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Radha, an aspiring… (Class 10 Maths Basic SQP 2024-25, Q37)

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MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 37

From the official CBSE sample question paper for 2024-25, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedPolynomials

Radha, an aspiring landscape designer, is tasked with creating a visually captivating pool design that incorporates a unique arrangement of fountains. The challenge entails arranging the fountains in such a way that when water is thrown upwards, it forms the shape of a parabola. The graph of one such parabola is given below.

The height of each fountain rod above water level is 10 cm. The equation of the downward-facing parabola representing the water fountain is given by .

Based on the above information, answer the following questions:

  1. (i)

    Find the zeroes of the polynomial p(x) from the graph.

    1 mark
  2. (ii)

    Find the value of x at which water attains maximum height.

    1 mark
  3. (iii)

    (A) If h is the maximum height attained by the water stream from the water level of the pool, then find the value of h.

    2 marks

  4. OR

    (iii)

    (B) At what point(s) on x-axis, the height of water above x-axis is 2 m?

    2 marks

Figure in the paper: Graph of a downward-facing green parabola on axes X'OX and YY'. On the Y-axis 1 unit = 1 m; on the X-axis 1 unit = 0.5 m. The curve crosses the X-axis at (1,0) and (4,0), peaks at roughly (2.5, 2.25) and extends below the axis. A vertical black rod is drawn at x = 1 from the water level line, which is a horizontal line at the level of the X-axis labelled 'Water level'. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

Open one hint at a time and try again before the next.

Hint 1

The zeroes are the x-values where the curve meets the x-axis.

Hint 2

The highest point of the parabola lies exactly midway between the two zeroes.

Hint 3

For the maximum height, find p at that x and remember the rod height. For a height of 2, set p(x) = 2 and solve the quadratic.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (i) The parabola cuts the x-axis at and , so the zeroes of are and . Check: .

    1 mark

  2. (ii) A parabola is symmetric about the vertical line midway between its zeroes. So the maximum occurs at .

    1 mark

  3. (iii)(a) Substitute : m.

    1 mark

  4. (iii)(a) Add the rod height above water, m: m.

    1 mark

  5. (iii)(b) Set : .

    ½ mark

  6. (iii)(b) Rearrange to get .

    ½ mark

  7. (iii)(b) Factorise: , so or .

    ½ mark

  8. (iii)(b) The required points on the x-axis are and .

    ½ mark

Answer: (i) 1 and 4; (ii) x = 5/2; (iii)(A) h = 2.35 m; (iii)(B) (2, 0) and (3, 0)

Where the marks are

  • Reads the zeroes 1 and 4 from the graph (1 mark)
  • Finds for the maximum height (1 mark)
  • (iii)(A): finds (1 mark)
  • (iii)(A): adds 0.10 m to get m (1 mark)
  • (iii)(B): forms (½ mark)
  • (iii)(B): simplifies to (½ mark)
  • (iii)(B): solves to get (½ mark)
  • (iii)(B): states the points and (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.