SAT Math Fundamentals

This course covers the core skills outlined in the SAT Math curriculum.

Students begin by taking a diagnostic assessment, which will identify their current knowledge frontier and any weaknesses in their foundational knowledge.

Once the student has completed the diagnostic assessment, our sophisticated algorithms will create a custom course that addresses any foundational weaknesses along with a plan for building on their existing strengths to attain the highest possible score.

Comparing SAT Math Fundamentals to the Traditional High-School Sequence

The following data gives the composition of the SAT Math Fundamentals course against the traditional math sequence.

• Prealgebra: 39%
• Algebra I: 39%
• Geometry: 19%
• Algebra II: 3%

For example, 39% of the topics in the SAT Math Fundamentals course are from Prealgebra.

The data below describes the proportion of each high school course whose topics feature in SAT Math Fundamentals.

• Prealgebra: 90%
• Algebra I: 82%
• Geometry: 63%
• Algebra II: 9%

For example, a student who's completed SAT Math Fundamentals will have completed at least 90% of Prealgebra.

Comparing SAT Math Fundamentals to the Integrated Math Sequence

The following data gives the composition of the SAT Math Fundamentals course against the integrated sequence.

• Prealgebra: 39%
• Integrated Math I: 37%
• Integrated Math II: 24%

For example, 37% of the topics in the SAT Math Fundamentals course are from Integrated Math I.

The data below describes the proportion of each high school course whose topics feature in SAT Math Fundamentals.

• Prealgebra: 90%
• Integrated Math I: 81%
• Integrated Math II: 37%

For example, a student who's completed the SAT Math Fundamentals course will have completed at least 81% of Integrated Math I.

Preliminaries

• Addition, subtraction, multiplication, and division with rational numbers, and solving real-world and mathematical problems involving these operations.
• Manipulating expressions involving exponents and radicals, fractional and negative exponents, and the rules of exponents and radicals.
• Applying the order of operations to evaluate complex expressions containing rational numbers, fractional and negative exponents, and radicals.
• Constructing, evaluating, simplifying, and factoring linear algebraic expressions.

Algebra - Linear Equations in One Variable

• Solving one-step and multi-step linear equations, including cases involving rational expressions, cross-multiplication, unknown coefficients, and multiple variables.
• Using linear equations to model and solve real-world and mathematical problems.

Algebra - Linear Equations in Two Variables

• Graphing linear equations, calculating and describing a graph's key features.
• Working with slope-intercept, point-slope, and standard forms of straight line equations and determining properties of lines presented in these forms.
• Finding equations of parallel and perpendicular lines.
• Using two-variable equations to solve contextual problems, including problems involving speed, distance, time, and acceleration.
• Solving two-variable systems of linear equations using substitution and elimination, including cases with fractional and decimal coefficients, systems with no solutions or infinitely many solutions, and explaining how the solutions relate to the intersection of two lines.
• Using two-variable systems to model and solve contextual problems.

Algebra - Linear Inequalities

• Solving single-variable linear inequalities, compound inequalities, and systems of inequalities and graphing their solutions.
• Interval notation, including unions and intersections.
• Solving two-variable linear inequalities and systems of inequalities using a graphical method.
• Using single-variable and two-variable inequalities in real-world modeling contexts.

Geometry - Points, Lines, & Angles

• Understanding and applying basic geometry concepts, including working with segments, angles, and their properties.
• Solve problems involving complementary, supplementary, corresponding, alternate, and consecutive angles.

Geometry - Polygons & Solids

• Solving problems with interior and exterior angles of triangles.
• Classifying triangles and applying the isosceles triangle theorem.
• Understanding and applying terminology related to geometry in three dimensions and identifying common three-dimensional shapes.

Geometry - Congruence & Similarity

• Applying the ASA, SAS, AAS, SSS, and HL congruence criteria, and the AA, SSS, and SAS similarity criteria.
• Applying the midpoint and proportionality theorems.
• Solving problems related to polygon and solid similarity, including area and volume scale factors.

Geometry - Length, Area & Volume

• Calculating perimeters and areas of polygons in the plane.
• Applying the distance and midpoint formulas.
• Solving problems related to the surface area and volume of three-dimensional figures, including cubes, rectangular solids, pyramids, cylinders, cones, and spheres.

Geometry - Circles

• Circle fundamentals: interiors and exteriors of circles, circular arcs, sectors, and segments.
• Calculating circumferences and areas of circles and circular sectors.
• Solving problems involving tangent lines to circles.
• Working with radians, including converting between radians and degrees and using radians to calculate arc lengths and areas of sectors.
• Equations of circles in the coordinate plane, including techniques for determining properties of circles from their algebraic equations.

Trigonometry

• The Pythagorean theorem and its converse.
• The 45-45-90 and 30-60-90 special right triangles.
• Using trigonometric ratios to calculate side lengths and angle measures in right triangles.
• Using the special trigonometric ratios and the relationship between sine and cosine in terms of cofunctions.
• Modeling and solving real-world problems using trigonometry.

Advanced Algebra - Functions

• Functions essentials, including representations of functions, the vertical line test, domain, range, global and local extrema, roots, end-behavior, increasing and decreasing functions, piecewise functions, and inverse functions in simple cases.

Advanced Algebra - Absolute Value

• Applying the rules of absolute value and solving simple absolute value equations.
• Sketching absolute value functions, including cases with translations, stretches, reflections, and composite transformations.
• Determining roots of transformed absolute value functions.

Advanced Algebra - Polynomials

• Polynomial fundamentals, including simplifying, adding, subtracting, multiplying, and factoring polynomials.
• Techniques for solving quadratic equations, including applying the zero product rule, completing the square, and the quadratic formula.
• Finding the discriminant of a quadratic equation and solving related problems.
• Performing graph transformations of simple quadratic curves, including cases with translations, stretches, reflections, and composite transformations.
• Finding the axis of symmetry and roots of a general quadratic function and plotting their graphs.
• Solving nonlinear systems of equations involving quadratic functions and lines.
• Using quadratic functions to model real-world situations, such as vertical motion, revenue, cost, and profit functions.
• Factoring higher-order polynomials using greatest common factors, differences of squares, and grouping, and solving polynomial equations using these techniques.

Advanced Algebra - Exponential Equations & Functions

• Exponential expressions and equations, including modeling exponential growth and decay situations in context.
• The domain, range, intercepts, asymptotes, roots, and end behavior of exponential functions.
• Using exponential functions to model and solve real-world problems.

Advanced Algebra - Rational and Radical Equations

• Adding, subtracting, multiplying, dividing, and simplifying rational expressions, and solving rational equations.
• Simplifying radical expressions and solving radical equations.

Problem-Solving: Ratios & Percentages

• Solving real-world and mathematical problems involving ratios, percentages, unit rates, and proportional relationships, including modeling and solving real-world and mathematical problems.
• Determining units in formulas, including rates of change, working with standard and non-standard units.
• Performing unit conversions using algebraic techniques, including converting between units of area and volume.

Data Analysis - Statistics & Probability

• Summarizing and representing data through concepts such as centrality, spread, skew, and outliers and using frequency tables, dot plots, box plots, and histograms to visualize data and interpret distributions.
• Using scatter plots to identify trends in bivariate data, estimating trend lines, interpreting trend line coefficients in context, understanding the correlation coefficient, and matching data with an appropriate regression model.
• Probability: single and compound events, Venn diagrams, conditional probability, and independent events.