# Your Math Help is on the Way!

### More Math Help

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Academic Systems Algebra Scope and Sequence

 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