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Questions and Answers
What skill is associated with item number 1?
What skill is associated with item number 1?
Adding and subtracting integers
What skill is associated with item number 23?
What skill is associated with item number 23?
Evaluating expressions
What skill is associated with item number 7?
What skill is associated with item number 7?
Multiplying and dividing integers
What skill is associated with item number 30?
What skill is associated with item number 30?
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What skill is associated with item number 45?
What skill is associated with item number 45?
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What skill is associated with item number 50?
What skill is associated with item number 50?
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What skill is associated with item number 66?
What skill is associated with item number 66?
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What skill is associated with item number 72?
What skill is associated with item number 72?
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What skill is associated with item number 54?
What skill is associated with item number 54?
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What skill is associated with item number 79?
What skill is associated with item number 79?
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What skill is associated with item number 86?
What skill is associated with item number 86?
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What is the result of $-9 + (-15)$?
What is the result of $-9 + (-15)$?
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What is the result of $2 + (-3)$?
What is the result of $2 + (-3)$?
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What is the result of $6 - 9$?
What is the result of $6 - 9$?
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What is the result of $-6 - 11$?
What is the result of $-6 - 11$?
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What is the result of $13 + 8$?
What is the result of $13 + 8$?
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What is the result of $-12 - (-10)$?
What is the result of $-12 - (-10)$?
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What is the result of $2(-7)$?
What is the result of $2(-7)$?
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What is the result of $-8 imes 2$?
What is the result of $-8 imes 2$?
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What is the result of $9 ext{ divided by } 3$?
What is the result of $9 ext{ divided by } 3$?
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What is the result of $25 ext{ divided by } (-5)$?
What is the result of $25 ext{ divided by } (-5)$?
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What is the result of $-30 ext{ divided by } (-6)$?
What is the result of $-30 ext{ divided by } (-6)$?
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What is the result of $-1(-7)$?
What is the result of $-1(-7)$?
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What is the perimeter of a rectangle with a length of 6 feet and a width of 3 feet?
What is the perimeter of a rectangle with a length of 6 feet and a width of 3 feet?
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What is the area of a square with a side length of 9 centimeters?
What is the area of a square with a side length of 9 centimeters?
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What is the result of $-6 + 5$?
What is the result of $-6 + 5$?
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What is the result of $1 - (-3)$?
What is the result of $1 - (-3)$?
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Complete the statement: 3 ____ 7.
Complete the statement: 3 ____ 7.
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Complete the statement: -1 ____ 4.
Complete the statement: -1 ____ 4.
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Complete the statement: -4 ____ -10.
Complete the statement: -4 ____ -10.
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Complete the statement: -6 ____ -3.
Complete the statement: -6 ____ -3.
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What is the value of $2x - 6$ when $x = 9$?
What is the value of $2x - 6$ when $x = 9$?
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What is the value of $-7 + 9x$ when $x = 3$?
What is the value of $-7 + 9x$ when $x = 3$?
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What is the value of $12x + 13$ when $x = 5$?
What is the value of $12x + 13$ when $x = 5$?
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What is the value of $-x - 12$ when $x = 4$?
What is the value of $-x - 12$ when $x = 4$?
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What is the value of $13 - 7x$ when $x = -10$?
What is the value of $13 - 7x$ when $x = -10$?
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What is the value of $11x + 17$ when $x = -6$?
What is the value of $11x + 17$ when $x = -6$?
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Which ordered pair corresponds to point U?
Which ordered pair corresponds to point U?
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Which ordered pair corresponds to point S?
Which ordered pair corresponds to point S?
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Which point is located in Quadrant II?
Which point is located in Quadrant II?
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What is $y$ in the equation $2x - y = 3$?
What is $y$ in the equation $2x - y = 3$?
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What is $y$ in the equation $3x + 2y = -4$?
What is $y$ in the equation $3x + 2y = -4$?
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What is $y$ in the equation $-2x = 6y + 3$?
What is $y$ in the equation $-2x = 6y + 3$?
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What is $y$ in the equation $0 = 7x - y + 12$?
What is $y$ in the equation $0 = 7x - y + 12$?
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What is the GCF of 45 and 9?
What is the GCF of 45 and 9?
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What is the GCF of 64 and 48?
What is the GCF of 64 and 48?
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What is the GCF of 25 and 10?
What is the GCF of 25 and 10?
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What is the GCF of 29 and 12?
What is the GCF of 29 and 12?
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What is the square root of 25?
What is the square root of 25?
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What is the square root of -81?
What is the square root of -81?
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What is the square root of -144?
What is the square root of -144?
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What is the greatest common factor of the sequence 3, 6, 9, 12, ...?
What is the greatest common factor of the sequence 3, 6, 9, 12, ...?
