The Ultimate TASC Math Formula Cheat Sheet

Preparing for the TASC (Test Assessing Secondary Completion) Math test can be challenging, but having a comprehensive formula cheat sheet can make the process much easier. This guide covers essential formulas you need to know for the TASC Math test, organized by topic to help you quickly find what you need.

TASC Math Formula Cheat Sheet

The TASC Math test assesses your knowledge and skills in various mathematical areas, including algebra, geometry, and data analysis. Mastering these formulas is crucial for solving problems efficiently and accurately. Use this cheat sheet to review and memorize key formulas before test day.

Algebra

Basic Algebraic Operations

• Addition and Subtraction of Like Terms:
  $a + a = 2a$ 

  $a – a = 0$ 

  
  

• Multiplication of Like Terms:
  $a \cdot a = a^2$ 
• Distributive Property:
  $a(b + c) = ab + ac$ 

  
  

Linear Equations

• Slope-Intercept Form:
  $y = mx + b$ 

  $m$ 

  is the slope, and $b$ 

  is the y-intercept.

• Standard Form:
  $Ax + By = C$ 

  
  

• Slope Formula:
  $m = \frac{y_2 – y_1}{x_2 – x_1}$ 

  ​​

• Point-Slope Form:
  $y – y_1 = m(x – x_1)$ 

  
  

Quadratic Equations

• Standard Form:
  $ax^2 + bx + c = 0$ 

  
  

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

  ​​

• Factoring:
  $ax^2 + bx + c = (px + q)(rx + s)$ 

  
  

Geometry

Perimeter and Area

• Rectangle:
  Perimeter: $P = 2(l + w)$ 

  Area: $A = lw$ 

  where $l$ 

  is the length and $w$ 

  is the width.

• Square:
  Perimeter: $P = 4s$ 

  Area: $A = s^2$ 

  where $s$ 

  is the side length.

• Triangle:
  Perimeter: $P = a + b + c$ 

  Area: $A = \frac{1}{2}bh$ 

  where $b$ 

  is the base and $h$ 

  is the height.

• Circle:
  Circumference: $C = 2\pi r$ 

  Area: $A = \pi r^2$ 

  where $r$ 

  is the radius.

Volume

• Rectangular Prism:
  $V = lwh$ 

  where $l$ 

  is the length, $w$ 

  is the width, and $h$ 

  is the height.

• Cube:
  $V = s^3$ 

  where $s$ 

  $s$ is the side length.

• Cylinder:
  $V = \pi r^2 h$ 

  where $r$ 

  is the radius and $h$ 

  is the height.

• Sphere:
  $V = \frac{4}{3} \pi r^3$ 

  where $r$ 

  is the radius.

Surface Area

• Rectangular Prism:
  $SA = 2lw + 2lh + 2wh$ 

  
  

• Cube:
  $SA = 6s^2$ 

  
  

• Cylinder:
  $SA = 2\pi r^2 + 2\pi rh$ 

  
  

• Sphere:
  $SA = 4\pi r^2$ 

  
  

Data Analysis and Probability

Statistics

• Mean (Average):
  $\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}$ 

  ​

• Median:
  The middle value is when the data set is ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.
• Mode:
  The value that appears most frequently in the data set.

Probability

• Probability of an Event:
  $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ 

  ​

• Addition Rule (Mutually Exclusive Events):
  $P(A \text{ or } B) = P(A) + P(B)$ 

  
  

• Multiplication Rule (Independent Events):
  $P(A \text{ and } B) = P(A) \times P(B)$ 

  
  

Trigonometry

Basic Trigonometric Ratios

• Sine:
  $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ 

  ​

• Cosine:
  $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ 

  ​

• Tangent:
  $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 

  ​

Pythagorean Theorem

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

  where $a$ 

  $a$ and $b$ 

  $b$ are the legs of a right triangle, and $c$ 

  $c$ is the hypotenuse.

Conversion Formulas

Metric System

• Length:
  $1 \text{ kilometer (km)} = 1000 \text{ meters (m)}$ 

  $1 \text{ meter (m)} = 100 \text{ centimeters (cm)}$ 

• Mass:
  $1 \text{ kilogram (kg)} = 1000 \text{ grams (g)}$ 

  $1 \text{ gram (g)} = 1000 \text{ milligrams (mg)}$ 

• Volume:
  $1 \text{ liter (L)} = 1000 \text{ milliliters (mL)}$ 

  
  

Imperial System

• Length:
  $1 \text{ mile (mi)} = 5280 \text{ feet (ft)}$ 

  $1 \text{ foot (ft)} = 12 \text{ inches (in)}$ 

  
  

• Mass:
  $1 \text{ pound (lb)} = 16 \text{ ounces (oz)}$ 

  
  

• Volume:
  $1 \text{ gallon (gal)} = 4 \text{ quarts (qt)}$ 

  $1 \text{ quart (qt)} = 2 \text{ pints (pt)}$ 

  $1 \text{ pint (pt)} = 2 \text{ cups (c)}$ 

  $1$

Temperature Conversion

• Celsius to Fahrenheit:
  $F = \frac{9}{5}C + 32$ 

  
  

• Fahrenheit to Celsius:
  $C = \frac{5}{9}(F – 32)$