Download Courses for the Proposed Developmental Sequence

Courses for the Proposed Developmental Sequence
The new curriculum would involve reorganizing the material contained in the current 3 semester
developmental mathematics program into 9 one credit hour courses. (Course objectives attached
to the end of this document.)
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MAT080 Integer Arithmetic
MAT081 Fractions, Decimals and Percents
MAT082 Linear Equations
MAT083 Systems of Linear Equations
MAT084 Polynomials
MAT085 Quadratics Equations and Circles
MAT086 Rational Functions
MAT087 Geometry
MAT088 Introduction to Trigonometry
Proposed Revised Structure for 08x Courses
MAT080 Integer
Arithmetic
MAT081 Fractions,
Decimals and Percents
MAT083 Systems of
Linear Equations
MAT082 Linear Equations
MAT087
Geometry
MAT084
Polynomials
MAT088
Introduction to
Trigonometry
MAT085 Quadratic
Equations and Circles
MAT086 Rational
Expressions and Equations
Proposed Courses and Associated Objectives
MAT080 – Integer Arithmetic
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Perform operations with signed numbers. BCM, chapter 10
Add, subtract, multiply, and divide whole numbers both with and without the use of a
calculator. BCM, chapter 1
Define whole number exponents and evaluate numerical expressions with whole numbers
exponents. BCM, section 1.6
Find the prime factorization of a number. BCM, section 1.7
Recognize, use and understand the commutative, the associative, and the distributive laws
of addition and multiplication. BCM, section 11.1
Know and use order of operations effectively. BCM, section 1.6, 2.8,
Define square root and evaluate numerical expressions with square roots. BCM, section
12.5
Perform arithmetic operations with square roots. BCM, section 12.5
Evaluate variable expressions given values for the variables. BCM, section 11.1
Formulate and solve applications with whole numbers and integers. Integrated
throughout. For instance, BCM Objectives 1.2A, 1.3C, 1.4C, 1.5D, 2.4D, 2.5D, 2.6C,
2.7C, all of chapter 6
Make estimates by developing a sense of relative number size. In various sections, for
instance BCM 3.2
Construct and interpret graphs and charts with appropriate scales. BCM, Sections 7.1,
7.2, 7.3
Use all arithmetic functions on a scientific calculator, including square, square root, and
power functions when available. See inside back cover of BCM
Use parentheses keys. See inside back cover of BCM
MAT081 – Fractions, Decimals and Percents
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Add, subtract, multiply, and divide arithmetic fractions and decimals both with and
without the use of a calculator. BCM, Sections 2.4, 2.5, 2.6, 2.7
Define negative exponents and simplify expressions containing them. Not covered in
BCM.
Write fractions in equivalent forms. . BCM, Section 2.3
Convert between decimals, fractions and percents (including rounding). . BCM, Section
5.1
Evaluate rational variable expressions given values for the variables. . BCM, Section
11.1
Solve basic ratio and proportion application problems. BCM, Chapter 4
Solve percent application problems. BCM, Chapter 5
Solve application problems involving both English and Metric measurement conversions.
BCM, Chapters 8 and 9.
Solve problems using scientific notation. Not covered in BCM
MAT082 – Linear Equations
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Graph using the rectangular coordinate system. Intermediate Algebra, Section 3.1
Find the slope of a line. Intermediate Algebra, Section 3.4
Find equations of lines using point-slope form, slope-intercept form and general form.
Intermediate Algebra, Section 3.5
Reduce all forms of line equations to slope intercept form. Intermediate Algebra,
Section 3.5
Graph linear equations in two variables. Intermediate Algebra, Section 3.3
Find equations of vertical and horizontal lines. Intermediate Algebra, Section 3.3
Identify parallel and perpendicular lines from their equations. Intermediate Algebra,
Section 3.6
Find equations of parallel and perpendicular lines. Intermediate Algebra, Section 3.6
Define and evaluate functions using function notation. Intermediate Algebra, Section
3.2
Formulate and solve problems involving linear equations and linear functions. See, for
instance, Intermediate Algebra, Objective 3.3D and 3.5C
Solve linear literal equations. Intermediate Algebra, Objective 2.1B
Solve linear inequalities. Intermediate Algebra, Section 2.4
Graph solutions of linear inequalities. Intermediate Algebra, Section 3.7
MAT083 – Systems of Linear Equations
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Solve 2 by 2 linear systems by graphing. Intermediate Algebra, Section 4.1
Solve 2 by 2 linear systems by substitution. Intermediate Algebra, Section 4.1
Solve 2 by 2 and 3 by 3 linear systems by elimination. Intermediate Algebra, Section
4.2
Solve 2 by 2 and 3 by 3 linear systems by row operations. Hardbound Intermediate
Algebra, Section 4.3
Solve applications problems involving 2 by 2 and 3 by 3 systems of linear equations.
