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7th Grade Math Algebra 1 Geometry H Algebra 2/Trig IB AI IB AA PreCalc 1 PreCalc 2 Calculus BC Calculus 2 SAT ACT

7th Grade Math

Unit 1: Building Community with Data
Statistical Questions → Ways to Collect Data → Representative Samples → Make a Histogram → Histogram Intervals → Compare Data Displays → Conclusions from Histograms →
Unit 2: Rational Numbers and Exponents
Square Roots of Perfect Squares → More Square Roots → Order of Operations with Negative Numbers → Order of Operations, Step by Step → Multiplying Fractions → Patterns with Negative Powers of 10 → Powers of 10 as Fractions and Decimals → Scientific Notation, Positive Powers → Scientific Notation, Negative Powers → Scientific Notation, Mixed Practice → Compare Numbers in Scientific Notation → Compare and Order Rational Numbers →
Supplemental
Adding and Subtracting Negative Fractions → Adding and Subtracting Rational Numbers → Negative Number Statements → Absolute Value → Multiplying and Dividing Rational Numbers → Multiply and Divide Negative Fractions → Equivalent Expressions with Negatives →
Unit 3: Expressions
Simplify Numerical Expressions → Model Equivalent Expressions → Simplify Algebraic Expressions → Distributing → Evaluate Expressions →
Unit 4: Equations and Inequalities
Solve Two-Step Equations → Check a Solution → Equations in Real Life → Solve Inequalities → Multiply or Divide by a Negative → Graph an Inequality → Inequalities in Real Life → Equations and Inequalities →
Unit 5: Proportional Relationships
Ratio Tables → Proportions → Convert Units → Percent of a Number → Slope and y = mx → Describe the Slope → Graph a Proportional Relationship → Tables, Equations, and Graphs →
Unit 6: Applications of Proportional Reasoning in Geometry
Similar Figures → Side Lengths in Similar Figures → Angles in Similar Figures → Scale Drawings → Dilations →
Unit 7: Rational Number Applications
Theoretical Probability → Experimental Probability → Theory and Experiment → Rational Numbers in Real Life →
Unit 8: Applications of Expressions and Equations in Geometry
Quadrilaterals → Angles in Quadrilaterals → Sides in Quadrilaterals → Volume of a Cylinder → Surface Area → Volume or Surface Area → Changing a Measurement →

Algebra 1

Unit 1: Solving Equations and Inequalities
Write Equations → Write Inequalities → Solve Multi-Step Equations → Clearing Fractions (Advanced Strategy) → Solve Multi-Step Inequalities → Literal Equations → One, None, or Infinitely Many Solutions →
Unit 2: Linear Equations
Key Features of Linear Functions → Transformations of y = x → Convert to Different Linear Equations → Write y = mx + b → Write Ax + By = C → Write y − y₁ = m(x − x₁) → Write the Equation of a Line → Parallel and Perpendicular Lines → Graph Linear Functions → Input and Output → Compare Linear Functions →
Unit 4: Systems of Equations and Inequalities
Write a System of Equations → Solve a System of Equations → One, None, or Infinitely Many Solutions → Write a Linear Inequality → Graph a Linear Inequality → Write a System of Inequalities → Graph a System of Inequalities → Check and Interpret Solutions → Systems with Three Lines → Systems with Three Variables →
Unit 6: Exponents, Radicals, and Linear Review
Translate Expressions → Evaluate Expressions → Multiply, Divide, and Raise Powers → Simplify Algebraic Fractions with Exponents → Simplify Square Roots and Cube Roots → Add, Subtract, and Multiply Radicals → Radicals as Rational Exponents → Key Features of Linear Functions → Parallel and Perpendicular Lines → Graph Linear Functions → Input and Output → Compare Linear Functions → Exponential Equations with the Same Base → Compare Methods for Simplifying Radicals → Rationalize a Monomial Denominator → Decompose Fractional Powers → Patterns as Functions → Exponential Curve of Best Fit →
Unit 7: Polynomials and Factoring
Add and Subtract Polynomials → Multiply Polynomials → Factor Quadratics (a = 1) → Factor Quadratics (a > 1) → Divide Polynomials → Equivalent Quadratic Expressions → Factor Quadratics in Two Variables → Factor Cubics and Quartics →
Unit 8: Quadratic Functions
Key Features of Quadratic Functions → Graph Quadratics with Transformations → Standard Form and Factored Form → Quadratic Regression → Quadratic Patterns as Functions →
Unit 9: Solving Quadratic Equations
Solve Quadratic Equations → How Many Real Solutions? → Complete the Square → Compare Methods for Solving Quadratics →
Unit 10: Functions and Two-Variable Data
Linear and Quadratic Features → Compare Linear, Quadratic, and Exponential → Write Bivariate Questions → Choose Variables → Choose a Sample → Read a Scatterplot → Draw Conclusions from Two-Variable Data → Patterns That Are Not Linear or Quadratic →

