Algebra Chapter 12 Flashcards

Study Notes

Types of Algebra Questions

Two main types: solving for a specific variable (x) or an overarching cosmic value (x).

Golden Rule of Algebra

Maintain balance in equations: any operation performed on one side must be equally applied to the other side.

Calculator Tip

Performing calculations by hand can be quicker than using a calculator for certain problems.

Working Backwards Strategy

Start with the possible middle answer.
If it's too large, select the next smaller option; if too small, choose the next larger option.

Ordering of Answers

Numerical answers on the ACT are arranged from least to greatest.

Reverse Question Aspect

Sometimes variable values are provided directly in the question, simplifying the process.

Definition of Polynomial

A polynomial is a type of equation regarded as easier on tests.

Cosmic Equation Explained

An equation where x does not have a specific value, exemplified by 4x - 5.

ACT English vs ACT Math Vocabulary

Key elements: is (=), zero (of x), percent (100), and relation symbols (more than +, less than -).

Plugging In Steps

Choose numbers for variables, solve the problem using these numbers, then check which answer choice aligns with your solution.

Nature of Cosmic Problems

Problems featuring variables in the answer choices are identified as cosmic problems.

Factoring in ACT Problems

Many test questions involve some form of factoring, such as the basic problem x^2 + 7x + 12.

FOIL Method

FOIL stands for First, Outer, Inner, Last; a method used for multiplying binomials.

Preferred Process in Problem Solving

Use POE (Process of Elimination) to narrow down choices.

Quadratic Problems

More complex factoring questions require setting a factorable expression equal to zero.

Quadratic Equation Solutions

Typically, quadratic equations yield two solutions, known as roots and zeros.

Caution When Working Backwards

Be aware that there may be two valid solutions in these scenarios.

Favorable Factor Forms

Key algebraic identities:
- ( x^2 - y^2 = (x+y)(x-y) )
- ( x^2 + 2xy + y^2 = (x+y)^2 )
- ( x^2 - 2xy + y^2 = (x-y)^2 )

Simultaneous Equations

Simultaneous equations involve two equations that share the same two variables.

Solving Variables

An equation cannot be solved with two variables using only one equation.

Understanding Inequalities

Example: ( 3x + 7 > 38 ) illustrates the formulation of an inequality.

Key Difference in Solving

Solving inequalities is similar to equalities, but multiplying/dividing by a negative flips the inequality sign.

Common Testing Topics

Logarithms are less frequently encountered on the ACT compared to other topics.

Logarithms Explained

Logarithms act as an alternative notation for expressing exponents.

Logarithm Equation Format

The expression ( \log_{x}y = z ) translates to ( x^z = y ).

Description

Explore the key concepts from Chapter 12 of Algebra through flashcards. Each card presents a term and its definition, covering essential rules and techniques for solving algebraic equations. Test your understanding and reinforce your foundational algebra skills with these interactive flashcards.

Algebra Chapter 12 Flashcards

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Questions and Answers

What are the two kinds of algebra questions?

What is the golden rule of algebra?

It is faster to do these problems by hand.

Working backwards involves starting with the ______ answer.

How are numerical answers presented on the ACT?

The reverse question makes the job easier by giving you the value for the variable.

What type of equation is considered easiest on the test?

What is a cosmic equation?

The abbreviation 'POE' stands for ______.

What is the main difference between solving inequalities and equalities?

What is logarithm notation for exponents?

What does the logarithm equation log(small x)y=z mean?