Mathematics Formulas Quiz

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Questions and Answers

What is the Slope Formula?

  • m=(y1+y2)/(x1+x2)
  • m=y1-y2/x1-x2
  • m=y2-y1/x2-x1 (correct)
  • m=(y2-y1)/(x2-x1) (correct)

What is the Point-Slope Form?

y-y1=m(x-x1)

What is the Pythagorean Theorem?

a²+b²=c²

How do you calculate the perimeter of a triangle?

<p>p=a+b+c</p>
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What is the Quadratic Formula?

<p>x = -b ± √(b² - 4ac)/2a</p>
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What is the Discriminant in a quadratic equation?

<p>b²-4ac</p>
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What is the Midpoint Formula?

<p>(x₁+x₂)/2, (y₁+y₂)/2</p>
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How is the Distance Formula expressed?

<p>d = √[(x₂ - x₁)² + (y₂ - y₁)²]</p>
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What is the Vertex of a Parabola formula?

<p>(-b/2a, f(-b/2a))</p>
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What is the Direct Variation equation?

<p>y=kx</p>
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What is the Inverse Variation equation?

<p>y=k/x</p>
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What is the Joint Variation equation?

<p>y=kxz</p>
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Flashcards

Slope Formula

m = (y₂ - y₁)/(x₂ - x₁)

Point-Slope Form

y - y₁ = m(x - x₁)

Pythagorean Theorem

a² + b² = c²

Triangle Perimeter

p = a + b + c

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Quadratic Formula

x = (-b ± √(b² - 4ac))/2a

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Discriminant

b² - 4ac

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Midpoint Formula

( (x₁ + x₂)/2, (y₁ + y₂)/2 )

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Distance Formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

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Parabola Vertex

(-b/2a, f(-b/2a))

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Direct Variation

y = kx

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Inverse Variation

y = k/x

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Joint Variation

y = kxz

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Study Notes

Slope Formula

  • Formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
  • Determines the slope between two points on a line.

Point-Slope Form

  • Formula: ( y - y_1 = m(x - x_1) )
  • Used to write the equation of a line given a point and its slope.

Pythagorean Theorem

  • Formula: ( a^2 + b^2 = c^2 )
  • Essential for calculating the length of a side in a right triangle, where ( c ) is the hypotenuse.

Perimeter of a Triangle

  • Formula: ( p = a + b + c )
  • Calculates the perimeter by summing the lengths of all three sides.

Quadratic Formula

  • Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )
  • Provides solutions for ( x ) in any quadratic equation of the form ( ax^2 + bx + c = 0 ).

Discriminant

  • Formula: ( b^2 - 4ac )
  • Helps in identifying the number of solutions for a quadratic equation.

Midpoint Formula

  • Formula: ( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) )
  • Used to calculate the midpoint of a line segment defined by two endpoints ((x_1, y_1)) and ((x_2, y_2)).

Distance Formula

  • Formula: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
  • Computes the distance between two points in a Cartesian plane.

Vertex of a Parabola

  • Formula: ( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) )
  • Identifies the vertex point of a quadratic function.

Direct Variation

  • Formula: ( y = kx )
  • Establishes a relationship where ( y ) is directly proportional to ( x ), with ( k ) as the constant of variation.

Inverse Variation

  • Formula: ( y = \frac{k}{x} )
  • Defines a relationship where ( y ) varies inversely with ( x ), again with ( k ) as the constant.

Joint Variation

  • Formula: ( y = kxz )
  • Indicates that ( y ) varies jointly with variables ( x ) and ( z ), with ( k ) as the constant of variation.

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