H Algebra 2/Trig

Unit 0 – Review
Order of Operations with Integers and absolute value → Polynomial Vocabulary → Fraction Operations → Simplifying Exponents → Properties Of Math → Multiplying Binomials → Simplifying Expressions → Factor Difference of Squares → Factor Quadratics (a = 1) → Factor Quadratics (a > 1) → Factor Quadratics - U-Substitution for x⁴ Polynomials → Factor Four-Term Polynomials → Algebraic Area → Simplify Radicals →
Supplemental
Simplify Exponents → Negative Exponents → Slope-Intercept Form → Write Equations of Lines → Linear Word Problems → Evaluate Functions → Absolute Value Equations → Absolute Value Inequalities → Systems of Linear Inequalities →
Unit 1 – Quadratics
Write Numbers with Imaginary Unit → Complex Number Operations → Powers of i → Solve by Factoring → Quadratic Formula → Discriminant → Sum and Difference of Cubes → Solve by Square Root → Completing the Square → Vertex Form Graphs → Quadratic Word Problems →
Unit 2 – Quadratic Graphs
Convert to Standard Form → Standard Form Graphs → Write Quadratics from Roots → Vertex Form from a Point → Equations from Graphs → Write Equations from Word Problems → Challenging Completing the Square Problems →

Review for Test
Quadratic Formula → Solve by Square Root → Completing the Square → Discriminant →
Unit 3 – Polynomial Functions
Degree and End Behavior → Zeros and Multiplicity → Equation from a Graph → Sketch a Polynomial → Divide by a Monomial → Polynomial Long Division → Sum and Difference of Cubes → Simplify a Power → Polynomial from Zeros → Find All Zeros → Solve Polynomial Equations → Zeros of a Difference of Powers → Polynomial Area → Zeros with a GDC → Factor Theorem → Remainder Theorem →
Unit 4 – Rational Functions
Divide Rational Expressions → Simplify Complex Fractions → Add and Subtract Rational Expressions → Solve Rational Equations → Solve Rational Inequalities → Direct, Inverse, or Joint → Direct Variation → Inverse Variation → Joint Variation → Combined Variation → Asymptotes and Holes → Graph a Rational Function →
Unit 7 – Exponential and Logarithmic Functions
Graph Exponential Functions → Graph Logarithmic Functions → Asymptote and Intercept → Exponential and Logarithmic Form → Evaluate Logarithms → Find the Inverse → Condense Logarithmic Expressions → Expand Logarithmic Expressions → Exponential Equations with the Same Base → Exponential Equations with Unlike Bases → Quadratic Exponential Equations → Write an Exponential from Points →
Unit 8 – Sequences, Series, and Probability and Statistics
Arithmetic Terms → Combinations → Permutations → Counting Principle → Empirical Rule → Normal Probabilities → Inverse Normal →

IB Analysis and Approaches

Unit 1
1A Exponents
Multiply, Divide, and Raise Powers → Simplify Algebraic Fractions with Exponents → Negative Exponents → Solve Exponential Equations → Solve Simultaneous Exponential Equations →
1B Scientific Notation

This class allows you to use the calculator heavily.

