Double Discovery Center


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The usual progression for Mathematics courses in high school is Integrated Algebra in 9th grade, Geometry in 10th grade, and Algebra 2/ Trigonometry in 11th grade. In 12th grade students may take other advanced courses such as Calculus, Statistics or Discrete Mathematics.

The resources below each subject include a link to the specific detailed concepts summarized on this page and a link to previous Regents exams, to give a better idea of the type of questions a student will be expected to answer. The further educational resources include links to Khan Academy, which mainly utilizes educational videos, Regents Prep, which reviews topics based on the Common Core requirements, and Sparknotes, which reviews more general material.

Integrated Algebra
Algebra 2/ Trigonometry


- Classify Real Numbers & their Properties
- Radicals
- Fractions, Decimals, Percents (Decrease/Increase and Discount), & Proportionality/Direct Variation
- Factorials, Absolute Values, & Exponential Expressions
Equations and Inequalities
- Translate Verbal Phrases into Mathematical Equations or Inequalities
- Linear Inequalities
- Solve Systems of Equations in Two Variables
- Linear & Quadratic Equations
- Equations with Several Variables (Literal Equations)
- Exponential Growth & Decay
Variables and Expressions
- Monomials and Polynomials
- Factoring
Patterns, Relations, & Functions
- Set-Builder & Interval Notation
- Set Properties
Trigonometric Functions
- Sine, Cosine, & Tangent Ratios
- Pythagorean Theorem
Coordinate Geometry
- Slope & Equations of Lines
- Graph Functions: Linear, Quadratic (Parabolic), Absolute Value, & Exponential
- Graph Linear Inequalities
- Properties of Parallel and Perpendicular Lines
- Area and Perimeter of Polygons, Circles, & Sectors of a Circle
- Volume and Surface Area of Rectangular Solids & Cylinders
Units of Measurement
- Convert Units
- Calculate Relative Error in Measurement
- Identify Data as Qualitative or Quantitative; Univariate or Bivariate; Biased or Unbiased
- Central Tendency
- Histogram, Cumulative Frequency Histogram, & Box-and-Whisker Plot
- Scatter Plots
- Percentile Rank
- Fundamental Principle of Counting
- Permutations
- Conditional Probability

More Resources
Specific Integrated Algebra Concepts
Sample Integrated Algebra Regents
→Further Educational Resources:
Khan Academy
Regents Prep


Geometric Relationships
- Properties of Perpendicular & Parallel Lines & Planes
- Properties of Prisms, Regular Pyramids, Cylinders, Right Circular Cone & Spheres
Constructions- Construct Bisectors, Parallel Lines & Equilateral Triangles using a Straightedge and Compass
- Concurrence of Medians, Altitudes, Angle Bisectors & Perpendicular Bisectors of Triangles
- Compound Loci
Informal & Formal Proofs
- Statements: Negation, Truth, Conjunction, Disjunction, Conditional & Biconditional
- Conditional Statements: Inverse, Converse, & Contrapositive
- Write a Proof Given a Hypothesis
- Angles of Intersecting Lines & Interior and Exterior Angles of Polygons
- Theorems involving Triangles: Congruence, Angles, Isosceles Triangle Theorem, Triangle Inequality Theorem, Similarity Theorems, Mean Proportionality, & Pythagorean Theorem & Converse
- Theorems involving Quadrilaterals: Parallelograms; Special Parallelograms (Rectangles, Rhombuses, Squares); & Trapezoids
- Theorems involving Circles: Chords, Tangents, Secants, Angles, Arcs, & Segments Intersected by a Circle
Transformational Geometry
- Isometries (Rotations, Reflections, Translations, & Glide Reflections)
- Similarities & Dilations
Coordinate Geometry
- Slope & Equations of Lines
- Midpoint & Length of a Line Segment
- Distance, Midpoint & Slope Formulas
- Solve a System of Equations Graphically
- Find the Equation of a Circle Given the Center and Radius

More Resources
Specific Geometry Concepts
Sample Geometry Regents
→Further Educational Resources:
Khan Academy
Regents Prep


- Negative & Fractional Exponents
- Radicals
- Polynomials
- Complex Numbers
- Sigma Notation
Equations & Inequalities
- Absolute Value Equations & Inequalities
- Quadratic Equations: Discriminant & Roots; Sum & Product of Roots; Inequalities; Completing the Square; Quadratic Formula
- Solve Systems of Equations involving One Linear Equation and One Quadratic Equation
- Direct & Inverse Variation
- Solve Rational Equations and Inequalities
- Solve Radical, Exponential & Logarithmic Equations
- Solve Polynomial Equations of Higher Degree
Variables & Expressions
- Factor Polynomials
- Evaluate & Simplify Exponential Expressions
- Evaluate & Simplify Logarithmic Expressions
- Evaluate & Simplify Radical Expressions
- Simplify Complex Fractions Expressions
Patterns, Relations, & Functions
- Geometric & Arithmetic Sequences
- Geometric & Arithmetic Series
- Binomial Theorem
- Relations
- Functions: Domain & Range; Functional Notation; Composition; Inverse; One-To-One & Onto; Transformations
Coordinate Geometry
- Equations of Circles
- Interpret Graphs of Polynomials of Higher Degree
- Interpret Graphs to Determine Properties of a Function
- Graph Exponential & Logarithmic Functions
Trigonometric Functions
- Six Trigonometric Functions, Co-functions and Reciprocals as Ratios of the Sides of a Right Triangle
- Inverse Trigonometric Functions
- Graphs of the Six Trigonometric Functions
- Unit Circle
- Reference Angles & Standard Position
- Arc Length
- Periodic Functions (Amplitude, Period, Frequency, & Phase Shift)
- Pythagorean Identities
- Sum & Difference Identities
- Double-Angle Identities
- Half-Angle Identities
- Law of Sines & Law of Cosines
- Area of Triangles and Parallelograms Using Trigonometry
Units of Measurement- Radian & Degree Measures
- Central Tendency
- Measures of Dispersion
- Normal Distribution
- Regression Models
- Permutations, Combinations & Fundamental Principle of Counting
- Theoretical & Empirical Probability
- Binomial Probability & Expansion

More Resources
Specific Algebra 2/ Trigonometry Concepts
Sample Algebra 2/ Trigonometry Regents
→Further Educational Resources:
Khan Academy
Regents Prep