Algebra 1

What you will learn

• Solve equations and inequalities.
• Graph lines and interpret slope.
• Use functions to connect inputs and outputs.
• Work with exponents and polynomials.
• Solve basic quadratic equations.

Common challenges

• Keeping equations balanced

  An equation stays true when you perform the same allowed operation on both sides. Write one operation per line so you can check it.

• Negative signs

  A minus sign can change an entire expression. Use parentheses and check your work with a simple substitution.

• Turning words into math

  Define the unknown and its units first. Translate one relationship at a time, then check whether your answer fits the situation.

Key concepts

Variable

A variable is a symbol representing a number. Its value may be unknown or may change.

Equivalent equations

Equivalent equations have the same solutions. Adding the same number to both sides preserves equality.

Slope

Slope measures vertical change divided by horizontal change between two points on a nonvertical line.

Function

A function assigns exactly one output to each input in its domain.

Systems

A solution to a system makes all its equations true at once. On a graph, it lies where their graphs meet.

Quadratic

A quadratic function has a squared variable as its highest power. Its graph is a parabola.

How to prepare

• Practice adding and multiplying signed numbers.
• Solve ten fraction and decimal problems without a calculator.
• Review order of operations with parentheses.
• Plot points in all four coordinate quadrants.

Study habits that help

• Keep an error log for sign and fraction mistakes.
• Check equation solutions by substitution.
• Describe what each graph says in a sentence.
• Mix a few older problems into each practice session.

What to expect

Typical workload

Moderate

Time outside class

Typically about 3 to 5 hours outside class; this varies by school and student.

Pace

Topics usually build on earlier skills, so short, regular practice helps.

How it is usually graded

Teachers typically use tests, quizzes, homework, and sometimes projects or classwork.

Skills that help

• Fraction arithmetic
• Careful notation
• Reading word problems
• Checking answers

What teachers usually expect

• Show the steps in your solution.
• Bring questions about mistakes.
• Complete practice before the next lesson.

Before you start

• Comfort with whole numbers, fractions, and decimals
• Basic ratios and percentages
• Experience with simple numerical expressions

These are general descriptions of a typical course. Workload, pace and prerequisites differ by school and instructor, so check with your counselor, advisor or the course catalog.

Where it can lead

• Business
• Computer science
• Engineering
• Social sciences

Flashcards

Practice questions

Vocabulary

Expression

Numbers, variables, and operations without an equality statement.

Equation

A statement that two expressions are equal.

Inequality

A comparison using symbols such as < or >.

Constant

A fixed value.

Domain

The allowed inputs of a function.

Range

The outputs a function actually produces.

Intercept

A point where a graph meets an axis.

Factor

A quantity multiplied by another to form a product.