||Determine domain & range; Evaluate functions; Determine
restrictions on domain.
||Perform operation on functions; Find composite functions.
||Graph linear equations; Find the zeros of linear functions.
||Write equations for lines given points and/or slopes.
||Determine if lines are parallel or perpendicular; Write
equations for parallel or perpendicular lines.
||Graph piecewise defined functions.
||Determine domain & range (1.1); Evaluate a function
for a given value (1.1); Determine the domain of an equation (1.1); Add,
subtract, multiply, and/or divide functions (1.2); Find the composition
of functions (1.2); Graph linear equations (1.3); Write the equation of
a line (1.4); Write the equation of a line parallel or perpendicular to
a given line (1.5); Graph absolute value and piecewise functions (1.7)
||Determine symmetry of functions
||Identify transformations of graphs; Use transformations
to graph functions.
||Determine the inverse of a function; Graph functions and
||Determine continuity of a function at a point; Determine
continuity of a function; Determine end behavior of a function.
||Determine the symmetries of a function (3.1); given a partial
graph and its symmetry relation, complete the graph (3.1); Given an equation,
describe its transformation in relation to its parent graph (3.2); Graph
a function given its parent graph (3.2); Find the inverse of a function
and determine if the inverse if a function (3.4); Graph a function and
its inverse on the same set of axes (3.4); Determine if a function is
continuous at a point (3.5); Determine the end behavior of a function
(3.5); Determine the interval(s) for which a function is increasing and
||Determine limits of functions at specified values.
||Determine limits of functions as x approaches ±
||Find the derivatives of functions using the definition of
||Use derivative rules to find the derivative.
||Determine relative minimum and maximum values of polynomial
functions; Determine inflection points; Graph polynomial functions.
||Determine limits as n approaches a constant, and
as n approaches ± infinity (Worksheet, 12.3); Find the derivative
of a function using the definition (Worksheet); Find the derivative of
a function using derivative rules (15.2); Find local minimum and maximum
values of a function (Worksheet); Find inflection points of a function
(Worksheet); Graph a function using its extrema (Worksheet)
||Determine asymptotes of functions; Graph rational functions.
||Determine the number of complex roots (Fundamental Theorem
of Algebra); Given the roots, write a polynomial of least degree.
||Solve quadratic equations by completing the square and quadratic
formula; Discuss the nature of the roots of polynomial functions.
||Determine if a binomial is a factor of a polynomial; Use
the Remainder & Factor Theorems to find roots of polynomials.
||Determine all horizontal, vertical and/or oblique asymptotes
for a rational function (3.7); Determine if a rational function has a
hole (3.7); Graph rational functions (3.7); Write a polynomial equation
of least degree given its roots (4.1); Solve a quadratic equation by completing
the square, and by using the quadratic formula (4.2); Use the discriminant
to discuss the nature of the roots of a quadratic equation (4.2); Use
the Factor and/or Remainder Theorems to determine the binomial factors
of a polynomial (4.2)
||Determine possible rational roots of a polynomial (Rational
Roots Theorem); Determine the maximum number of real positive and real
negative roots of a polynomial (Descartes' Rule of Signs).
||Approximate the location of the real roots of a polynomial
function; Determine the upper and lower bounds for the real roots of a
||Solve rational equations and inequalities; Complete partial
||Solve radical equations and inequalities.
||List all possible rational roots of a polynomial equation,
then determine which ones are actual roots (4.4); Determine the number
of possible positive real and negative real roots of a polynomial equation
(4.4); Determine between which consecutive integers the roots of a polynomial
are located (4.5); approximate the zeros of a function to the nearest
hundredth (4.5); Determine the least upper bound and the greatest lower
bound for the roots of a polynomial function (4.5); Solve rational equations
(4.6); Solve radical equations and inequalities (4.7).
||Simplify numerical & algebraic expressions involving
exponents (use the rules of exponents).
||Graph exponential functions.
||Solve problems involving e.
||Convert between logarithmic & exponential form; Evaluate
logarithmic expressions; Solve logarithmic equations.
