Questions and Answers
What is the slope-intercept form of a linear equation?
In slope-intercept form, what does 'm' represent?
slope
In slope-intercept form, what does 'b' represent?
y-intercept
What is the formula for direct variation?
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What is the formula to find the slope of a line between two points?
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What is the formula for the circumference of a circle?
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What is the area formula for a triangle?
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What is the area formula for a rectangle or parallelogram?
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What is the area formula for a trapezoid?
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What is the area formula for a circle?
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What is the lateral surface area formula of a prism?
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What is the lateral surface area formula of a cylinder?
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What is the total surface area formula of a prism?
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What is the total surface area formula of a cylinder?
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What is the formula for the volume of a prism?
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What is the formula for the volume of a pyramid?
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What is the formula for the volume of a sphere?
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What is the Pythagorean Theorem?
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What is the formula for simple interest?
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What is the formula for compound interest?
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Study Notes
Slope-Intercept Form
- Equation is expressed as y = mx + b.
- m represents the slope of the line.
- b indicates the y-intercept where the line crosses the y-axis.
Direct Variation
- Represented by the equation y = kx, where k is a constant.
Slope Calculation
- Formula for the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).
Circle Measurements
- Circumference (C) can be calculated using C = 2πr (radius) or C = πd (diameter).
- Area (A) of a circle is given by A = πr².
Triangle and Rectangle Measurements
- Area of a triangle is calculated using A = 1/2 * base (b) * height (h).
- Area of a rectangle or parallelogram is A = base (b) * height (h).
Trapezoid Area
- The area of a trapezoid can be found using A = 1/2 * (b1 + b2) * height (h), where b1 and b2 are the lengths of the two parallel sides.
Prism and Cylinder Surface Areas
- Lateral surface area of a prism is S = Perimeter of base (P) * height (h).
- For a cylinder, lateral surface area is S = 2πr * height (h).
Total Surface Area Calculations
- Total surface area of a prism is S = Ph + 2B, where B is the area of the base.
- Total surface area of a cylinder is S = 2πrh + 2πr².
Volume Calculations
- Volume of a prism is calculated using V = Base area (B) * height (h).
- Volume of a pyramid is V = 1/3 * Base area (B) * height (h).
- Volume of a sphere is given by V = 4/3πr³.
Pythagorean Theorem
- Used to determine the relationship between the sides of a right triangle with the formula a² + b² = c², where c is the hypotenuse.
Interest Calculations
- Simple interest (I) is calculated using I = Principal (P) * rate (r) * time (t).
- Compound interest can be represented by the formula A = P(1 + r)ᵗ, where t is the number of compounding periods.
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Description
This quiz covers essential geometry formulas including slope-intercept form, circle measurements, and area calculations for various shapes such as triangles, rectangles, and trapezoids. Test your knowledge on how to apply these formulas effectively.