YOUR TOPIC-BY-TOPIC GUIDE FOR THE ALEKS PIE

COORDINATED WITH

MATH 101: COLLEGE ALGEBRA

Louisiana Tech University

Review: (Sections 2.1-2.2)
               LEq: (completes 23 topics out of this slice)

                     Integer and rational numbers

                     Integer, rational, and irrational numbers
                     Evaluation of a linear expression in two variables
                     Evaluation of a polynomial in one variable
                     Translating expressions, basic

                     Translating sentences into mathematical expressions, basic
                     Writing an inequality
                     Distributive Property, simple
                     Distributive Property, advanced
                     Combining like terms, basic
                     Additive property of equality: Problem type 1
                     Additive property of equality: Problem type 2
                     Additive property of equality: Problem type 3
                     Multiplicative property of equality: Problem type 1
                     Multiplicative property of equality: Problem type 2
                     Solving a linear equation: Problem type 1
                     Solving a linear equation: Problem type 2
                     Solving a linear equation: Problem type 3
                     Solving a linear equation with several occurrences of the variable: Problem type 1
                     Solving a linear equation with several occurrences of the variable: Problem type 2
                     Solving a linear equation with several occurrences of the variable: Problem type 3
                     Solving a linear equation with several occurrences of the variable: Problem type 4
                     Solving a linear equation with several occurrences of the variable: Problem type 5

 Section 2.4:

                LEq: (completes 29 topics out of this slice)

                     Solving a linear inequality: Problem type 1
                     Solving a linear inequality: Problem type 2
                     Solving a linear inequality: Problem type 3
                     Solving a linear inequality: Problem type 4
                     Graphing a linear inequality on the number line

                     Word problem with linear inequalities

Section 2.5:

                LEq: (completes 31 topics out of this slice)

                     Graphing a compound linear inequality on the number line
                     Writing a compound inequality

Section 2.6:

                LEq: (completes 35 topics out of this slice)
                     Solving a linear equation with absolute value: Problem type 1
                     Solving a linear equation with absolute value: Problem type 2
                     Solving a linear inequality with absolute value
                     Graphing a linear inequality with absolute value on the number line

Review:
                LEq: (completes 39 topics out of this slice)          

                      Word problem on proportions: Problem type 2

                      Word problem with percent and money: Problem type 1

                      Sides of polygons having the same perimeter

                      Area and perimeter of a rectangle

                Gr&Fn: (completes 4 topics out of this slice)
                     Reading a point in the coordinate plane
                     Plotting a point in the coordinate plane
                     Solutions to a linear equation in two variables: Problem type 1
                     Solutions to a linear equation in two variables: Problem type 2            

Section 3.1:

                 Gr&Fn: (completes 10 topics out of this slice)

                     Graphing a line given the x and y intercepts
                     Graphing a line given the equation in slope-intercept form
                     Graphing a line given the equation in standard form
                     Graphing the line through a given point with a given slope
                     Determining the slope of a line given its graph
                     Graphing a vertical or horizontal line

                 Cnc: (completes 2 topics out of this slice)
                      Midpoint of a line segment in the plane
                      Distance between two points in the plane

Sections 3.2-3.3:

                 Gr&Fn: (completes 19 topics out of this slice)            
                     Y-intercept of a line
                     X and Y intercepts of a line given the equation in standard form
                     Finding the slope of a line given its equation
                     Writing the equation of a line given the slope and the y-intercept
                     Writing the equation of a line given the slope and a point
                     Writing the equation of the line through two given points
                     Writing the equations of vertical and horizontal lines through a given point
                     Writing the equation of the line through a given point and parallel to a given line
                     Writing the equation of the line through a given point and perpendicular to a given line

Review:

                  Gr&Fn: (completes 22 topics out of this slice)
                     Set builder notation
                     Union and intersection of sets
                     Intervals

Sections 4.1-4.3:
                  SEq: (completes 3 topics out of this slice)            
                     Solving a system of linear equations
                     Inconsistent system of linear equations
                     Consistency and independence of a system of linear equations            
Review: (Sections 5.1-6.3)
                  E&Po: (completes 35 topics out of this slice)

                     Product rule of exponents
                     Quotients of exponent expressions
                     Power Rule
                     Writing a positive number without a negative exponent
                     Writing a negative number without a negative exponent
                     Quotient of exponents and negative exponents
                     Product rule of exponents in a multivariate monomial
                     Ordering numbers with positive exponents
                     Ordering numbers with negative exponents
                     Scientific notation with positive exponent
                     Scientific notation with negative exponent
                     Addition of polynomials
                     Multiplication of monomials
                     Multiplication of two binomials
                     Squaring a binomial
                     Multiplication of polynomials
                     Degree of a multivariate polynomial
                     Division of a polynomial by a binomial with no remainder
                     Division of a polynomial by a binomial with remainder

                     Factoring a quadratic trinomial with leading coefficient 1
                     Factoring a quadratic trinomial with leading coefficient greater than 1
                     Factoring a perfect square
                     Factoring the product of a quadratic trinomial with a monomial
                     Roots of a quadratic equation with leading coefficient 1
                     Roots of a quadratic equation with leading coefficient greater than 1
                     Roots of a product of polynomials
                     Roots of a sum of polynomials
                     Writing a quadratic equation given the roots and the leading coefficient
                     Factoring a Difference of Squares
                     Factoring the difference of two fourth powers
                     Factoring the sum or difference of two cubes
                     Greatest common factor of two monomials
                     Least common multiple of two monomials
                     Factoring a multivariate polynomial by grouping: Problem type 1
                     Factoring a multivariate polynomial by grouping: Problem type 2