Write Numbers in Standard Form → Multiply and Divide in Standard Form → Add and Subtract in Standard Form → Standard Form with a, b, c, and d → Standard Form Applications →
1C Logarithms
Evaluate Logs Without a Calculator → Solve Log Equations → Simplify Logarithmic Expressions → Inverse Properties of Logs and Exponentials → Solve Exponential Equations Using Logs → Logarithm Applications →
12A Law of Exponents and Rational Expressions
Evaluate Rational Exponents → Negative Rational Exponents → Write in the Form axp → Solve Equations with Rational Exponents →
12B Logarithms
Evaluate Logs Exactly → Solve Log Equations → Log Laws → Change of Base → Exponential Equations with a Calculator → Exponential Equations with Natural Logs →
Unit 2
5A Volumes and Surface Area of Three Dimensional Solids
Spheres and Hemispheres → Cones → Pyramids → Compound Solids →
5B Rule of Trigonometry
Right Triangles → Angle Between Two Lines → Sine Rule → Cosine Rule → Area of a Triangle →
5C Applications of Trigonometry
Angles in a Cuboid → Angles in a Pyramid and a Cone → Bearings → Elevation and Depression →
18A Radian Measure of Angles
Convert Degrees to Radians → Convert Radians to Degrees → Points on the Unit Circle → Arc Length and Sector Area → Segments → Find the Radius or the Angle → Compound Shapes →
18B Trigonometric Functions
Related Angles: Sine → Related Angles: Cosine → Tangent Relationships → Exact Values → The Ambiguous Case → Exact Lengths and Simplifying →

Calculus BC

AP Calculus BC, unit by unit.

Review
Evaluate Trig Functions without a Calculator →
Unit 1: Limits and Continuity
Limits by Substitution → Algebraic Limits → Limits from Graphs and Tables → Which Statement About a Limit Is True → Estimate a Limit from a Table → Piecewise Limits → Trig Limits → Squeeze Theorem → Choose a Method for a Limit → Types of Discontinuity → Continuity at a Point → Removing Discontinuities → Asymptotes → Infinite Limits and Limits at Infinity → Intermediate Value Theorem → Justify with the Intermediate Value Theorem →
Unit 2: Differentiation: Definition and Fundamental Properties
Average Rate of Change → Difference Quotients → The Derivative as a Limit → Find a Derivative from the Definition → Estimate a Derivative → Where a Function Is Differentiable → Power Rule and Basic Rules → Derivatives of Sine, Cosine, e^x, and ln x → Product Rule → Quotient Rule → Derivatives of Tangent, Cotangent, Secant, and Cosecant → Tangent Lines →
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
The Chain Rule → Chain Rule from Tables and Graphs → Implicit Differentiation → Derivatives of Inverse Functions → Find g'(a) for an Inverse → Inverse Trigonometric Derivatives → Choosing a Derivative Rule → Higher-Order Derivatives →
Unit 4: Contextual Applications of Differentiation
The Meaning of the Derivative → Straight-Line Motion → Rates of Change in Context → Related Rates → Linear Approximation → L'Hospital's Rule →
Unit 5: Analytical Applications of Differentiation
The Mean Value Theorem → Critical Points and the Extreme Value Theorem → Increasing, Decreasing, and Local Extrema → Absolute Extrema on a Closed Interval → Concavity and the Second Derivative Test → Graphs of a Function and Its Derivatives → Optimization → Horizontal and Vertical Tangents →
Unit 6: Integration and Accumulation of Change
Riemann Sums → Definite Integrals and Their Properties → The Fundamental Theorem and Accumulation Functions → Antiderivatives → Integration by Substitution → Integration by Parts → Partial Fractions and Completing the Square → Improper Integrals → Choosing an Integration Technique →
Unit 7: Differential Equations
Writing and Verifying Differential Equations → Slope Fields → Euler's Method → Separation of Variables → Exponential Models → Logistic Models →
Unit 8: Applications of Integration
Average Value of a Function → Motion with Integrals → Accumulation in Context → Area Between Curves → Volumes with Known Cross Sections → Disc and Washer Volumes → Arc Length →
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Derivatives of Parametric Equations → Second Derivatives and Parametric Arc Length → Vector-Valued Functions → Motion in the Plane → Polar Derivatives → Area of Polar Regions →
Unit 10: Infinite Sequences and Series
Geometric Series → The nth-Term Test for Divergence → Integral Test and p-Series → Comparison Tests → Alternating Series → The Ratio Test → Interval of Convergence → Error Bounds → Taylor Polynomials → Taylor and Maclaurin Series →

