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HPC
Final Exam
Test Expectations
Name_________________
MATH FINAL
Tuesday, May 26, 2013
8:20-9:50

Chapter 9: Probability and Functions of a Random Variable
 Sec. 9-2: Appropriately use words that are used to describe probability: random
experiment, trial, outcomes, simple event, event, equally likely, sample space, and
probability.
 Sec. 9-3: Calculate the number of outcomes in an event or sample space.
Appropriately distinguish between independent and mutually/non-mutually
exclusive events.
 Sec. 9-4: Given a description of a permutation, find the probability of getting that
permutation if an arrangement is selected at random. Appropriately use
vocabulary: permutation, fixed position, restricted position, and factorial.
 Sec. 9-5: Calculate the number of different combinations containing r elements
taken from a set containing n elements. Appropriately use the following
definitions and properties: Computation for number of combinations,
combination, symbols for numbers of combinations and permutations.
 Sec. 9-6: Calculate the probability of two events including the intersection, union,
and complementary events.

Chapter 10: Vectors
 Given two vectors, finds the resultant vector by adding or subtracting them.
 Sec. 10-2: Given the components of a two-dimensional position vector, find its
length, a unit vector in its direction, a scalar multiple of it, and its direction angle.
Given two-dimensional position vectors, find their sum and their difference.
 Sec. 10-3: Given the components of a three-dimensional position vector, find their
lengths, add them, subtract them and use the results to analyze real-world
problems. If a position vector terminated in their first octant, sketch it on graph
paper.
 Sec. 10-4: Given two vectors, find their dot product. Use the result to find the
angle between the vectors and the projection of one vector on the other. Apply the
definitions of Dot Product and Projections of Vectors.
 Sec. 10-5: Given a point on a plane and a vector perpendicular to the plane, find
the particular equation of the plane and use it to find other points on the plane.

Chapter 11: Matrix Transformations and Fractal Figures
 Perform matrix operations and algebra to calculate the sums, differences,
products, determinants and inverses of matrices.

 Sec. 11-3: Given a dilation, rotation and translation, write a matrix that will
perform the transformation when it is multiplied by a point matrix representing a
figure. Find the fixed point to which the images are attracted.
 Sec. 11-5: Given several different transformations, perform them iteratively,
starting with a pre-image, and plot the remaining images.
 Algebraically iterate a function.
Chapter 12: Analytic Geometry of Conic Sections
 Sec. 12-1: Given a quadratic equation with two variables, plot its graph and
formulate conclusions.
 Sec. 12-2: Given a Cartesian or parametric equation of a conic section, sketch or
plot the graph, and given the graph, find an equation.
 Sec. 12-3: Given the equation of a conic section, sketch the surface generated by
rotating it about one of its axes, and find the area or volume of a figure inscribed
wither on the plane region bounded by the graph or in the solid region bounded
by the surface.
 Sec. 12-4: Given the equation of a conic section, find the foci, the directrix, and the
eccentricity, and vice versa.
 Sec. 12-5: Plot a conic section rotated by a specified angle to the coordinate axes.
Identify a rotated conic from its Cartesian equation. Plot a rotated conic using its
Cartesian or parametric equations.

Chapter 13: Polar Functions
 Sec. 13-1: Given an equation in polar coordinates, plot the graph on polar
coordinate paper.
 Sec. 13-2: Given a polar equation, identify and/or plot the graph. Given a polar
graph, identify and/or write its equation. Given the polar equation of a conic
section, transform it to Cartesian coordinates.

 Sec. 13-3: Given two polar curves, find the intersection points (numerically,
graphically, algebraically).
 Sec. 13-4: Perform algebraic operations on complex numbers in polar form.

Chapter 14: Sequences and Series
 Sec. 14-1: Given a few terms in a sequence or series of numbers, find more terms.
Given a series, find the sum of a specified number of terms.
 Sec. 14-2: Represent sequences explicitly and recursively. Given information
about a sequence, find a term given its term number, and find the term number of
a given term.
 Sec. 14-3: Given a series, find a specified partial sum, or find the number of terms
if the partial sum is given. Use sigma notation to write partial sums. Given a
power of a binomial, expand it as a binomial series.
 Use mathematical induction to prove a conjecture.

Chapter 15: Functions, Limits, and Derivatives
 Sec. 15-1: Apply properties of cubic functions and their graphs.
 Sec. 15-2: Use long or synthetic division to determine quadratic factors.
 Sec. 15-3: Given a set of points, find the particular equation of the polynomial
function that fits the data exactly or fits the best for a given degree.

Calculus Unit
 Evaluate integrals and sketch the result.
 Calculate the first derivative of a polynomial function.
 Evaluate first and second derivatives to draw conclusions about the graph of
functions.