Math Final
Tuesday, May 26th
10:20 – 11:50
Final Exam Expectations

Sec. 8-5: Use the Binomial Theorem to calculate binomial coefficients. Use binomial
coefficients to write binomial expansions. Use Pascal’s Triangle to calculate binomial
coefficients.

Sec. 8-6: Appropriately use vocabulary: permutation, fixed position, restricted position,
and factorial. Calculate the number of different permutations and combinations
containing r elements taken from a set containing n elements. Appropriately use the
following definitions and properties: Computation for number of combinations,
permutations, symbols for numbers of combinations and permutations

Sec. 8-7: Find the probability of various events in a dice-rolling experiment. Calculate the
probability of two events including the intersection, union, and complementary events.
Given a description of a permutation, find the probability of getting that permutation if
an arrangement is selected at random.

Use the ratio and/or comparison test to determine if a series converges or diverges.

Use Binomial Probability to calculate probabilities.

Sec. 9-1: Recognize a conic as the intersection of a plane and a double-napped cone.
Write equations of circles in standard form. Write equations of parabolas in standard
form. Use the reflective property of parabolas to solve real-life problems.

Sec. 9-2: Write equations of ellipses in standard form. Use properties of ellipses to model
and solve real-life problems. Find eccentricities of ellipses.

Sec. 9-3: Write equations of hyperbolas in standard form. Find asymptotes of and graph
hyperbolas. Use properties of hyperbolas to solve real-life problems. Classify conics from
their general equations.

Sec. 9-4: Use the discriminant to classify conics.

Sec. 9-5: Evaluate sets of parametric equations for given values of the parameter. Graph
curves that are represented by sets of parametric equations. Rewrite sets of parametric
equations as single rectangular equations by eliminating the parameter. Find sets of
parametric equations for graphs.

Given the equation of a conic section, sketch the surface generated by rotating it about
one of its axes.

Sec. 9-6: Plot points and find multiple representations of points in the polar coordinate
system. Convert points from rectangular to polar form and vice versa. Convert equations
from rectangular to polar form and vice versa.

Sec. 9-7: Graph polar equations by point plotting. Use symmetry as a sketching aid. Use
zeros and maximum r-values as sketching aids. Recognize special polar graphs. Write
polar equations given the polar graph.

Sec. 9-8: Define conics in terms of eccentricities. Write and graph equations of conics in
polar form. Transform conics expressed in Cartesian from to polar form.

Algebraically determine points of intersection for polar equations.

Sec. 10-2: Find the component forms of, the unit vectors in the same direction of, the
magnitudes of, the dot products of, and the angles between vectors in space. Determine
whether vectors in space are parallel or orthogonal.

Sec. 10-3: Find cross products of vectors in space. Use geometric properties of cross
products of vectors in space. Use triple scalar products to find volumes
of parallelepipeds.

Sec. 10-4: Find parametric and symmetric equations of lines in space. Find equations of
planes in space.
Statistics
A. Interpreting graphical displays of distributions of data
(dotplots, stemplots, histogram, boxplot)
1. Center and spread
2. Clusters and gaps
3. Outliers and other unusual features
4. Shape
B. Summarizing distributions of data
1. Measuring center: median, mean
2. Measuring spread: range, interquartile range, standard deviation
3. Measuring position: quartiles, percentiles, standardized scores (z-scores)
4. Using boxplots
5. The effect of changing units on summary measures
C. Comparing distributions of data
(dotplots, back-to-back stemplots, parallel boxplots)
1. Comparing center and spread: within group, between group variation
2. Comparing clusters and gaps
3. Comparing outliers and other unusual features
4. Comparing shapes
D. Transformations of Data Sets
1. Adding a constant to all values of a data set
2. Multiplying a constant by all values of a data set
E. The normal distribution
1. Properties of the normal distribution (65-95-99.7)
2. Calculating z-scores
3. Using z-score tables of the normal distribution
4. The normal distribution as a model for measurements
 Sec. 11-1: Use the definition of a limit to estimate limits. Determine whether limits of
functions exist. Use properties of limits and direct substitution to evaluate limits.

Sec. 11-2: Use the dividing out technique to evaluate limits of functions. Use the
rationalizing technique to evaluate limits of functions. Approximate limits of functions
graphically and numerically. Evaluate one-sided limits of functions.

Sec. 11-3: Use a tangent line to approximate the slope of a graph at a point. Use the limit
definition of slope to find exact slopes of graphs. Find derivatives of functions and use
derivatives to find slopes of graphs.

Sec. 11-4 Evaluate limits of functions at infinity. Find limits of sequences.

Sec. 11-5 Use rectangles to approximate areas of plane regions.
Calculus Unit

Estimate and interpret rates of change

Estimate and interpret instantaneous rates of change

Interpret f  and f  with respect to a given situation

Calculate the first derivative of a function using the Power Rule

Use integral notation to represent an area under a curve

Use calculator programs LSUM and RSUM to estimate area under a curve

Use the midpoint method to estimate area under a curve

Applications of definite integrals