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### Semester 1 REview

Honors Analysis

1.1: Counting Problems

- Fundamental Counting Principle
- Factorial Calculations (No Calculator!)
- Permutation Calculation (No Calculator!)
- Arrangement Problems (Permutations): n!
- Circular Arrangements: (n – 1)!
- Unique arrangements of letters in words

1.2 Combinations

- Combinations Formula (by hand)
- Combinations & Fundamental Counting Principle
- Distinguish between perm/comb

1.3 Intro to probability

- Calculate Probability/Odds
- Create a sample space to determine prob.
- Prob of Union of Events (OR Problems)
- Remember: If events aren’t mutually exclusive, the intersection must be subtracted!!
- Probability of Intersections (AND Problems)
- Adjust for independent vs. dependent events (such as replacement)
- Calculate probability of the complement
- Reword probability scenarios using AND/OR

1.4 Extended Probability

- Use combinations to calculate complex probabilities (specifically when order doesn’t matter)
- Conditional Prob: P(A | B) (Probability of Event A given that Event B has occurred)
- P(A | B) =

1.5 Geometric Probability

- Know 30-60-90 & 45-45-90 triangle patterns
- Find basic areas (circles, triangles, rectangles, trapezoids…)
- Subtract areas of shapes from other regions to find partial areas

1.6 Mathematical Expectation (Expected Value)

- (Calculated as sum of the products of the probability of each event and the gain/loss)

Unit 2 Topics

- Misleading graphs
- Quantitative vs. Categorical Variables
- Graph Types:
- Bar graph vs. Histogram
- Frequency table vs. Relative Frequency Table
- Stem Plot
- Pie Chart/Circle Graph
- Comparative Bar Chart
- Dot Plot

Unit 2 Topics

- Five Point Summary (quartiles, IQR)
- Box Plot
- Standard Deviation (By hand, calc)
- Basic Normal Curve (given simple curve)
- Z-Scores
- Calculate probabilities using Z-scores

Unit 3 topics

- Calculate Slope
- Graph linear equations using a table
- Graph linear equations using x & y intercepts
- Graph linear equations using slope-int form
- Horizontal lines: y = k
- Vertical lines: x = k
- Perpendicular lines: Negative Recip. Slopes
- Graph functions to find intersection point
- Write equations of lines using pt-slope form:

Unit 3 topics

- Graph 2-variable data using a scatter plot
- Approximate equation of line of best fit
- Use graphing calculator (STAT/lists) to create linear regression line
- Use linear equations to make predictions about data
- Evaluate positive/negative correlation of data
- Calculate midpoint:

Unit 3 topics

- Solve linear equations
- Write linear equations based on application problems
- Write linear equations involving supplements and complements
- Write median equation (passes through triangle vertex and mdpt of opposite side)
- Write equation of perpendicular bisector of side (passes through midpoint; perpendicular to slope of side)
- Write equation of altitude of triangle (passes through vertex; slope perpendicular to base)

UNIT 3 topics

- Solve systems using substitution
- Solve systems using elimination
- Find intersection point of medians (centroid), altitudes (orthocenter), perpendicular bisectors (circumcenter)
- Solve systems of three variables
- Write equation of parabola using a system of three variables.

Unit 4 Topics

- Evaluate, analyze, and graph piecewise functions
- Write the equation of piecewise functions
- Determine domain and range of a function using the graph (or given a function such as
- Determine values that make piecewise functions continuous
- Evaluate Greatest Integer Function values
- Modular Arithmetic

Unit 4 Topics

- Solve distance = rate * time word problems (use chart setup!)
- Calculate average rate of change of a function from a table or function
- Estimate instantaneous rate of change of a function
- Estimate definite integrals by counting blocks on a graph (WATCH OUT FOR GRAPH SCALE!!)
- Calculate definite integrals by calculating areas (constant functions, linear functions, etc.)
- Estimate definite integrals (area under the curve) using the Trapezoidal Rule (may be given function OR a table of values – always best to draw a graph first!!)
- Determine units for rate problems (y unit divided by x unit!)
- Determine units for integral/area problems (x unit times y unit!)

Unit 5 Topics

- Factoring Methods:
- Factor out the GCF
- Difference of Squares
- Trinomial (FOIL Pattern)
- Grouping

- Find vertex of a parabola by completing the square
- Solve a quadratic using the quadratic formula
- Solve a quadratic by factoring

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