Intermediate Algebra, Objective 4.1C and Section 4.4
MAT084 – Polynomials The material for this course, with the exception of objective 12, is
covered in Intermediate Algebra, Chapter 5. I think that objective was meant fo5
MAT085.
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Define and identify polynomials.
Add and subtract polynomials.
Multiply polynomials.
Factor a monomial from a polynomial.
Factor expressions that are quadratic in form.
Factor expressions that are the sum and difference of cubes.
Factor expressions that can be factored by grouping.
Divide polynomials by monomials.
Divide poloynomials by binomials using long division.
Solve polynomial equations.
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Solve applications involving polynomial equations.
Simplify algebraic monomials inside a square root. Intermediate Algebra, Section 7.2
MAT085 – Quadratic Equations and Circles
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Simplify square roots of non-square numbers. Intermediate Algebra, Section 7.2
Simplify square roots of variable expressions. Intermediate Algebra, Section 7.2
Solve quadratic equations by factoring and the square root property. Intermediate
Algebra, Section 8.1
Solve quadratic equations by completing the square. Intermediate Algebra, Section 8.2
Solve quadratic equations by using the quadratic formula. Intermediate Algebra,
Section 8.3
Find the vertex and axis of symmetry of a parabola. Intermediate Algebra, Section 9.1
Graph a parabola by finding the vertex, intercepts, and additional points. Intermediate
Algebra, Section 9.1
Graph a circle given its equation in standard or general form. Intermediate Algebra,
Section 11.2
Use completing the square to graph circles and parabolas. Intermediate Algebra,
Section 11.1 and 11.2
Compare the graphing traits of functions and non-functions. Intermediate Algebra,
Section 9.2
Apply the vertical line test. Intermediate Algebra, Section 9.2
Determine the range of a function. Intermediate Algebra, Section 3.1, 9.1
Solve application problems with quadratic equations. Intermediate Algebra, Section 8.6
MAT086 – Rational Expressions and Equations
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Simplify rational expressions by factoring. Intermediate Algebra, Objective 6.1B
Determine the domain of a rational function . Intermediate Algebra, Objective 6.1A
Multiply and divide algebraic fractions. Intermediate Algebra, Objective 6.1C and
6.1D
Add and subtract algebraic fractions. Intermediate Algebra, Section 6.2
Simplify complex fractions. Intermediate Algebra, Section 6.3
Evaluate complicated formulas including complex fractions using a scientific calculator.
Not covered
Solve rational equations that reduce to linear or quadratic form. Intermediate Algebra,
Objectives 6.4A and 6.5A
Solve and evaluate literal equations. Intermediate Algebra, Section 2.4
Solve application problems with rational equations. Intermediate Algebra, Objectives
6.4B, 6.5B, 6.5C
MAT087 – Geometry With few exceptions, this is BCM, Chapter 12.
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Classify polygons.
Classify quadrilaterals as parallelograms, kites (No), trapezoids, isosceles trapezoids,
rectangles, rhombi, and squares.
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Classify triangles as scalene, isosceles or equilateral.
Classify angles, and measure angles using a protractor.
Classify triangles as acute, right or obtuse.
Relate the sides and angles of similar and congruent triangles.
Solve applications involving similar triangles.
Use and understand the Pythagorean Theorem
Define a circle.
Use a ruler (No) to measure lengths in both English and Metric units.
Find perimeter and area of triangles, quadrilaterals and compound shapes.
Find circumference and area of circles.
Calculate the surface area and volume of cones, spheres, prisms, pyramids and cylinders.
MAT088 – Introduction to Trigonometry This would have to come from our College
Algebra and Trig (CAT) text (new edition will publish soon) or College Trigonometry (CT)
which is not being revised.
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Convert between radians and degrees. CAT 5.1, CT 2.1
Find reference angles for angles measured in degrees. CAT 5.3, CT 2.3
Know the exact trigonometric ratios in a 30º-60º-90º triangle and 45 º-45º -90º triangle.
CAT 5.2, CT 2.2
Evaluate the six trigonometric functions of general angles measured in degrees. CAT 5.3,
CT 2.3
Evaluate inverse trigonometric values to degree measure. CAT 6.5, CT 3.5
Evaluate the six trigonometric functions of general angles measured in radians. CAT 5.3,
CT 2.3
Evaluate inverse trigonometric values to radians. CAT 6.5, CT 3.5
Find values of the six trigonometric functions using right triangles. CAT 5.2, CT 2.2
Solve applications using right triangle trigonometry. CAT 5.2, CT 2.5