                  Rat:  (completes 12 topics out of this slice)           
                     Multiplying rational expressions, Type 1
                     Multiplying rational expressions: Problem type 2
                     Dividing rational expressions
                     Adding rational expressions with common denominator
                     Adding rational expressions
                     Adding rational expressions with different denominators
                     Adding and subtracting rational expressions: Problem type 2
                     Adding and subtracting rational expressions: Problem type 1
                     Ratio of quadratic polynomials: Problem type 1
                     Ratio of quadratic polynomials: Problem type 2
                     Ratio of quadratic polynomials: Problem type 3
                     Ratio of multivariate polynomials

Section 6.4:

                  Rat: (completes 14 topics out of this slice)

                     Complex fraction: Problem type 1
                     Complex Fraction: Problem type 2 

Section 6.6:

                  Rat: (completes 21 topics out of this slice)
                      Restriction on variable in a denominator
                      Solving a simple equation with rational expressions: Problem type 1
                      Solving a simple equation with rational expressions: Problem type 2
                      Solving a simple equation with rational expressions: Problem type 3
                      Solving an equation with rational expressions: Problem type 1
                      Solving an equation with rational expressions: Problem type 2
                      Solving an equation with rational expressions: Problem type 3

Sections 2.3 & 6.7:

                   LEq: (completes 42 topics out of this slice)

                      Word problem on linear equations: Problem type 1
                      Word problem on linear equations: Problem type 2
                      Word problem on proportions: Problem type 1                     
                   SEq: (completes 8 topics out of this slice)  
                      Word problem on systems of linear equations: Problem type 1
                      Word problem on systems of linear equations: Problem type 2
                      Word problem on systems of linear equations: Problem type 3
                      Word problem on systems of linear equations: Problem type 4
                      Word Problem with percent and money: Problem type 2

Review:

                  Rat: (completes 22 topics out of this slice)
                      Algebraic symbol manipulation

Section 7.1:

                  R&Q: (completes 5 topics out of this slice)  

                      Rational exponents: Basic
                      Rational exponents: Negative exponents and fractional bases
                      Rational exponents: Power of power
                      Solving an equation with positive rational exponent
                      Solving an equation with negative rational exponent    

Sections 7.2-7.4:
                  R&Q: (completes 16 topics out of this slice)       
                     Square root simplification
                     Simplifying a radical expression
                     Square root addition
                     Simplifying a sum of radical expressions
                     Square root multiplication
                     Simplifying the product of two radicals
                     Simplifying a product of radical expressions: Problem type 1
                     Simplifying a product of radical expressions: Problem type 2
                     Simplifying a product of radical expressions: Problem type 3
                     Rationalizing the denominator of a radical expression
                     Rationalizing the denominator of a radical expression using conjugates

Section 7.5:

                  R&Q: (completes 26 topics out of this slice)

                     Pythagorean theorem
                     Solving an equation with radicals: Problem type 1
                     Solving an equation with radicals: Problem type 2
                     Solving an equation with radicals: Problem type 3
                     Solving an equation with radicals: Problem type 4               
                     Cube root of an integer
                     Even root property
                     Odd root property
                     Solving an equation with exponent using the even-root property
                     Solving an equation with exponent using the odd-root property

Section 7.6:

                  R&Q: (completes 30 topics out of this slice)
                     Addition and subtraction of complex numbers
                     Multiplication of complex numbers
                     Division of complex numbers
                     Powers of i            

Sections 8.1, 8.2,  8.4:

                  R&Q: (completes 36 topics out of this slice)

                      Completion of the square
                      Quadratic formula
                      Complex solutions of a quadratic equation
                      Discriminant of a quadratic equation
                      Discriminant of a quadratic equation with parameter
                      Word problem solving quadratic equations, irrational roots

Section 8.3 & 11.2:
                  Cnc: (completes 3 topics out of this slice)

                      Graph of a parabola

                  R&Q: (completes 39 topics out of this slice)

                      Graphing a parabola: Problem type 1.
                      Graphing a parabola: Problem type 2.
                      Graphing a parabola

Sections 3.5, 9.1, 9.3, Appendix B-8 & B-9:

                  Gr&Fn: (completes 39 topics out of this slice)

                      Domain and range of a relation
                      Function tables
                      Graphing integer functions
                      Domain and range of an integer function
                      Domain and range of a real function
                      Relations and functions: The vertical line test
                      Sum of two linear functions
                      Product of two linear functions
                      Quotient of two functions
                      Vertical translation of the graph of a function
                      Horizontal translation of the graph of a function
                      Inversible and non-inversible functions: The horizontal line test
                      Inverse of a linear function
                      Inverse of a rational function
                      Composition of two integer functions: Problem type 1
                      Composition of two integer functions: Problem type 2
                      Composition of two real functions

 Sections 10.1-10.3:         
                  Ex&Log: (completes 8 topics out of this slice)
                      Translating a logarithmic equation into an exponential equation and conversely
                      Evaluating a logarithmic expression
                      Product rule for logarithms
                      Quotient rule for logarithms
                      Power rule for logarithms                    
                      Sketching an exponential function
                      Sketching a logarithmic function
                      Translation of logarithmic and exponential graphs

Section 10.4:

                  Ex&Log: (completes 12 topics out of this slice)

                      Solving a logarithmic equation: Problem type 1
                      Solving a logarithmic equation: Problem type 2
                      Solving an exponential equation: Problem type 1
                      Solving an exponential equation: Problem type 2

Section 11.3:

                  Cnc: (completes 6 topics out of this slice)  

                      Graph of a circle
                      Writing the equation of a circle given the center and an arbitrary point
                      Writing the equation of a circle given the endpoints of a diameter

Section 11.4:

                 Cnc: (completes 9 topics out of this slice)
                      Graph of an ellipse centered at the origin
                      Graph of an ellipse with an arbitrary center
                      Graph of a hyperbola centered at the origin