Questions and Answers
Write an algebraic expression for six more than a number.
6 + n or n + 6
Write an algebraic expression for twelve less than the product of three and a number.
3n - 12
Write an algebraic expression for four divided by the difference between a number and seven.
4/(n - 7)
Evaluate: 32 ÷ 4 + 2³ - 3.
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Evaluate: (2 × 4)²/7 + 3².
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Find the value of the expression a² + 2ab + b² if a = 6 and b = 4. A. 68, B. 92, C. 100, D. 121
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Evaluate: 13 + (16 - 4²).
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Evaluate: 2/9[9 ÷ (7 - 5)].
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Evaluate: 37 + 29 + 13 + 21.
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Write the equivalent expression for 4(x + 3).
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Simplify the expression (5p - 2)(-3).
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Write and evaluate an expression for the total typical number of tickets sold by three locations in four weeks.
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Solve for x in the equation 3x - 9 = 12.
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Solve for y in the equation y² - 5y - 11 = 13.
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Write an equation to find C, the total monthly cost for m minutes given the plan includes a flat fee of $29 and $0.12 per minute.
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Determine the outputs as ordered pairs from the given set: X: -2, 1, 3, 4, Y: 4, 2, 0, -2.
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Express the relation shown in each table, mapping, or graph as a set of ordered pairs for Domain: -3, -1, 1, 3 and Range: -2, 0, 2, 4.
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Determine the domain and range for the relation {(2, 5), (-1, 3), (0, -1), (3, 3), (-4, -2)}. A. F - D: {2, -1, 0, 3, -4}, R: {5, 3, -1, 3, -2} B. G - D: {5, 3, -1, 3, -2}, R: {2, -1, 0, 3, 4} C. H - D: {0, 1, 2, 3, 4}, R: {-4, -3, -2, -1, 0} D. J - D: {2, -1, 0, 3, -4}, R: {2, -1, 0, 3, 4}
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Determine whether the relation {(2, 3), (-1, 3), (0, 4), (3, 2), (-2, 3)} is a function.
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If f(x) = 5 − 2x, find g(3) given g(x) = x² + 7x.
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If f(x) = 5 − 2x, find f(-6y).
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Identify if the function graphed is linear or nonlinear.
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Study Notes
Algebraic Expressions
- Six more than a number is represented as 6 + n or n + 6.
- Twelve less than the product of three and a number is 3n - 12.
- Four divided by the difference between a number and seven is expressed as 4/(n - 7).
Evaluating Expressions
- Evaluating 32 ÷ 4 + 2³ - 3 results in 13.
- For (2 × 4)²/7 + 3², the evaluation yields 4.
- To find a² + 2ab + b² given a = 6 and b = 4, the value is 100.
More Evaluations
- Evaluating 13 + (16 - 4²) simplifies to 13.
- 2/9[9 ÷ (7 - 5)] evaluates to 1.
- Summing 37 + 29 + 13 + 21 results in 100.
Simplifying Expressions
- Distributing 4(x + 3) leads to 4x + 12.
- The expression (5p - 2)(-3) simplifies to -15p + 6.
Real-Life Applications
- The total number of movie tickets sold in four weeks across three theaters is 5296 tickets.
- The total monthly cost C for a cell phone plan with a flat fee of $29 plus $0.12 per minute is calculated as C = 29 + 0.12m. For m = 50, C = 35.
Relations and Functions
- The set of ordered pairs for the relation X: {-2, 1, 3, 4} and Y: {4, 2, 0, -2} is {(-2, 4), (1, -2), (3, 0), (4, -2)}.
- Another set of ordered pairs from Domain: {-3, -1, 1, 3} and Range: {-2, 0, 2, 4} includes {(-3, 2), (-3, 4), (-1, 0), (1, -2), (3, 0)}.
Domain and Range
- For the relation {(2, 5), (-1, 3), (0, -1), (3, 3), (-4, -2)}, the correct domain and range is D: {2, -1, 0, 3, -4} and R: {5, 3, -1, 3, -2}.
Function Determination
- The relation {(2, 3), (-1, 3), (0, 4), (3, 2), (-2, 3)} qualifies as a function since every input corresponds to exactly one output.
Function Values
- For the functions f(x) = 5 - 2x and g(x) = x² + 7x, g(3) evaluates to 30, while f(-6y) results in 5 + 12y.
Graph Analysis
- The graphed function is nonlinear; it has no intercepts other than the origin, is positive for all x, and is increasing. There are no relative extrema, and its end behavior shows that as x increases, y increases, indicating a slower growth rate as time progresses.
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Description
Test your skills with this practice test for 8th grade Algebra Chapter 1. The flashcards cover translating verbal expressions into algebraic expressions, helping you understand key concepts and improve problem-solving techniques. Challenge yourself with a variety of examples to enhance your learning.
