Algebra 2: Topic Outline

I. Intro to Functions unit

1.Function basics

  • Function concept and f(x) notation
  • Ways to represent or describe functions: formula, table, graph, verbal
  • Finding an output given an input, or an input given an output
  • Deciding whether a table/graph shows a function or not
  • Identifying domain and range
  • Concept of zeros

2.Graphing calculator use, including intersections, zeros, maximum and minimum

3.Solving equations

  • Solving equations with linear functions algebraically
  • Solving equations using the intersection of two graphs on your calculator

4. Solving inequalities graphically and algebraically

5.Composite and inverse functions

  • Given two functions f(x) and g(x) as formulas, tables, or graphs, finding and using the composite function g(f(x))
  • Using various meanings of the concept that two functions are inverses of each other
  • Given a function f(x), finding its inverse f –1(x) using tables (reverse columns), graphs(reverse coordinates), or formulas (“change and solve”)

II. Linear functions

Finding the slope using m = or a table or a graph

Point-slope form f(x) = m(x – h) + k

Slope-intercept form f(x) = mx + b

  • Graphs of linear functions

Graphing point-slope lines, using a starting point and the slope

Horizontal lines (y = #) and vertical lines (x = #)

Parallel lines (equal slopes) and perpendicular lines (opposite reciprocal slopes)

  • Evaluating and solving

Given an input, finding an output (evaluating)

Given an output, finding an input (solving equations)

Solving inequalities and double inequalities

  • Finding composite functions and inverse functions
  • Modeling (application) problems

Meaning of slope: a rate or a speed

Turning word problems into function formulas

Domain and range

Evaluating/solving (see above) and giving the meaning of the answer in the problem context

III. Logs and exponents

Basic properties of exponents

Use of negative and fractional exponents

Simplifying and rewriting expressions using exponent properties. Combining like terms, but not combining unlike terms.

  • Logarithms

Solving bx = c using x = logbc; on calculator: LOG(c)/LOG(b)

Finding values of logs by interpreting them as questions

Converting between exponential and logarithmic equations

  • Exponential functions
  • Exponential modeling (application problems)

Setting up an exponential function using a starting value and a multiplier

Answering input-output questions (evaluating and solving).

IV. Quadratic Functions:

  1. Three forms
  2. Standard Form:
  3. Factored Form:
  4. Vertex Form:

You need to be able to transform functions from one form to another. The skills you need to do this are 1) factoring, 2) multiplying, and 3) completing the square,

  1. Properties of quadratic functions
  2. Zeros: find them by: 1) factoring, 2) taking square roots (if appropriate) or 3) using the quadratic formula.
  3. Vertex: Three ways to find the x coordinate: average the zeros for factored form, use for standard form and just look at the equation for vertex form. Once you find x, plug in to find y. In the calculator section of the test, you can find the vertex by finding the maximum or minimum using the 2nd Trace command.
  4. End behavior
  1. Graphing a quadratic function in vertex form and factored form.
  2. Writing a formula for a quadratic function given a graph. Use either factored form or vertex form depending on the information you are given.
  3. Solving quadratic equations. (“Find the value(s) of x that make the equation true.”)
  4. Quadratic application problems (projectiles).

V. Polynomials:

1.Graph a polynomial function in factored form. To do this you need to know:

  1. End behavior
  2. Zeros and multiplicity
  3. Y-intercept

2.Factoring a cubic equation:

3.Write a polynomial function from a graph when you know the shape and some points.

4.Dividing polynomials using long division

VI. Systems and Matrices

  • Solving linear systems by substitution and elimination methods (only for 2 equations, 2 variables)
  • Solving linear systems by matrix elimination method

Doing row operations by yourself

Getting the reduced matrix from calculator rref command

  • Recognizing whether a system has one solution, no solutions, or infinitely many solutions
  • Word problems involving linear systems

VII. Counting and Probability

  • Probabilities in situations where the outcomes are equally likely.

Probability of a single outcome = .

Probability of an event = .

Using counting methods (such as C, P, or !) to find “the total number of outcomes” and/or “the number of outcomes in the event.”

  • Probabilities involving “and”, “or”, “not” (here A and B stand for events)

P(not A) = 1 – P(A)

P(A or B) = P(A) + P(B) – P(A and B)

P(A or B) = P(A) + P(B) if A and B are mutually exclusive because then P(A and B) = 0

Venndiagrams.

  • Dependent and independent events

If events A and B are dependent (the outcome of A affects the likelihood of B):
P(A and B) = P(A) · P(B | A) where P(B | A) means prob. of B given A

If events A and B are independent:
P(A and B) = P(A) · P(B)

  • Repeated binomial experiments: For an action having two equally-likely outcomes (suchas a coin flip) done n times, the probability of getting a certain outcome r-out-of-n times is
  • Expected value (multiply each outcome times its probability, then add)
  • Conditional probability in tree diagrams and in tables