Semester 1 REview

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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.

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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
• 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