Regents Prep Math B

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On-line
Multiple-Choice Questions

Interactive Games and Puzzles
for Math B

PowerPoint Interactive Review Activity for Math B (Level 1)
Play On-Line.
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Each subtopic below contains a lesson page, an interactive student practice page, and a
teacher resource page. Sections denoted with * have Graphing Calculator references.

1. Mathematical Reasoning (5-10% of Regents Exam)

A. Vocabulary Sheet for Proofs
B. Theorem/Properties Sheet for Proof
C. Direct Euclidean Proofs
D. Direct Analytic Proofs (Coordinate Geometry)
E. Indirect Euclidean Proofs

What Proofs
Have Been Asked
on Math B?

Why Study Proofs?

2. Numbers & Numeration (5-10% of Regents Exam)

A. Nature of the Roots / Sum and Product of the Roots

      B. Algebraic Fractions
      1. Rationalize Denominators
      2. Simplify Algebraic Fractions (Polynomial Denominators)

     C. Simplify Complex Fractions

      D. Complex Numbers
      1. Imaginary Unit *
      2. Standard Form of Complex Numbers *

3. Operations (5-10% of Regents Exam)

A. Operations with Fractions with Polynomial Denominators
      1. Multiply and Divide Rational Fractions
      2. Add and Subtract Rational Fractions

B. Exponents
      1. Laws of Rational Exponents
      2. Evaluate Expressions with Fractional Exponents

C. Complex Numbers
      1. Simplify Square Roots with Negative Numbers *
      2. Add and Subtract Complex Numbers *
3. Cyclic Nature of the Powers of i *
4. Multiply and Divide Complex Numbers (including Conjugates) *
      5. Absolute Value of Complex Numbers

D. Transformations
1. Apply Transformations on Figures and Functions in the Coordinate Plane
      3. Identify Isometries, Both Direct and Opposite
      4. Graphically Represent the Inverse of a Function *
5. Use Slope and Midpoint to Demonstrate Transformations
6. Use Transformations to Investigate Relationships of Two Circles
7. Using Translation and Reflection to Investigate Parabolas
      8. Apply the Composition of Transformations

E. Determine Value of Compound (Composite) Functions

4. Modeling/Multiple Representation (15-25% of Regents Exam)

A. Symbolic Representation of Problem Situations
1. Express Quadratic, Circular, Exponential, and Logarithmic Functions in Problems
2. Use Symbolic Form to Represent an Explicit Rule for a Sequence
3. Define and Graph an Inverse Variation (Hyperbola)

     B. Exponents
    1. Use Positive, Negative, and Zero Exponents
      2. Scientific Notation

C. Exponential and Logarithmic Functions
1. Rewrite Log Equations as Exponential Equations
      2. Solve Log Equations and Exponential Equations
3. Rewrite Expressions Involving Exponents and Logarithms
      4. Investigating Exponential Graphs
      5. Reflections of Exponential Graphs

D. Trigonometry
1. Use Law of Sines and Law of Cosines
          (in a variety of problems involving the resolution of forces)
2. Unit Circle including Use of Radian Measure, Sine, Cosine, Tangent, and
          Reciprocal Trigonometric Functions
      3. Use Reference Angle, Amplitude and Period

      E. Conic Sections
1. Recognize Conic Sections: Circles, Parabolas, Hyperbolas, Ellipses
      2. Write Equations of Circles Given Center and Radius and Determine
          Radius and Center Given Equation
      3. Recognize Parabola by Equation and be able to graph, find axis of symmetry,
          y-intercepts, turning point, maximum or minimum
      4. Graph quadratics noting where the graph crosses the x-axis or that it does not.

