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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: 5
    4

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    0 / 4

    An 8km long straight beach is represented by the x-axis from x=0km to x=8km. Two lifeguard stations are located at A(2,2) and B(6,2), where the y-coordinate is the distance inland in km.


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    The beach manager decides that each point on the sand should be patrolled by the nearer station.

    1. Write down the equation of the straight line that separates the patrol zones of stations A and B.

      [2]

    A swimmer has an emergency at P(3,4).

    1. Determine, and justify, which station will watch over the swimmer.

      [2]
    5

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    The point U has coordinates (6,−3) and the point V has coordinates (−2,7). The point W has coordinates (1,−1).

    1. Write down the coordinates of X, the midpoint of line segment UV. 

      [2]
    2. Find the gradient of the line WX.

      [2]
    3. Find the equation of WX. Write your answer in the form

      ax+by+d=0

      where a,b,d∈Z.

      [2]
    6

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    A biker climbs a mountain with a slope of 8%. He bikes a distance of 12km along the road to reach a summit at an altitude of 1675m.

    1. Show that he has climbed 960m.

      [1]

    The relationship between the height h (in meters) of the biker above sea level and the distance d (in kilometers) travelled along the road can be modeled by

    h=ad+b.
    1. Find the values of a and b.

      [2]
    2. State the significance of the value of b in this context.

      [1]
    7

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