Prerequisite Comparison Sheet – exit skills of Math 31 and entry skills for Math 32
Exit Skills for Math 31
Upon successful completion of Math 31, the student will be able to:
Exit Skills for Math 31
Upon successful completion of Math 31, the student will be able to:
A. Solve linear, quadratic and literal equations and systems of linear equations and inequalities
B. Graph linear equations and inequalities.
C. Factor polynomials at an elementary level.
D. State and apply the quadratic formula
E. Add, subtract, multiply and divide polynomials, square roots and rational expressions
F. Simplify complex fractions, square roots and exponential expressions
G. Solve introductory level equations with rational and radical expressions.
H. Translate and solve algebraic word problems in a single variable
I. Define and use properties of equality and inequality.
J. Recognize and use common mathematical language to describe mathematical processes in either written or verbal form.
K. Apply units of measurements in the solution of algebraic applications as appropriate.
Entry Skills for Math 32
Prior to enrolling in Math 32 students should be able to:
1. Solve a proportion. M81 (5)
2. Add and multiply monomials and polynomials. M31 (6)
3. Solve a quadratic equation by factoring, completing square and quadratic formula. M31 (1)
4. Simplify square roots. M31 (6)
5. Simplify and perform basic operations to numerical fractions. M81 (3)
6. Solve first degree equations in a single variable over the rational. M31 (1)

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7. Apply properties of equality and order. M31 (11)
8. Solve word problems involving first degree equations in a single variable. M31 (9)
9. Solve equations involving square roots. M31 (8)

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Santa Monica College
Student Learning Outcomes
Date: Fall 2010
Course Name and Number: Math 32, Plane Geometry
Student Learning Outcome(s):
1. Given an argument, students will determine if it is valid and will provide a counterexample if it
2. Using geometric definitions, postulates and theorems, students will write a proof of a given statement. is invalid.
Demonstrate how this course supports/maps to at least one program and one institutional learning outcome . Please include all that apply:
1. Program Outcome(s):
The student will demonstrate an appreciation and understanding of mathematics in order to develop creative and logical solutions to various abstract and practical problems.
2. Institutional Outcome(s):
The student will obtain the knowledge and academic skills necessary to access, evaluate, and interpret ideas, images, and information critically in order to communicate effectively, reach conclusions, and solve problems.

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Textbook: Koeberlein, Elementary Algebra for College Students, 5 th ed, 2011, Brooks/Cole
The online portion of logic, sections L1 and L2 is available at: http://www.wadsworth.com/cgiwadsworth/course_products_wp.pl?fid=M20b&product_isbn_issn=9781439047903&discipline_number=1
&token=
COMMENTS on the new edition of the text:
1. Logic Appendices (L1 and L2) now appear only online. Note that the material in the logic sections is discussed again in less detail in parts of Chapters 1 and 2.
2. You’ll see that in the proposed day-by-day schedule. Sections 1.3 & 1.4 precede Sections 1.1 & 1.2.
This is because students find Chapter 1 very confusing as terms appear and are used but not necessarily clearly defined.
3. On page 4, the author gives a quick study box for the types of reasoning and then goes on to explain how we use them in mathematics. Unfortunately his choice of words in this box confuses the students. He talks about “validating a theory” and one of our the new skills is to “determine if an argument is valid”. The explanations on pages 5 & 6 were clear.
4. Introductory problems involving bearing and elevation/depression appear in Section 1.2, #49, Section
2.4, #35 & 36 and Section 5.5, #26. There is no formal discussion of these topics in these sections.
5. Chapter 11 uses only right triangle trigonometry assumes all angles are acute so the students get the false idea that one only need hit an inverse trig key on the calculator to obtain an angle given a trig function value. A handout will be available to help with this.