||Simplify numerical and variable expressions involving exponents
(11.1); Convert between radical & exponential notation (11.1); Solve
equations involving exponents (11.1);; Graph exponential functions (11.2);
Solve problems involving exponential functions (11.2); Convert between
exponential & logarithmic form (11.4); Solve equations involving logarithms
(11.4); Graph logarithmic functions (11.4).
||Use properties of logarithms to evaluate logarithmic expressions;
Use the change of base formula; Solve logarithmic & exponential equations;Graph
||Convert between logarithmic & exponential form; Solve
logarithmic & exponential equations.
||Convert between decimal degree and degree minute second
notation; Find coterminal angles; Determine reference angles.
||Use trigonometry to determine the measure of the angles
of right triangles.
||Use trigonometry on the unit circle.
||Evaluate logarithms using the change of base formula (11.5
& 11.6); Solve exponential and/or logarithmic equations (11.5 &
11.6); Convert between decimal degrees and degree minute second notation
(5.1); Find the measure of the reference angle (5.1); given 2 sides of
a right triangle, find all 6 trigonometric values for one of its acute
angles (5.2); Given the measure of a central angle on the unit circle,
find the values of all 6 trigonometric functions (5.2); Given an ordered
pair that lies on the terminal side of a central angle, find the values
of all 6 trigonometric functions (5.2); Given one trigonometric value
and the quadrant the terminal side of the angle lies in, find the values
of the remaining 5 trigonometric functions (5.2).
||Convert between radian and degree measure; Find arc length;
Find the area of a sector.
||Use the graphs of sine and cosine.
||Determine amplitude and period for sine & cosine; Graph
sine & cosine functions.
||Determine the phase shift for sine & cosine; Graph sine
& cosine functions.
||Convert between degree and radian measure (6.1); Use the
arc length formula(6.1); Use the area of a sector formula (6.1); Identify
the period, amplitude, and phase shift of the graph of a trigonometric
function (6.4 & 6.5); Graph trigonometric functions (6.4 & 6.5).
||Graph tangent & cotangent.
||Graph secant & cosecant.
||Determine the inverse of trigonometric functions; Graph
trigonometric functions & their graphs.
||Identify & use basic trigonometric identities.
||Identify the period, amplitude, and phase shift of the graph
of a trigonometric function (6.4, 6.5, 6.7); Graph trigonometric functions
(6.4, 6.5, 6.7); Graph trigonometric functions and their inverses (6.8);
Simplify trigonometric expressions (7.1).
||Verify trigonometric identities.
||Verify trigonometric identities.
||Use sum & difference identities to evaluate trigonometric
||Use double & half angle identities to evaluate trigonometric
||Given the value of a trigonometric function and a quadrant,
find the exact value of another trigonometric function (7.1); Express
a trigonometric function as a related function in the first quadrant (7.1);
Verify trigonometric identities (7.2); Use the sum and/or difference identities
to find the exact value of a trigonometric function (7.3); find the exact
value of sine, cosine, and/or tangent, given the values of sine and/or
cosine (7.3); Use the double and/or half angle formulas to find the exact
value of a trigonometric function (7.4); Given the value of sin x,
cos x, or tan x, find the exact value of sin 2x,
COs 2x, tan 2x, sin (1/2x), COs (1/2x), and/or
||Solve trigonometric equations.
||Determine the magnitude and direction of vectors; Add &
subtract vectors; Find equal, opposite & parallel vectors.
||Add, subtract, & multiply vectors; Find the magnitude
of resultants; Find ordered pairs that represent vectors.
||Determine if two vectors are perpendicular.
||Solve trigonometric equations for the principal solution
or over a specified interval (7.5); Determine the magnitude and direction
of a vector (8.1); Find the magnitude and direction of the resultant when
adding, subtracting and/or multiplying two vectors (8.1); Given vectors
a and b, find the ordered pair that represents vector ab,
and the magnitude of vector ab (8.2); Find the ordered pair that
represents the sum, difference and/or scalar product of two vectors (8.2);
Find the magnitude of a vector and write the vector as the sum of unit
vectors (8.2); Find the inner product of two vectors and determine if
the vectors are perpendicular (8.4); Solve problems representing applications
of vectors (8.5).
