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ALEKS Math Flashcards
52 Questions
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ALEKS Math Flashcards

Created by
@WellRunHydrogen

Questions and Answers

What is the Quadratic Formula?

-b±[√b²-4ac]/2a

What is the formula for Slope?

(y₂-y₁)/(x₂-x₁)

What is the Slope-Intercept form?

y=mx+b

What is the factored form of a³-b³?

<p>(a-b)(a²+ab+b²)</p> Signup and view all the answers

What is the factored form of a³+b³?

<p>(a+b)(a²-ab+b²)</p> Signup and view all the answers

What is the factored form of a²-b²?

<p>(a-b)(a+b)</p> Signup and view all the answers

What is the factored form of a²-2ab+b²?

<p>(a-b)²</p> Signup and view all the answers

What is the factored form of a²+2ab+b²?

<p>(a+b)²</p> Signup and view all the answers

What is the expanded form of (a+b)(c+d)?

<p>ac+ad+bc+bd</p> Signup and view all the answers

What does a(b+c) equal?

<p>ab+ac</p> Signup and view all the answers

What is the sine ratio?

<p>opposite ÷ hypotenuse</p> Signup and view all the answers

What is the cosine ratio?

<p>adjacent ÷ hypotenuse</p> Signup and view all the answers

What is the tangent ratio?

<p>opposite ÷ adjacent</p> Signup and view all the answers

What is the formula for Direct Variation?

<p>y=kx</p> Signup and view all the answers

What is the formula for Inverse Variation?

<p>y=k/x</p> Signup and view all the answers

What is the Slope-Intercept form?

<p>y=mx+b</p> Signup and view all the answers

What is the Point-Slope form?

<p>y-y₁=m(x-x₁)</p> Signup and view all the answers

What is the Standard form of a linear equation?

<p>Ax + By=C</p> Signup and view all the answers

What does Undefined refer to in mathematics?

<p>When there is a vertical line that has different y points, but the same x point</p> Signup and view all the answers

What does Zero refer to in mathematics?

<p>When there is a horizontal line that has different x points, but the same y point</p> Signup and view all the answers

What happens when you divide by a negative number in an inequality?

<p>You must flip the sign</p> Signup and view all the answers

How do you graph < or > on a coordinate plane?

<p>dotted line</p> Signup and view all the answers

How do you graph ≥ or ≤ on a coordinate plane?

<p>solid line</p> Signup and view all the answers

How do you graph ≥ or > on a coordinate plane?

<p>shade upwards or to the right</p> Signup and view all the answers

How do you graph ≤ or < on a coordinate plane?

<p>shade downwards or to the left</p> Signup and view all the answers

What does Infinitely many solutions mean?

<p>when the system of equations have the same slope and y-intercept</p> Signup and view all the answers

What does One solution mean?

<p>when the system of equations have different slopes</p> Signup and view all the answers

What does No solution mean?

<p>when the system of equations have the same slope but different y-intercepts</p> Signup and view all the answers

What is the Linear parent function?

<p>y=x or f(x)=x</p> Signup and view all the answers

What is the Elimination method?

<p>solving systems by adding or subtracting equations to eliminate a variable</p> Signup and view all the answers

What is the solution of the system of linear equations?

<p>Any ordered pair in a system that makes all the equations true</p> Signup and view all the answers

What is the Graphing method?

<p>Graphing the system of equations and finding the point at which they intersect</p> Signup and view all the answers

What is the Substitution method?

<p>Replacing one variable with an equivalent expression containing the other variable</p> Signup and view all the answers

What is an Absolute value equation?

<p>A V-shaped graph that points upward or downward</p> Signup and view all the answers

What is Translation in graphing?

<p>A shift of a graph horizontally, vertically, or both</p> Signup and view all the answers

What is the Area of a circle?

<p>Πr²</p> Signup and view all the answers

What is the Area of a square?

<p>s², where s = length of a side</p> Signup and view all the answers

What is the Area of a triangle?

<p>½(base x height) [or (base x height)÷2]</p> Signup and view all the answers

What is the Area of a trapezoid?

<p>½(b₁ +b₂) x h [or (b₁ +b₂) x h÷2]</p> Signup and view all the answers

What is the Perimeter of a rectangle?

<p>2Length + 2width [or (length + width) x 2]</p> Signup and view all the answers

What is the Perimeter of a square?

<p>4s (where s = length of a side)</p> Signup and view all the answers

What is the Perimeter (circumference) of a circle?

<p>2 pi r</p> Signup and view all the answers

What is the Area of rectangle, square, parallelogram?

<p>A=bh</p> Signup and view all the answers

What is the Area of a sector?

<p>x°/360 times (∏r²), where x is the degrees in the angle</p> Signup and view all the answers

What is the length of a sector?

<p>x°/360 times (2 pi r), where x is the degrees in the angle</p> Signup and view all the answers

What is a Circle?

<p>The set of points which are all the same distance (its radius) from a certain point (the center)</p> Signup and view all the answers

What is a Radius (Radii)?

<p>A segment connecting the center of a circle to any point on the circle</p> Signup and view all the answers

What is a Diameter?

<p>The distance across the circle through the center of the circle.</p> Signup and view all the answers

What is a Chord?

<p>The distance from one point on the circle to another point on the circle</p> Signup and view all the answers

What is a Sector?

<p>The part of a circle that looks like a piece of pie.</p> Signup and view all the answers

What is an Arc?

<p>Part of a circle connecting two points on the circle</p> Signup and view all the answers

What is a Central Angle?

<p>An angle whose vertex is the center of the circle</p> Signup and view all the answers

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.

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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.

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