6. Chapter 7 (Locus of P): A handout will be available to discuss parabola as a locus of points.
7. Chapter 9 (Surface Area and Volume): A handout will be available to help with this
COMMENTS on Formula Sheets on Exams:
The students are expected demonstrate knowledge of definitions, postulates, and standard theorems in chapter 1, 2, 3, 5 and 11. Since the material in the later sections is used primarily to develop their critical thinking skills, it is up the individual instructor to decide whether or not a formula sheet/study card provided either by the instructor or by the student may be used on the exams on chapter 6, 8, and 9 as well as the final.
COMMENTS on Math 32 as a Prerequisite for Math 2, Precalculus
This course was re-designed to better prepare students for their work in Math 2. The following Math 2 entry skills, which correspond to Math 32 objectives, should be given prominence in all Math 32 sections.
A. Without the use of study aids, be able to identify in a diagram: supplementary angles, complementary angles, acute angle, obtuse angle, right angle, circle, sector, arc, radius, center, diameter, circumference, chord, secant, tangent, triangle, hypotenuse, isosceles triangle, equilateral triangle, square, rectangle, parallelogram, parallel lines, and perpendicular lines. Sketch examples that accurately illustrate the definitions. [Maps to obj 11]
B. Use properties of right triangles, including Pythagorean Theorem and right-triangle trigonometry, properties of parallel lines, and the method of similar triangles in order to solve application problems including but not limited to those involving bearing and angle of elevation/depression. [Maps to obj 9]
C. From memory, state and use formulas to calculate the perimeter and area of polygons, sectors, and circles, and the volume and surface area of rectangular boxes and circular cylinders. [Maps to obj]
D. Read a written argument and determine if it is valid. [Maps to obj 5]
E. Given the statement of a theorem, identify its hypothesis and conclusion, state its converse, inverse and contrapositive, and identify which of these three can be used in place of the original statement.
[Maps to obj 3,4]
F. Set up and complete simple direct and indirect proofs. [Maps to obj 7]

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This schedule assumes a standard meeting schedule of 1 hr 20 min with 2 class meetings per week.
Session
1
2
A Sample Schedule for Math 32 – 16 Week Semester
Text Section/Activity
L.1 Online Logic Appendix: Truth Tables
L.2 Online Logic Appendix: Valid Arguments
1.3 Early Definitions and Postulates
1.4 Angles and their Relationships
Assignment/Notes
L.1 # odds
L.2 # odds
1.3 #1, 2, 8, 9, 11, 14, 15, 17, 25, 29, 31, 37
1.4 #1, 3, 5-8, 10, 12, 15, 19, 23, 25, 27, 31, 33, 35
3 1.1 Sets, Statements, and Reasoning
1.2 Informal Geometry and Measurement
1.1 #1-55 odd
1.2 #7, 9, 10, 11, 13, 15, 19, 27, 33-49 odd
4
5
6
7
8
1.5 Introduction to Geometric Proof
1.6 Relationships: Perpendicular Lines
1.7 The Formal Proof of a Theorem
2.1 The Parallel Postulate and Special Angles
2.2 Indirect Proof
Review
1.5 #1 – 23 odd, 27, 29, 31
1.6 #1 – 21 odd
1.7 #1-31 odd
2.1 #1-33 odd
2.2 #1-1-27 odd, 16
NOTE: Chapter 1 Review differs from Chapter 1 Test. Chapter 1
Review provides students practice on "Sometimes, Always, Never" type questions as well as the type where they are given information and have to draw a conclusion. The Chapter review has constructions that require the students to use reasoning skills while the test has the student demonstrate memorized constructions.
Chapter 1 Review: at least the odds
Chapter 2 Review: #2-5 (Note - Lines are NOT given parallel but answers assume they are!) #6, 17, 30-33, 37-39
Chapter 2 Test: #1, 3, 4
Exam 1 on Topics Covered Day 1-7
 Recognize a statement and determine its negation.
 Determine the truth value for compound statements.
 Given a conditional statement expressed implicitly, rewrite the statement in the standard “If – then” form.
 Given a conditional statement, identify the hypothesis, the conclusion, its converse, inverse, and contrapositive and know which are logically equivalent.