||Convert between parametric equations & linear equations;
Write the vector equation parallel to a given line.
||Solve motion problems using parametric equations.
||Graph points in polar coordinates; Graph polar equations;
Find the distance between two points.
||Graph polar equations; Write polar equations that meet specified
||Solve problems representing applications of vectors (8.5,
8.7); Write the vector equation of a line passing through a given point
parallel to a given vector (8.6); Convert between parametric equations
for a line and slope-intercept form (8.6); Graph points given in polar
form (9.1); Find the distance between two points given in polar form (9.1);
Graph polar equations (9.2).
||Convert between polar & rectangular coordinates; Convert
equations between polar & rectangular form.
||Convert equations between linear & normal form; Find
the length & angle of the normal from the origin.
||Find the distance from a point to a line; Find the distance
between two parallel lines; Write equations of lines that bisect angles.
||Convert equations between polar & rectangular form.
||Convert points & equations between polar & rectangular
form (9.3); Write the standard form of an equation given the length of
the normal segment & the angle the normal segment makes with the positive
x-axis (7.6); Write a standard form equation in normal form &
find the length of the normal & the measure of the angle it makes
with the positive x-axis (7.6); Find the distance between a point
and a line (7.7); Find the distance between two parallel lines (7.7);
Convert equations between rectangular and polar form (9.4); Graph polar
||Simplify expressions involving complex numbers.
||Solve equations involving complex numbers; Convert numbers
between complex & polar form.
Find distance & midpoint; Prove statements using coordinate proofs.
||Write equations form and graph circles.
||Simplify expressions containing complex numbers (9.5); Solve
equations involving complex numbers (9.6); Graph complex numbers and find
their absolute value (9.6); Write complex numbers in polar form (9.6);
Find the length and midpoint of a segment, given its endpoints (10.1);
Prove statements using coordinate proofs (10.1); Convert between general
and standard forms for the equations of circles (10.2); Graph circles
(10.2); Given a graph, write the equation for a circle (10.2).
||Write equations for and graph ellipses.
||Write equations for and graph hyperbolas.
||Write equations for and graph parabolas.
||Graph conic sections; Convert equations for conic sections
between rectangular & polar form.
||Convert between general & standard forms for the equations
of ellipses (10.3); and hyperbolas (10.4); Graph ellipses (10.3); and
hyperbolas (10.4); Given a graph, write the equation for an ellipse (10.3);
and a hyperbola (10.4); Determine if an equation's graph is a circle,
parabola, ellipse, or hyperbola, then graph it (10.5); Rewrite a general
form equation into standard form, then identify the conic section and
graph it (10.6).
||Determine the next terms of arithmetic sequences; Find the
sum of arithmetic sequences.
||Determine the next terms of geometric sequences; Find the
sum of geometric sequences.
||Write repeating decimals as fractions; Determine if the
sum of an infinite series converges or diverges.
||Determine if an infinite series converges or diverges.
||Find the common difference and the next several terms in
an arithmetic sequence (12.1); Find the specified term of an arithmetic
sequence (12.1); Find the sum of an arithmetic sequence (12.1); Find the
common ratio and the next several terms of a geometric sequence (12.2);
Given the common ratio and a term in a geometric sequence, find the first
term (12.2); Determine if the sum of a series exists, and if it does,
find the sum (12.3); Use the ratio and/or comparison test to determine
if a series is convergent or divergent (12.4).
||Use sigma notation; Expand a binomial; Write a series using
||Use Pascal's triangle & the Binomial Theorem to expand
||Use the exponential & trigonometric series & Euler's
Formula to estimate values for e, the natural logarithm, and trigonometric
||Write an expression in expanded form and then find its sum
(12.5); Write a series using sigma notation (12.5); Use Pascal's triangle
to expand a binomial (12.6); Use the Binomial Theorem to expand a binomial
(12.6); Find the specified term for a binomial expansion (12.6); Use the
exponential series to find an approximation for e to a power or
the natural logarithm of a number (12.7); Use the trigonometric series
to approximate sine or cosine (12.7); Use Euler's formula to write a complex
number in exponential form (12.7)