Basic Math Formulas Flashcards

Geometry Formulas

• Perimeter of a Square: P = 4s, where s is the length of a side.
• Perimeter of a Rectangle: P = 2l + 2w, where l is length and w is width.
• Circumference of a Circle: C = 2πr or C = πd, where r is radius and d is diameter.
• Area of a Square: A = s², where s is the length of a side.
• Area of a Rectangle: A = lw, where l is length and w is width.
• Area of a Parallelogram: A = bh, where b is base length and h is height.
• Area of a Triangle: A = ½bh, where b is base and h is height.
• Area of a Trapezoid: A = ½(b₁ + b₂)h, where b₁ and b₂ are the lengths of the bases and h is height.
• Area of a Circle: A = πr², where r is radius.

Surface Area and Volume Formulas

• Surface Area of a Rectangular Prism: SA = 2lw + 2wh + 2lh.
• Surface Area of a Prism: SA = ph + 2B, where p is perimeter of the base and B is area of the base.
• Surface Area of a Cylinder: SA = 2πr² + 2πrh.
• Surface Area of a Pyramid: SA = B + ½pl, where B is base area and l is slant height.
• Surface Area of a Cone: SA = πrl + πr², where r is radius and l is slant height.
• Surface Area of a Sphere: SA = 4πr², where r is radius.
• Volume of a Cube: V = s³, where s is the length of a side.
• Volume of a Prism: V = Bh, where B is the area of the base and h is height.
• Volume of a Pyramid: V = ⅓Bh.
• Volume of a Cone: V = ⅓πr²h.
• Volume of a Sphere: V = (4/3)πr³.

Algebraic Formulas

• Slope Formula: m = (y₂ - y₁) / (x₂ - x₁).
• Slope-Intercept Form: y = mx + b, with m as slope and b as y-intercept.
• Point-Slope Form: y - y₁ = m(x - x₁), where (x₁, y₁) is a specific point on the line.
• Standard Form (Linear Equations): Ax + By = C, where A and B are not both zero and A is not negative.
• Standard Form (Quadratic Equations): ax² + bx + c = 0.
• Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a).
• Standard Form (Quadratic Functions): y = ax² + bx + c.
• Intercept Form (Quadratic Functions): y = a(x - p)(x - q), where p and q are x-intercepts.
• Vertex Form (Quadratic Functions): y = a(x - h)² + k.

Sequences and Interest Formulas

• Arithmetic Sequence Definition: Each term increases by a constant value called the common difference.
• Arithmetic Sequence Formula: a₁ + (n - 1)d.
• Geometric Sequence Definition: Defined recursively as Aₙ = A(n-1) * r, where r is the common ratio.
• Simple Interest Formula: I = Prt, where I is interest, P is principal, r is rate, and t is time.
• Compound Interest Formula: A = P(1 + r/n)^(n*t), where n is the number of compounding periods.

Coordinate Geometry

• Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²], used to calculate distance between two points.
• Midpoint Formula: ((x₁ + x₂) / 2, (y₁ + y₂) / 2), finds the midpoint between two points.
• Distance Traveled Formula: d = rt, where r is rate and t is time.

Temperature Conversion

• Temperature Conversion Formula: C = 5/9 (F - 32), to convert Fahrenheit to Celsius.