 Use elementary logical reasoning to determine if a given argument is valid.
 Use counterexamples to disprove a fallacy.
 Demonstrate understanding of basic geometric terms
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on segments, angles, perpendicular lines, and parallel lines to determine additional information.
 Construct geometric figures using a straightedge and compass.
 Complete simple indirect proofs
9 2.3 Proving Lines Parallel
2.4 The Angles of a Triangle
10 2.5 Convex Polygons
3.1 Congruent Triangles
11 3.2 CPCTC
3.3 Isosceles Triangles
3.4 Constructions
12 3.5 Inequalities in a Triangle
2.3 odds
2.4 # 1-37 odd
2.5 #1-33 odd
3.1 # 1, 3, 5, 9 – 25, 27, 31, 33, 39,
3.2 odds
3.3 #1 – 11 odd, 19 – 29 odd, 33 – 41 odd
3.4 # 2, 7, 13, 14, 20 (more hw for them to practice constructions)
3.5 # 1 – 10, 13, 15, 19, 23, 25, 27, 31 – 37 odd

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Session Text Section/Activity
4.1 Properties of a Parallelogram
13 4.2 The Parallelogram and Kite (Kite optional)
4.3 The Rectangle, Square, and Rhombus
14 Review
5.1 Ratios, Rates, and Proportions
4.1 # 1-15 odd, 21, 23, 29
Assignment/Notes
4.2 # 1, 2, 3, 7, 8, 9, 11, 13, 19, 21, 23, 29, 31
4.3 # 1 – 23 odd, 27, 28, 33, 39
Chapter 2 Review 7-35 odds, 41, 42
Chapter 2 Test # 1-9, 12-19
Chapter 3 Review #1-29 odd
Chapter 3 Test # 3-8
Chapter 4 Review # 1, 4-17, 23, 25, 29, 31
15 Exam 2 on Topics Covered Day 1-14 with Emphasis on Sections 2.3 & 2.4, Chapter 3, Chapter 4 – (exclude 5.1)
 Continuation of topics from Exam 1
 Demonstrate understanding of basic geometric terms, including but not limited to parallel lines, polygons, congruent triangles, rectangles, squares, rhombi.
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on polygons, congruency, triangles, parallelograms, segments, angles, perpendicular lines, and parallel lines to determine additional information.
 Use deductive arguments to write direct and/or indirect proofs.
 Construct geometric figures using a straightedge and compass.
5.1 # 1, 5, 9, 13, 21, 24, 25
16 5.2 Similar Polygons
5.3 Proving Triangles Similar
5.2 # 1-25 odd, 29, 31
5.3 # 1-39 odd
17 5.4 The Pythagorean Theorem
5.5 Special Right Triangles
5.4 # 7-21 odd, 25, 26, 31, 33
5.5 # odds
5.5 Comment: Students must memorize 30-60-90 theorem and 45-45-90 theorem! For 30-60-90 and 45-45-90 triangles, students must be able to a) determine an angle given information about length(s) of sides and b) determine length(s) of sides given information about angle measures, all without the aid of a calculator.
18 11.1 The Sine Ratio and Applications
11.2 The Cosine Ratio and Applications
11.1 # 1, 5, 7, 9, 15, 19, 21, 25, 27-33 odd, 34, 35
11.2 # 1, 5, 7, 9, 11, 17, 21, 25, 27, 29-35 odd
11.1-2 Comment : The theory of similar right triangles started in 5.5 is continued in Chapter 11 where other size angles are studied. With the aid of a calculator students must learn to approximate sides of triangles other than for 30-60-90 and 45-45-
90 and estimate angles
19 11.3 The Tangent Ratio and Applications
11.4 Applications with Acute Triangles
7.3 More about regular polygons – finding apothem and radius
11.3 # 1-31 odd, 37-45 odd, 42
11.4 # 1-33 odd
7.3 #14, 16, 17, 21, 22, 26 plus Handout
11.4 Comment: Students need not memorize formulas for Law of Cosines and Law of Sines for Math 32 (but they must for
Math 2) Students must realize calculators inability to produce obtuse angles on the screen if Law of Sines is used.
