## Podcast Beta

## Questions and Answers

What is the point slope form of a linear equation?

What does sin equal in a right triangle?

opposite/hypotenuse

What is the formula for the difference of cubes?

a³-b³=(a-b)(a²+ab+b²)

What is the Point Distance Formula?

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What is the area formula for a square?

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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 area formula for a triangle?

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What is the formula for the circumference of a circle?

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How is distance calculated in relation to rate and time?

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What is the formula for the volume of a cube?

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What is the volume formula for a rectangular prism?

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What is the volume formula for a cone?

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What is the formula for the volume of a sphere?

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What is the tangent in trigonometry?

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What is the Exponential Decay Formula?

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What is the Exponential Growth Formula?

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What is the surface area formula for a rectangle?

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What is the midpoint formula?

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Perpendicular lines are ___ (ex. 5, -1/5).

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What does cosine equal in a right triangle?

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What is the surface area formula for a cube?

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What is the area formula for a circle?

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What is csc in trigonometry?

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What is sec in trigonometry?

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What is cot in trigonometry?

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What is the Arc Length Formula?

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Parallel lines have ___ slopes.

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What is the formula for work in terms of job rate?

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What is the Mixture Formula?

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What are the x and y values of the unit circle?

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What is the area formula for an equilateral triangle?

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What are the Triangle Congruence Theorems?

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What transformation occurs for 90 degrees clockwise rotation?

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What transformation occurs for 90 degrees counterclockwise rotation?

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What transformation occurs for 180 degrees rotation?

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What is the formula for sin(A+B)?

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What transformation occurs for 270 degrees clockwise rotation?

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What transformation occurs for 270 degrees counterclockwise rotation?

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What is the Law of Sines?

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What is the formula for the volume of a cylinder?

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What is the volume formula for a pyramid?

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What is the formula for cos(A+B)?

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What is the Law of Cosines formula?

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What is the formula for sin(2x)?

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What is the formula for cos(2x)?

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What is the formula for tan(2x)?

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What is the formula for sin(A-B)?

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What is the formula for cos(A-B)?

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What is the formula for the area of a trapezoid?

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What are the Pythagorean Identities?

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What does the measurement of the central angle equal?

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What is an inscribed angle?

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What is the angle formed by a tangent and a chord?

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What is the angle formed by the intersection of two chords?

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What is the angle outside the circle?

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What is the area formula for a hexagon?

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## Study Notes

### Point Slope Form

- Represents the equation of a line using a known point (x1, y1) and slope m: ( y - y_1 = m(x - x_1) )

### Trigonometric Ratios

- Sine (sin): Ratio of the length of the opposite side to the hypotenuse in a right triangle: ( \text{sin} = \frac{\text{opposite}}{\text{hypotenuse}} )
- Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse: ( \text{cos} = \frac{\text{adjacent}}{\text{hypotenuse}} )
- Tangent (tan): Ratio of sine to cosine: ( \text{tan} = \frac{\text{opposite}}{\text{adjacent}} )

### Difference of Cubes Formula

- Can be factored as: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) )

### Distance and Midpoint Formulas

- Point Distance Formula: Calculates distance between two points ((x_1, y_1)) and ((x_2, y_2)): ( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} )
- Midpoint Formula: Finds the midpoint of a segment connecting two points: ( \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) )

### Area Formulas

- Area of Square: ( A = s^2 )
- Area of Rectangle: ( A = lw )
- Area of Parallelogram: ( A = bh )
- Area of Triangle: ( A = \frac{1}{2}bh ) or ( A = \frac{bh}{2} )
- Area of Circle: ( A = \pi r^2 )
- Area of Trapezoid: ( A = \frac{1}{2}(b_1 + b_2)h )
- Area of Equilateral Triangle: ( \frac{s^2 \sqrt{3}}{4} )
- Area of Hexagon: ( \frac{3\sqrt{3}}{2}a^2 )

### Circumference and Volume Formulas

- Circumference of Circle: ( C = 2\pi r )
- Volume of Cube: ( V = s^3 )
- Volume of Rectangular Prism: ( V = lwh )
- Volume of Cone: ( V = \frac{1}{3} \pi r^2 h )
- Volume of Sphere: ( V = \frac{4}{3} \pi r^3 )
- Volume of Cylinder: ( V = \pi r^2 h )
- Volume of Pyramid: ( V = \frac{1}{3} lwh )

### Exponential Functions

- Exponential Growth Formula: ( y = a(1 + r)^t )
- Exponential Decay Formula: ( y = a(1 - r)^t )

### Trigonometric Identities

- Pythagorean Identities:
- ( \sin^2 x + \cos^2 x = 1 )
- ( \tan^2 x + 1 = \sec^2 x )
- ( 1 + \cot^2 x = \csc^2 x )

- Double Angle Formulas:
- ( \sin(2x) = 2 \sin x \cos x )
- ( \cos(2x) = \cos^2 x - \sin^2 x )
- ( \tan(2x) = \frac{2 \tan x}{1 - \tan^2 x} )

### Geometric Angle Formulas

- Inscribed Angle: Measures half of the arc it intercepts.
- Angle Formed by a Tangent and a Chord: Equal to half the measure of the intercepted arc.
- Angle Formed by Intersection of Two Chords: Average of measures of the arcs intercepted.
- Angle Outside the Circle: Difference between larger and smaller arcs, divided by 2.

### Slope Relationships

- Parallel lines have equal slopes.
- Perpendicular lines have slopes that are opposite reciprocals, e.g., if one slope is ( 5 ), the other is ( -\frac{1}{5} ).

### Job and Mixture Formulas

- Work Rate Formula: ( \text{Job} = \text{Work Rate} \times \text{Time} )
- Mixture Formula: ( (\text{percentage of solution}) \times (\text{volume of solution}) = \text{amount of liquid} )

### Unit Circle Values

- ( x ) and ( y ) coordinates are represented by ( ( \cos, \sin ) ) respective to angles.

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## Description

Test your knowledge of essential algebraic formulas with this flashcard quiz. Covering topics such as point slope form, the sine function, and the area of various shapes, this quiz is perfect for those preparing for the Accuplacer exam. Enhance your understanding of advanced algebra and functions with these key concepts.