Questions and Answers
What is the result of simplifying -8 × 7 − (16 - 8)^2?
-120
Evaluate 7a + b if a = 2 and b = -6.
8
What is the range of f(x) = 3x if the domain is {-1, 0, 1}?
{-3, 0, 3}
Evaluate f(x) = -4x + 5 if x = -3.
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Simplify 7x^2 + 5x + 4x.
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Simplify 7(2x + y) + 6(x + 5y).
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Evaluate |26 - r| + 7 if r = 9.
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Simplify 6x(-4y).
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Simplify (17 + 15) / 8.
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Solve -3/4 y = 8/20.
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Solve 8(x - 5) = 12(4x - 1) + 12.
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A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot?
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If f(x) = 7 - 2x, find f(3) + 6.
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Chaps is beginning an exercise program that calls for 30 push-ups each day for the first week. Each week thereafter, she has to increase her push-ups by 2. Which week will be the first one in which she will do 50 push-ups a day?
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A line with a slope of -1 passes through points at (2, 3) and (5, y). Find the value of y.
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How many solutions exist for the system of equations 2x - 3y = 14 and 4x - 6y = 21?
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When solving the following system, what is x? 5x - 12y = 6 and 7x + y = 3.
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If 4x + 5y = 6 and 7x + 5y = 3, what is the value of y?
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Use substitution to solve the system of equations y = -2x and 5x + 3y = 4. What is the solution?
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Use elimination to solve the system of equations x + 3y = -6 and 2x + 3y = -9. What is the solution?
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If 4 + 7 + 6 = 4 + 7 + 6 + n, what is the value of n?
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Solve for x. 4(x + 6) = 3(x + 14).
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Find the slope of the line y = -2/3 x + 8.
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Solve |-2x + 6| = 7.
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Study Notes
Simplification and Evaluation Concepts
- Simplify expressions using basic algebraic operations, e.g., -8 × 7 − (16 - 8)² results in -120.
- Evaluate expressions at given variable assignments, e.g., 7a + b where a=2 and b=-6 results in 8.
- Understand and find the range of a function given its domain, e.g., f(x) = 3x for domain {-1, 0, 1} leads to range {-3, 0, 3}.
Function Evaluation and Algebraic Manipulations
- Calculate function values by substituting inputs, e.g., f(x) = -4x + 5 at x=-3 results in 17.
- Combine like terms in polynomial expressions, e.g., 7x² + 5x + 4x simplifies to 7x² + 9x.
- Apply distributive property for simplification, e.g., 7(2x + y) + 6(x + 5y) simplifies to 20x + 37y.
Absolute Values and Reductions
- Compute absolute values, as in |26 - r| + 7 with r=9 results in 24.
- Simplify algebraic expressions with multiplication, e.g., 6x(-4y) results in -24xy.
- Simplify fractions and basic arithmetic, e.g., (17 + 15) / 8 simplifies to 4.
Solving Equations
- Solve linear equations for one variable, e.g., -3/4y = 8/20 results in y = -8/15.
- Find solutions to equations by isolating terms, e.g., 8(x - 5) = 12(4x - 1) + 12 leads to x = -1.
- Calculate percent increases in real-world contexts, e.g., a dealership increasing 180 cars by 25% results in 225 cars.
Function Application in Sequences
- Evaluate piecewise functions at given points, e.g., with f(x)=7-2x, finding f(3)+6 results in 7.
- Analyze sequences of push-ups with increasing daily goals, determining that the first week to do 50 push-ups is week 11.
Geometry and Solving Systems of Equations
- Evaluate solutions to linear systems, identifying y for points (2, 3) and (5, y) with slope -1, results in y=0.
- Determine the existence of solutions in equations, understanding when a system yields no solutions, e.g., two equations resulting in a contradiction yields 0 solutions.
- Utilize substitution and elimination methods to solve systems of equations, such as (5x + 3y = 4 and y = -2x) leading to the solution (-4, 8).
Characteristics of Lines
- Determine slopes from equations, e.g., slope of y = -2/3x + 8 is -2/3.
- Solve absolute value equations to find multiple solutions, as | -2x + 6 | = 7 leads to solutions {-1/2, 13/2}.
Studying That Suits You
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Prepare for your Honors Algebra 1 final exam with these flashcards that cover key concepts. Each card provides a problem to solve or a concept to simplify, ensuring you have a thorough understanding of the material. Test your knowledge and improve your skills before the exam.
