• INTEGRATED MODERN ALGEBRA 

     

     

     

    ALL WORK WILL BE POSTED ON GOOGLE CLASSROOM.

     

     

    Overview 

    The curriculum for Integrated Modern Algebra is based on the belief that mastery in learning takes place over an extended period. When a skill or concept is introduced and practiced, students develop familiarity with it. This course intends to enable students to move toward independent learning within the context of review and extension of these skills with an introduction to topics essential for further study of mathematics. Emphasis is placed on the reinforcement of fundamental skills and concepts. The course focuses on families of functions, including linear, quadratic, exponential, and rational functions. Students are introduced to the complex number system. Other topics of study include trigonometry and data trends. As this course follows Algebra 1 and Geometry, students who complete this course will meet the NJDOE three-year mathematics graduation requirement. Students who complete and wish to continue to pursue mathematics at Wall High School can enroll in Algebra 2 CP. As this is a non-required precursor for Algebra 2 CP, students who have completed Algebra 2 CP are not eligible to take this course.

     

     

     

    Syllabus

     

     

    Unit 1

     

    • Simplify algebraic expressions

    • Add, subtract, and multiply polynomial expressions

    • Solve Linear Equations of all types (one step, two step, multi-step, variables on both sides)

    • Define and apply definitions of angle, perpendicular lines, parallel lines, and line segment.

    • Understand and apply angle relationships including complementary angles, supplementary angles, congruent angles, linear pairs, and vertical angles.

    • Understand and apply the angle addition postulate.

    • Understand and apply segment relationships including bisector, congruent segments, and midpoint.

    • Understand and apply the segment addition postulate.

    • Apply volume and area formulas for cylinders, pyramids, cones, and spheres.

    • Solve literal equations

    Unit 2

    • Understand and apply the Pythagorean Theorem

    • Understand and apply the Distance Formula

    • Understand and apply the Midpoint Formula

    • Solve Right Triangles with Trigonometric Functions (only in degrees to find both angles and sides)

    •  Understand and apply the Cofunction Theorem. example: cos(30)=sin(60)

    • Introduce Secant, Cosecant, and Cotangent trigonometric functions for right triangles.

    • Define and apply circles vocabulary: central angles, inscribed angle, diameter, semi-circle, center, radius, chord, measure of an arc.

    • Find the arc length of a circle using proportion with circumference.

    • Find the area of a sector using a proportion with area.

    • Write a standard-form circle equation given a graph or information such as center, radius, area, and circumference.

    Unit 3

    • Use the definition of a function to determine whether a relationship is a function. 

    • Use function notation once a relation is determined to be a function. 

    • Evaluate functions for given inputs in the domain. 

    • Operations with function notation.

    • Interpret Functions in real life problems

    • Identify characteristics of graphs of functions including domain and range, increasing and decreasing, maximum and minimum, end behavior, positive and negative, and discontinuity.

    • Calculate and interpret the average rate of change of a function over a specified interval. 

    • Estimate the rate of change from a graph.

    Unit 4

    • Given tables of values determine which represent linear functions and explain reasoning. 

    • Write a linear function in different but equivalent forms to reveal and explain different properties of the function. These forms include slope-intercept form, standard form and point-slope form each revealing different properties. 

    • Rearrange the equation of a line into different forms.

    • Graph linear functions from a table, an equation or a described relationship. 

    • Identify key characteristics from the graph and equations.

    • Find slopes of parallel and perpendicular lines and write equations for such. 

    • Graph piecewise-defined functions.

    Unit 5

    • Solve systems of linear equations through an algebraic method and check answers for correctness. 

    • Recognize when linear systems have one solution, no solutions or infinitely many solutions. 

    • Translate algebraic verbal equations to represent linear systems and solve those systems. 

    • Solve systems of linear equations through a graphical approach both by hand and with a graphing calculator. 

    • Find approximate solutions when appropriate. Explain why graphical approaches may only lead to approximate solutions while an algebraic approach produces precise solutions that can be represented graphically or numerically. 

    • Graph the solutions to a linear inequality.

    • Graph the solution set to a system of linear inequalities.

    • Solving basic linear inequalities.

    • Solving compound inequalities.

    Unit 6

    • Simplify square roots.

    • Operations with complex numbers. 

    • Solve quadratic equations by inspection: taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. 

    • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.

    • Relate the value of the discriminant to the type of root to expect for the graph of a quadratic function. 

    • Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 

    • Solve a simple System consisting of a linear equation and a quadratic equation in two variables algebraically.

    • Solve a simple System consisting of quadratic equations in two variables algebraically.

    Unit 7

    • Investigate the graph of quadratic functions through the use of the graphing calculator. 

    • Recognize transformations of the parent f(x) = x2 as vertical f(x) = x2 + k, horizontal f(x + k), stretch or reflections. 

    • Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. 

    • Graph quadratic functions given in vertex form through the process of generating points in function notation and apply the meaning of symmetry to plot points. 

    • Recognize that different forms of quadratic functions reveal different key features of its graph.

    • Relate the value of the discriminant to the type of root to expect for the graph of a quadratic function.

    • Interpret models of quadratic functions given as equations or graphs. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

    • Solve a simple System consisting of a linear equation and a quadratic equation in two variables graphically.

    • Solve a simple System consisting of quadratic equations in two variables graphically.

    Unit 8

    • Understand and apply the Laws of Exponents 

    • Graph Exponential functions and discuss key features including intercepts, transformations, and horizontal asymptotes.

    • Switch from radical form to rational exponents and vice versa

    • Graph square roots functions and discuss key features including intercepts and transformations.

    • Perform addition, subtraction, multiplying and dividing with square root functions.

    • Graph and analyze piecewise functions containing linear, quadratic, exponentials and square root functions.

    • Solve radical and exponential equations and discuss extraneous solutions.

     

    Unit 9

    • Simplify rational expressions

    • Identify excluded values and discuss as domain restrictions and discontinuities

    • Multiply rational expressions

    • Divide rational expressions

    • Solve rational equations and check for extraneous solutions.