   F. Modeling
      1. Model Composition of Transformations
2. Model Quadratic Inequalities Algebraically
3. Model Quadratic Inequalities Graphically
      4. Represent Graphically the Sum and Difference of Two Complex Numbers

G. Solve Systems of Equations and Real World Problems
1. Linear
2. Quadratic
3. Trigonometric
      4. Exponential

5. Measurement (15-20% of Regents Exam)

A. Geometry in a Circle
1. Angles Formed by Radii, Chords, Tangents and Secants
      2. Measure of Segments Related to a Circle

B. Right Triangle Trigonometry
      1. Special Angles 30, 45, 60
        2. Right Triangle Proportions

C. Trigonometric Functions
1. Unit Circle Including Sine, Cosine, Tangent, and Their Reciprocals,
          Coordinates (cos A, sin A)
      2. Amplitude and Period
      3. Reflection in y = x
      5. Inverse Functions

D. Derive and Apply Formulas
      1. Radian Measure Definition
2. Degree - Radian Conversion
      3. Reference and Coterminal Angles
      4. Derivation of Sine, Cosine, Tangent, and Their Reciprocals
      5. Sum and Difference of Two Angles
      6. Double and Half Angles for Sine and Cosine
      7. Vectors

E. Triangle Information Gained From Trigonometry
      1. Area of a Triangle Using Trigonometry
      2. Law of Sines
      3. Law of Cosines
      4. Ambiguous Case

F. Statistics
1. Normal Curve (interpretations based on Mathematics B Regents Examination
          formula sheet)
      2. Normal Curve/Distribution
      3. Standard Deviation
4. Bias / Random Sample
5. Choose Appropriate Statistical Measures
      6. Scatter Plots
      7. Lines of Best Fit

H. Derive Formulas to Find Measures
1. Pythagorean Theorem
2. Perimeter of Polygon
3. Circumference of Circle
4. Area of Polygons
5. Volume of Solids

6. Uncertainty (Probability) (10-15% of Regents Exam)

A. Determine effects of changing the parameters of graphs of linear, quadratic,
           exponential, trigonometric, and circular functions

B. Discrete and Continuous Probability
1. Measure of Central Tendency
2. Use of Sigma Notation
3. Measures of Dispersion
4. Range
5. Mean Absolute Deviation
6. Variance and Standard Deviation Using the Calculator
           (for population and sample data)
8. Binomial Theorem
9. Normal Approximation for the Binomial Distribution
     10. Probability of exactly, at least, or at most r successes in n trials of a Bernoulli
           experiment

C. Curve Fitting
1. Linear Regression
2. Logarithmic Regression
3. Exponential Regression
4. Power Regression
5. Linear Correlation Coefficient

D. Examining Data -- Making Predictions
1. Domain and Range
2. Interpolate and Extrapolate from Graphs
          (linear, quadratic, trigonometric, circular, exponential and logarithmic functions)

7. Patterns & Functions (15-25% of Regents Exam)

A. Function Vocabulary and Notation
1. Definition of a Relation and Function
2. Determining if a Relation is a Function
3. Definition of Inverse Function *
      4. Notation for Absolute Value, Composite Functions
5. Expressing Exponential Functions as Logs
6. Functions: Inverse, Exponential, Logarithmic

B. Ways to Represent and Work with Functions
1. Represent and Analyze Exponential, Logarithmic, Quadratic, and
          Trigonometric Functions
      2. Relate Algebraic Expressions to the Graphs of Functions
      3. Use Transformations to Investigate the Relationships Between Functions
      4. Find the Solution of Quadratic Equations Both Algebraically and Graphically
      5. Use the Discriminant to Determine Roots: Rational, Irrational, Imaginary
      6. Evaluate Composite Functions
      7. Transformations that Provide Congruence: Reflections, Translations, Rotations *
      8. Direct Isometries
      9. Opposite (Indirect) Isometries
     10. Dilations
     11. Inverse Functions (reflections in the line y = x)

C. Using Identities
1. Quotient Identities
2. Reciprocal Identities
3. Pythagorean Identities

D. Solving Equations
1. Quadratic Equations *
      2. Fractional Equations
      3. Radical Equations *
      4. Logarithmic Equations
      5. Exponential Equations
      6. Absolute Value Equations *
      7. Linear Inequalities *
      8. Absolute Value Inequalities *
9. Quadratic Inequalities
10. First-Degree Trigonometric Equations
11. Quadratic Trigonometric Equations
      E. Standard Deviation for Grouped Data

      F. Use of Double-Angle and Half-Angle Formulas

Contact Person: Donna M. Roberts (donrob@twcny.rr.com)

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