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Math B2/B3 |
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Math B2/B3
Scope and Sequence
Schenectady High School Department of Mathematics
J. Brendese
I. Preliminaries
A. Family of Numbers/The Language of Mathematics
B. Numbers, Density, & the Real Number Line
C. Properties of Numbers & First-Degree Equations/Inequalities [2-4, p. 685]
D. Linear Equations & Slopes [2-1]
E. Inverse Variation [8-1, 8-2]
F. Two-Variable Equations & Inequalities [2-5, p. 687]
G. Solving Systems of Equations Algebraically & Graphically [4.1, 4.2]
B. Rational Expressions
i. Reduced to Lowest Terms/Undefined [8-4]
ii. Multiplication [8-4]
iii. Division [8-4]
iv. Addition/Subtraction [8-5, p. 695]
v. Complex Fractions
C. Solving Fractional Equations [8-6]
D. Absolute-Value Equations [1-5, p. 686]
E. Absolute-Value Inequalities [2-4, p.686]
F. Roots and Radicals [p. 691 and supplement]
i. nth degree & Simplifying
ii. Operations
iii. Rationalizing
G. Solving Radical Equations
A. Complex/Imaginary Numbers [5.6]
B. Operations on Complex Numbers [5.6, p. 375]
C. Graphing on the Complex Plane & Magnitude [NY1 and supplement]
IV. Functions
A. Relations vs. Functions [1-3]
B. One-to-One Functions: Domains and Ranges [1-3 and supplement]
C. Types of Functions
D. Compositions of Functions [1-4]
E. Transformations as Functions: Composition
F. Transformations as Functions: Shifting Functions [1-5]
G. Inverse Functions (Domain/Range) [5-4]
V. Quadratic Equations
A. The Parabolic Function [5.5]
B. Solving Quadratic Equations with Imaginary Roots [5-8]
C. Nature of Roots [5-8]
D. Applications of the Parabolic Function [5.2]
E. Quadratic Inequalities [NY2]
VI. Conics
A. Equation of a Circle [10-3]
B. Ellipses [10-4]
C. Hyperbolas [10-5]
VII. Trigonometric Functions
A. The Right Triangle [9-6]
B. Angles and the Unit Circle [9.2]
C. The Six Trigonometric Functions [9.4/9.5 and NY8]
D. Using Triangles to Find Unknown Trig Values [9.6]
E. Trigonometric Functions & Radian Measure [9-3 and supplement]
F. Reference Angles [9-2]
VIII. Trigonometric Graphs
A. Graphs of y = sin x & y = cos x [9-4, 9-5]
B. Amplitude, Frequency, & Period [9-4, 9-5]
C. Sketching Trigonometric Functions [9-4, 9-5, and p. 421]
D. Transformations of Trigonometric Graphs [NY6]
E. Inverse Trigonometric Functions [9-6 and supplement]
A. Area of a Triangle [NY23]
B. Law of Sines [9-7]
C. The Ambiguous Case [p. 449]
D. Law of Cosines [9-7]
E. Forces
F. Solving Triangles
A. Quotient and Reciprocal Identities [NY9]
B. Pythagorean Identities [NY9]
C. Sum/Difference of Angles Identities [NY11]
D. Functions of Double Angles [NY11]
E. Functions of Half Angles
F. Solving Trigonometric Equations [NY10]
XI. Exponents
A. Laws of Exponents [p. 688]
B. Negative & Zero Exponents [p. 688]
C. Scientific Notation [p.690]
D. Fractional Exponents [6-1]
E. Equations with Fractional/Negative Exponents [7.5]
F. Exponential Equations
X11. Logarithms
A. Logarithmic Form of an Equation [7.3]
B. Product, Quotient, & Power Rules [7.4]
C. Logarithmic Equations/“Unsolvable” Exponential Equations [7.5]
D. Graphing the Exponential & Logarithmic Function (Transformations) [7.3]
XIII. Probability
A. Bernoulli Experiments [11-6]
B. Bernoulli Experiments: “At Least/At Most” [11-6 and supplement]
XIV. Statistics
A. Sigma Notation
B. Standard Deviation [11-3, 11-4]
C. Normal Curve [11-7]
A. Plotting Data
B. Recognizing & Fitting Curves [NY7]
a. Linear
b. Exponential
C. Predictions
XVI. Topical Review
A. Ratio & Percents
B. Geometric Proofs:
i. Basic Definitions
ii. Equation of a Line/Types of Lines
iii. Properties of Quadrilaterals
iv. Coordinate Geometry Proofs
v. Methods of Proof (Triangles)
vi. Triangle Proofs
vii. Circle Theorems
viii. Circle Proofs
C. Transformations on the Coordinate Plane (Order/Isometries)
D. Continuous review of Previously Covered Topics