20 Review Chapter 5 Review # 8g, 12, 13, 14, 16, 1 – 25 odd, 31, 33, 38, 40c, 41
Chapter 11 Review # 1-30
21 Exam 3 on Topics Covered Day 1-20 with Emphasis on Chapters 5 and 11
 Continuation of topics from Exams 1 & 2
 Demonstrate understanding of basic geometric terms, including but not limited to polygons, similar triangles, right triangles, sine of an angle, cosine of an angle, tangent of an angle
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on polygons, similarity and right-triangle trigonometry to determine additional information including problems involving bearing and angle of elevation/depression
 Use deductive arguments to write direct and/or indirect proofs.
 Construct geometric figures using a straightedge and compass
22 6.1 Circles and Related Segments and Angles
6.2 More Measures in the Circle
6.1 # 1 – 21 odd, 31, 33, 40
6.2 # 1-27 odd

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Session Text Section/Activity
23 6.3 Line & Segment Relationships in the Circle
7.1 Locus of Points
6.3 # 1-21 odd, 25, 27
7.1 # 1-29 odd #14, #20
Assignment/Notes
24
26
Supplement Locus of Points - Circle, Parabola
8.1 Area and Initial Postulates
25 8.2 Perimeter and Area of Polygons
8.3 Regular Polygons and Area
8.4 Circumference and Area of a Circle
Construct geometric figures using a straightedge and compass.
8.1 # 1-25 odd, 55
8.2 # 1-29 odd, 33, 34, 35
8.3 # 1-33 odd
8.4 # 1-43 odd
8.5 # 1, 3, 5, 13-21 odd, 22,25, 27, 29, 30
Handout
8.5 More Area Relationships in the Circle
27 Selected problems from Chapter 9 on Surface Area and Volume
28 Additional work on Chapter 9 or
Possible 4th Exam on Topics Covered Days 1 – 27with Emphasis on Chapter 6, Section 7.1, Chapter 8
 Continuation of topics from Exam 1 – 3
 Demonstrate understanding of basic geometric terms, related to the circle including but not limited to circle, sector, arc, radius, center, diameter, circumference, secant, chord, tangent
 Demonstrate understanding of basic geometric terms, related to the polygon including but not limited to radius, side length, apothem
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on circles and polygons to determine additional information.
 From memory, state and use formulas to calculate the perimeter and area of polygons and circles
 Given a written description of a locus be able to identify the figure and construct the set of points satisfying the conditions using a straightedge and compass.
 From memory, state and use formulas to calculate the perimeter and area of polygons and circles, and the volume and surface area of rectangular boxes and circular cylinders.
Chapter 6 Review # 1-34
Chapter 7 Review # 7-17
Chapter 8 Review skip 7
29 Review

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A Sample Schedule for Math 32 – 6 week Semester
This schedule assumes a standard meeting schedule of 2 hr 05 min with 4 class meetings per week.
Session
1
2
3
4
Text Section/Activity
L.1 Online Logic Appendix: Truth Tables
L.2 Online Logic Appendix: Valid Arguments
1.3 Early Definitions and Postulates
1.4 Angles and their Relationships
1.1 Sets, Statements, and Reasoning
1.2 Informal Geometry and Measurement
1.5 Introduction to Geometric Proof
1.6 Relationships: Perpendicular Lines
1.7 The Formal Proof of a Theorem
1.7 Continued
2.1 The Parallel Postulate and Special Angles
2.2 Indirect Proof
Assignment/Notes
L.1 odds
L.2 odds
1.3 #1, 2, 8, 9, 11, 14, 15, 17, 25, 29, 31, 37
1.4 #1, 3, 5-8, 10, 12, 15, 19, 23, 25, 27, 31, 33, 35
1.1 #1-55 odd
1.2 #7, 9, 10, 11, 13, 15, 19, 27, 33-49 odd
1.5 #1 – 23 odd, 27, 29, 31
1.6 #1 – 21 odd
1.7 #1-23 odd
1.7 #25-31 odd
2.1 #1-33 odd
2.2 #1-27 odd, 16
5
7
8
9
Review
2.3 Proving Lines Parallel
NOTE: Chapter 1 Review provides practice on "Sometimes, Always,
Never" type questions as well as the type where they are given information and have to draw a conclusion. The Chapter review has constructions that require the students to use reasoning skills while the test has the student demonstrate memorized constructions.
