Take your skills to a higher level with the SAT Math Level 2 Subject Test. If you’ve covered all the requirements for SAT Math Level 1, plus elementary functions (pre-calculus) or trigonometry or both, then you’re ready for SAT Math Level 2.

– College Board

# Introduction to SAT Math Level 2

The SAT Math Level 2 Subject Test covers the same material as the Mathematics Level 1 test — with the addition of trigonometry and elementary functions (precalculus). If you performed well in these courses, taking this test gives you the opportunity to highlight your abilities and showcase your interest in higher-level mathematics.

## Anticipated Skills

- Number and operations
- Algebra and functions
- Geometry and measurement (coordinate, three-dimensional, and trigonometry)
- Data analysis, statistics and probability

## Recommended Preparation

More than three years of college-preparatory mathematics, including two years of algebra, one year of geometry, and elementary functions (precalculus) or trigonometry or both.

### Number and operations

- Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences, series, vectors

### Algebra and functions

- Expressions, equations, inequalities, representation and modeling, properties of functions (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, periodic, piecewise, recursive, parametric)

### Geometry and measurement

- Coordinate: Lines, parabolas, circles, ellipses, hyperbolas, symmetry, transformations, polar coordinates
- Three-dimensional: Solids, surface area and volume (cylinders, cones, pyramids, spheres, prisms), coordinates in three dimensions
- Trigonometry: Right triangles, identities, radian measure, law of cosines, law of sines, equations, double angle formulas

### Data analysis, statistics, and probability

Mean, median, mode, range, interquartile range, standard deviation, graphs and plots, least squares regression (linear, quadratic, exponential), probability

## Choosing Between Math Levels 1 and 2

If you have taken trigonometry or elementary functions (precalculus) or both, received grades of B or better in these courses, and are comfortable knowing when and how to use a scientific or graphing calculator, you should select the Level 2 test. If you are sufficiently prepared to take Level 2, but elect to take Level 1 in hopes of receiving a higher score, you may not do as well as you expect. You may want to consider taking the test that covers the topics you learned most recently, since the material will be fresh in your mind. You should also consider the requirements of the colleges and programs you are interested in.

#### Course Materials

#### Logarithmic Graphs

- Dilation from the x-axis
- Dilation from the y-axis
- Dilation from the base
- Translation of Logarithmic Graphs
- Reflection of Logarithmic Graphs
- Transformations of Logarithmic Graphs to base e
- Dilation of Logarithmic Graphs to base e
- Translation of Logarithmic Graphs to base e
- Reflection of Logarithmic Graphs to base e
- Graphs of Logarithmic Functions
- Absolute Values

#### Transformations

- Basic Rules of Transformations
- Transformation of Parabolas
- Transformation of Cubic Graphs
- Transformation of Quartic Graphs
- Transformation of Power Functions
- Transformation of Hyperbola
- Transformation of Square Root Graphs
- Transformation of Absolute Value Graphs
- Reflection of Cubic Graphs
- Axes of Symmetry
- Shifts by Axes

#### Conic Sections

- Parabola Symmetrical to y-axis
- Parabola Symmetrical to x-axis
- Transformation of Parabola Symmetrical to y-axis
- Transformation of Parabola Symmetrical to x-axis
- Eccentricity of Ellipse
- Definition of Ellipse
- Transformation of Ellipse
- Drawing Hyperbolae
- Eccentricity of Hyperbolae
- Transformation of Hyperbolae
- Finding the Equation of Hyperbola

#### Arithmetic Sequences and Series

- Identifying Arithmetic Sequences
- First Term and Common Difference of Arithmetic Sequences
- Finding a Term from a Rule
- Set up a Rule
- Finding the number of Terms
- Applications
- Sum of an Arithmetic Series
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Terms from Sum
- Sigma Notation of Arithmetic Series

#### Geometric Sequences and Series

- Identifying Geometric Sequences
- First Term and Common Ratio of Geometric Sequences
- Finding a Term from a Rule
- Set up a Rule
- Finding the number of Terms
- Applications
- Compound Interest
- Finding Unknown Values
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Number of Terms
- Sigma Notation of Geometric Series
- Finding the Number of Terms

#### Probability

- Listing Outcomes
- 2-Dimensional Grids
- Tree Diagrams for Sample Spaces
- Addition Rule of Probability
- Mutually Exclusive Events
- Independent Events
- Probability Tables
- Estimating Probabilities from Data
- Using Grids to Find Probabilities
- Venn Diagram
- Basic Tree Diagrams
- Further Tree Diagrams
- Conditional Probability
- Further Conditional Probability