Math

• Linear Equations


  Equations in the form y=mx+b, where y = y-value, x = x-value, b = constant, m = slope
• Linear Equations


  • Useful for a variety of problems
  • Represented by a graph with a simple, straight line
• Solving for characteristics of a linear equation


  1. Plug in known values

  2. Use isolation technique to isolate unknown variable
• Unknowns to solve for in linear equations

  • y-intercept
  • x-intercept
  • Slope
  • Constant
• Quadratic Equations


  Equations with a variable in the second power
• Quadratic Equations


  • Graphs are parabolas, which are conic sections
  • Standard form is y=a(x-h)^2+k, with vertex at (h,k)
• Geometric formulas


  • Angles of a triangle: 180 degrees
  • Area of a triangle: (base*height)/2
  • Pythagorean Theorem: a^2+b^2=c^2
  • Trigonometry: SOH CAH TOA
  • Area of a circle: pi*r^2
  • Circumference of a circle: 2*pi*r
  • Length of arc: (angle/360)*2*pi*r
  • Sum of angles in a quadrilateral: 360 degrees
  • Area of a parallelogram: base*height
  • Angle of regular polygon: 180(n-2)/n
  • Volume of cube: s^3
  • Volume of cuboid: l*w*h
  • Volume of sphere: 4/3*pi*r^3
  • Volume of cylinder: pi*r^2*h
  • Volume of cone: 1/3*pi*r^2*h
• Functions


  Equations where each x-value has only one corresponding y-value
• Functions


  • Can be tested using vertical line test
  • Different types include rational, quadratic, etc.
• Absolute Value


  Value between vertical lines |x| becomes positive
• Logarithms


  Notation log_b(x) = y means b^y = x
• Common logarithms use base 10
• The absolute value only turns negatives into positives, and not the other way around
• Logarithms are quite confusing to handle, because initially, they don't make intuitive sense and seem pretty useless, but as you go on learning about them in your formal classes, you will eventually understand their purpose
• Logarithms


  logbx=y means that b raised to y is equal to x
• Common logarithms


  Logarithms for which the base b is equal to 10, written as log x=y
• Natural logarithms


  Logarithms that make use of the constant e as the base, written as ln x=y
• The value of e is roughly 2.718
• Trigonometry involves a very special type of function which shows the relationship between two sides of a triangle and an angle
• Radians


  Another way to express the degree of an angle, in terms of pi (π), where x degrees is x(π/180) radians and y radians is y(180/π) degrees
• Basic trigonometric identities


  • tan θ = sin θ / cos θ
  • cot θ = cos θ / sin θ
  • sin θ = 1 / csc θ
  • cos θ = 1 / sec θ
  • tan θ = 1 / cot θ
  • csc θ = 1 / sin θ
• Pythagorean trigonometric identities


  • sin2θ + cos2θ = 1
  • tan2θ + 1 = sec2θ
  • cot2θ + 1 = csc2θ
• Factoring


  1. DOTS (Difference of Two Squares): x2 - y2 = (x + y)(x - y)

  2. DOTC (Difference of Two Cubes): x3 - y3 = (x - y)(x2 + xy + y2)

  3. Sum of Two Cubes: x3 + y3 = (x + y)(x2 - xy + y2)

  4. Quadratic Equations (no coefficient for x): x2 + bx + c = (x + a)(x + b)

  5. Quadratic Equations (coefficient for x): ax2 + bx + c = (2x + a)(3x - b)