College Algebra / **Math 12 - 32189 - Fall 2008**

(Prof. Latham) **Course Syllabus**

The fol lowing is the list of problems covered in each chapter of the textbook

**Barnett/Ziegler/Byleen: College Algebra, 7th Ed. (McGraw-Hill)(*).**

**Completion through Chapter 1 (53 / 53 new items) **
Sep / 10 / 2008

alge013: Solving a linear equation with several occurrences of the variable:
Problem type 3

alge014: Solving a word problem using a linear equation: Problem type 1

alge020: Solving a linear inequality: Problem type 2

alge021: Solving a linear inequality: Problem type 3

alge024: Product rule of exponents

alge025: Power rule: Negative exponents

alge026: Quotients of expressions involving exponents

alge027: Power rule: Positive exponents

alge028: Product rule of exponents in a multivariate monomial

alge029: Simplifying a polynomial expression

alge030: Multiplying monomials

alge038: Factoring a multivariate polynomial by grouping: Problem type 1

alge040: Factoring a quadratic with leading coefficient greater than 1

alge041: Factoring a product of a quadratic trinomial and a monomial

alge042: Factoring with repeated use of the difference of squares formula

alge044: Factoring a sum or difference of two cubes

alge045: Finding the roots of a quadratic equation with leading coefficient 1

alge048: Finding the roots of a quadratic equation with leading coefficient
greater than 1

alge060: Solving a rational equation that simplifies to a linear equation:
Problem type 1

alge061: Solving a linear equation with several occurrences of the variable:
Problem type 2

alge076: Solving a system of linear equations

alge078: Solving a word problem using a system of linear equations: Problem type
1

alge080: Simplifying a radical expression : Problem type 1

alge084: Simplifying a sum of radical expressions

alge086: Rationalizing the denominator of a radical expression

alge088: Rationalizing the denominator of a radical expression using conjugates

alge089: Solving an equation with radicals: Problem type 1

alge173: Solving a word problem using a linear equation: Problem type 3

alge179: Solving a linear equation with several occurrences of the variable:
Problem type 5

alge180: Multiplying polynomials

alge194: Graphing a line given its equation in slope-intercept form

alge195: Graphing a line given its equation in standard form

alge196: Graphing a line through a given point with a given slope

alge198: Graphing a vertical or horizontal line

alge205: Solving a rational equation that simplifies to a linear equation:
Problem type 2

alge207: Solving a linear inequality: Problem type 4

alge209: Solving a linear equation with several occurrences of the variable:
Problem type 4

alge211: Solving a quadratic equation needing simplification

alge219: Solving a word problem using a linear equation: Problem type 2

alge249: Rational exponents: Powers of powers

alge250: Rational exponents: Basic

alge251: Rational exponents: Negative exponents and fractional bases

alge624: Factoring a difference of squares

alge631: Finding the slope of a line given its equation

alge637: Determining the slope of a line given its graph

alge640: Simplifying a product of radical expressions

alge681: Solving equations written in factored form

alge704: Solving a word problem using a linear equation: Problem type 4

alge705: Factoring a quadratic with leading coefficient 1

alge708: Polynomial long division: Linear divisor

alge710: Simplifying a ratio of polynomials: Problem type 1

scinot001: Converting between decimal numbers and numbers written in scientific
notation

scinot002: Multiplying and dividing numbers written in scientific notation

**Completion through Chapter 2 (30 / 83 new items)**
Sep / 24 / 2008

alge018: Graphing a linear inequality in the plane: Problem type 1

alge071: Writing the equation of a line given the slope and a point on the line

alge072: Writing the equation of the line through two given points

alge073: Writing the equations of vertical and horizontal lines through a given
point

alge091: Solving an equation with radicals: Problem type 3

alge094: Completing the square

alge095: Solving a quadratic equation using the quadratic formula

alge103: Solving an equation involving absolute value: Basic

alge167: Solving an equation involving absolute value: Advanced

alge169: Solving an inequality involving absolute value

alge170: Solving an inequality involving absolute value: Basic

alge182: Solving an equation with radicals: Problem type 4

alge184: Solving a word problem using a system of linear equations: Problem type
2

alge206: Solving a rational equation that simplifies to a linear equation:
Problem type 3

alge225: Graphing a linear inequality in the plane: Problem type 2

alge252: Graphing a parabola: Problem type 1

alge253: Graphing a parabola: Problem type 2

alge524: Solving a word problem using a quadratic equation with irrational roots

alge701: Writing equations and drawing graphs to fit a narrative

alge703: Solving a word problem using a quadratic equation with rational roots

alge707: Finding the discriminant of a quadratic equation

alge771: Solving a quadratic inequality

geom807: Slopes of parallel and perpendicular lines: Problem type 1

pcalc048: Adding and subtracting complex numbers

pcalc049: Multiplying complex numbers

pcalc050: Dividing complex numbers

pcalc051: Solving a quadratic equation with imaginary roots

pcalc053: Simplifying a power of i

set004: Set builder and interval notation

set005: Union and intersection of intervals

**Completion through Chapter 3 (26 / 109 new items)** Oct / 8 / 2008

alge127: Quotient of two functions

alge129: Composition of two functions: Advanced

alge130: Inverse functions: Advanced

alge132: Distance between two points in the plane

alge168: Graphing an equation involving absolute value in the plane

alge185: Vertical translation of the graph of a function

alge191: Midpoint of a line segment in the plane

alge254: Graphing a parabola: Problem type 3

alge255: Graphing a quadratic inequality

fun004: Domain and range: Problem type 2

fun010: Vertical line test

fun011: Horizontal line test

fun012: Inverse functions: Basic

fun016: Domain and range: Problem type 1

fun018: Introduction to functions: Notation and graphs

fun019: Sum, difference, and product of two functions

fun020: Vertical and horizontal translations of the graph of a function

fun021: Composition of two functions: Domain and range

fun022: Composition of two functions: Basic

fun023: Piecewise-defined functions

geom808: Slopes of parallel and perpendicular lines: Problem type 2

pcalc064: Graphing a circle given its equation in general form

pcalc065: Writing an equation of a circle given its center and a point on the
circle

