Mathematics Quarter 1 - Quadratic Equations
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Questions and Answers

What is the total perimeter represented by the 16m of fencing materials?

  • 32m
  • 16m (correct)
  • 8m
  • 4m
  • The equation representing the usage of 16 meters of fencing around rectangular land can be expressed as $2(length + width) = 16$.

    True (A)

    What does 'quadratic equation' refer to?

    An equation that can be written in the form $ax^2 + bx + c = 0$

    The equation for the perimeter can be represented as $2(length + width) = ______$.

    <p>16</p> Signup and view all the answers

    Match the following terms with their meanings:

    <p>Perimeter = The total distance around a shape Quadratic equation = An equation of degree 2 Fencing materials = Materials used to enclose an area Length and Width = Dimensions of a rectangle</p> Signup and view all the answers

    What is the degree of the equation $x^2 + 3x - 15 = 0$?

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

    A quadratic equation can have a degree of 3.

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

    What is the standard form of a quadratic equation?

    <p>ax^2 + bx + c = 0</p> Signup and view all the answers

    In the equation $x^2 + 3x - 15 = 0$, the value of c is ______.

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

    Which of the following represents a quadratic equation?

    <p>x^2 + 4 = 3x (D)</p> Signup and view all the answers

    The equation $(x - 5)(2x + 3) = 7$ is a quadratic equation.

    <p>True (A)</p> Signup and view all the answers

    What is the value of a in the equation $3x^2 + 2x - 9 = 0$?

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

    Match the following quadratic equations with their respective coefficients:

    <p>$3x^2 + 2x - 9 = 0$ = a = 3, b = 2, c = -9 $x^2 + 3x - 15 = 0$ = a = 1, b = 3, c = -15 $2x^2 - 5x + 1 = 0$ = a = 2, b = -5, c = 1 $x^2 + 4x + 4 = 0$ = a = 1, b = 4, c = 4</p> Signup and view all the answers

    Which equation represents the area of a rectangular window with width x and length x + 6?

    <p>$x^2 + 6x - 315 = 0$ (D)</p> Signup and view all the answers

    The sum of two numbers is always greater than their product.

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

    What is the product of two consecutive even integers if their product is stated to be 288?

    <p>288</p> Signup and view all the answers

    The quadratic equation representing the situation where the square of a number added to 8 times the number results in 100 is __________.

    <p>$x^2 + 8x - 100 = 0$</p> Signup and view all the answers

    Match the equations with their corresponding descriptions:

    <p>$x^2 + 6x - 315 = 0$ = Area of a window $x(16 - x) = 48$ = Product of two numbers $x^2 + 2x - 288 = 0$ = Product of two consecutive even integers $x^2 + 8x - 100 = 0$ = Square of a number added to a multiple of the number</p> Signup and view all the answers

    The equation $2x^2 - 7x - 8 = 0$ is quadratic.

    <p>True (A)</p> Signup and view all the answers

    What is the first step in solving for two numbers whose product is 48 and sum is 16?

    <p>Set up the equation $16 - x$ for the second number (C)</p> Signup and view all the answers

    A quadratic equation can have up to two real solutions.

    <p>True (A)</p> Signup and view all the answers

    What values represent 'a', 'b', and 'c' in the equation $2x^2 - 7x - 8 = 0$?

    <p>a = 2, b = -7, c = -8</p> Signup and view all the answers

    A rectangular prism's volume is calculated using the formula V = length x width x height. If the height is 3 m, the volume is 18 m3, and the length is three times the width, then w represents the ______.

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

    In the equation $x^2 + 6x - 315 = 0$, the coefficient of x is __________.

    <p>6</p> Signup and view all the answers

    Match the equations with their types:

    <p>$2x^2 - 7x - 8 = 0$ = Quadratic $-14x - 15 = 0$ = Linear $9w^2 - 18 = 0$ = Quadratic $x + 5 = 0$ = Linear</p> Signup and view all the answers

    Which equation represents a linear equation?

    <p>$-14x - 15 = 0$ (C)</p> Signup and view all the answers

    The equation $(x + 6)^2 = 12x$ is quadratic.

    <p>True (A)</p> Signup and view all the answers

    If the length of a window is 6 cm more than its width and the area is 315 cm², how would you represent the width in the quadratic equation?

