Algebra 1 Final Exam Review
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Questions and Answers

What is the simplified result of $4 - 2$?

  • 2 (correct)
  • 0
  • –8
  • 4

    • If a store owner marks up jeans by 200% and sells them for $36, what was the original price?

  • $18 (correct)
  • $72
  • $12
  • $30

    • The expression $30 × 10^{-1}$ is greater than which of the following?

  • 3
  • 30
  • 0.3 (correct)
  • 0.3 × 10^{1}

    • In the expression $2√x + 3 = 5$, what operation should be done first to isolate $x$?

    <p>Subtract 3 (B)</p> Signup and view all the answers

    What is the degree of the polynomial $3x^{77} + 10x^{33} + 11x + 2$?

    <p>77 (D)</p> Signup and view all the answers

    Identify the arithmetic sequence from the following options.

    <p>8, 10, 13, 17, 22 (C)</p> Signup and view all the answers

    What is the factored form of $x^{2} - 5x - 14$?

    <p>($x + 2)(x - 7) (D)</p> Signup and view all the answers

    What is the GCF of $12x^{3}y$ and $21x^{2}y^{2}$?

    <p>$6xy$ (D)</p> Signup and view all the answers

    What is the result of multiplying $(4x - 5)(3x + 2)$?

    <p>$12x^{2} - 7x - 10$ (D)</p> Signup and view all the answers

    What is the result of simplifying $\sqrt{50} \cdot \sqrt{18} \cdot \frac{1}{30}$?

    <p>$\frac{1}{3}$ (D)</p> Signup and view all the answers

    Which of the following expressions cannot represent the sum of 5 and a number?

    <p>5x (C)</p> Signup and view all the answers

    For the equation $3x^2 + 5x + 2 = 0$, what best describes the solution(s)?

    <p>no real solution (B)</p> Signup and view all the answers

    What are the solutions to the equation $x^2 + 5x - 6 = 0$?

    <p>$x = 2, -3$ (C)</p> Signup and view all the answers

    Solve the inequality $8k + 4k + 2 < -10$. What is the range of k?

    <p>$k &lt; -2$ (C)</p> Signup and view all the answers

    Which statement is true about the equation $x^2 = -100$?

    <p>It has no real solution. (C)</p> Signup and view all the answers

    Solve the equation $-7(2x - 4) + 3(-2x + 5)$ for x. What is the simplified expression?

    <p>$-8x + 43$ (D)</p> Signup and view all the answers

    What are the x- and y-intercepts of the line represented by $3x - 4y = 12$?

    <p>x-int: (4, 0); y-int: (0, 3) (C)</p> Signup and view all the answers

    True or False: For any real number x, $\sqrt{x^2} = x$.

    <p>Only for positive x (A)</p> Signup and view all the answers

    Flashcards

    Simplifying 4 - 2

    The result of subtracting 2 from 4 is 2.

    -31.25 + (-7.621)

    Adding two negative numbers results in a larger negative number.

    Markup of 200%, jeans for $36

    The original price of jeans if the marked-up price is $36 and the markup is 200% is $12.

    Solving 6x = 23

    To solve for x, divide both sides of the equation by 6; This isolates the variable x.

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    Solving x > 2 or x < 3

    x is greater than 2 or x is less than 3.

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    Arithmetic Sequence

    A sequence where each term after the first is found by adding a constant to the previous term.

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    Polynomial Degree 3x^77 +10x^33+11x+2

    The highest power of the variable in the polynomial determines its degree.

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    Factoring x^2-5x-14

    Factoring this quadratic expression results in two binomials that multiply to the expression (x + 2) (x - 7).

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    (2x + 5)(3x + 2)

    Multiplication of the two binomials yields the expression 6x^2 + 19x + 10.

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    GCF of 12x³y and 21x²y²

    The greatest common factor (GCF) of 12x³y and 21x²y² is 3x²y.

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    Simplifying √50 ⋅ √18 ÷ √30

    The process of combining square roots involves simplifying the square roots, then multiplying or dividing them by combining like terms.

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    Convert 2√3 x 3 to radical form

    The given expression, 2√3 x 3, represents multiplying 2, √3 and 3, yielding 6√3.

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    Convert √8y to exponential form

    √8y = (8y) ^ (1/2) = (2^3 * y)^ 1/2 = 2^ (3/2) * y^ (1/2).

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    √x² = x (True or False for all real numbers x)

    This statement is true for all non-negative values of x but only the absolute value is valid for all real values of x. |-2| = 2

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    Solve (2x - 5)² + 16 = 25

    To solve the equation, isolate 'x' by applying algebraic rules. Square root both sides, then isolate x.

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    Solve x² + 5x = 6

    Move all terms to one side, then factor and equate the factors to zero to find the value of x.

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    x² = -100 (real solution)

    There are no real solutions to the equation x² = -100 since the square of any real number is non-negative.

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    Solution to 3x² + 5x + 2 = 0

    The equation has two rational solutions.

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    Solve 8k + 4k + 2 < -10

    Simplify by combining like terms, then isolate k to find the solution with a one-sided inequality.

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    -7(2x - 4) + 3(-2x + 5) simplification

    Distribute the terms then combine like terms.

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    Study Notes

    Algebra 1 Final Exam Review

    • Simplification: Example: 31.25 + (-7.621) = 23.629
    • Equation Solving: Example: 2x + 3 = 5; x = 1
    • Arithmetic Sequences: Identify sequences. Examples are provided but not listed here.
    • Scientific Notation: Example: 0.000081217 = 8.1217 x 10⁻⁵
    • Inequalities: Example: n > 6
    • Factoring: Examples include factoring quadratics and finding GCFs.
    • Radicals: Example: √50 - √18 = √25² - √23² = 5√2 – 3√2 = 2√2
    • Exponents: Example: Convert 2y³ to radical form.
    • Linear Equations: State the slope and y-intercept of 3x + 9y = 18 (m = -1/3, b = 2).
    • Graphing: Find the x and y intercepts of 3x – 4y = 12 (x-int: (4, 0); y-int: (0, -3).
    • Quadratic Equations: Example: 4x² - 25 = 0; x = ±5/2
    • Functions: Check graphs for direct variation and relations, including determining whether it's a function.
    • Polynomials: Examples for multiplication, division.

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    Algebra 1 Final Exam - PDF

    Description

    Prepare for your Algebra 1 final exam with this comprehensive review quiz. It covers key concepts such as simplification, equation solving, arithmetic sequences, and more, providing examples and essential problem-solving strategies. Test your knowledge on various topics, including functions and polynomials.

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