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

UNIT | TOPICS |
---|---|

Operations | - 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 |

Shapes | - 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 |

Statistics | - 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 |

Probability | - Fundamental Principle of Counting - Permutations - Conditional Probability |

**More Resources**

→Specific Integrated Algebra Concepts

→Sample Integrated Algebra Regents

→Further Educational Resources:

Khan Academy

Regents Prep

Sparknotes

## GEOMETRY

UNIT | TOPICS |
---|---|

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 |

Locus | - 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

Sparknotes

## ALGEBRA 2/ TRIGONOMETRY

UNIT | TOPICS |
---|---|

Operations | - 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 |

Statistics | - Central Tendency - Measures of Dispersion - Normal Distribution - Regression Models |

Probability | - 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

Sparknotes