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Passport to Advanced Math

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More Lessons for SAT Math
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We have lots of free resources and videos to help you prepare for the SAT. These materials are for the redesigned SAT which is for you if you are taking the SAT in March 2016 and beyond.

Passport to Advanced Math questions build on the knowledge and skills tested on the Heart of Algebra questions. It is recommended that you build your proficiency with the Heart of Algebra questions before attempting the Passport to Advanced Math questions.

Passport to Advanced Math includes questions that test your ability to
• work with expressions involving exponentials, integer and rational powers, radicals or fractions with a variable in the denominator.
• add, subtract, multiply polynomials and divide polynomials by a linear expression.
• solve a quadratic equation, a radical equation, a rational equation or a system consisting of linear equation and a nonlinear equation.
• manipulate an equation in several variables to isolate a required variable.
• understand functions and their graphs.

There are many ways that you can be tested and practicing different types of questions will help you to be prepared for the SAT.

The following video lessons will show you how to solve a variety of Passport to Advanced Math questions in different situations.

Operations with Polynomials and Rewriting Expressions

You will need to know how to foil and factor quadratics. You may be asked to rewrite expressions by recognizing structures for eg. difference of squares.

Quadratic Functions and Equations

Make sure you know the following methods to solve quadratic equations:
1. Factoring
2. Completing the Square
3. Quadratic Formula
4. Using a calculator (if permitted)
5. Use of structure

Exponential Functions, Equations, and Expressions and Radicals

You may be asked to build a function that models a given situation. An exponential function models a situation in which a quantity is multiplied by a constant factor for each time period.
If it increases with time then it is exponential growth, represented by the function y = a(1 + r)t
If it decreases with time then it is exponential decay, represented by the function y = a(1 - r)t where a is the initial population, r is the rate of growth or decay, and t is the number of time intervals that have elapsed.

You may be asked to solve radical equations. When solving radical equations, we usually square both sides of the equation. This may result in a root that may not be a solution to the original equation. So, always remember to check your solutions with the original equation. Radicals can also be written as fractional or rational exponents.

Dividing Polynomials by a Linear Expression, Solving Rational Equations, and Manipulating Rational Expressions

You will need to work with rational expressions, including fractions with a variable in the denominator. When solving for a variable, the first step will be to try to clear the variable from the denominator.

You will need to know how to perform long division of a polynomial by a linear expression.

Systems of Equations: Linear and nonlinear

You may be asked to solve a systems of equations where one equation is linear and the other equation is quadratic or nonlinear equation.

Relationships between Algebraic and Graphical Representations of Functions

You are required to know and apply the following relationships: intercepts, domain and range, maximum and minimum values, increasing and decreasing, end behavior, asymptotes, symmetry, and transformations.

Function Notation

You may be asked to evaluate a function or the composition of two functions. You may be asked to interpret the value of a function in the context.

Analyzing more Complex Equations in Context

You may be asked to analyze equations and functions. You need to know how to isolate a required quantity.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

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