Algebra Class 10 Quiz
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Questions and Answers

What value should be added to both sides of the equation $x^2 + 16x = 2$ to complete the square?

  • -16
  • 16
  • 8
  • 64 (correct)

    • What is the solution of the equation $(-8x + 6) + 8 = -7(x + 4)$?

  • {-10} (correct)
  • {-26}
  • {-42}
  • {42}

    • What is the result of the operation $(4 + 4i) - (-9 + i)$ expressed in standard form?

  • 13 - 3i
  • -13 - 3i
  • 13 + 3i (correct)
  • -5 + 5i

    • Using the square root property, what are the solutions to the equation $(2x - 1)^2 = 9$?

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

    What is the result when using the quadratic formula on $16x^2 + 1 = 3x$?

    <p>$\frac{3 \pm 55}{32}$</p> Signup and view all the answers

    What is the profit the vendor makes from selling 600 pretzels?

    <p>$511</p> Signup and view all the answers

    What is the domain and range of the relation {(9, 4), (-6, -4), (-7, -1), (-7, -9)}?

    <p>domain = {-6, -7, 9}; range = {-4, -1, 4, -9}</p> Signup and view all the answers

    Which set-builder notation correctly represents the interval [-4, 1)?

    <p>{x | -4 ≤ x &lt; 1}</p> Signup and view all the answers

    Which equation represents the line in point-slope form with a slope of 9, passing through the point (4, 3)?

    <p>y - 3 = 9(x - 4)</p> Signup and view all the answers

    What does the function $P(x) = 0.65x - 89$ model?

    <p>The relationship between the number of pretzels sold and the profit made</p> Signup and view all the answers

    What is the slope-intercept form of the line passing through (5, 2) and perpendicular to the line whose equation is y = 9x + 7?

    <p>y = -9x - 47</p> Signup and view all the answers

    What is the domain of the function f(x) = 1/(x + 6)?

    <p>(-∞, -6) ∪ (-6, ∞)</p> Signup and view all the answers

    What is the midpoint of the line segment between the points (4, 5) and (1, 8)?

    <p>(3, 13/2)</p> Signup and view all the answers

    For a quadratic function with a vertex at (-1, -6) that opens upwards, what can be inferred about its range?

    <p>[-6, ∞)</p> Signup and view all the answers

    If the slope of a line is 9, what would be the slope of a line perpendicular to it?

    <p>-1/9</p> Signup and view all the answers

    What is the equation of a line that has a slope of 9 and passes through the point (0, 0) in slope-intercept form?

    <p>y = 9x</p> Signup and view all the answers

    What does the inequality $x^2 + y^2 \leq 36$ represent in a Cartesian plane?

    <p>A circle with a radius of 6 centered at the origin</p> Signup and view all the answers

    Which inequality describes a line that intercepts the x-axis at 2 and the y-axis at 8?

    <p>4x + y \leq 8</p> Signup and view all the answers

    What is the maximum value of y that satisfies both inequalities when represented graphically?

    <p>5</p> Signup and view all the answers

    Which graph represents the solution to the inequalities $x^2 + y^2 \leq 36$ and $8x + 2y \leq 16$ correctly?

    <p>Graph C</p> Signup and view all the answers

    In the inequality $8x + 2y \leq 16$, what is the slope of the boundary line?

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

    At which point do the inequalities $x^2 + y^2 \leq 36$ and $8x + 2y \leq 16$ intersect?

    <p>(2, 0)</p> Signup and view all the answers

    Which of these points lies outside the feasible region defined by the inequalities?

    <p>(5, 0)</p> Signup and view all the answers

    If we increase the right-hand side of the inequality $8x + 2y \leq 16$ to 20, what effect does this have?

    <p>The feasible region expands</p> Signup and view all the answers

    What is the solution set for the inequality $(x - 3)(x + 2) > 0$?

    <p>(-∞, -2) ∪ (3, ∞)</p> Signup and view all the answers

    If y varies directly as x, and y = 6 when x = 5, what is y when x = 10?

    <p>12</p> Signup and view all the answers

    What is the expected rabbit population next April given the growth formula $y = 190(2.7)^{0.09t}$ and starting with 190 rabbits?

    <p>555</p> Signup and view all the answers

    What is the approximate value of $e^{1.6}$ rounded to three decimal places?

    <p>4.349</p> Signup and view all the answers

    What is the exact solution to the logarithmic equation log 3 (x + 4) = 2?

    <p>{13}</p> Signup and view all the answers

    Which choice correctly represents the cost function C(x) for a business selling vases at $30 each with supplies costing $17 per vase and an initial investment of $26,000?

    <p>C(x) = 17x + 26,000</p> Signup and view all the answers

    Which equation represents the equivalent exponential form of $log_2 32 = x$?

    <p>$2^x = 32$</p> Signup and view all the answers

    What is the equivalent logarithmic form of $2^{-3} = 8$?

    <p>$log_{1/2} 2 = -3$</p> Signup and view all the answers

    Using the substitution method, what is the solution to the system of equations 5x - 4y = 147 and x = 5y?

    <p>{(7, 35)}</p> Signup and view all the answers

    From the addition method, what is the solution for the system of equations 6x + 7y = 30 and 6x + 2y = 60?

    <p>{(-12, 6)}</p> Signup and view all the answers

    What does the expression $log_2 (xy)$ expand to using properties of logarithms?

    <p>$log_2 x + log_2 y$</p> Signup and view all the answers

    What is the solution for x in the equation $(x - 3)(x + 2) = 0$?

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

    If you invested $8800 to sell vases costing $12 each and selling at $23, how many units must be sold to break even?

    <p>801 units</p> Signup and view all the answers

    What is the solution set for the system of inequalities -4x - y = -24 and y = x^2 - 8?

