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Questions and Answers
What is the area of a parallelogram with a base of 10 and a height of 5?
What is the area of a parallelogram with a base of 10 and a height of 5?
- 50 (correct)
- 15
- 100
- 25
The Law of Sines states that $a/sin(A) = b/sin(B) = c/cos(C)$
The Law of Sines states that $a/sin(A) = b/sin(B) = c/cos(C)$
False (B)
What is the equation for the area of a circle?
What is the equation for the area of a circle?
A = πr²
The quadratic formula is used to find the roots of a quadratic equation in the form of $ax^2 + bx + c = 0$. The formula is: $x = (-b ± √______) / (2a)$
The quadratic formula is used to find the roots of a quadratic equation in the form of $ax^2 + bx + c = 0$. The formula is: $x = (-b ± √______) / (2a)$
What does m represent in the standard form of a linear equation, $y = mx + b$?
What does m represent in the standard form of a linear equation, $y = mx + b$?
The volume of a cubic/rectangular prism is calculated by $V = πr^2h$.
The volume of a cubic/rectangular prism is calculated by $V = πr^2h$.
What is the formula for the Law of Cosines?
What is the formula for the Law of Cosines?
In trigonometry, $sin(θ)$ is defined as opposite over ______.
In trigonometry, $sin(θ)$ is defined as opposite over ______.
Allison is reading a 300-page book. She plans to read the same number of pages every day until she finishes the book. If she reads 20 more pages per day than she currently plans to read, it will take Allison 4 fewer days to complete the book. How many pages per day is Allison currently planning to read?
Allison is reading a 300-page book. She plans to read the same number of pages every day until she finishes the book. If she reads 20 more pages per day than she currently plans to read, it will take Allison 4 fewer days to complete the book. How many pages per day is Allison currently planning to read?
If $x^a = x^b$, then $a + b = 1$
If $x^a = x^b$, then $a + b = 1$
When simplifying $(2x^4y^3)^6 / (4xy^{-4})$, what is the coefficient?
When simplifying $(2x^4y^3)^6 / (4xy^{-4})$, what is the coefficient?
When 40 percent of a number is increased by 20, the result is 4 less than the number. The number is ______.
When 40 percent of a number is increased by 20, the result is 4 less than the number. The number is ______.
Match each trigonometric function with its equivalent ratio:
Match each trigonometric function with its equivalent ratio:
Arthur charges an initial fee of $12, plus an $8 per-hour fee. Lolita charges an initial fee of $20, plus a $5 per-hour fee. For how much time would the two need to shovel for Lolita's overall fee to be cheaper than Arthur's overall fee?
Arthur charges an initial fee of $12, plus an $8 per-hour fee. Lolita charges an initial fee of $20, plus a $5 per-hour fee. For how much time would the two need to shovel for Lolita's overall fee to be cheaper than Arthur's overall fee?
$(x + y)^2 = x^2 + y^2$ is a true statement
$(x + y)^2 = x^2 + y^2$ is a true statement
At a fall festival, you can purchase 1 cup of candy corn and 1 cup of apple cider for $3.50. You can also purchase 2 cups of candy corn and 3 cups of apple cider for $9.75. What is the price of one cup of apple cider?
At a fall festival, you can purchase 1 cup of candy corn and 1 cup of apple cider for $3.50. You can also purchase 2 cups of candy corn and 3 cups of apple cider for $9.75. What is the price of one cup of apple cider?
The endpoints of a line segment are (-4, 12) and (3, -5). The midpoint of the segment is (______, 3.5)
The endpoints of a line segment are (-4, 12) and (3, -5). The midpoint of the segment is (______, 3.5)
Line k has equation $y = 3x – 5$ and is graphed in the standard xy-coordinate plane. Which of the following lines is perpendicular to k and crosses through the point (2, -1)?
Line k has equation $y = 3x – 5$ and is graphed in the standard xy-coordinate plane. Which of the following lines is perpendicular to k and crosses through the point (2, -1)?
When two lines are parallel, their slopes are negative reciprocals of each other.
When two lines are parallel, their slopes are negative reciprocals of each other.
In the figure above (isosceles triangular roof with a 30 foot base and 15 foot height) a 10-foot support crossbeam is installed parallel to the base of the roof at a distance x feet from the base. What is the value of $x$?
