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Academic Systems Algebra Scope and Sequence

Academic Systems Intermediate Algebra

Lesson Concept Objectives Hours
Topic EII: Essentials of Algebra
EII.A Real Numbers and
Exponents
(reviews 1.1, 1.3, 6.1)
Real Numbers and Notation a) Number line and notation: sets, ordering symbols,
grouping symbols, exponents, and absolute value
b) Operations on signed numbers
c) Properties of real numbers: commutative law, associative
law, distributive law, additive and multiplicative identities,
inverses
1 hour
Integer Exponents a) Nonnegative integer exponents
b) Properties of exponents
1 hour
Lesson Total 2 hours
EII.B Polynomials
(reviews 2.1, 6.2, 7.1,7.2)
Polynomial Operations a) Algebra building blocks: constants,
variables, terms and coefficients
b) Evaluating polynomials
c) Adding and subtracting polynomials
d) Multiplying and dividing polynomials
1 hour
Factoring
Polynomials
a) Factoring out the greatest common factor
b) Factoring by grouping
c) Factoring trinomials
d) Factoring a difference of 2 squares
e) Factoring sums and differences of 2 cubes
f) Factoring using a combination of methods
1 hour
Lesson Total 2 hours
EII.C Equations and
Inequalities
(reviews 2.2, 2.4)
Linear a) Solving linear equations
b) Solving linear inequalities
2 hours
Lesson Total 2 hours
EII.D Rational Expressions
(reviews 8.1, 8.2)
Rational Expressions a) Negative integer exponents
b) Writing rational expressions in lowest terms
c) Multiplying and dividing rational expressions
d) Adding and subtracting rational expressions
1 hour
Rational Equations a) Solving equations that contain rational expressions 1 hour
Lesson Total 2 hours
EII.E Graphing Lines
(reviews 3.1, 4.1, 4.2)
Graphing Lines a) The coordinate system
b) Graphing lines
1 hour
Finding Equations a) Slope and intercepts
b) Finding the equation of a line
1 hour
Lesson Total 2 hours
EII.F Absolute Value
(new material)
Solving Equations a) Solving |x| = a
b) Solving |Ax + B| = a
c) Solving |Ax + B| = |Cx + D|
2 hours
Solving Inequalities a) Solving absolute value inequalities 1 hour
Lesson Total 3 hours

Topic 9: Rational Exponents and Radicals

9.1 Roots and Radicals Square Roots and
Cube Roots
a) Definition of square root and cube root
b) Radicand, radical
c) Principal square root
d) Multiplication and division properties
e) Simplifying a square root or a cube root of a whole number
f) Simplifying a square root or a cube root of simple
monomial expression
 1 hour
Radical Expressions a) Simplifying radical expressions
b) Like radical terms
c) Simplifying a sum or difference of radical expressions
d) Multiplying radical expressions
e) Conjugates
f) Rationalizing the denominator
g) Solving radical equations
2 hours
Lesson Total 3 hours
9.2 Rational Exponents Roots and Exponents a) The nth root of a number
b) Definition of a1/n and am/n
c) Properties of rational exponents
1 hour
Simplifying Radicals a) Simplifying radicals 1 hour
Operations on
Radicals
a) Multiplying radical expressions
b) Dividing radical expressions
c) Adding and subtracting radical expressions
2 hours
Lesson Total 4 hour

Topic 10: Quadratic Equations

10.1 Quadratic Equations I Solving by Factoring a) The standard form of a quadratic equation
b) Putting a quadratic equation into standard form
ax^2 + bx + c = 0; a ≠ 0
c) Solving quadratic equations of the form
ax^2 + bx = 0 by factoring
d) Solving quadratic equations of the form
ax^2 + bx + c = 0 by factoring
1 hour
Solving by Square
Roots
a) Finding square roots
Roots b) Solving quadratic equations of the form ax^2 = b
c) Solving quadratic equations of the form (ax + b)^2 = c
1 hour
Lesson Total 2 hour
10.2 Quadratic Equations II Completing the Square a) Solving quadratic equations of the form
x^2 + bx + c = 0 by completing the square
b) Solving quadratic equations of the form
ax^2 + bx + c = 0, a ≠ 1, by completing the square
1 hour
The Quadratic
Formula
a) Introducing the quadratic formula
b) Using the quadratic formula to solve
quadratic equations of the form ax^2 + bx + c = 0
c) Using the discriminant of a quadratic equation to
determine the nature of the solutions of the equation
1 hour
Explore a) Solving Equations 1 hour
Lesson Total 3 hour
10.3 Complex Numbers Complex Number
System
a) Definition of complex numbers
b) Powers of i
c) Operations on complex numbers
2 hours
Lesson Total 2 hour

