Honors Analysis
 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
 Combinations
Formula (by hand)
 Combinations & Fundamental Counting
Principle
 Distinguish between perm/comb
 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
 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) =
𝑃(𝐴∩𝐵)
𝑃(𝐵)
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

𝑛
 𝑘=1 𝑃
𝐴𝑘 𝑎𝑘
(Calculated
as sum of the
products of the probability of
each event and the gain/loss)
 Misleading
graphs
 Quantitative vs. Categorical Variables
 Graph Types:
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Bar graph vs. Histogram
Frequency table vs. Relative Frequency Table
Stem Plot
Pie Chart/Circle Graph
Comparative Bar Chart
Dot Plot
 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
 Calculate
 Graph
Slope 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
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:
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
 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:
𝑥1 +𝑥2 𝑦1 +𝑦2
,
2
2
 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)
 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.
 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
𝑦 = 2𝑥 + 4
 Determine values that make piecewise
functions continuous
 Evaluate Greatest Integer Function values
 Modular Arithmetic
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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!)
 Factoring
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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