NC MATH 1 EOC STUDY GUIDE

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📘 NC Math 1 EOC Study Guide

🧮 UNIT 1: Expressions, Equations & Inequalities

Key Concepts:

* Order of Operations (PEMDAS)

* Solving Linear Equations (one-step, multi-step, with variables on both sides)

* Solving Inequalities (flip inequality when multiplying/dividing by a negative)

* Literal Equations – Solve for a specific variable

Example:

Solve:

3(x - 4) + 2 = 2x + 1

Distribute → Combine like terms → Isolate variable → Solve

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📊 UNIT 2: Functions

Key Concepts:

* Function Notation: f(x) means the output of function f when x is input

* Determine if Relation is a Function: Passes vertical line test

* Domain & Range

* Linear vs. Nonlinear Functions

Key Formulas:

* Slope: m = (y₂ - y₁) / (x₂ - x₁)

* Slope-Intercept Form: y = mx + b

* Point-Slope Form: y - y₁ = m(x - x₁)

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📐 UNIT 3: Linear Functions

Key Concepts:

* Graphing Linear Functions

* Finding Slope from Graph, Table, or Two Points

* Parallel & Perpendicular Lines:

* Parallel: same slope

* Perpendicular: negative reciprocal slope

Word Problems:

* Convert words to equations (e.g., "total cost = fixed fee + rate × time")

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📈 UNIT 4: Systems of Equations & Inequalities

Key Concepts:

* Solve Systems by:

* Graphing

* Substitution

* Elimination

* Solutions: One solution, no solution, infinitely many

* System of Inequalities: Graph each inequality, shade solution region

Tip:

* Check solution by plugging into *both* equations

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🔢 UNIT 5: Exponents & Exponential Functions

Exponent Rules:

* Product Rule: x^a * x^b = x^(a+b)

* Quotient Rule: x^a / x^b = x^(a-b)

* Power Rule: (x^a)^b = x^(a*b)

* Negative Exponent: x^(-a) = 1/x^a

Exponential Functions:

* Growth: y = a(1 + r)^t

* Decay: y = a(1 - r)^t

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📉 UNIT 6: Descriptive Statistics

Key Concepts:

* Mean, Median, Mode, Range

* Box Plots

* Standard Deviation: Measures data spread

* Scatter Plots & Correlation:

* Positive, Negative, or No Correlation

* Line of Best Fit

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📏 UNIT 7: Quadratics (If included on your test)

Quadratic Functions:

* Standard Form: y = ax^2 + bx + c

* Vertex Form: y = a(x - h)^2 + k

* Axis of Symmetry: x = -b/(2a)

* Vertex: Maximum or minimum point

* Factoring to Solve: Set y = 0, then factor

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🧠 Test-Taking Strategies

* Use Graphing Calculator wisely for checking graphs & calculations

* Underline Key Words in word problems

* Plug In Answers (back-solve when possible)

* Check Your Work especially signs and decimal points

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📄 FORMULA SHEET (Memorize or Know How to Use)

| Concept | Formula/Rule |

| -------------------- | ------------------------- |

| Slope | m = (y₂ - y₁)/(x₂ - x₁) |

| Slope-Intercept Form | y = mx + b |

| Point-Slope Form | y - y₁ = m(x - x₁)

| Exponential Growth | y = a(1 + r)^t |

| Exponential Decay | y = a(1 - r)^t |

| Standard Form Quad. | y = ax^2 + bx + c

| Axis of Symmetry | x = -b / (2a) |