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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: 4
    1

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    0 / 4

    The function h(x)=2x+5 models the cost (in dollars) of renting a scooter for x hours.

    1. Write down the cost of renting the scooter for 3 hours.

      [1]
    2. Solve h(x)=15.

      [1]
    3. State the gradient of the function and explain what it represents in this context.

      [2]
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    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]
    3

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    The line L passes through the points P(1,2) and Q(5,−2).

    1. Find the slope of L.

      [1]
    2. Determine an equation for L in the form y=mx+c.

      [2]
    3. Find the midpoint of [PQ].

      [2]
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    The line L1​ passes through the points A(1,−2) and B(1,3).

    1. Write down the equation of L1​.

      [1]

    A second line, L2​, is perpendicular to L1​ and passes through C(−4,5).

    1. Find the equation of L2​ in the form y=mx+c.

      [2]

    The point P lies on L1​, and the point Q lies on L1​ and L2​.

    1. Given that P is equidistant from A and Q, find the coordinates of P.

      [2]
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