Questions and Answers
What are the two kinds of algebra questions?
What is the golden rule of algebra?
Whatever you do to one side of an equation, you have to do to the other side.
It is faster to do these problems by hand.
True
Working backwards involves starting with the ______ answer.
Signup and view all the answers
How are numerical answers presented on the ACT?
Signup and view all the answers
The reverse question makes the job easier by giving you the value for the variable.
Signup and view all the answers
What type of equation is considered easiest on the test?
Signup and view all the answers
What is a cosmic equation?
Signup and view all the answers
The abbreviation 'POE' stands for ______.
Signup and view all the answers
What is the main difference between solving inequalities and equalities?
Signup and view all the answers
What is logarithm notation for exponents?
Signup and view all the answers
What does the logarithm equation log(small x)y=z mean?
Signup and view all the answers
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 ).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
