formulas

 

Foundational Formulas Across College Prep

1. College Algebra / Pre-Calculus

• Quadratic Formula: $x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}$

• Discriminant: $D = b^2 - 4ac$ (determines root types)

• Polynomial Identities: $(a+b)^2 = a^2 + 2ab + b^2$, $(a-b)^2$, $a^2 - b^2$, etc.

• Exponential/Logarithmic Basics & Properties for simplifying expressions.

These are the algebraic fundamentals that act as building blocks for calculus, statistics, and quantitative reasoning. CollegeVine+4The Princeton Review+4Reddit+4

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2. ACT / Entry-Level Math

• Sequence formulas:

  • Arithmetic: $a_n = a_1 + (n - 1)d$

  • Geometric: $a_n = a_1 \cdot r^{(n-1)}$

• Coordinate Geometry: slope $\frac{y_2 - y_1}{x_2 - x_1}$, midpoint, distance

• Algebra shortcuts: FOIL, variation formulas, sum/product of roots, etc. CollegeVine

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3. Chemistry & Physical Sciences

• Gas Laws: Ideal Gas $PV = nRT$, Boyle’s Law, Charles’s Law

• Solution Chemistry: Molarity M = \frac{\text{moles}}\text{volume}, Dilution $M_i V_i = M_f V_f$

• Reaction Metrics: Percent yield, percent composition, basic thermochemical equations
  Wikipedia+11Eastern Connecticut State University+11CollegeVine+11

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4. Physics Basics (Mechanics & Energy)

• Newton’s Laws: $F = ma$

• Energy Formulas: $KE = \frac{1}{2}mv^2$, $PE = mgh$, Total $E = KE + PE$

• Motion: $v = v_0 + at$, $d = v_0 t + \frac{1}{2}at^2$

• Gravity: $F = \frac{G m_1 m_2}{r^2}$, Relativity: $E = mc^2$
  Learner+2Reddit+2UWorld Grad School

📘 Core Formula Families for College Entry

1. Algebra / Functions

• Quadratic formula:
  $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Slope of a line:
  $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Point-slope & slope-intercept form:
  $y - y_1 = m(x - x_1), \quad y = mx + b$

• Distance formula:
  $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• Midpoint:
  $\Big(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\Big)$

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2. Geometry

• Area of a triangle: $A = \tfrac{1}{2}bh$

• Area of a circle: $A = \pi r^2$

• Circumference of a circle: $C = 2\pi r$

• Pythagorean theorem: $a^2 + b^2 = c^2$

• Surface area & volume:

  • Cube: $V = s^3$

  • Rect prism: $V = lwh$

  • Cylinder: $V = \pi r^2 h$

  • Sphere: $V = \tfrac{4}{3}\pi r^3$

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3. Trigonometry (entry-level)

• SOHCAHTOA ratios

• Special triangles (30-60-90, 45-45-90) side relationships

• Radians to degrees: $\pi \text{ rad} = 180^\circ$

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4. Statistics / Probability

• Mean: $\bar{x} = \frac{\text{sum of values}}{n}$

• Probability: $P = \frac{\text{favorable outcomes}}{\text{total outcomes}}$

• Permutations/Combinations basics

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5. Physics (the few entry must-knows)

• Speed: $v = \frac{d}{t}$

• Force: $F = ma$

• Work: $W = Fd$

• Potential energy: $PE = mgh$

• Kinetic energy: $KE = \tfrac{1}{2}mv^2$

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6. Chemistry (baseline)

• Density: $\rho = \frac{m}{V}$

• Molarity: $M = \frac{\text{moles}}{\text{liters}}$

• Ideal gas law: $PV = nRT$

• Percent yield: $\frac{\text{actual}}{\text{theoretical}} \times 100\%$

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👉 This “core bank” is what SAT, ACT, and college placement tests actually expect.
Graduate entrance exams (GRE/MCAT/LSAT) build on this, but if you want entry-level college readiness for health, science, or pre-law kids — this is the backbone.