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Oroville Union High School District |
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Mathematics Curriculum |
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Mathematics - Precalculus |
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Measuring Angles: Degrees & Radians
The learner will be able to
understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 1.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.1. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Right Angle Trigonometry,
Radian Measure.
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Sine and Cosine
The learner will be able to
know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 2.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Circular Functions,
Laws of Sines and Law of Cosines.
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Trig. Identity: cos 2(x) + sin 2(x) =1
The learner will be able to
know the identity cos 2 (x) + sin 2 (x) = 1.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 3.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 5.1 & 5.2. [Textbook]. |
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Pythagorean Theorem
The learner will be able to
prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 3.1. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 5.1 & 5.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Trigonometric Identities of a Single Variable,
Trigonometric Identities II,
Trigonometric Equations.
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Other Trigonometric Identities
The learner will be able to
prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x) = 1. For example, students use this identity to prove that sec 2 (x)Ê =Ê tan 2 (x) + 1.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 3.2. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 5.1 & 5.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Trigonometric Identities of a Single Variable,
Trigonometric Identities II,
Trigonometric Equations.
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Graphing Functions
The learner will be able to
graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 4.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.5. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Graphing Trigonometric Functions.
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Tangent & Cotangent Functions
The learner will be able to
know the definitions of the tangent and cotangent functions and can graph them.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 5.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 4.2 & 4.6. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Three More Trigonometric Functions,
Graphing Trigonometric Functions.
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Secant & Cosecant Functions
The learner will be able to
know the definitions of the secant and cosecant functions and can graph them.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 6.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.6. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Three More Trigonometric Functions,
Graphing Trigonometric Functions.
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Tangent of an Angle
The learner will be able to
know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 7.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 12.3. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Circular Functions.
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Inverse & Trigonometric Functions
The learner will be able to
know the definitions of the inverse trigonometric functions and can graph the functions.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 8.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.7. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Inverse Trigonometric Functions.
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Values of Trigonometric Functions
The learner will be able to
compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 9.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Sines & Cosines: Addition Formulas
The learner will be able to
demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/or simplify other trigonometric identities.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 10.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 5.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Trigonometric Identities II.
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Sines & Cosines: Angle Formulas
The learner will be able to
demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 11.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 5.5. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Trigonometric Identities II.
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Sides & Angles in Right Triangles
The learner will be able to
use trigonometry to determine unknown sides or angles in right triangles.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 12.0. |
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Instructional Resources |
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Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 4.3. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Law of Sines and Law of Cosines.
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Laws of Sines & Cosines
The learner will be able to
know the law of sines and the law of cosines and apply those laws to solve problems.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 13.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.1 & 6.2. [Textbook]. |
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CPM Foundations for Algebra: Year 1, CPM Educational Program, First Edition. v. 2.0, 2001., Modules: [Textbook]. Trigonometry:
Law of Sines and Law of Cosines.
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Area of a Triangle
The learner will be able to
determine the area of a triangle, given one angle and the two adjacent sides.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 14.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.1 & 6.2. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Right Angle Trigonometry,
Law of Sines and Law of Cosines.
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Polar Coordinates
The learner will be able to
be familiar with polar coordinates. In particular, they can determine
polar coordinates of a point given in rectangular coordinates and vice versa.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 15.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 10.6. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Polar Coordinates.
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Equations in Rectangular Coordinates
The learner will be able to
represent equations given in rectangular coordinates in terms of polar coordinates.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 16.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 10.6. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Polar Coordinates.
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Complex Numbers in Polar Form
The learner will be able to
are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 17.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 6.5. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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DeMoivre's Theorem
The learner will be able to
know DeMoivre’s theorem and can give nth roots of a complex number given in polar form.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 18.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 6.5. [Textbook]. |
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PLATO Learning Inc., 2000, Modules: [Software]. Trigonometry:
Polar Coordinates.