Topic 11: Functions and Graphing

11.1 Functions Functions and Graphs a) Definition of a function
b) Function as an ordered pair of numbers
c) Finding function values given a formula
d) Function notation: y = f(x)
e) Graphing simple functions
f) Domain and range of a function
g) The vertical line test
1 hour
Linear Functions a) Graphs of linear functions
b) Graphs of absolute value functions
1 hour
Quadratic Functions a) Graphs of quadratic functions
b) Intercepts of quadratic functions
1 hour
Explore a) Functions and Graphs 1 hour
Lesson Total 4 hour
11.2 The Algebra of
Functions
The Algebra of
Functions
a) The sum and difference of functions
b) The product and quotient of functions
c) The composition of functions
2 hours
Inverse Functions a) Finding the inverse and the equation of the inverse
b) Defining one-to-one and checking whether a function has
an inverse that is a function
c) Graphing inverse functions
2 hours
Lesson Total 4 hour

Topic 12: The Exponential and Logarithmic Functions

12.1 Exponential Functions The Exponential Function a) Recognizing and graphing an exponential function
b) Applications of the exponential function
c) The algebra of exponential functions
2 hours
Lesson Total 2 hour
12.2 Logs and Their
Properties
The Logarithmic Function a) Converting from exponents to logarithms & logarithms to exponents
b) Recognizing and graphing a logarithmic function
1 hour
Lesson Total 1 hour
12.3 Applications of Logs Natural and Common
Logs
a) Base e and natural logarithms
Logs b) Finding logs in base 10 and finding powers of 10, using a calculator
c) Finding logs in base e and powers of e, using a calculator
d) Change of base formula
1 hour
Solving Equations a) Solving exponential equations
b) Solving logarithmic equations
1 hour
Lesson Total 2 hour
Topic 13: More Nonlinear Equations and Inequalities
13.1 Nonlinear Equations Solving Equations a) Solving polynomial equations by factoring
b) Solving quadratic-type equations by factoring or by
substitution
1 hour
Radical Equations a) Solving
b) Solving a
c) Solving
d) Solving equations that contain rational exponents
1 hour
Explore a) Graphing
Lesson Total 3 hour
13.2 Nonlinear Systems Solving Systems a) The solution of a nonlinear system
b) Solving nonlinear systems by graphing
c) Solving nonlinear systems by the addition method
d) Solving nonlinear systems by the substitution method
1 hour
Explore a) Graphing Systems 1 hour
Lesson Total 2 hour
13.3 Inequalities Quadratic Inequalities a) Solving quadratic inequalities 2 hours
Rational Inequalities a) Solving rational inequalities 1 hour
Explore a) Graphing Inequalities 1 hour
Lesson Total 4 hour

Topic 3: Introduction to Graphing

3.1 Introduction to
Graphing
Plotting Points a) The xy-plane
b) The x-axis and y-axis
c) The origin
d) Ordered pairs
e) The x-coordinate (abscissa), the y-coordinate (ordinate)
f) Plotting ordered pairs of numbers
g) Labeling the four quadrants
h) Determining the quadrant in which a point lies
i) The signs of the coordinates in each quadrant
1 hour
Rise and Run a) Subscript notation
b) Geometric interpretation of rise and run
c) Algebraic definition of rise and run
1 hour
The Distance Formula a) Pythagorean Theorem
b) The distance formula
c) The equation of a circle
0.5 hours
Explore a) Plotting Points 0.5 hours
Lesson Total 3 hour

Topic 4: Graphing Linear Equations and Inequalities

4.1 Graphing Equations Graphing Lines I a) Definition of a linear equation in two variables
b) Recognizing linear equations in two variables
c) Solutions of linear equations
d) Graphing a linear equation by plotting ordered pairs
2 hours
Graphing Lines II a) Equations and graphs of horizontal and vertical lines
b) The intercepts of a line
c) Graphing a linear equation by finding the intercepts
1 hour
Slope of a Line a) Definition of the slope of a line
b) Positive slope, negative slope, zero slope, undefined
slope
c) Graphing a line given a point and the slope
d) Parallel and perpendicular lines
2 hours
Lesson Total 5 hour
4.2 The Equation of a Line Finding the Equation I a) Finding the equation of a line given a point on the line and the slope of the line
b) The point-slope form of the equation of a line
c) Finding the equation of a line given two points on the line
1 hour
Finding the Equation II a) The slope-intercept form of the equation of a line
b) Finding the equation of a horizontal line
c) Finding the equation of a vertical line
d) Finding the equation of a line parallel or perpendicular to
a given line
2 hours
Lesson Total 3 hour
4.3 Graphing Inequalities Linear Inequalities a) Ordered pairs as solutions of linear inequalities
b) Graphing inequalities
2 hours
Lesson Total 2 hour