Chapter 1 Review: at least the odds
Chapter 2 Review: #2-5 (Note - Lines are NOT given parallel but answers assume they are!) #6, 17, 30-33, 37-39
Chapter 2 Test: #1, 3, 4
Exam 1 on Topics Covered Days 1-4
 Recognize a statement and determine its negation.
 Determine the truth value for compound statements.
 Given a conditional statement expressed implicitly, rewrite the statement in the standard “If – then” form.
 Given a conditional statement, identify the hypothesis, the conclusion, its converse, inverse, and contrapositive and know which are logically equivalent.
 Use elementary logical reasoning to determine if a given argument is valid.
 Use counterexamples to disprove a fallacy.
 Demonstrate understanding of basic geometric terms
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on segments, angles, perpendicular lines, and parallel lines to determine additional information.
 Construct geometric figures using a straightedge and compass.
 Complete simple indirect proofs
2.3: odds
2.4 The Angles of a Triangle
3.1 Congruent Triangles
3.2 CPCTC
3.3 Isosceles Triangles
3.4 Constructions
3.5 Inequalities in a Triangle
4.1 Properties of a Parallelogram
2.4 # 1-37 odd
3.1 # 1, 3, 5, 9 – 25, 27, 31, 33, 39
3.2 odds
3.3 #1 – 11 odd, 19 – 29 odd, 33 – 41 odd
3.4 # 2, 7, 13, 14, 20
3.5 # 1 – 10, 13, 15, 19, 23, 25, 27, 31 – 37 odd,
4.1 # 1-15 odd, 21, 23, 29

Session
10
11
12
13
14
15
16
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Text Section/Activity
4.2 The Parallelogram and Kite (Kite optional)
4.3 The Rectangle, Square, and Rhombus
Assignment/Notes
4.2 # 1, 2, 3, 7, 8, 9, 11, 13, 19, 21, 23, 29, 31
4.3 # 1 – 23 odd, 27, 28, 33, 39
Review
5.1 Ratios, Rates, and Proportions
Chapter 2 Review 7-35 odds, 41, 42
Chapter 2 Test # 1-9, 12-19
Chapter 3 Review #1-29 odd
Chapter 3 Test # 3-8
Chapter 4 Review # 1, 4-17, 23, 25, 29, 31
Exam 2 on Topics Covered Days 1-9 with Emphasis on Sections 2.3 & 2.4, Chapters 3 and 4
 Continuation of topics from Exam 1
 Demonstrate understanding of basic geometric terms, including but not limited to parallel lines, polygons, congruent triangles, rectangles, squares, rhombus.
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on polygons, congruency, triangles, parallelograms, segments, angles, perpendicular lines, and parallel lines to determine additional information.
 Use deductive arguments to write direct and/or indirect proofs.
 Construct geometric figures using a straightedge and compass
5.1 # 1, 5, 9, 13, 21, 24, 25
2.5 Convex Polygons
5.2 Similar Polygons
5.3 Proving Triangles Similar
2.5 #1-33 odd
5.2 # 1-25 odd, 29, 31
5.3 # 1-39 odd
5.4 The Pythagorean Theorem
5.5 Special Right Triangles
5.4 # 7-21 odd, 25, 26, 31, 33
5.5 # odds
11.1 The Sine Ratio and Applications 11.1 # 1, 5, 7, 9, 15, 19, 21, 25, 27-33 odd, 34, 35,
5.5 Comment: Students must memorize 30-60-90 theorem and 45-45-90 theorem! For 30-60-90 and 45-45-90 triangles, students must be able to a) determine an angle given information about length(s) of sides and b) determine length(s) of sides given information about angle measures, all without the aid of a calculator.