    <p>{(4, 8), (-8, 56)}</p> Signup and view all the answers

    Which of the following is the revenue function for selling vases at $30 each, based on the previous investment?

    <p>R(x) = 30x</p> Signup and view all the answers

    What values must be rejected from the logarithmic expression log 3 (x + 4) = 2?

    <p>x &lt; -4</p> Signup and view all the answers

    What is the domain of the polynomial function f(x) = 2(x - 3)(x + 6)4?

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

    What are the zeros of the function f(x) = 2(x - 3)(x + 6)4, and how do they behave at the x-axis?

    <p>3, multiplicity 1, crosses x-axis; -6, multiplicity 4, touches x-axis and turns around</p> Signup and view all the answers

    Using the Rational Zero Theorem, which of the following is a complete list of all possible rational zeros for f(x) = 5x^4 - x^2 + 2?

    <p>±1, ±2, ±5, ±1/2</p> Signup and view all the answers

    What are the vertical asymptotes for the rational function f(x) = (x + 4)/(x(x + 5))?

    <p>x = 0 and x = -5</p> Signup and view all the answers

    Which of the following describes the multiplicity of the zeros found in f(x) = 2(x - 3)(x + 6)4?

    <p>3 has multiplicity 1; -6 has multiplicity 4</p> Signup and view all the answers

    What is the range of the function f(x) = 2(x - 3)(x + 6)4?

    <p>[-6, ∞)</p> Signup and view all the answers

    What is the behavior of the graph at x = 3 for the polynomial function f(x) = 2(x - 3)(x + 6)4?

    <p>The graph crosses the x-axis</p> Signup and view all the answers

    What can be concluded about the vertical asymptote of f(x) = (x + 4)/(x(x + 5))?

    <p>The function approaches infinity as it nears the vertical asymptote</p> Signup and view all the answers

    Study Notes

    Multiple Choice Questions

    • Question 1: To solve x² + 16x = 2 by completing the square, add 64 to both sides of the equation.
    • Question 2: The solution to the linear equation (-8x + 6) + 8 = -7(x + 4) is {42}.
    • Question 3: (4 + 4i) - (-9 + i) = 13 + 3i.
    • Question 4: The solution to the equation (2x – 1)² = 9 is {-1, 2}.
    • Question 5: The solution to the quadratic equation 16x² + 1 = 3x using the quadratic formula is (3 + √55)/32.
    • Question 6: The domain of the relation {(9, 4), (-6, −4), (−7, −1), (-7, −9)} is {-6, -7, 9} and the range is {-4, -1, 4, −9}.

    Intervals

    • Question 7: The interval [-4, 1) in set-builder notation is {x | -4 ≤ x < 1}.

    Functions

    • Question 8: P(600) = $390 (profit for selling 600 pretzels).
    • Question 9: The equation for the line with slope 8/8 passing through (4, 3) is y - 3= (x - 4).
    • Question 10: The equation of the line passing through (5, 2) and perpendicular to y = 1/9x + 7 in slope-intercept form is y = -9x + 47.
    • Question 11: The domain of the function f(x) = 1/(x - 6) is all real numbers except 6.
    • Question 12: The midpoint of the line segment with endpoints (4, 5) and (1, 8) is (5/2, 13/2).

    Quadratic Functions

    • Question 13: A quadratic function with vertex (-1, -6) and opening upwards has a domain of (-∞, ∞) and a range of [-6, ∞).

    Polynomials

    • Question 14: For f(x) = 2(x − 3)(x + 6)⁴, the zeros are x = 3 (multiplicity 1) and x = -6 (multiplicity 4). The graph touches the x-axis and turns around at x = 3 and crosses the x-axis at x = −6.

    Rational Functions

    • Question 15: The possible rational zeros of f(x) = 5x⁴ - x² + 2 are ±1/5, ±1/2, ±1 and ±2.
    • Question 16: The vertical asymptote for f(x) = (x + 4)/(x(x + 5)) is x = 0.

    Polynomial Inequalities

    • Question 17: The solution to the inequality (x − 3)(x + 2) > 0 is (-2, 3).

    Exponential and Logarithmic Functions

    • Question 18: If y varies directly as x, and y = 6 when x = 5, then y = 12 when x = 10.
    • Question 19: The approximate rabbit population in the next April, using the given function, is expected to be 554.
    • Question 20: e¹·⁶ ≈ 4.953 (rounded to three decimal places).
    • Question 21: log₂32= x is equivalent to 2x = 32.
    • Question 22: The equivalent logarithmic form of 2⁻³ = ¹⁄₈ is log₂1/8 = –3.
    • Question 23: log₃(y³/x⁷) = 3log₃x - 7log₃y
    • Question 24: The solution to log₃(x + 4) = 2 is x = 10.

    Systems of Equations

    • Question 25: The solution to the system of equations 5x - 4y = 147 and x = 5y is (35, 7).
    • Question 26: The solution to the system of equations 6x + 7y = 30 and 6x + 2y = 60 is (12, -6)
    • Question 27: The cost function C(x) = 17x + 26,000 and the revenue function R(x) = 30x
    • Question 28: The break-even point in this business scenario is 800 units.
    • Question 29: The solution to the system -4x - y = -24 and y = x² - 8 is (4, 8) and (-8, 56).

    Systems of Inequalities

    • Question 30 The solution graph of the system of inequalities x² + y² ≤ 36 and 8x + 2y ≤ 16 is shown in image C.

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    Final Exam Review PDF

    Description

    Test your knowledge of algebraic concepts with this quiz designed for 10th-grade students. It covers topics such as completing the square, solving linear and quadratic equations, and understanding functions and intervals. Each question challenges you to apply your algebra skills effectively.

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