Questions and Answers
What is the additive inverse of -5?
What is the multiplicative inverse of 2/3?
The associative property involves changing the order of addition or multiplication.
False
What are rational numbers?
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What is the output for x when the fraction 6/x is undefined?
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What is the value of x that makes the fraction x/x + 2 undefined?
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What are the values of x that make the fraction (x² - 9)/(x² + 7x + 10) undefined?
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What is the area formula for a triangle?
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What is the formula for the area of a rectangle?
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What is the formula for the area of a square?
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What is the circumference formula?
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If the diameter of a circle is 22, what is the approximate circumference?
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How is the area of a trapezoid calculated?
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What is the intersection of sets A = {1,3,5,7,9} and B = {1,2,3,4,5,6}?
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What is the union of sets E = {1,3,5,7,9} and F = {2,4,6,8}?
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What represents the complement of set A = {6,7}?
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What represents the complement of set B = {3,5,7}?
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The ___ of two (or more) sets consists of all elements in both sets with no common elements listed more than once.
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The ___ of two (or more) sets consists of the elements the sets have the same values.
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Study Notes
Key Algebra Concepts and Definitions
- Additive Inverse: The opposite of a number; e.g., -a/2 becomes a/2, and -5 becomes 5.
- Multiplicative Inverse: The reciprocal of a number; e.g., 5 becomes 1/5, and 2/3 becomes 3/2.
- Associative Property: Changes grouping of numbers; e.g., A(BC) changes to B(AC).
- Commutative Property: Changes order of numbers; e.g., a + b = b + a and ab = ba.
- Rational Numbers: Any number that can be expressed as a fraction.
- Rational Expression: An algebraic fraction with polynomial numerator and denominator, where the denominator cannot be zero.
Fraction and Expression Evaluations
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Fraction Undefined Conditions:
- 6/x is undefined when x = 0.
- x/(x+2) is undefined when x = -2.
- (x² - 9)/(x² + 7x + 10) is undefined for x = -2 and x = -5.
Simplifying Rational Expressions
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Steps to Simplify:
- Factor both numerator and denominator.
- Simplify the factors.
- Eliminate common factors between numerator and denominator.
- Example: 42/63 simplifies to 2/3.
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Example Simplifications:
- 56x²y/70x³y² simplifies to 4/5xy.
- (x² - 2x - 15)/(x² - x - 12) simplifies to (x - 5)/(x - 4).
- Multiplication and division can also be simplified similarly.
Set Theory Concepts
- Intersection of Sets: Elements common to multiple sets, denoted by ∩; e.g., A ∩ B = {1, 3, 5} for A = {1, 3, 5, 7, 9} and B = {1, 2, 3, 4, 5, 6}.
- Union of Sets: All elements from both sets without duplicates, denoted by ∪; e.g., E ∪ F = {1, 2, 3, 4, 5, 6, 7, 8, 9} for E = {1, 3, 5, 7, 9} and F = {2, 4, 6, 8}.
Complement and Set Operations
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Complement: The elements not in a specified set; e.g.:
- Complement of A = {1, 2, 3, 4, 5} for A = {6, 7}.
- Complement of B = {1, 2, 4, 6} for B = {3, 5, 7}.
- Complement of A ∩ Complement of B = {1, 2, 4}.
Geometry Formulas
- Circumference: Distance around a circle; C = 2πr or C = πd.
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Area Formulas:
- Triangle: A = (1/2)bh.
- Rectangle: A = bh.
- Square: A = s².
- Trapezoid: A = 1/2(b₁ + b₂)h, e.g., A = 806 for bases 20 and 42, height 26.
Perimeter and Shape Evaluations
- Perimeter of Equilateral Triangle: For side length represented by x + 5, perimeter is 3(x + 5) = 3x + 15.
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Perimeter of Rectangle: Length (x) is less than width (x - 3) can be solved for given perimeter conditions, resulting in:
- Length = 34 yards, Width = 31 yards.
Advanced Circle Calculations
- Circumference Calculation Example: For a circle with a diameter of 22, C ≈ 69.12 rounded to nearest hundredth.
- Area of Shaded Region: Found by determining the total area and subtracting the area of unshaded portions.
Mathematical Approaches
- Finding Areas of Different Shapes: The shaded region can be calculated by subtracting the unshaded area from the total area.
Studying That Suits You
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Description
Prepare for the Algebra 1 Regents exam with these flashcards covering key concepts. Each card provides a definition and examples of important terms, such as Additive Inverse and Multiplicative Inverse, to help reinforce your understanding. Utilize these flashcards for quick review and effective study.
