Podcast
Questions and Answers
What is the Quadratic Formula?
What is the Quadratic Formula?
-b±[√b²-4ac]/2a
What is the formula for Slope?
What is the formula for Slope?
(y₂-y₁)/(x₂-x₁)
What is the Slope-Intercept form?
What is the Slope-Intercept form?
y=mx+b
What is the factored form of a³-b³?
What is the factored form of a³-b³?
What is the factored form of a³+b³?
What is the factored form of a³+b³?
What is the factored form of a²-b²?
What is the factored form of a²-b²?
What is the factored form of a²-2ab+b²?
What is the factored form of a²-2ab+b²?
What is the factored form of a²+2ab+b²?
What is the factored form of a²+2ab+b²?
What is the expanded form of (a+b)(c+d)?
What is the expanded form of (a+b)(c+d)?
What does a(b+c) equal?
What does a(b+c) equal?
What is the sine ratio?
What is the sine ratio?
What is the cosine ratio?
What is the cosine ratio?
What is the tangent ratio?
What is the tangent ratio?
What is the formula for Direct Variation?
What is the formula for Direct Variation?
What is the formula for Inverse Variation?
What is the formula for Inverse Variation?
What is the Slope-Intercept form?
What is the Slope-Intercept form?
What is the Point-Slope form?
What is the Point-Slope form?
What is the Standard form of a linear equation?
What is the Standard form of a linear equation?
What does Undefined refer to in mathematics?
What does Undefined refer to in mathematics?
What does Zero refer to in mathematics?
What does Zero refer to in mathematics?
What happens when you divide by a negative number in an inequality?
What happens when you divide by a negative number in an inequality?
How do you graph < or > on a coordinate plane?
How do you graph < or > on a coordinate plane?
How do you graph ≥ or ≤ on a coordinate plane?
How do you graph ≥ or ≤ on a coordinate plane?
How do you graph ≥ or > on a coordinate plane?
How do you graph ≥ or > on a coordinate plane?
How do you graph ≤ or < on a coordinate plane?
How do you graph ≤ or < on a coordinate plane?
What does Infinitely many solutions mean?
What does Infinitely many solutions mean?
What does One solution mean?
What does One solution mean?
What does No solution mean?
What does No solution mean?
What is the Linear parent function?
What is the Linear parent function?
What is the Elimination method?
What is the Elimination method?
What is the solution of the system of linear equations?
What is the solution of the system of linear equations?
What is the Graphing method?
What is the Graphing method?
What is the Substitution method?
What is the Substitution method?
What is an Absolute value equation?
What is an Absolute value equation?
What is Translation in graphing?
What is Translation in graphing?
What is the Area of a circle?
What is the Area of a circle?
What is the Area of a square?
What is the Area of a square?
What is the Area of a triangle?
What is the Area of a triangle?
What is the Area of a trapezoid?
What is the Area of a trapezoid?
What is the Perimeter of a rectangle?
What is the Perimeter of a rectangle?
What is the Perimeter of a square?
What is the Perimeter of a square?
What is the Perimeter (circumference) of a circle?
What is the Perimeter (circumference) of a circle?
What is the Area of rectangle, square, parallelogram?
What is the Area of rectangle, square, parallelogram?
What is the Area of a sector?
What is the Area of a sector?
What is the length of a sector?
What is the length of a sector?
What is a Circle?
What is a Circle?
What is a Radius (Radii)?
What is a Radius (Radii)?
What is a Diameter?
What is a Diameter?
What is a Chord?
What is a Chord?
What is a Sector?
What is a Sector?
What is an Arc?
What is an Arc?
What is a Central Angle?
What is a Central Angle?
Study Notes
Algebraic Formulas and Concepts
- Quadratic Formula: ( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) used to solve quadratic equations.
- Slope: Represents the rate of change; calculated as ( \frac{y_2 - y_1}{x_2 - x_1} ).
- Slope-Intercept Form: ( y = mx + b ) where ( m ) is the slope and ( b ) is the y-intercept.
Factoring and Algebraic Identities
- Difference of Cubes: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ).
- Sum of Cubes: ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ).
- Difference of Squares: ( a^2 - b^2 = (a - b)(a + b) ).
- Perfect Square Trinomials:
- ( a^2 - 2ab + b^2 = (a - b)^2 )
- ( a^2 + 2ab + b^2 = (a + b)^2 ).
Algebraic Operations
- Product of Sums: ( (a + b)(c + d) = ac + ad + bc + bd ).
- Distributive Property: ( a(b + c) = ab + ac ).
Trigonometric Ratios
- Sine Ratio: Given by the formula ( \text{opposite} ÷ \text{hypotenuse} ).
- Cosine Ratio: Given by the formula ( \text{adjacent} ÷ \text{hypotenuse} ).
- Tangent Ratio: Given by the formula ( \text{opposite} ÷ \text{adjacent} ).
Variation Types
- Direct Variation: Defined by the equation ( y = kx ), where ( k ) is a constant.
- Inverse Variation: Defined by the equation ( y = \frac{k}{x} ).
Linear Equation Forms
- Point-Slope Form: ( y - y_1 = m(x - x_1) ) used to define linear equations.
- Standard Form: Written as ( Ax + By = C ), with specific criteria for A, B, and C.
- Characteristics of Solutions:
- Infinitely Many Solutions: Same slope and y-intercept.
- One Solution: Different slopes.
- No Solution: Same slope, different y-intercepts.
Graphing Techniques
- Graphing inequalities involves using dotted lines for ( < ) or ( > ) and solid lines for ( \geq ) or ( \leq ).
- Shading direction based on inequality signs: upwards/right for ( \geq ) or ( > ), downwards/left for ( \leq ) or ( < ).
System of Equations Methods
- Elimination Method: Involves adding or subtracting equations to remove a variable.
- Substitution Method: Replacing a variable in one equation with an expression from another.
Geometric Area and Perimeter Formulas
- Area of a Circle: ( \pi r^2 ).
- Area of a Square: ( s^2 ) where ( s ) is the length of a side.
- Area Formulas:
- Triangle: ( \frac{1}{2} \times \text{base} \times \text{height} ).
- Trapezoid: ( \frac{1}{2}(b_1 + b_2) \times h ).
- Perimeter of Rectangles and Squares:
- Rectangle: ( 2 \times \text{Length} + 2 \times \text{Width} ).
- Square: ( 4s ).
Circle Properties
- Definition: A set of points equidistant from a center point.
- Radius: A line segment from the center to any point on the circle.
- Diameter: The longest distance across the circle, twice the length of the radius.
- Chord: A line segment connecting two points on the circle.
- Sector: A "pie slice" of a circle defined by two radii and an arc.
- Arc: A segment of the circumference connecting two points.
- Central Angle: An angle whose vertex is located at the center of the circle.
Graph Transformations
- Translation: Shifts the graph horizontally, vertically, or both, maintaining its shape and size.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of key mathematical concepts with these ALEKS flashcards. Covering topics such as quadratic formulas and polynomial identities, this quiz helps reinforce critical algebraic principles. Perfect for students preparing for exams or looking to boost their math knowledge.
