ASU Math Placement Exam Flashcards

Distance Formula: Calculate the distance between two points ((x₁, y₁)) and ((x₂, y₂)) using (d = \sqrt{(x₂ - x₁)² + (y₂ - y₁)²}).
Area of a Triangle: Determine the area using the formula (A = \frac{1}{2}bh), where (b) is the base and (h) is the height.
Area of a Rectangle: Calculated as (A = lw), with (l) representing length and (w) representing width.

Volume of a Rectangular Prism: Find the volume by (V = lwh).
Square Yard to Square Feet Conversion: One square yard is equivalent to nine square feet (1yd² = 9ft²).

Equation of a Circle: Defined as ((x - h)² + (y - k)² = r²), where ((h, k)) is the center and (r) is the radius.
Area of an Equilateral Triangle: Use the formula (A = \frac{s² \sqrt{3}}{4}), with (s) being the length of a side.

Conversion of Exponents to Logs: (a^y = x) can be expressed as (y = \log_a(x)).
Addition of Logs: For products, (log(xy) = log(x) + log(y)).
Subtraction of Logs: For quotients, (log\left(\frac{x}{y}\right) = log(x) - log(y)).

Vertex Form of Quadratic Functions: Expressed as (y = a(x - h)² + k) where ((h, k)) is the vertex.
Triangle Similarity Statements:
- Not all right triangles are similar; this statement is false.
- All squares are considered similar; this statement is true.
- All congruent rectangles are similar; this statement is true.
- All equiangular triangles are similar; this statement is true.
- All equilateral triangles are also similar; this statement is true.

Arc Length Formula: The length of an arc can be found with (L = 2\pi r \left(\frac{m⁰}{360⁰}\right)), connecting the arc length to the circle's radius and central angle.
Perimeter of a Circle: Commonly referred to as the circumference, calculated with (P = 2\pi r).
Area of a Circle: Computed using (A = \pi r²), where (r) is the radius.