SAT® Preparation Course
Unit 3: Passport to Advanced Math
Passport to Advanced Math questions include topics that are especially important for students to master before studying advanced math. Chief among these topics is the understanding of the structure of expressions and the ability to analyze, manipulate, and rewrite these expressions. This domain also includes reasoning with more complex equations, and interpreting and building functions.
What will my child learn?
Students will:
SAT.PAM.01 Create a quadratic or exponential function or equation that models a context. The equation will have rational coefficients and may require multiple steps to simplify or solve the equation.
SAT.PAM.02 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 in order to solve.
SAT.PAM.03 Solve a system of one linear equation and one quadratic equation. The equations will have rational coefficients.
SAT.PAM.04 Add, subtract, and multiply polynomial expressions and simplify the result. The expressions will have rational coefficients.
SAT.PAM.05 Understand the relationship between zeros and factors of polynomials, and use that knowledge to sketch graphs. Students will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of a polynomial based on other information provided.
SAT.PAM.06 Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms.
SAT.PAM.07 Rewrite simple rational expressions. Students will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result. The expressions will have rational coefficients.
SAT.PAM.08 Solve an equation in one variable that contains radicals or contains the variable in the denominator of a fraction. The equation will have rational coefficients, and the student may be required to identify when a resulting solution is extraneous.
SAT.PAM.09 Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.
SAT.PAM.10 Create an equivalent form of an algebraic expression by using structure and fluency with operations.
SAT.PAM.11 Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.
SAT.PAM.12 Interpret parts of nonlinear expressions in terms of their context. Students will make connections between a context and the nonlinear equation that models the context to identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation.
SAT.PAM.13 Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation.
SAT.PAM.14 Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions.
Students will:
SAT.PAM.01 Create a quadratic or exponential function or equation that models a context. The equation will have rational coefficients and may require multiple steps to simplify or solve the equation.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 2 - F.LEA.2) | Algebra 2 (Unit 2 - F.LE.A.2) | Algebra 2 (Unit 3 - F.IF.C.8)
- Check for Understanding: College Board - item 15 | Ivy Global - item 1 | Learnerator - Quadratic & exponential functions
SAT.PAM.02 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 in order to solve.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 3 - A.REI.B.4, A.REI.B.4a, A.REI.B.4b)
- Check for Understanding: College Board - item 3 | Ivy Global - item 5 | Learnerator - Solving quadratic equations
SAT.PAM.03 Solve a system of one linear equation and one quadratic equation. The equations will have rational coefficients.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 3 - A.REI.C.7)
- Check for Understanding: College Board - item 23 | Ivy Global - item 8
SAT.PAM.04 Add, subtract, and multiply polynomial expressions and simplify the result. The expressions will have rational coefficients.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 4 - A.APR.A.1)
- Check for Understanding: College Board - item 5 | Ivy Global - item 6 | Learnerator - Operations on polynomials
SAT.PAM.05 Understand the relationship between zeros and factors of polynomials, and use that knowledge to sketch graphs. Students will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of a polynomial based on other information provided.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 3 - A.SSE.B.3) | Algebra 2 (Unit 4 - A.APR.B.2)
- Check for Understanding: College Board - item 28 | Ivy Global - item 11
SAT.PAM.06 Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 5 - N.RN.A.1, N.RN.A.2)
- Check for Understanding: College Board - item 6 | Ivy Global - item 3
SAT.PAM.07 Rewrite simple rational expressions. Students will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result. The expressions will have rational coefficients.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 6 - N.RN.A.2, A.APR.D.6)
- Check for Understanding: College Board - item 29 | Ivy Global - item 9 | Learnerator - Radicals & rational exponents
SAT.PAM.08 Solve an equation in one variable that contains radicals or contains the variable in the denominator of a fraction. The equation will have rational coefficients, and the student may be required to identify when a resulting solution is extraneous.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 6 - A.REI.A.2)
- Check for Understanding: College Board - item 18 | Ivy Global - item 7 | Learnerator - Solving radical & rational equations
SAT.PAM.09 Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 3 - F.IF.C.8)
- Check for Understanding: College Board - item 7 | Ivy Global - item 2
SAT.PAM.10 Create an equivalent form of an algebraic expression by using structure and fluency with operations.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 3 - A.SSE.B.3)
- Check for Understanding: Ivy Global - item 4 | Ivy Global - section 3, item 4
SAT.PAM.11 Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 2 - A.CED.A.4)
- Check for Understanding: College Board - item 4 | Ivy Global - item 13 | Learnerator - Isolating quantities using structure
SAT.PAM.12 Interpret parts of nonlinear expressions in terms of their context. Students will make connections between a context and the nonlinear equation that models the context to identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 3 - A.SSE.A.1) | Algebra 2 (Unit 2 - F.LE.B.5)
- Check for Understanding: College Board - item 14 | Ivy Global - item 10
SAT.PAM.13 Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 1 (Unit 2 - F.IF.C.7 & Unit 3 - F.IF.C.7) | Algebra 2 (Unit 6 - F.IF.C.7)
- Check for Understanding: College Board - item 7 | Ivy Global - item 14 | Learnerator - Non-linear relationships between two variables
SAT.PAM.14 Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions.
- Alignment to HCPSS Math Course(s) & Course Standard(s): Algebra 2 (Unit 2 - F.IF.A.3)
- Check for Understanding: Ivy Global - item 12 | Learnerator - Function notation
Tools and Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! |
More 4 U
The Khan Academy has produced videos of worked examples of concepts found in the Passport to Advanced Math portion of the new SAT®. Khan Academy also has four official practice exams from College Board. |