Questions and Answers
What is the formula for the perimeter of a square?
What is the formula for the perimeter of a rectangle?
What is the circumference of a circle?
What is the formula for the area of a square?
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What is the area formula for a rectangle?
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What is the formula for the area of a triangle?
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What is the formula for the area of a circle?
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What is the surface area formula for a rectangular prism?
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What is the volume of a cube?
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What is the slope formula?
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What is the slope-intercept form of a linear equation?
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What is the quadratic formula?
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What is the formula for simple interest?
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What is the distance formula?
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Study Notes
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.
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Test your knowledge of essential math formulas with these flashcards. Learn the perimeter and area formulas for various shapes including squares, rectangles, circles, and parallelograms. Perfect for students looking to reinforce their understanding of basic geometry.