In the figure above (isosceles triangular roof with a 30 foot base and 15 foot height) a 10-foot support crossbeam is installed parallel to the base of the roof at a distance x feet from the base. What is the value of $x$?
Flashcards
Square/Rectangle Area
Square/Rectangle Area
Area of a square or rectangle. s = side length, l = length, w = width.
Parallelogram/Rhombus Area
Parallelogram/Rhombus Area
The area of a parallelogram or rhombus. b = base, h = height.
Triangle Area
Triangle Area
Area of a triangle. b = base, h = height, A and B are adjacent sides, C is the angle between sides A and B.
Trapezoid Area
Trapezoid Area
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Circle Area & Circumference
Circle Area & Circumference
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Cubic/Rectangular Prism Volume
Cubic/Rectangular Prism Volume
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Cylinder Volume
Cylinder Volume
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sin θ
sin θ
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cos θ
cos θ
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tan θ
tan θ
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csc θ
csc θ
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sec θ
sec θ
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cot θ
cot θ
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tan θ Identity
tan θ Identity
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sin² θ + cos² θ
sin² θ + cos² θ
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Law of Sines
Law of Sines
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Law of Cosines
Law of Cosines
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Standard form of a line
Standard form of a line
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Slope (m)
Slope (m)
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Quadratic formula
Quadratic formula
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Study Notes
- This guide serves as a quick reference for essential ACT Math strategies and content.
- There is no formula sheet on the ACT, making it necessary to know formulas and how to use them.
Strategy: Working Backwards
- The most effective method is to work backwards by beginning with the middle value option.
- To work backwards, find the solution for one of the answers provided.
Strategy: Translating Words to Math
- Fixed rate and variable equations are crucial mathematical concepts
- Setting up an expression that represents the total charge for each person is essential when translating words to math
- The fixed cost remains constant and becomes part of the expression as-is
- The per-hour cost is multiplied by the number of hours and added to the fixed rate.
- Setting the two expressions equal to each other helps find the "break even" point, where fees are the same.
Strategy: Simple Algebra and Percentages
- Translate word problems into equations for efficiency
- To increase or decrease a # by a certain %, multiply the original # by 1 ± the decimal equivalent of the %.
- Increase: "20% more than 150" = 150 * (1 + 0.2) = 180
- Decrease: "70% less than 400" = 400 * (1 – 0.7) = 120
- "5 more than a number" translates to x + 5
- "5 less than a number" translates to x - 5
- "30 percent of a number" translates to 0.3x
- "increased by" translates to +
- decreased by" translates to -
Strategy: Systems of Equations
- The ACT typically presents systems of linear equations.
- "Infinite solutions" means the equations represent the same line so coefficients are proportional
- Parallel lines have no solutions since they do not intersect.
Strategy: Exponents
- Know the following rules:
- x^(a) * x^(b) = x^(a+b)
- (x^a)/(x^b) = x^(a-b)
- (x^a)^(b) = x^(a * b)
- x^-a = 1/(x^a)
- x⁰ = 1
- Anything raised to 0 equals 1
- (x + y)² DOES NOT = x² + y²
- (x + y)² = (x + y)(x + y) = x² + 2xy + y²
- √(x² + y²) DOES NOT = x + y
Strategy: Averages
- The formula to use is Avg = (Sum of #s) / (# of #s)
Strategy: Distance On The XY-Plane
- Create a right triangle using the points
- Apply the Pythagorean theorem to find the missing length
- Formula used: a² + b² = c²
Strategy: Midpoint
- To find the midpoint of a segment, you must average the endpoints
- Always read carefully to determine whether you’re being given two endpoints, or an endpoint and a midpoint
- Sketches can eliminate unreasonable answer choices
Strategy: Coordinate Geometry
- Perpendicular lines have negative reciprocal slopes, which are "flips" of each other.
- Parallel lines have the same slope.
Strategy: Similar Triangles
- Directly solving is not always possible
- Separate both triangles to solve for the missing element
Strategy: Angles
- Extend lines to reveal simple angle relationships
- When line segments are parallel, take advantage of their positioning
Strategy: Trigonometry
- Employ SOH-CAH-TOA to solve for trig functions
- Cosine = Adjacent / Hypotenuse
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