ASU Math Placement Exam Flashcards

Study Notes

Distance and Area Formulas

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 and Unit Conversion

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).

Circle and Triangle Properties

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.

Logarithmic Properties

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)).

Function Forms and Similarity Principles

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.

Circle Measurements

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.

Description

Prepare for the ASU Math Placement Exam with these essential flashcards. Each card covers important mathematical formulas and concepts such as the distance formula, area of various shapes, and the equation of a circle. Boost your understanding and confidence in math before the exam.