Honors Algebra 1 Final Exam Review
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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.

<p>17</p> Signup and view all the answers

Simplify 7x^2 + 5x + 4x.

<p>7x^2 + 9x</p> Signup and view all the answers

Simplify 7(2x + y) + 6(x + 5y).

<p>20x + 37y</p> Signup and view all the answers

Evaluate |26 - r| + 7 if r = 9.

<p>24</p> Signup and view all the answers

Simplify 6x(-4y).

<p>-24xy</p> Signup and view all the answers

Simplify (17 + 15) / 8.

<p>4</p> Signup and view all the answers

Solve -3/4 y = 8/20.

<p>-8/15</p> Signup and view all the answers

Solve 8(x - 5) = 12(4x - 1) + 12.

<p>-1</p> Signup and view all the answers

A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot?

<p>225</p> Signup and view all the answers

If f(x) = 7 - 2x, find f(3) + 6.

<p>7</p> Signup and view all the answers

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?

<p>11</p> Signup and view all the answers

A line with a slope of -1 passes through points at (2, 3) and (5, y). Find the value of y.

<p>0</p> Signup and view all the answers

How many solutions exist for the system of equations 2x - 3y = 14 and 4x - 6y = 21?

<p>0</p> Signup and view all the answers

When solving the following system, what is x? 5x - 12y = 6 and 7x + y = 3.

<p>-30/79</p> Signup and view all the answers

If 4x + 5y = 6 and 7x + 5y = 3, what is the value of y?

<p>2</p> Signup and view all the answers

Use substitution to solve the system of equations y = -2x and 5x + 3y = 4. What is the solution?

<p>(-4, 8)</p> Signup and view all the answers

Use elimination to solve the system of equations x + 3y = -6 and 2x + 3y = -9. What is the solution?

<p>(-3, -1)</p> Signup and view all the answers

If 4 + 7 + 6 = 4 + 7 + 6 + n, what is the value of n?

<p>0</p> Signup and view all the answers

Solve for x. 4(x + 6) = 3(x + 14).

<p>18</p> Signup and view all the answers

Find the slope of the line y = -2/3 x + 8.

<p>-2/3</p> Signup and view all the answers

Solve |-2x + 6| = 7.

<p>{-1/2, 13/2}</p> Signup and view all the answers

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}.

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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.

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