**SAT****® Preparation Course**

**Unit 3: Passport to Advanced Math**

**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.

Algebra 1 (Unit 2 - F.LEA.2) | Algebra 2 (Unit 2 - F.LE.A.2) | Algebra 2 (Unit 3 - F.IF.C.8)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 3 - A.REI.B.4, A.REI.B.4a, A.REI.B.4b)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 3 - A.REI.C.7)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 4 - A.APR.A.1)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 1 (Unit 3 - A.SSE.B.3) | Algebra 2 (Unit 4 - A.APR.B.2)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 1 (Unit 5 - N.RN.A.1, N.RN.A.2)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 6 - N.RN.A.2, A.APR.D.6)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 6 - A.REI.A.2)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 3 - F.IF.C.8)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 1 (Unit 3 - A.SSE.B.3)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 1 (Unit 3 - A.SSE.A.1) | Algebra 2 (Unit 2 - F.LE.B.5)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 1 (Unit 2 - F.IF.C.7 & Unit 3 - F.IF.C.7) | Algebra 2 (Unit 6 - F.IF.C.7)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**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.

Algebra 2 (Unit 2 - F.IF.A.3)**Alignment to HCPSS Math Course(s) & Course Standard(s):**

**Check for Understanding:**Ivy Global - item 12 | Learnerator - Function notation

Tools and TechnologyDesmos 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 UThe 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. |