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ICSE Class 10 Algebra: Simultaneous Linear Equations & Quadratics — practice questions

Explore 50 free Algebra: Simultaneous Linear Equations & Quadratics questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: Simultaneous Linear Equations & Quadratics questions and exercises with answers

Showing questions 1–30 of 50.

Quick quadratic picksRead the answer and worked solution →The vertical line of the coordinate system is the:Read the answer and worked solution →The coordinates of the origin are:Read the answer and worked solution →The axes divide the plane into how many quadrants?Read the answer and worked solution →A point is written in the form:Read the answer and worked solution →The number line studied in earlier grades is:Read the answer and worked solution →In Quadrant III, a point has:Read the answer and worked solution →What is the largest number of real roots a quadratic equation can have?Read the answer and worked solution →The square of any odd integer, when divided by 8, leaves remainderRead the answer and worked solution →The point (0, -5) lies onRead the answer and worked solution →The mid-point of the segment joining (2, 3) and (6, 7) isRead the answer and worked solution →If P(2, 3) is shifted 4 units right and 1 unit down, the new co-ordinates areRead the answer and worked solution →The point P(-3, -4) lies inRead the answer and worked solution →Proving the first identityRead the answer and worked solution →The list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?Read the answer and worked solution →Match each triangle similarity criterion with its condition:Read the answer and worked solution →In a right triangle with legs a and b, the altitude h drawn to the hypotenuse c satisfiesRead the answer and worked solution →Tap the word in each sentence that is wrong. The correct fix appears below.Read the answer and worked solution →If the two lines of a pair of linear equations are parallel, the pair hasRead the answer and worked solution →Solve: 2x + 3 = 7. What is x?Read the answer and worked solution →Match each condition for lines a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0:Read the answer and worked solution →If an AP has first term $a=6$ and common difference $d=-3$, which of the following is the correct AP?Read the answer and worked solution →Point (3, k) is the midpoint of segment joining (1, 4) and (5, 6). Find k.Read the answer and worked solution →The common difference of the AP 3, 1, −1, −3, … is:Read the answer and worked solution →Which of these is NOT an AP?Read the answer and worked solution →Find the distance of (3, 4) from the origin.Read the answer and worked solution →For ax² + bx + c, the sum of roots equals:Read the answer and worked solution →A polynomial of degree 2 is called a:Read the answer and worked solution →True or false on coordinate geometryRead the answer and worked solution →Which field is named as an application of coordinate geometry?Read the answer and worked solution →

Worked practice questions

Quick quadratic picks

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Questions
  1. Question
    Degree of a quadratic equation
    Choices
    1. 1
    2. 3
    3. 2
    Correct choice
    2
  2. Question
    Roots when b² - 4ac is negative
    Choices
    1. No real roots
    2. Two equal
    3. Two distinct
    Correct choice
    No real roots
  3. Question
    Roots when b² - 4ac is positive
    Choices
    1. One root
    2. Two distinct
    3. Two equal
    Correct choice
    Two distinct
  4. Question
    The roots of x² - 4 = 0
    Choices
    1. 4 and -4
    2. 0 only
    3. 2 and -2
    Correct choice
    2 and -2
Instructions
Pick the right answer before the next one arrives.
_Source: syllabus Mathematics, Ch 4 'Quadratic Equations' (jemh104)_

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The vertical line of the coordinate system is the:

  1. n-axis
  2. y-axis
  3. x-axis
  4. z-axis
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Correct answer: B. y-axis

1. The two axes are drawn at right angles to each other. 2. The horizontal one is the x-axis. 3. The vertical one is called the y-axis. 4. So the answer is the y-axis. _Source: syllabus Mathematics, Ch 1 'Orienting Yourself: The Use of Coordinates'_

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The coordinates of the origin are:

  1. (0, 1)
  2. (1, 0)
  3. (0, 0)
  4. (1, 1)
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Correct answer: C. (0, 0)

1. The origin is where the two axes cut each other. 2. It is zero units along both axes. 3. So its coordinates are (0, 0). 4. The answer is (0, 0). _Source: syllabus Mathematics, Ch 1 'Orienting Yourself: The Use of Coordinates'_

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