to success in entry-level college mathematics courses.

#### Test Taking Strategies for ACT Mathematics

The mathematics test is a 60-question, 60-minute test designed to assess the mathematical skills students have typically acquired in courses taken up to the beginning of grade 12. Most questions are self-contained. Some questions may belong to a set of several questions.

#### Imaginary Numbers on the ACT

Imaginary numbers were discovered or invented as a way to take the square root of a negative number. You can’t do that by real numbers. If you take the square root of -1, you get imaginary number i.

#### Right Triangles and Pythagorean Theorem

Out of all the ACT Math topics tested, the triangle is the most commonly tested Geometric shape. The Pythagorean Theorem and the properties of right triangles are especially tested.

#### Properties of Numbers: Factors, Multiples and Divisibility

Learning the basics of numbers and their properties is crucial for success on the ACT Math Test.

factor, or divisor, of a number is a positive integer that evenly divides into that number. For example, 4 is a factor of 12 because 12/4 is an integer, 3. All integers have 1 and themselves as factors. For example, there are six factors for the number 12 - 1, 2, 3, 4, 6, 12.

#### Trigonometry

There are very few trigonometry questions on the ACT Mathematics Test. The questions test the basic trigonometric ratios which are related to right triangles.

#### Plane Geometry

Plane Geometry questions test plane geometry concepts such as Properties and Relations of Plane Figures.

Plane figures include Triangles; Circles; Rectangles; Parallelograms; Trapezoids; Angles, Parallel Lines, and Perpendicular Lines; Perimeter, Area, and Volume.

#### Coordinate Geometry

The Coordinate Geometry (Cartesian Coordinate Plane) questions test coordinate geometry concepts such as Number Line Graphs; Equation of a Line; Slope; Parallel and Perpendicular Lines; and Distance and Midpoint Formulas.

#### Intermediate Algebra

The Intermediate Algebra (ninth or tenth grade level) questions test intermediate algebraic concepts such as Quadratic Formula; Radical and Rational Expressions; Inequalities and Absolute Value Equations; Sequences; Systems of Equations; Logarithms; Roots of Polynomials; and Matrices.

#### Elementary Algebra

The Elementary Algebra (eighth or ninth grade level) questions test elementary algebraic concepts such as Functions; Polynomial Operations and Factoring Simple Quadratic Expressions; Linear Inequalities with One Variable; and Properties of Integer Exponents and Square Roots.

#### Pre-Algebra

The Pre-Algebra (seventh or eighth-grade level) questions test basic algebraic concepts such as operations Using Whole Numbers, Fractions, and Decimals; Square Roots; Exponents; Scientific Notation; Ratios, Proportions, and Percent; Linear Equations with One Variable; Absolute Value; and Simple Probability.