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  • Perplex
    IB Math AISL
    /
    Cartesian plane & lines
    /

    Problems

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    Problem Bank - Cartesian plane & lines

    Access custom-built, exam-style problems for cartesian plane & lines. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 6
    14

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    A square park is modeled by the region 0≤x≤8 and 0≤y≤8 (all distances in meters).

    There are three refreshment kiosks.

    • Kiosk A is at the point (2,6).

    • Kiosk B is at the point (2,b).

    • Kiosk C is at the point (6,6).

    A Voronoi diagram of the park's kiosks is shown below:

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    Every visitor is served by the nearest kiosk.

    1. Show that V has coordinates (4,5).

      [4]
    2. Determine the value of b.

      [3]
    3. Determine the fraction of the park served by Kiosk A.

      [2]
    15

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    Let f(x)=log4​(7x+4).

    1. For the function f, write down

      1. the largest possible domain of f.

        [2]
      2. the range of f.

        [1]
    2. Find

      1. f(3).

        [1]
      2. f−1(2).

        [2]
    3. For the curve y=f(x), find

      1. the x-intercept.

        [1]
      2. the y-intercept.

        [1]

    The line y=2x−1 intersects the curve y=f(x) at P and Q.

    1. Find the distance between P and Q.

      [5]
    16

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