2. Objectives for Algebra, Geometry,
Trigonometry, and Calculus.
Algebra,Geometry,Trigonometry, andCalculus,but
rather to give you a sound understanding of what
each of these are and how, and why, they are
used.My hope is that this will allow you to make
informed decisions in the future when choosing math
classes.
3. Definitions
Algebra – the study of mathematical operations and their application to solving equations
Geometry – the study of shapesAlgebra is a prerequisiteTrigonometry – the study of
triangles and the relationships between the lengths of their sides and the angles between
those sides.Algebra and Geometry are prerequisites
Calculus – the mathematical study of changeDifferential Calculus – concerning rates of
change and slopes of curvesIntegral Calculus – concerning accumulation of quantities and
the areas under curves
Algebra, Geometry, and Trigonometry are prerequisites
4. Algebra Properties
Commutative Property a + b = b + a , ab = ba
Associative Property (a + b) + c = a + (b + c),(ab)c = a(bc)
Distributive Property a(b + c) = ab + ac
5. Rules of signs Order of Operations
Negative (-) can go anywhere.
Two negatives = positiveOrder of Operations
Parenthesis and Exponents first, thenMultiply and Divide, thenAdd and Subtract
6. Exponents and Polynomials
𝒙 𝟐
= x times x
𝒙 𝟑 = x times x times x times
Polynomials 𝒙 𝟐
+ 4x + 37𝒙 𝟑
- 5𝒙 𝟐
+ 12x – 7
Factoring 𝒙 𝟐 + 4x + 3 = (x + 1)(x + 3)
8. Solving Equations 3x + 3 = 2x + 6 solve
for x
Subtract 2x from each side
3x + 3 – 2x = 2x + 6 – 2x
x + 3 = 6
Subtract 3 from each side
x = 6 – 3X = 3 (answer)
9. Equations of Lines Standard Form:
y = mx + b, where
m is slope of line and
Positive slope = ___
Negative slope = ___
Zero slope = ___
b is the y-axis intercept