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  • Perplex
    IB Math AIHL
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    Cartesian plane & lines
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    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: 5
    13

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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:

    Powered by Desmos


    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]
    14

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    Consider the points A(−3,5) and B(5,−1) with midpoint M. The line L passes through M and is perpendicular to [AB].


    Find the equation of L, giving your answer in the form y=mx+c.

    [5]
    15

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    Flannery is a wizard brewing a batch of potions. She wants to brew some luck potions and some flight potions. Each contains the same rare specialized ingredients, dove feather dust and purple snake scales. A luck potion uses 3 pinches of dove feather dust and 2 purple snake scales. A flight potion uses 2 pinches of dove feather dust and 5 purple snake scales.


    Flannery has 24 pinches of dove feather dust and 38 purple snake scales available. She wants to use all of the ingredients without leftovers.

    1. Find the amount of each potion Flannery should make to use all of her supplies,

      [3]

    After Flannery gets her ingredients out of the cellar, her familiar, orange cat named Ferguson, knocks over the jar of dove feather dust, spilling 4 pinches onto the floor and rendering them unusable. Flannery decides to brew fewer potions, but keep the same ratio of luck to flight potions. She cannot partially brew a potion.

    1. Find the maximum number of each kind of potion that she can now brew.

      [4]
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