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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

Semester 1 REview

Honors Analysis

1 1 counting problems
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
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
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
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
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 topics1
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
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 topics1
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 topics2
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 topics3
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
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 topics1
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
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