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What is the notation for the nth term in the arithmetic sequence 3, 6, 9, 12,...?
What is the notation for the nth term in the arithmetic sequence 3, 6, 9, 12,...?
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What is the transformation from the graph of $f(x) = x$ to $g(x) = -x - 1$?
What is the transformation from the graph of $f(x) = x$ to $g(x) = -x - 1$?
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Study Notes
Arithmetic Operations
- Addition and subtraction of integers: understanding negative values and their implications.
- Examples:
- (-9 + (-15) = -24)
- (2 + (-3) = -1)
- (6 - 9 = -3)
Multiplication and Division
- Fundamental operations involving integers, especially with negative numbers.
- Examples:
- (2 \times (-7) = -14)
- (-8 \div 2 = -4)
- (9 \div 3 = 3)
Geometry Applications
-
Perimeter of a rectangle:
- Formula: (P = 2(length + width))
- Given dimensions: 6 feet (length), 3 feet (width) results in (P = 2(6 + 3) = 18) feet.
-
Area of a square:
- Formula: (A = side^2)
- Given side length: 9 cm results in (A = 9^2 = 81) cm².
Number Graphing
- Placement of numbers on a coordinate plane, identifying quadrants based on coordinates.
- Example coordinates: A(4, 2), B(-1, 3), C(-5, -3).
Evaluating Expressions
- Substituting values into algebraic expressions to solve for results.
- Examples:
- For (2x - 6) with (x = 9), calculate (2(9) - 6 = 12).
- For (-x - 12) with (x = 4), calculate (-4 - 12 = -16).
Systems of Linear Equations
- Techniques for solving equations through graphing to find points of intersection.
- Graph equations such as (y = 2x + 1) and (y = -1x + 1).
Inequalities
- Understanding and graphing solutions to inequalities like (p + 6 > 9) or (3x - 4 < 2).
- Solutions depicted on a number line, showcasing permissible values.
Greatest Common Factor (GCF)
- Finding GCF of pairs of numbers to simplify fractions or expressions.
- Example: GCF of 45 and 9 is 9.
Transformations of Functions
- Understanding shifts in graph appearances through transformations, e.g., reflection or translation.
- Transformations can be described for functions (f(x) = x) to (g(x) = -x - 1).
Histograms
- Representing data visually using frequency distribution.
- Example: Display time spent on cell phones daily, categorized into intervals such as 0-1 hours, 2-3 hours, etc.
Comparing Real Numbers
- Skills in comparing values using symbols: <, >, or =.
- Example: (3 < 7), (-4 > -10).
Key Skills Summary
- Proficiency in adding, subtracting, multiplying, and dividing integers.
- Evaluating expressions, plotting points, and understanding geometry basics.
- Graphing equations and inequalities to find solutions visually.### Skills Overview
- Emphasizes graphing linear functions as a foundational skill in algebra.
- Order of operations is crucial for simplifying expressions and solving equations.
- Finding square roots is an essential skill for various algebraic operations.
Graphing Linear Functions
- Multiple items focus on graphing linear functions, indicating its importance in understanding linear relationships.
- Repeated emphasis suggests a deep understanding is necessary for success in upcoming concepts.
Order of Operations
- Understanding and applying the order of operations is vital for accurate problem-solving.
- Essential for simplifying complex expressions and evaluating mathematical statements correctly.
Finding Square Roots
- Techniques for finding square roots are highlighted, reflecting their role in solving equations and simplifying expressions.
- Essential for working with quadratic equations and understanding polynomial functions.
Writing Equations for Arithmetic Sequences
- Ability to write equations for arithmetic sequences showcases skills in identifying patterns and trends in data.
- Related to understanding linear functions and their representations.
Simplifying Algebraic Expressions
- Simplifying algebraic expressions is key to solving more complex equations and understanding function behavior.
- Mastery is indicated through repeated focus on various aspects of algebraic simplification.
Evaluating Expressions
- Evaluating expressions is a significant skill, particularly those involving square roots and multiple variables.
- Critical for applying algebraic concepts in real-world scenarios and advanced mathematics.
Factoring Trinomials
- Multiple entries cover factoring perfect square trinomials, emphasizing its importance in polynomial factorization techniques.
- Understanding factorization aids in solving quadratics and simplifying expressions.
System of Linear Equations
- Solving systems of linear equations by graphing is a critical skill for visualizing relationships between equations.
- Mastery aids in solving real-world problems that involve multiple constraints.
Transforming Linear Functions
- Transforming linear functions focuses on understanding how changes to variables affect the overall function.
- Important for exploring advanced topics in functions and their applications.
Data Displaying
- Skills in displaying data enhance the understanding of linear relationships and their visual representations.
- Essential in statistics and interpreting real-life situations through graphs and charts.
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