Questions and Answers
What is the Distance Formula?
d=√(x₁-x₂)² + (y₁-y₂)²
Select the correct formula for Slope.
What is the equation for Slope Intercept?
y=mx+b
How is the Midpoint Formula calculated?
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What does PEDMAS stand for?
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What is the standard form of a Quadratic Equation?
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What is the Quadratic Formula?
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How do you calculate Percent?
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What is the rule for multiplying powers with the same base?
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What happens when dividing powers with the same base?
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What is the rule for raising a power to another power?
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What does a Negative Exponent represent?
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What does a Rational Exponent signify?
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What is the Absolute Value of -3?
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What does FOIL stand for in algebra?
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What is the formula for the Area of a Triangle?
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What is the Pythagorean Theorem for right triangles?
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What is the formula for the Area of a Rectangle?
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What is the formula for the Area of a Parallelogram?
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What is the formula for the Area of a Square?
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What is the formula for the Circumference of a Circle?
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What is the formula for the Area of a Circle?
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Study Notes
Distance Formula
- Formula: ( d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} )
- Used to calculate distance between two points on a coordinate plane.
Slope
- Formula: ( \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1} )
- Indicates the steepness of a line; positive slope rises, negative slope falls.
Slope Intercept Form
- Equation: ( y = mx + b )
- ( m ) represents slope, and ( b ) is the y-intercept.
Midpoint Formula
- Formula: ( \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) )
- Provides the midpoint between two points in a coordinate system.
PEDMAS
- Acronym representing the order of operations: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
- Essential for solving mathematical expressions correctly.
Quadratic Equation
- Standard form: ( ax^2 + bx + c = 0 )
- Represents a parabolic function; can have two, one, or no real solutions.
Quadratic Formula
- Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )
- Used to find roots of a quadratic equation; handles cases when factors are not obvious.
Percent Formula
- Formula: ( \text{Part} = \text{Percent} \times \text{Whole} )
- Facilitates calculation of percentage values in various scenarios.
Multiplication of Power Exponents
- Rule: ( x^m \cdot x^n = x^{m+n} )
- You add exponents when multiplying like bases.
Dividing Power Exponents
- Rule: ( \frac{x^m}{x^n} = x^{m-n} )
- You subtract exponents when dividing like bases.
Raising Power to Powers
- Rule: ( (x^m)^n = x^{m \cdot n} )
- You multiply exponents when raising a power to another power.
Negative Exponent
- Definition: ( x^{-n} = \frac{1}{x^n} )
- Indicates the reciprocal of the base raised to a positive exponent.
Rational Exponent
- Notation: ( \sqrt[n]{x} )
- Represents the nth root of ( x ).
Absolute Value
- Definition: ( |x| ) represents the distance of ( x ) from zero on a number line.
- Example: ( |-3| = 3 )
FOIL Method
- Technique for multiplying binomials: First, Outside, Inside, Last.
- Example: ((x - 3)(x + 5) = x^2 + 2x - 15)
Factoring Difference of Squares
- Formula: ( a^2 - b^2 = (a - b)(a + b) )
- Useful for simplifying expressions and solving equations.
Area of a Triangle
- Formula: ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} )
- Represents the space contained within a triangle.
Pythagorean Theorem
- Formula: ( a^2 + b^2 = c^2 )
- Applies to right triangles; ( a ) and ( b ) are legs, ( c ) is the hypotenuse.
- Notable special triangles: 3-4-5, 30-60-90, 5-12-13, 45-45-90.
Area Formulas
- Rectangle: ( \text{Area} = \text{length} \times \text{width} )
- Parallelogram: ( \text{Area} = \text{base} \times \text{height} )
- Square: ( \text{Area} = (\text{side})^2 )
Circumference of a Circle
- Formula: ( \text{Circumference} = 2\pi r )
- Represents the distance around the circle.
Area of a Circle
- Formula: ( \text{Area} = \pi r^2 )
- Represents the space contained within the circle.
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Description
This quiz features essential math formulas for the ACT, including the Distance Formula, Slope, and Slope Intercept. Each card provides a definition along with an example to help you master the key concepts. Use these flashcards to prepare effectively for the math section of the ACT exam.