Topic 5: Solving Linear Systems

5.1 Solving Linear
Systems
Solution by Graphing a) The solution of a linear system
b) Graphing linear systems
c) Systems with a unique solution
d) Systems with no solutions
e) Systems with an infinite number of solutions
1 hour
Solution by Algebra a) Solving linear systems by the substitution method: one
solution, no solution, and an infinite number of solutions
b) Solving linear systems by the elimination method: one solution,
no solution, and an infinite number of solutions
1.5 hours
Explore a) Exploring Graphing Linear Systems 0.5 hours
Lesson Total 3 hour
5.2 Problem Solving Using Linear Systems a) Number problems
b) Interest problems
c) Coin problems
d) Mixture problems
2 hours
Lesson Total 2 hour
5.3 Systems of Inequalities Solving Linear Systems a) Solving systems of linear inequalities by graphing 1 hour
Explore a) Exploring Solving Linear Systems 1 hour
Lesson Total 2 hour

Topic 6: Exponents and Polynomials

6.1 Exponents Properties of
Exponents
a) Definition of exponent, power, and base
b) Multiplication property
c) Division property
d) Powers raised to powers
e) Products raised to powers
f) Quotients raised to powers
g) The zero exponent
2 hours
6.2 Polynomial
Operations I
Adding and
Subtracting
a) Definition of polynomial, term, and coefficient
b) Evaluating a polynomial
c) The degree of a term and a polynomial
d) Writing the terms of a polynomial in descending order
e) Definition of a monomial, binomial, and trinomial
f) Recognizing like or similar terms
g) Combining like or similar terms
h) Polynomial addition
i) Polynomial subtraction
2 hours
Multiplying and
Dividing
a) Multiplying a monomial by a monomial
b) Multiplying a polynomial by a monomial
c) Dividing a monomial by a monomial
d) Dividing a polynomial by a monomial
2 hours
Lesson Total 4 hour
6.3 Polynomial
Operations II
Multiplying Binomials a) Multiplying binomials by the "FOIL" method
b) Perfect squares, product of the sum and difference of two terms
1.5 hours
Multiplying and
Dividing
a) Multiplying a polynomial by a polynomial
b) Dividing a polynomial by a polynomial
1.5 hours
Explore a) Multiplying Binomials 1 hour
Lesson Total 4 hour

Topic 7: Factoring

7.1 Factoring
Polynomials I
Greatest Common Factor a) Finding the greatest common factor (GCF) of a set of
monomials
b) Factoring a polynomial by finding the GCF when the GCF is a
monomial
2 hours
Grouping a) Factoring a polynomial by finding the GCF when the GCF is a
binomial
b) Factoring a polynomial with four terms by grouping
2 hours
Lesson Total 4 hour
7.2 Factoring
Polynomials II
Trinomials I a) Factoring trinomials of the form x^2 + bx+ c;
x^2 + bxy+ cy^2;
1 hour
Trinomials II a) Factoring trinomials of the form ax^2 + bx + c, a ≠ 1, by trialand-error
b) Factoring trinomials of the form ax^2 + bx + c, a ≠ 1, by grouping
c) Solving quadratic equations by factoring
2 hours
Explore a) Exploring Factoring 1 hour
Lesson Total 4 hour
7.3 Factoring by Patterns Recognizing Patterns a) Factoring a perfect square trinomial
b) Factoring a difference of two squares
c) Factoring a sum and difference of two cubes
d) Factoring using a combination of methods
2 hours
Lesson Total 2 hour