    <p>Let w be the width.</p> Signup and view all the answers

    What quadratic equation represents the situation where a rectangular field has an area of 120m² and the length is 12m longer than the width?

    <p>$x^2 - 12x - 120 = 0$ (D)</p> Signup and view all the answers

    The length of each window being 4 less than the square of the width can form a quadratic equation.

    <p>True (A)</p> Signup and view all the answers

    What quadratic equation represents the area of a square with a side length of 12 cm?

    <p>$s^2 = 144$</p> Signup and view all the answers

    The perimeter of a rectangular lot is represented by the equation _____ and the area is represented by _____ .

    <p>2L + 2W = 46, L * W = 132</p> Signup and view all the answers

    Match the situation with the corresponding quadratic equation:

    <p>Field with area 120m² and length 12m longer = $x^2 - 12x - 120 = 0$ Window area of 315cm² with length 6cm more than width = $x^2 - 6x - 315 = 0$ Square area of 144cm² = $s^2 = 144$ Lot area of 132m² and perimeter 46m = $x^2 - 46x + 132 = 0$</p> Signup and view all the answers

    Which of the following forms the correct quadratic equation for a rectangular lot with an area of 132m² and a perimeter of 46m?

    <p>$x^2 - 23x + 132 = 0$ (D)</p> Signup and view all the answers

    The equation $s(s + 1) = 144$ accurately represents the area of a square with side s.

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

    Write an example of a real-life situation that can lead to a quadratic equation.

    <p>A gardener wants to create a rectangular flower bed with a specific area given certain constraints.</p> Signup and view all the answers

    Which of the following is the standard form of a quadratic equation?

    <p>$a x^2 + b x + c = 0$ (B)</p> Signup and view all the answers

    The equation $3x + 5 = 0$ is a quadratic equation.

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

    What is the value of 'c' in the equation $x^2 - 6x + 2 = 0$?

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

    The quadratic equation in standard form is represented as __________.

    <p>$a x^2 + b x + c = 0$</p> Signup and view all the answers

    Which equation represents a quadratic when factored form is presented?

    <p>$2x^2 + 7x = 15$ (B)</p> Signup and view all the answers

    Match the following quadratic equations with their corresponding values of a, b, and c:

    <p>$x^2 - 6x + 2 = 0$ = a = 1, b = -6, c = 2 $x^2 + 2x + 1 = 0$ = a = 1, b = 2, c = 1 $2x^2 + 7x - 15 = 0$ = a = 2, b = 7, c = -15 $3x^2 - 3x = 0$ = a = 3, b = -3, c = 0</p> Signup and view all the answers

    The equation $(x - 1)^2 + 3 = 2x + 1$ has a constant term of 1.

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

    In the equation $(x + 5)(2x - 3) = 2(x + 1)$, what are the values of a, b, and c in standard form?

    <p>$a = 4, b = 19, c = -17$ (A)</p> Signup and view all the answers

    Study Notes

    Mathematics Quarter 1-Module 1 - Illustrating Quadratic Equations

    • Learning Code: M9AL-Ia-1

    • Topic: Illustrating quadratic equations

    • Focus: Understanding and representing quadratic equations in various contexts.

    • Key Concepts:

      • Quadratic equation: A second-degree polynomial equation that can be written in the form ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0.

      • Standard form: The form ax² + bx + c = 0 where 'a' is the coefficient of the x² term, 'b' is the coefficient of the x term, and 'c' is the constant term.

      • Quadratic Term: The term containing x².

      • Linear Term: The term containing x.

      • Constant Term: The term that does not contain x.

    • Illustrative examples:

      • Word Problems: Real-world scenarios involving area, perimeter, and product of numbers can lead to quadratic equations.
      • Geometric problems, like those involving rectangles and prisms.
      • Visual representations support the concept of a quadratic relationship between variables.
    • Application:

      • Ability to write quadratic equations to model real-life situations.
      • Solve quadratic equations and identify their solutions.
      • Determine values of variables a, b, and c within quadratic equations.
      • Recognize when an equation is or is not quadratic.

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    Description

    Explore the fundamentals of quadratic equations in this quiz, designed for Mathematics Quarter 1, Module 1. Understand how to illustrate and represent these equations through various contexts and real-world problems. Test your knowledge on standard forms, terms, and applications of quadratic equations.

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