SAT Math

DESMOS Hacks!
Desmos Problems→
Algebra – Linear Equations in one variable
⭐ Infinitely Many Solution→ ⭐ No Solutions→ ⭐ How Many Solution→ Equivalent Solutions→ Interpret Terms In Context→ Word Problems→ ⭐ Verbals Descriptions to Algebra→ Evaluate Expression→ Solve Equations→
Algebra – Linear Functions
Evaluate Linear Functions→ Solve Linear Functions→ Interpret Slope and y-int in Context→ Find Slope and Intercepts→ Write Equations of Linear Functions→ Linear Word Problems and Models→ Linear Functions from Graphs and Tables→
Algebra – Linear Equations in Two Variables
Perpendicular Lines (Slope)→ Parallel Lines→ Writing Equations of Lines→ Finding Slope and Intercepts→ Real World Applications→ Linear Relationships from Tables and Graphs→ Mixture, Cost, and Total-value problems→
Algebra – Systems of two linear equations in two variables
Find Specific Value in a System→ Systems with No Solutions→ Systems with Infinite Solutions→ Graphing Systems & Intersection Points→ Writing Systems from Word Problems→
Algebra – Linear inequalities in one or two variables
Graph Linear Inequalities→ Systems of Linear Inequalities→ Writing Inequalities from Word Problems→ Solving for Minimum or Maximum Values→ Interpreting Tables and Ordered Pairs→
Advanced Algebra – Nonlinear equations in one variable and systems of equations in two variables
Solving Quadratic Equations in One Variable→ Systems Involving Linear + Quadratic Equations→ Solving for a Variable in Terms of Others→ Modeling with Nonlinear Equations from Word Problems→ Systems with Absolute Value or Other Nonlinear Functions→
Advanced Algebra – Nonlinear Functions
⭐ Quadratic Functions→ ⭐ Exponential Functions→ Function Notation→ Function Transformations→ Interpreting Graphs, Tables, and Intercepts in Context→ Polynomial, Rational, and Absolute Functions→ Modeling with Nonlinear Functions from Word Problems→
Advanced Algebra – Equivalent Expressions
Factoring Polynomials→ Simplifying Expressions with Exponents and Radicals→ Combining Like Terms and Using the Distributive Property→ Rewriting Rational Expressions→ Equivalent Forms of Quadratic Expressions→ Finding Constants in Equivalent Expressions→
Problem Solving and Data Analysis -Ratios, rates, proportional relationships, and units
Unit Conversions (Length, Volume, Time)→ Rates and Constant Speed/Distance Problems→ Proportional Relationships→ Rates and Constant Speed/Distance Problems→ Population Density and Area→ Density, Mass, and Volume→ Scale Models and Similar Figures→
Problem Solving and Data Analysis -Percentages
Percent Increase and Decrease→ Finding the Original Value Given Percent Change→ Calculating “What Percent” and “Percent Of”→ Percent Greater or Less Than→ Multi-Step Percent Problems (Successive Changes)→ Applied Percent Problems (Tips, Discounts, Growth)→
Problem Solving and Data Analysis -One-variable data: Distributions and measures of center and spread
Median and Mode→ Mean Calculations and Comparisons→ Range and Spread (Including Standard Deviation)→ Box Plots and Histograms→ Effects of Adding/Removing Data Points→ Frequency Tables and Dot Plots→
Problem Solving and Data Analysis – Two-variable data: Models and scatterplots
Scatterplots and Residuals→ Slope and Rate of Change→ Line of Best Fit→ Select Best Model→ Predictions and Interpretations→ Line Graphs and Two Variable Graphs→
Problem Solving and Data Analysis – Probability and conditional probability
Basic Probability→ Frequency Tables→ Joint Probability→ Conditional Probability→ Compound Events – And, Or, Neither→ Geometric Probability Models→
Geometry and Trigonometry – Area and Volume
⭐ Area of 2D Shapes→ Surface Area→ Volume of Prisms and Cubes→ Volume of Cylinders→ Similar Figures and Scale Factor→ Composite Figures→
Geometry and Trigonometry – Lines, angles, and triangles
Parallel Lines→ Triangle Angle Sum and Missing Angles→ Congruent Triangles→ Similar Triangles and Proportions→ Isosceles Triangles→ Exterior Angles, Vertical Angles, and Linear Pairs→
Geometry and Trigonometry – Right Triangles and trigonometry
Pythagorean Theorem→ Special Right Triangles→ Trig Ratios→ Similar Right Triangles and Trig→ Use Trig to find Missing Sides and Angles→ Trig Applications and Composite Figures→
Geometry and Trigonometry – Circles
Circle Equations→ Find Circle Center and Radius→ Arc Length, Central Angles, and Inscribed Angles→ Tangents to Circles→ Points on, in, and outside Circles→ Circle Transformations and Applications→
SAT Resources
Factoring Quadratics where a=1 →
Super Challenge!
Geometry→