Topic 8: Rational Expressions

8.1 Rational Expressions I Multiplying and Dividing a) Determining when a rational expression is undefined
b) Writing a rational expression in lowest terms
c) Multiplying rational expressions
d) Dividing rational expressions
e) Simplifying a complex fraction
1 hour
Adding and Subtracting a) Adding rational expressions with the same denominator
b) Subtracting rational expressions with the same
denominator
1 hour
Lesson Total 2 hour
8.2 Rational
Expressions II
Negative Exponents a) Notation
b) Scientific notation
1 hour
Multiplying and Dividing a) Reducing a rational expression of the form
(a -b)/(b-a)
b) Multiplying rational expressions
c) Dividing rational expressions
d) Simplifying a complex fraction
1 hour
Adding and Subtracting a) Finding the least common denominator of two or more
rational expressions
b) Adding rational expressions with different denominators
c) Subtracting rational expressions with different
denominators
d) Simplifying a complex fraction
1 hour
Lesson Total 3 hour
8.3 Equations with
Fractions
Solving Equations a) Solving equations with rational expressions
b) Solving for an unknown in a formula involving a rational
expression
2 hour
Lesson Total 2 hour
8.4 Problem Solving Rational Expressions a) Ratio and proportion
b) Distance problems
c) Work problems
d) Variation
2 hours
Lesson Total 2 hour

Topic F3: Proportional Reasoning II

F3.1 Ratio and Proportion Ratios a) Notation
b) Equivalent ratios
c) Rates
d) Applications
2 hours
Proportions a) Setting up a proportion
b) Solving a proportion
c) Similar triangles
d) Applications
3 hours
Explore a) Inverting Ratios
b) Similar Figures
1 hour
Lesson Total 4-6 hours
F3.2 Percent Definition a) Percent as a fraction
b) Percent as a decimal
c) “Benchmark” percents
d) Applications
2 hours
Converting a) Converting among fractions, decimals and percents
b) Percent increase and decrease
c) Applications
3 hours
Solving Percent
Problems
a) Setting up and solving proportions
b) Setting up and solving other equations
c) Applications
3 hours
Explore a) A Survey
b) Computing Tips
c) A Percent Question
1 hour
Lesson Total 6-8 hours

Topic F5: Geometry

F5.1 Geometry I Geometric Figures a) Point, line, line segment, ray
b) Polygons
c) Measuring angles
d) Angles: acute, right, obtuse, straight
e) Relationships between angles: complementary,
supplementary, adjacent, vertical
f) Applications
3 hours
Explore a) Tiling with Polygons
b) What’s the Sum?
1 hour
Lesson Total 4hours
F5.2 Geometry II Perimeter and Area a) Perimeter of a polygon
b) Area of a polygon
c) Area of a rectangle, square, parallelogram, triangle,
trapezoid
d) Circumference of a circle
e) Area of a circle
f) Perimeter and area of composite figures
g) Applications
2 hours
Surface Area and
Volume
a) Surface area of a solid
b) Volume of a solid
c) Surface area and volume of a rectangular prism
d) Surface area and volume of a cylinder
e) Volume of a cone
f) Volume of a sphere
g) Composite figures
h) Applications
3 hours
Explore a) Don’t Fence Me In
b) Why π?
c) Packaging Products
1 hour
Lesson Total 4-6 hours
F5.3 Geometry III Triangles and
Parallelograms
a) Angle sum of a triangle
b) Congruent triangles
c) Isosceles and equilateral triangles
d) Right triangles
e) The Pythagorean Theorem
f) Parallel lines and transversals
g) Properties of parallelograms
h) Applications
2 hours
Similar Polygons a) Similar polygons
b) Similar triangles
c) Applications
3 hours
Explore a) Congruent Triangles
b) Door to Door
1 hour
Lesson Total 4-6 hours

Topic F6: Interpreting Data

F6.1 Units of Measurement US/English Units a) Measures: length, weight, time, volume
b) Converting from one unit to another
c) Adding and subtracting measurements
d) Applications
2 hours
The Metric System a) The metric system: length, mass, volume
b) Fahrenheit and Celsius scales
c) Converting between US and metric units
d) Applications
3 hours
Explore a) Sizing it Up
b) Choosing Units
1 hour
Lesson Total 4-6 hours
F6.2 Interpreting Graphs Data and Graphs a) Reading data from graphs
b) Graphing data
c) Pictographs
d) Bar graphs
e) Circle graphs
f) Line graphs
g) Applications
2 hours
Explore a) Collecting and Picturing Data
b) Graphs in the News
1 hour
Lesson Total 2-3 hours
F6.3 Introduction to
Statistics
Statistical Measures a) Mean
b) Median
c) Mode
d) Box-and-whisker plots
e) Applications
2 hours
Explore a) Collecting Data
b) Where’s the Middle?
1 hour
Lesson Total 2-3 hours