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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


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