Algebra 1 STAAR Reference Sheet & Formula Chart
Official Texas TEA formulas for linear forms, quadratic equations, exponential functions, and exponent laws for the High School Algebra 1 EOC Assessment.
Linear Forms & Rate of Change (TEKS A.2B, A.2C, A.3A)
Standard, slope-intercept, and point-slope equations for linear relationships.
| Linear Form | Standard Equation | Key Parameters & Meaning |
|---|---|---|
| Slope-Intercept Form | y = mx + b | m is rate of change (slope); b is y-intercept (0, b). |
| Point-Slope Form | y - y₁ = m(x - x₁) | m is slope; (x₁, y₁) is any known point on the line. |
| Standard Form | Ax + By = C | A, B, and C are integers with A ≥ 0; A and B are not both zero. |
| Slope of a Line | m = (y₂ - y₁) / (x₂ - x₁) | Rise over run between points (x₁, y₁) and (x₂, y₂). |
| Direct Variation | y = kx | k = y / x | Constant of variation k (line passes through 0, 0). |
Quadratic & Exponential Functions (TEKS A.6A, A.7A, A.8A, A.9C)
Standard forms, vertex models, quadratic formula, and growth/decay functions.
| Function Type | Formula / Equation | Explanation & Notes |
|---|---|---|
| Quadratic Functions | f(x) = ax² + bx + c | Standard form; c is the y-intercept; a ≠ 0 determines concavity. |
| f(x) = a(x - h)² + k | Vertex form; (h, k) represents the parabola vertex coordinate. | |
| x = (-b ± √(b² - 4ac)) / (2a) | Quadratic formula to calculate roots/zeros when ax² + bx + c = 0. | |
| x = -b / (2a) | Axis of symmetry vertical line through parabola vertex. | |
| Exponential Functions | f(x) = abˣ | a is initial value (y-intercept at x = 0); b is growth/decay factor (b > 0, b ≠ 1). |
| A(t) = a(1 ± r)ᵗ | Exponential growth (+) or decay (-) where r is percent rate as a decimal. |
Properties of Exponents & Sequence Formulas (TEKS A.11B, A.12D)
Official algebraic exponent laws and arithmetic/geometric sequence equations.
Properties of Exponents
- Product of Powers: aᵐ · aⁿ = aᵐ⁺ⁿ
- Quotient of Powers: aᵐ / aⁿ = aᵐ⁻ⁿ
- Power of a Power: (aᵐ)ⁿ = aᵐⁿ
- Power of a Product: (ab)ⁿ = aⁿbⁿ
- Rational Exponents: aᵐ/ⁿ = ⁿ√(aᵐ)
- Negative Exponent: a⁻ⁿ = 1 / aⁿ
- Zero Exponent: a⁰ = 1 (a ≠ 0)
Sequence Formulas (nth term)
aₙ = a₁ + (n - 1)d
Where a₁ is first term, d is common difference, and n is term position.
aₙ = a₁ · rⁿ⁻¹
Where a₁ is first term, r is common ratio, and n is term position.
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Algebra 1 STAAR Reference Sheet FAQs
Common questions about using the Texas Algebra 1 formula chart, calculator guidelines, and quadratic equations.
What equations are included on the official Algebra 1 STAAR formula chart?
The official Texas Algebra 1 EOC Mathematics Reference Materials chart provides formulas for Linear Forms (slope-intercept y = mx + b, point-slope y - y₁ = m(x - x₁), standard form Ax + By = C, slope m = (y₂ - y₁) / (x₂ - x₁)), Quadratic Functions (standard form ax² + bx + c, vertex form a(x - h)² + k, quadratic formula x = (-b ± √(b² - 4ac)) / (2a), axis of symmetry x = -b / (2a)), Exponential Functions (f(x) = abˣ), and complete Properties of Exponents.
Are sequence formulas included on the Algebra 1 reference sheet?
Yes. The chart includes the nth term formula for an arithmetic sequence: aₙ = a₁ + (n - 1)d (where d is common difference), and the nth term formula for a geometric sequence: aₙ = a₁ · rⁿ⁻¹ (where r is common ratio).
Is a graphing calculator required on the Algebra 1 STAAR EOC exam?
Yes! State testing policy requires that every student participating in the Texas Algebra 1 End-of-Course (EOC) assessment must have continuous access to a graphing calculator (such as TI-84 Plus, TI-Nspire CX, or the embedded digital Desmos calculator).
How do students use the quadratic formula from the chart to find zeros?
When given a quadratic equation in standard form ax² + bx + c = 0, students identify coefficients a, b, and c, and substitute them into x = (-b ± √(b² - 4ac)) / (2a). The discriminant b² - 4ac determines whether the equation has two real solutions, one real solution, or two complex solutions.