11.1-2 Comment: The theory of similar right triangles started in 5.5 is continued in Chapter 11 where other size angles are studied. With the aid of a calculator students must learn to approximate sides of triangles other than for 30-60-90 and
45-45-90 and estimate angles.
11.2 The Cosine Ratio and Applications
11.3 The Tangent Ratio and Applications
11.4 Applications with Acute Triangles
7.3 More about regular polygons
11.2 # 1, 5, 7, 9, 11, 17, 21, 25, 27, 29-35 odd
11.3 # 1-31 odd, 37-45 odd,
11.4 # 1-33 odd
7.3 #14, 16, 17, 21, 22, 26
11.4 Comment: Students need not memorize formulas for Law of Cosines and Law of Sines for Math 32 (but they must for Math 2) Students must realize calculators inability to produce obtuse angles on the screen if Law of Sines is used.
Review
6.1 Circles and Related Segments and Angles
Chapter 5 Review # 8g, 12, 13, 14, 16, 17 – 25 odd, 31, 33, 38, 40c,
41
Chapter 11 Review # 1-30
Exam 3 on Topics Covered Days 1-14 with Emphasis on Chapters 5 and 11
 Continuation of topics from Exam 1 & 2
 Demonstrate understanding of basic geometric terms, including but not limited to polygons, similar triangles, right triangles, sine of an angle, cosine of an angle, tangent of an angle
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on polygons, similarity and right-triangle trigonometry to determine additional information including problems involving bearing and angle of elevation/depression
 Use deductive arguments to write direct and/or indirect proofs.
 Construct geometric figures using a straightedge and compass.
6.1 # 1 – 21 odd, 31, 33, 40

Session
17
18
19
20
21
22
23
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Text Section/Activity
6.2 More Measures in the Circle
6.3 Line and Segment Relationships in the Circle
7.1 Locus of Points
6.2 # 1-27 odd
6.3 # 1-21 odd, 25, 27,
7.1 # 1-29 odd
Assignment/Notes
Supplement Locus of Points - Circle, Parabola
8.1 Area and Initial Postulates
8.2 Perimeter and Area of Polygons
8.3 Regular Polygons and Area
8.4 Circumference and Area of a Circle
8.5 More Area Relationships in the Circle
8.1 # 1-25 odd, 55
8.2 # 1-29 odd, 33, 34, 35
8.3 # 1-33 odd
8.4 # 1-43 odd
8.5 # 1, 3, 5, 13-21 odd, 22,25, 27, 29, 30
Review
Selected problems from Chapter 9 on Surface
Area and Volume
Chapter 6 Review # 1-34
Chapter 7 Review # 7-17
Chapter 8 Review skip 7
Additional work on Chapter 9 or
Exam 4 on Topics Covered Days 1-20 with Emphasis on Chapter 6, Section 7.1 and Chapter 8
 Continuation of topics from Exam 1 – 3
 Demonstrate understanding of basic geometric terms, related to the circle including but not limited to circle, sector, arc, radius, center, diameter, circumference, secant, chord, tangent
 Demonstrate understanding of basic geometric terms, related to the polygon including but not limited to radius, side length, apothem
 Given partial information on a geometric figure use the definitions, properties, postulates and theorems on circles and polygons to determine additional information.
 From memory, state and use formulas to calculate the perimeter and area of polygons and circles
 Given a written description of a locus be able to identify the figure and construct the set of points satisfying the
conditions using a straightedge and compass.
Review
 Continuation of topics from Exam 1-4
 From memory, state and use formulas to calculate, the volume and surface area of rectangular boxes and circular cylinders.