SAT Exam Syllabus for Maths

Heart of Algebra

• Create, solve, or interpret a linear expression or equation in 1 variable.
• Create, solve, or interpret linear inequalities in 1 variable.
• Build a linear function that models a linear relationship between 2 quantities.
• Create, solve, and interpret systems of linear inequalities in 2 variables.
• Create, solve, and interpret systems of 2 linear equations in 2 variables.
• Algebraically solve linear equations (or inequalities) in 1 variable.
• Algebraically solve systems of 2 linear equations in 2 variables.
• Interpret the variables and constants in expressions for linear functions.
• Understand connections between algebraic and graphical representations.

Problem Solving and Data Analysis:

• Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.
• Solve single- and multistep problems involving percentages.
• Solve single- and multistep problems involving measurement quantities, units, and unit conversion.
• Use scatterplot, linear, quadratic, or exponential models to describe how the variables are related.
• Use the relationship between 2 variables to investigate key features of the graph.
• Compare linear growth with exponential growth.
• Use 2-way tables to summarize categorical data and relative frequencies and calculate conditional probability.
• Make inferences about population parameters based on sample data.
• Use statistics to investigate measures of center of data. Analyze shape, center, and spread.
• Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods.
• The reports may consist of tables, graphs, or text summaries.

Passport to Advanced Math:

• Create a quadratic or exponential function or equation that models a context.
• Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.
• Create equivalent expressions involving rational exponents and radicals, which includes simplifying or rewriting in other forms.
• Create an equivalent form of an algebraic expression by using structure and fluency with operations.
• Solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation to solve.
• Add, subtract, and multiply polynomial expressions. Simplify the result. The expressions will have rational coefficients.
• Solve an equation in 1 variable that contains radicals or contains the variable in the denominator of a fraction.
• Solve a system of 1 linear equation and 1 quadratic equation.
• Rewrite simple rational expressions.
• Interpret parts of nonlinear expressions in terms of their context.
• Understand the relationship between zeros and factors of polynomials. Use that knowledge to sketch graphs.
• Understand a nonlinear relationship between 2 variables by making connections between their algebraic and graphical representations.
• Use function notation, and interpret statements using function notation.
• Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation.

Additional Topics in Math:

• Solve problems using volume formulas.
• Use trigonometric ratios and the Pythagorean theorem to solve applied problems involving right triangles.
• Add, subtract, multiply, divide, and simplify complex numbers.
• Convert between degrees. Use radians to determine arc lengths. Use trigonometric functions of radian measure.
• Apply theorems about circles to find arc lengths, angle measures, chord lengths, and areas of sectors.
• Use concepts and theorems about congruence and similarity to solve problems about lines, angles, and triangles.
• Use the relationship between similarity, right triangles, and trigonometric ratios. Use the relationship between sine and cosine of complementary angles.
• Create or use an equation in 2 variables to solve a problem about a circle in the coordinate plane.