Topics for Review

At the start of the semester, these are topics we will review in order to be sure that each of you have the tools needed for success in Honors Calculus and in future classes.

Pre-Calculus Formulas

Equations of a Line
Point-Slope Form: y-y₀=m(x-x₀)
General (or standard) Form: Ax+By=C
Horizontal Line: y=b

Two-Point Form: y-y₁=[ (y₂-y₁)/(x₂-x₁) ](x-x₁)
Slope-Intercept Form: y=mx+b
Vertical Line: x=a

Geometric Formulas
Rectangle (width w, height h): Area=wh, Perimeter=2w+2h
Rectangle (base b, height h): Area=½bh
Trapezoid (parallel sides h₁ and h₂, and distance between parallel sides w): Area=½(h₁+h₂)w

Circle (radius r): Area=πr², Circumference: 2πr
Sphere (radius r): Volume=4/3 πr³, Surface Area: 4πr²

Logarithms and Exponentials

1. y=b^x is equivalent to log_b(y)=x
   
2. y=ln x if and only if x=e^y=exp(y)
   
3. ln e^x=x
   
4. e^{ln x}=x
   
5. e^xe^y=e^x+y
6. e^x/e^y=e^x-y
7. (e^x)^y=e^xy

8. e⁰=1
9. ln(xy)=ln x+ln y
10. ln(x/y)=ln x-ln y
11. ln(x^y)=ylnx
12. ln 1=0
13. ln e=1

Other Topics for Discussion

• What successful homework looks like
  
• Properties of fractions (addition, subtraction, multiplication, division, and simplification)
• Properties of trigonometric functions
• Trigonometric identities
• Properties of exponents, natural logarithms, and log base-e
• Properties of logarithms (change of base, addition, subtraction, multiplication, division, and simplification)