pcalc066: Writing an equation of a circle given the endpoints of a diameter

pcalc114: Even and odd functions

pcalc605: Graphing a circle given its equation in standard form

**Completion through Chapter 4 (16 / 125 new items)** Oct / 22 / 2008

alge709: Polynomial long division: Quadratic divisor

pcalc092: Partial fraction decomposition

pcalc108: Sketching the graph of a rational function: Problem type 1

pcalc109: Sketching the graph of a rational function: Problem type 2

pcalc115: Solving a word problem by finding a local extremum of a polynomial
function

pcalc117: Synthetic division

pcalc118: Remainder theorem

pcalc123: Using a given zero to write a polynomial as a product of linear
factors

pcalc700: Finding a polynomial of a given degree with given zeros

pcalc701: Finding all potential zeros of a polynomial given by the rational
zeros theorem

pcalc702: Using the rational zeros theorem to find zeros of a polynomial

pcalc703: Using the conjugate zeros theorem to find all zeros of a polynomial

pcalc704: Solving a word problem involving a polynomial of degree 3

pcalc705: N zeros theorem and conjugate zeros theorem

pcalc706: Choosing the form of a rational function given its graph

pcalc738: Inferring properties of a polynomial function from its graph

**Completion through Chapter 5 (15 / 140 new items)** Oct / 29 / 2008

alge107: Change of base for logarithms

alge108: Exponential and logarithmic equations

alge111: Solving an exponential equation: Problem type 1

alge112: Solving an exponential equation: Problem type 2

alge113: Solving a logarithmic equation: Problem type 2

alge177: Solving a word problem using an exponential equation: Problem type 1

alge178: Solving a word problem using an exponential equation: Problem type 2

alge232: Evaluating a logarithmic expression

alge233: Solving a logarithmic equation: Problem type 1

alge712: Sketching the graph of an exponential function: Basic

pcalc102: Translating the graph of a logarithmic or exponential function

pcalc103: Sketching the graph of an exponential function: Advanced

pcalc104: Sketching the graph of a logarithmic function

pcalc708: Basic properties of logarithms

pcalc737: Solving a word problem using an exponential equation: Problem type 3

**Completion through Chapter 6 (13 / 153 new items)** Nov / 5 / 2008

alge075: Classifying a system of linear equations

alge077: Creating an inconsistent system of linear equations

alge079: Graphing a system of linear inequalities

alge172: Solving a word problem using a system of linear equations: Problem type
5

alge192: Solving a word problem using a system of linear equations: Problem type
4

alge224: Solving a word problem using a system of linear equations: Problem type
3

pcalc093: Solving a word problem using a system of linear inequalities

pcalc094: Solving a word problem using linear programming

pcalc095: Linear programming

pcalc098: Solving a system of nonlinear equations

pcalc099: Consistency and independence of a system of linear equations

pcalc709: Addition of matrices and multiplication of a matrix by a scalar

pcalc712: Gauss-Jordan elimination with a 2x2 matrix

**Completion through Chapter 7 (10 / 163 new items)** Nov / 12 / 2008

pcalc039: Multiplication of matrices: Basic

pcalc040: Finding the inverse of a 2x2 matrix

pcalc041: Finding the inverse of a 3x3 matrix

pcalc042: Finding the determinant of a 2x2 matrix

pcalc043: Finding the determinant of a 3x3 matrix

pcalc045: Cramer's rule: Problem type 1

pcalc046: Augmented matrix and solution set of a system of linear equations

pcalc047: Cramer's rule: Problem type 2

pcalc710: Multiplication of matrices: Advanced

pcalc711: Using the inverse of a matrix to solve a system of linear equations

**Completion through Chapter 8 (12 / 175 new items)** Nov / 19 / 2008

pcalc080: Finding the first terms of a sequence

pcalc082: Factorial expressions

pcalc087: Binomial formula

pcalc088: Permutations and combinations: Problem type 1

pcalc089: Permutations and combinations: Problem type 2

pcalc090: Permutations and combinations: Problem type 3

pcalc713: Arithmetic and geometric sequences: Identifying and writing in
standard form

pcalc715: Arithmetic sequences

pcalc717: Geometric sequences

pcalc718: Sum of the first n terms of an arithmetic sequence

pcalc719: Sum of the first n terms of a geometric sequence

pcalc720: Sum of a geometric series

**Completion through Chapter 9 (15 / 190 new items)**
Dec / 1 / 2008

pcalc067: Graphing a parabola with a horizontal or a vertical axis

pcalc068: Writing an equation of a parabola given the vertex and the focus

pcalc069: Finding the focus of a parabola

pcalc071: Graphing an ellipse given its equation in general form

pcalc072: Finding the foci of an ellipse

pcalc073: Writing an equation of an ellipse given the foci and the major axis
length

pcalc074: Writing an equation of an ellipse given the center, an endpoint of an
axis, and

the length of the other axis

pcalc076: Graphing a hyperbola given its equation in general form

pcalc077: Finding the foci of a hyperbola

pcalc078: Writing an equation of a hyperbola given the foci and the vertices

pcalc079: Writing an equation of a hyperbola given the foci and the asymptotes

pcalc096: Graphing a system of nonlinear inequalities: Problem type 1

pcalc734: Graphing an ellipse given its equation in standard form

pcalc735: Graphing a hyperbola given its equation in standard form

pcalc736: Classifying conics given their equations

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