Common Core Algebra 1 Regents Exam Cheat Sheet

Introduction

This cheat sheet is designed to help students prepare for the Common Core Algebra 1 Regents Exam. It contains essential formulas, concepts, and strategies to help you succeed on the exam. Remember, this is a reference tool to aid your memory, not a replacement for thorough studying and understanding of the material.

Linear Equations and Functions

Key Concepts:

• Parallel lines have equal slopes: m = m
• Perpendicular lines have slopes that are negative reciprocals: m m = -1
• Positive slope: line rises from left to right
• Negative slope: line falls from left to right

Systems of Equations

Methods of Solution:

• Graphing: Plot both equations and find the intersection point
• Substitution: Solve one equation for a variable and substitute into the other
• Elimination: Add or subtract equations to eliminate a variable

Special Cases:

• Infinite Solutions: Same line, same slope and y-intercept
• No Solution: Parallel lines, same slope but different y-intercepts
• One Solution: Lines have different slopes

Quadratic Functions

Key Concepts:

• The axis of symmetry is x = -b/(2a) or x = h
• The vertex is at (h, k) in vertex form
• The y-intercept is y = c in standard form
• The discriminant (b - 4ac) determines the number of real roots:
  • If positive: two real roots
  • If zero: one real root
  • If negative: no real roots

Exponential Functions

Properties of Exponents:

• Product of Powers: a^m a^n = a^(m+n)
• Quotient of Powers: a^m a^n = a^(m-n)
• Power of a Power: (a^m)^n = a^(mn)
• Zero Exponent: a^0 = 1
• Negative Exponent: a^-n = 1/(a^n)
• Fractional Exponent: a^(m/n) = (na)^m

Factoring Polynomials

Common Factoring Techniques:

• Greatest Common Factor (GCF): Factor out the largest term common to all terms
• Difference of Squares: a - b = (a + b)(a - b)
• Perfect Square Trinomial: a + 2ab + b = (a + b)
• Sum/Difference of Cubes: a + b = (a + b)(a - ab + b), a - b = (a - b)(a + ab + b)

Method	When to Use
GCF	When all terms share a common factor
Difference of Squares	When you have a - b
Trinomial Factoring	For ax + bx + c when a 0
Factor by Grouping	For four-term polynomials

Inequalities

Functions

Key Concepts:

• Domain: Set of all possible input values (x-values)
• Range: Set of all possible output values (y-values)
• Function Notation: f(x) represents the output when x is the input
• Vertical Line Test: A graph represents a function if every vertical line intersects the graph at most once
• One-to-One Function: A function where each output corresponds to exactly one input
• Composition: (f g)(x) = f(g(x))
• Inverse Function: If f(x) = y, then f^(-1)(y) = x

Statistics

Measures of Central Tendency:

Measures of Dispersion:

Graphing Techniques

Parent Functions:

• Linear: y = x
• Quadratic: y = x
• Absolute Value: y = |x|
• Exponential: y = b^x (where b > 0, b 1)
• Square Root: y = x

Transformations of Functions:

• Vertical Shift: y = f(x) + k (up if k > 0, down if k < 0)
• Horizontal Shift: y = f(x - h) (right if h > 0, left if h < 0)
• Vertical Stretch/Compression: y = af(x) (stretch if |a| > 1, compress if 0 < |a| < 1)
• Horizontal Stretch/Compression: y = f(bx) (compress if |b| > 1, stretch if 0 < |b| < 1)
• Reflection: y = -f(x) (reflects across x-axis), y = f(-x) (reflects across y-axis)

Word Problem Strategies

• Read the problem at least twice
• Identify what you need to find
• Determine the given information
• Set up equations or inequalities
• Solve carefully
• Check your answer in the context of the problem

Exam Tips

• Manage your time wisely - allocate more time to questions worth more points
• Read all instructions carefully
• Show all your work - partial credit is often awarded
• Check your answers if time permits
• Don't leave any questions blank
• Use the calculator only when allowed and necessary
• Use the reference sheet provided with the exam

Common Mistakes to Avoid

• Forgetting to check for extraneous solutions
• Mixing up formulas
• Calculation errors (especially with negative numbers)
• Incorrectly applying transformations to functions
• Rounding too early in multi-step problems
• Forgetting units in word problems
• Confusing independent and dependent variables