Grade 2 Mathematics Worksheet Notes

Mathematics Worksheet for Grade 2 - Second Semester, 2023/24

I. Problems to Attempt:

1. Vector Problem:

  • Problem Statement: Find the coordinates of the terminal point Q on the x-axis for a vector v, given that the initial point is (0,4) and the magnitude of the vector is 40\sqrt{40} units.

  • Understanding the Problem:

    • We are given the initial point of a vector v, which is (0,4).
    • The terminal point Q lies on the x-axis, meaning its y-coordinate is 0. So, Q has the form (x, 0).
    • The magnitude (or length) of the vector v is given as 40\sqrt{40}. We need to find the x-coordinate of point Q.

  • Steps to Solve:

    1. Define the Vector:
      • The vector v can be represented as the difference between the terminal and initial points:
        v=Q−(0,4)=(x,0)−(0,4)=(x,−4)v = Q - (0, 4) = (x, 0) - (0, 4) = (x, -4)
    2. Magnitude of the Vector:
      • The magnitude of vector v is calculated as:
        ∣∣v∣∣=x2+(−4)2||v|| = \sqrt{x^2 + (-4)^2}
    3. Use Given Magnitude:
      • We know ∣∣v∣∣=40||v|| = \sqrt{40}, so:
        x2+16=40\sqrt{x^2 + 16} = \sqrt{40}
    4. Solve for x:
      • Square both sides:
        x2+16=40x^2 + 16 = 40
      • Subtract 16 from both sides:
        x2=40−16=24x^2 = 40 - 16 = 24
      • Take the square root of both sides:
        x=±24=±4⋅6=±26x = \pm \sqrt{24} = \pm \sqrt{4 \cdot 6} = \pm 2\sqrt{6}
    5. Coordinates of Terminal Point Q:
      • Therefore, the coordinates of the terminal point Q are (26,0)(2\sqrt{6}, 0) or (−26,0)(-2\sqrt{6}, 0).

  • Final Answer: The coordinates of the terminal point Q are (26,0)(2\sqrt{6}, 0) and (−26,0)(-2\sqrt{6}, 0).

2. Data Problem:
  • The content of the data problem is not provided in the given extract. Therefore, cannot create notes for it.