Podcast
Questions and Answers
What is the formula for circumference?
What is the formula for circumference?
- C = πd (correct)
- C = πr^2
- C = 4s
- C = 2πr
What is the area of a circle formula?
What is the area of a circle formula?
- A = lw
- A = 1/2 bh
- A = πr^2 (correct)
- A = 4s
What is the longest side of a right triangle called?
What is the longest side of a right triangle called?
hypotenuse
What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
What is the formula for the perimeter of a square?
What is the formula for the perimeter of a square?
What is the formula for the perimeter of a rectangle?
What is the formula for the perimeter of a rectangle?
What is the area of a triangle formula?
What is the area of a triangle formula?
What does 'SA' represent in surface area formulas?
What does 'SA' represent in surface area formulas?
What is the formula for the volume of a cylinder?
What is the formula for the volume of a cylinder?
What is the formula for calculating mean?
What is the formula for calculating mean?
What is the median?
What is the median?
How is the range calculated?
How is the range calculated?
What is the symbol for squared?
What is the symbol for squared?
What is the formula for simple interest?
What is the formula for simple interest?
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Study Notes
Geometric Formulas
- Circumference of a circle: C = πd
- Area of a circle: A = πr²
- Hypotenuse: Longest side of a right triangle
- Pythagorean Theorem: a² + b² = c²
- Perimeter of a square: P = 4s
- Perimeter of a rectangle: P = 2l + 2w
- Perimeter of a triangle: P = a + b + c
- Area of a square: A = s²
- Area of a rectangle: A = lw
- Area of a parallelogram: A = bw
- Area of a triangle: A = ½bh
- Area of a trapezoid: A = ½h(b₁ + b₂)
Surface Area Formulas
- Surface area of a rectangular/right prism: SA = ph + 2B
- Surface area of a cylinder: SA = 2πrh + 2πr²
- Surface area of a pyramid: SA = ½ps + B
- Surface area of a cone: SA = πrs + πr²
- Surface area of a sphere: SA = 4πr²
Volume Formulas
- Volume of a rectangular/right prism: V = Bh
- Volume of a cylinder: V = πr²h
- Volume of a pyramid: V = ⅓Bh
- Volume of a cone: V = ⅓πr²h
- Volume of a sphere: V = ⅔πr³
Financial and Statistical Concepts
- Simple interest formula: I = Prt
- Distance formula: d = rt (where r = rate, t = time)
- Total cost calculation: Total Cost = (number of units) x (price per unit)
- Mean (average): Total of values divided by the number of values
- Median: Middle value in a sorted data set or average of two middle values
- Mode: Most frequently occurring number in a data set
- Range: Difference between the largest and smallest numbers
Calculating Statistical Values
- Calculating Mean: Sum all numbers and divide by count
- Calculating Mode: List numbers in order and identify the most frequent
- Calculating Median: Sort numbers, find middle value, and average two middle values if applicable
- Calculating Range: Subtract smallest number from largest
Specific Examples
- Range of the numbers 2, 4, 6, 8, 12, 16 is 14
- Mode of the numbers 7, 12, 1, 5, 7, 8 is 7
- Median of the numbers 7, 12, 1, 5, 7, 8 is 7.5
- Mean of the numbers 5, 8, 17, 20, 0 is 10
Linear Equations
- Slope of a line: Change in y / Change in x
- Slope-intercept form: y = mx + b (m is slope, b is y-intercept)
- Point-slope form: y - y₁ = m(x - x₁)
- Standard form of an equation: y = ax² + bx + c
- Quadratic formula utilized for solving quadratic equations (not provided in the initial text)
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