Algebra Class Quiz - Expressions and Operations
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Questions and Answers

What is the primary mathematical operation used to combine expressions in algebra?

  • Differentiation
  • Integration
  • Addition (correct)
  • Multiplication
  • Which expression represents exponentiation?

  • 6 / 2
  • 5^2 (correct)
  • 4 - 1
  • 2 + 3
  • What is the correct process to simplify the expression 3(a + 2) + 2a?

  • 6a + 3
  • 5a + 6 (correct)
  • 5a + 3
  • 3a + 6
  • Which operation does NOT typically involve solving for an unknown variable?

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

    In the context of algebra, what does factoring an expression commonly achieve?

    <p>Finding solutions to equations</p> Signup and view all the answers

    What is the simplified form of the expression $ rac{x^{2}-2x-8}{4-x^2}$?

    <p>$ rac{-(x+2)(x-4)}{(x-2)(x+2)}$</p> Signup and view all the answers

    When simplifying the expression $a^{2} - 7a + 6$ over $2a^{3} - 3a^{2}$, what is the first step required?

    <p>Factoring $2a^3 - 3a^2$ into $a^2(2a - 3)$</p> Signup and view all the answers

    What is the result of simplifying $8x^{2} - 12x - 5$ divided by $3x^{2} + 4x + 1$?

    <p>A proper fraction with no further simplification possible</p> Signup and view all the answers

    What expression represents the product of $6y^3 - 36y^2$ and $10-3y-4y^2$?

    <p>A polynomial of degree 5</p> Signup and view all the answers

    Which of these statements is incorrect regarding the polynomial operation involving $3x^{2}+4x+1$?

    <p>It should always equal zero for proper simplification.</p> Signup and view all the answers

    What is the least common denominator (LCD) of the fractions $ rac{3}{4}$ and $ rac{28}{x-3}$?

    <p>$4(x-3)$</p> Signup and view all the answers

    When simplifying the equation $ rac{5x}{3} = 18$, what integer value can x equal?

    <p>54</p> Signup and view all the answers

    For the equation $ rac{4}{9} = rac{27}{?}$, what value should replace the question mark to create an equivalent fraction?

    <p>36</p> Signup and view all the answers

    Which step is NOT involved in solving the equation $ rac{3}{4} - x = rac{28}{x-3}$?

    <p>Factoring the equation</p> Signup and view all the answers

    In solving equations that include fractions, which of the following is crucial for obtaining accurate results?

    <p>Finding a common denominator before combining fractions</p> Signup and view all the answers

    What is the result of simplifying the expression $\frac{2y - x}{4y^{2} - x^{2}}$?

    <p>$\frac{(2y - x)}{(2y - x)(2y + x)}$</p> Signup and view all the answers

    In the simplification of $\frac{2x^{2} - 11x + 12}{27 - 18x}$, which of the following represents a factor of the numerator?

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

    What is the correct result when simplifying $\frac{(2p - 7)^{3}/9}{(7 - 2p)^{4}/3}$?

    <p>$\frac{(2p - 7)^{3}}{(2p - 7)^{4}}$</p> Signup and view all the answers

    When simplifying $\frac{6y - 14}{9y - 21} \div \frac{y^{2}}{35}$, what expression remains after simplification?

    <p>$\frac{35(y - 2)}{9y - 21}$</p> Signup and view all the answers

    What result do you obtain when simplifying $\frac{r^{2}}{(r^{2} - s^{2}) \cdot (r + s)} \div (r + s)^{2}$?

    <p>$\frac{1}{(r + s) \cdot (r - s)}$</p> Signup and view all the answers

    What is the simplified result of $ rac{4}{15} igg/ rac{5}{6}$?

    <p>$ rac{8}{25}$</p> Signup and view all the answers

    What is the simplest form of $ rac{9a^{4}}{6ab} igg/ rac{4y}{18}$?

    <p>$ rac{3a^{3}}{2y}$</p> Signup and view all the answers

    Calculate the simplified result of $ rac{2m^{2}}{m^{2}-9} igg/ rac{10}{21} igg/ rac{1}{5}$.

    <p>$ rac{21m^{2}}{m^{2}-9}$</p> Signup and view all the answers

    What is the correct simplification for $ rac{3}{5} igg/ rac{2}{10}$?

    <p>$ rac{3}{1}$</p> Signup and view all the answers

    What is the simplest form of $ rac{5}{16} igg/ rac{6}{4} igg/ rac{7}{4} igg/ rac{1}{7}$?

    <p>$ rac{5}{1}$</p> Signup and view all the answers

    What is the least common denominator (LCD) for the fractions 1/6 and 5/9?

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

    When rewriting the fraction 2a-b/12 with its least common denominator, which of the following numerators would be correct if the least common denominator is found to be 60?

    <p>10(2a-b)</p> Signup and view all the answers

    In the provided program to calculate the LCD, which part of the program checks if Q is an integer?

    <p>60 IF Q=INT(Q) THEN</p> Signup and view all the answers

    When given the fractions 1/8, 3/5, and 2a-b/12, which is the correct approach to find their least common denominator?

    <p>Identify the prime factors of each denominator to find the highest powers.</p> Signup and view all the answers

    What is the product of $4 imes \frac{7}{8}$ expressed in simplest form?

    <p>$\frac{7}{4}$</p> Signup and view all the answers

    What is the simplified result of $(-\frac{2}{5})^2 \cdot \frac{8}{5}$?

    <p>$\frac{16}{25}$</p> Signup and view all the answers

    What is the simplified form of $\left(\frac{4}{7}x^{2} \cdot \frac{8}{9}x\right)$?

    <p>$\frac{32}{63}x^3$</p> Signup and view all the answers

    What is the area of a triangle with a base of $\frac{3}{4} x$ cm and height $\frac{8}{9} x$ cm?

    <p>$\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{8}{9} x^2$</p> Signup and view all the answers

    What is the volume of a cube with each edge measuring $\frac{4n}{5}$ in?

    <p>$\frac{64n^3}{125}$</p> Signup and view all the answers

    What total dollar cost in dollars is represented by $\frac{4y}{3}$ eggs if each dozen costs $d$ dollars?

    <p>$\frac{4yd}{12}$</p> Signup and view all the answers

    What is the simplified form of $\left(-\frac{4}{x}\right)^{2} \cdot \left(-\frac{4}{y}\right)$?

    <p>$\frac{16}{x^2y}$</p> Signup and view all the answers

    What is the final simplified result of the expression $\frac{(10x^4)}{6x - 12} \cdot \frac{x^2 - x - 2}{4x}$?

    <p>$\frac{5x^2}{3(x - 2)}$</p> Signup and view all the answers

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