Questions and Answers
What does 'xy' represent?
What does 'x ≤ y' mean?
Is less than or equal to
What does 'x ≥ y' mean?
Is greater than or equal to
What is the formula for solving indirect measurement?
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What makes two figures similar?
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How would I find out if two ratios are proportional?
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How would I solve a monomial problem like (3x²)(4x⁵)?
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If you see (5xy⁵), what exponent would you use on x?
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How would I solve a monomial problem like 15m⁵/3m²?
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How would I solve a monomial problem like (2a²b⁶)⁴?
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Make a proportion for '20 is 50% of what number?'
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Make a proportion for 'What is 50% of 40?'
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Make a proportion for '20 is what percent of 40?'
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What is the formula for finding the percent of change?
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What is the formula for finding simple interest?
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What order do the quadrants go in from left to right?
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What would a positive quadratic function look like on a graph?
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What is the formula for slope?
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What is the formula for circumference?
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What is the formula for area of a circle?
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What is the formula for the Pythagorean theorem?
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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 trapezoid?
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What is the formula for surface area of a rectangular prism?
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What is the formula for volume of a rectangular prism?
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What is the formula for volume of a cube?
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What is the formula for surface area of a cube?
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What is the formula for surface area of a cylinder?
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Study Notes
Inequalities and Symbols
- xy: Represents "is greater than."
- x≤y: Means "is less than or equal to," including y on the number line.
- x≥y: Means "is greater than or equal to," including y on the number line.
Indirect Measurement
- Formula: x/y = x/y.
- Visualize as a larger object casting a shadow, correlating height and shadow length for both smaller and larger objects.
Similar Figures
- Two figures are similar if the lengths of corresponding sides are proportional and corresponding angles are equal.
Proportional Ratios
- To determine if two ratios are proportional:
- Simplifying: Reduce both fractions to their simplest form.
- Cross Products: Multiply across the equals sign; if products are equal, ratios are proportional.
Monomials Operations
- Multiplication: For (3x²)(4x⁵), combine coefficients (3 and 4), multiply them, and add exponents (x² and x⁵).
- Exponent on x in (5xy⁵): x has an exponent of 1 (x¹).
- Division: For 15m⁵/3m², divide coefficients (15 by 3) and subtract exponents (m⁵ - m²).
- Exponentiation: In (2a²b⁶)⁴, apply distributive property for each factor.
Proportions and Percent Problems
- Proportion for "20 is 50% of what number":
- 20/50 = x/100.
- Proportion for "what is 50% of 40":
- x/50 = 40/100.
- Proportion for "20 is what percent of 40":
- 20/x = 40/100.
Percent Change and Simple Interest
- Formula for Percent Change: amount of change / original amount.
- Formula for Simple Interest (I): I = p × r × t, where p is principal, r is the interest rate, and t is time in years.
Quadrants and Graphs
- Quadrants are labeled II, I, III, IV from left to right.
- A positive quadratic function on a graph resembles a "smiley face."
Geometry Formulas
- Slope: slope = rise/run or change in y/change in x.
- Circumference of a circle: circumference = π × diameter.
- Area of a circle: area = π × r².
- Pythagorean theorem: a² + b² = c².
- Area of a triangle: area = ½ × base × height.
- Area of a trapezoid: area = (b1 + b2) × height × ½.
- Surface area of a rectangular prism: SA = 2(width × length + width × height + length × height).
- Volume of a rectangular prism: V = area of base × height.
- Volume of a cube: V = s³ (s = side length).
- Surface area of a cube: SA = 6s².
- Surface area of a cylinder: SA = 2πr² + 2πrh.
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