Pre-DP Precalculus: Scope And Sequence (Units & Topics)



Pre-AP Geometry Overview (Units & Topics)

Unit 0: Algebra 1 Review (Aug. 27-30; Quiz Sept. 4-5)

Solving Linear Equations

Solving Quadratic Equations

Factoring Quadratics

Using the Quadratic Formula

Unit 1: Essential Elements of Geometry (Sept. 3-12; Test Sept. 17)

Textbook: Chapter 1

Unit Question: How do we construct figures to represent problem situations?

Points, Lines, Planes, Segments, & Rays

Congruence

Postulates & Axioms

Bisectors & Midpoints

The Distance Formula

Measuring & Classifying Angles

Complementary, Supplementary, & Vertical Angles

Classifying Polygons

Perimeter & Area of Polygons

Circumference & Area of Circles

Unit 2: Logic, Reasoning, & Proof (Sept. 12 – Sept. 26; Test Oct. 1)

Textbook: Chapter 2

Unit Question: How do we draw valid conclusions from our observations?

Patterns & Inductive Reasoning

Conditional (if-then) Statements

Deductive Reasoning

Using Deductive Reasoning on Postulates & Diagrams

Using Deductive Reasoning on Algebraic Properties

Proving Statements Using Flow Proofs

Proving Statements Using Two-Column Proofs

Proofs of Angle Pair Relationships

Unit 3: Parallel & Perpendicular Lines (Sept. 27 – Oct. 8; Test Oct. 15)

Textbook: Chapter 3

Unit Question: What are the possible relationships between lines in the plane?

Identifying Line Pairs & Their Angles

Parallel Lines & Transversals

Proving Lines Are Parallel

Slopes of Lines in the Coordinate Plane

Linear Functions & Their Graphs

Proving Lines are Perpendicular

Unit 4: Triangle Congruence (Oct. 10-24; Test Oct. 29)

Textbook: Chapter 4

Unit Question: How can we tell when two things are exactly the same?

Triangle Sum Properties

Properties of Congruent Triangles

The Side-Side-Side Postulate

The Side-Angle-Side Postulate & the HL Theorem

The Angle-Side-Angle Postulate

The Angle-Angle-Side Theorem

Proving Triangles Congruent

Solving Problems Using Congruent Triangles

Isosceles & Equilateral Triangles

Translating, Reflecting, & Rotating Polygons

Unit 5: Triangle Properties & Relationships (Oct. 25 – Nov. 11; Test Nov. 12)

Textbook: Chapter 5

Unit Question: Where are the most important parts of a structure?

Midsegments & Coordinate Proofs

Perpendicular Bisectors

Angle Bisectors of Triangles & the Incenter

Medians of Triangles & the Centroid

Altitudes of Triangles & the Orthocenter

Inequalities in One Triangle

Inequalities in Two Triangles

Indirect Proof

Unit 6: Similar Polygons (Nov. 13 – Dec. 3; Test Dec. 10)

Textbook: Chapter 6

Unit Question: How can we measure things that are too far away to touch?

Ratios, Proportions, & Geometric Means

Proportional Reasoning & Problem-Solving

Properties of Similar Polygons & Scale Factors

The Angle-Angle Postulate

The Side-Side-Side Similarity Theorem

The Side-Angle-Side Similarity Theorem

Triangle Proportionality

Dilating Polygons

Unit 7 Part 1: Right Triangles (Dec. 4 – Dec. 9; unit will be continued in January)

Textbook: Chapter 7 Sections 1-3

Unit Question: Why do we use right angles in architecture & engineering?

The Pythagorean Theorem & Its Converse

Classifying Triangles

Similar Right Triangles

Semester Review (Dec. 11-13)

Semester Exams (Dec. 16-19)

Unit 7 Part 2: Special Right Triangles and Trigonometry (Jan. 6 – 17; Test Jan. 21)

Textbook: Chapter 7 Sections 4-7 & Extension

Unit Question: How can we measure lengths and angles we can’t reach?

Special Right Triangles (45-45-90 and 30-60-90)

The Trigonometric Ratios

Using the Tangent Ratio

Using the Sine and Cosine Ratios

Using Inverse Trigonometric Functions

Solving Right Triangles

The Law of Sines

The Ambiguous Case

The Law of Cosines

Unit 8: Quadrilaterals (Jan. 25 – Feb. 3; Test Feb. 4)

Textbook: Chapter 8

Unit Question: How do we construct parts of stable structures?

Angle Measures in Polygons

Properties of Parallelograms

Parallelogram Proofs

Properties of Rhombi, Rectangles, and Squares

Properties of Trapezoids and Kites

Identifying Types of Quadrilaterals

Unit 9: Circles (Feb. 5-17; Test Feb. 25)

Textbook: Chapter 10

Unit Question: How do we measure distances and angles without straight lines?

Circles, Tangent Lines, & Their Properties

Arc Measures

Properties of Chords

Inscribed Angles & Inscribed Polygons

Relationships of Angles, Chords, and Secants

Segment Lengths in Circles

Equations of Circles & Their Graphs

Unit 10: Measuring Lengths and Areas (Feb. 28 – Mar. 3; Test Mar. 10)

Textbook: Chapter 11

Unit Question: How are side lengths and areas related for different shapes?

Areas of Triangles & Parallelograms

Areas of Other Quadrilaterals

Perimeters & Areas of Similar Figures

Circumference & Arc Length

Areas of Circles & Sector Areas

Areas of Regular Polygons

Geometric Probability

The Sine-Area Rule & Heron’s Formula

Areas of Irregular Polygons

Finding Areas of Triangles Using Trigonometric Ratios

Spring Break (March 11-15)

Unit 11: Solids, Surface Area, and Volume (Mar. 4 – Apr. 2; Test Apr. 14)

Textbook: Chapter 12

Unit Question: How are the edge lengths, side areas, and volumes of solids related?

Types of Solids & Their Properties

Surface Areas of Prisms & Cylinders

Surface Areas of Pyramids & Cones

Volumes of Prisms & Cylinders

Volumes of Pyramids & Cones

Surface Areas & Volumes of Spheres

Properties of Similar Solids

Unit 12: Transformations & Vectors (Apr. 3 – 23; Test Apr. 28)

Textbook: Chapter 9

Unit Question: How do we represent changes of a figure in a coordinate plane?

Defining a Vector

Translations Using Vectors

Decomposing a Vector

Matrices & Their Properties

Reflections

Rotations

Compositions of Transformations

Identifying Symmetry

Dilations

Unit 13: Probability & Volumes of Revolution (Apr. 24 – May 18; Test May 19)

Textbook: Supplemental handouts

Unit Question: How can we determine how likely an event is?

Permutations & Combinations

Experimental & Theoretical Probability

Independent & Dependent Events

Probabilities With and Without Replacement

Conditional Probabilities & Two-Way Tables

The Side-Angle-Side Similarity Theorem

Defining Solids of Revolution

Finding Volumes of Revolution

Semester Review (May 20-22)

Semester Exams (May 26-29)

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