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Applications of Trigonometry
The learner will be able to
are adept at using trigonometry in a variety of applications and word problems.
| Strand |
Scope |
Source |
| Trigonometry |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Trigonometry, 19.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapters 5 & 6. [Textbook]. |
| · |
PLATO Learning Inc., 2000, Modules: [Software]. No PLATO modules are available for this learning expectation at this time. |
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Polar Coordinates & Vectors in the P
The learner will be able to
be familiar with, and can apply, polar coordinates and vectors in the plane. In particular, they can translate between polar and rectangular coordinates and can interpret polar coordinates and vectors graphically.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 1.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.3 & 10.7. [Textbook]. |
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Arithmetic of Complex Numbers
The learner will be able to
be adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables. They know the proof of DeMoivre’s theorem.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 2.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 2.4 & 6.5. [Textbook]. |
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Proofs by Mathematical Induction
The learner will be able to
give proofs of various formulas by using the technique of mathematical induction.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 3.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 9.4. [Textbook]. |
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Fundamental Theorem of Algebra
The learner will be able to
know the statement of, and can apply, the fundamental theorem of algebra.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 4.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 2.5. [Textbook]. |
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Conic Sections
The learner will be able to
be familiar with conic sections, both analytically and geometrically.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 5.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 10.1, 10.2, & 10.3. [Textbook]. |
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Quadratic Equation in Two Variables
The learner will be able to
take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components (foci, asymptotes, and so forth).
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 5.1. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 10.1, 10.2, 10.3, & 10.4. [Textbook]. |
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Geometric Description of a Conic Section
The learner will be able to
take a geometric description of a conic section, for example, the locus of points whose sum of its distances from (1, 0) and (-1, 0) is 6, and derive a quadratic equation representing it.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 5.2. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter 10. [Textbook]. |
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Roots & Poles of a Rational Function
The learner will be able to
find the roots and poles of a rational function and can graph the function and locate its asymptotes.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 6.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 2.6 & 10.6. [Textbook]. |
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Graphing Functions & Equations
The learner will be able to
demonstrate an understanding of functions and equations defined parametrically and can graph them.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 7.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 12.1. [Textbook]. |
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Limit of a Sequence & Function
The learner will be able to
be familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether certain sequences converge or diverge.
| Strand |
Scope |
Source |
| Mathematical Analysis |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Mathematical Analysis, 8.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 12.1 & 12.2. [Textbook]. |
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Gauss-Jordan Elimination
The learner will be able to
solve linear equations in any number of variables by using Gauss-Jordan elimination.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 1.0. |
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Instructional Resources |
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| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 7.1, 7.2, & 7.3. [Textbook]. |
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Interpreting Linear Systems
The learner will be able to
interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 2.0. |
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Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 7.3, 8.1, & 8.2. [Textbook]. |
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Rectangular Matrices: Echelon Form
The learner will be able to
reduce rectangular matrices to row echelon form.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 3.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 8.1. [Textbook]. |
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Matrices & Vectors: Addition
The learner will be able to
perform addition on matrices and vectors.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 4.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.3 & 8.2. [Textbook]. |
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Matrices & Vectors: Multiplication
The learner will be able to
perform matrix multiplication and multiply vectors by matrices and by scalars.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 5.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.3, 6.4, & 8.2. [Textbook]. |
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Linear Systems: Solutions
The learner will be able to
demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 6.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 7.3. [Textbook]. |
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Geometric Interpretation of Vectors
The learner will be able to
demonstrate an understanding of the geometric interpretation of vectors and vector addition (by means of parallelograms) in the plane and in three-dimensional space.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 7.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 6.3 & 6.4. [Textbook]. |
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Solution Sets of Systems of Equations
The learner will be able to
interpret geometrically the solution sets of systems of equations. For example, the solution set of a single linear equation in two variables is interpreted as a line in the plane, and the solution set of a two-by-two system is interpreted as the intersection of a pair of lines in the plane.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 8.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 7.1 & 7.2. [Textbook]. |
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Inverse to a Square Matrix
The learner will be able to
demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 9.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 8.3. [Textbook]. |
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Determinants of 2'2 & 3'3 Matrices
The learner will be able to
compute the determinants of 2 ´ 2 and 3 ´ 3 matrices and are familiar with their geometric interpretations as the area and volume of the parallelepipeds spanned by the images under the matrices of the standard basis vectors in two-dimensional and three-dimensional spaces.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 10.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Section 8.4. [Textbook]. |
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Inverse to 2'2 & 3'2 Matrices
The learner will be able to
know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 ´ 2 and 3 ´ 3 matrices using row reduction methods or Cramer’s rule.
| Strand |
Scope |
Source |
| Linear Algebra |
Master |
CA: Mathematics Content Standards, December 1997, Grades 8-12, Linear Algebra, 11.0. |
| |
Instructional Resources |
| |
| · |
Precalculus with Limits: A Graphing Approach, Houghton Mifflin Company, 2001, Chapter-Sections 8.3, 8.4, & 8.5. [Textbook]. |
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