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IB Mathematics: Applications and Interpretation HL · 12.8: Voronoi Diagrams · 12.8.7

Voronoi diagrams: exam review Exam review Answers

Section A: short questions

    1. (a) A: 5.83, B: 3.16, C: 4.47
    2. (b) B
    3. (c) On the edge between the cells of A and B
    4. (d) roads and travel time (the model uses only the straight-line distance)
    1. (a) \((1, 5)\)
    2. (b) \(y=-\frac{3}{2}x+\frac{13}{2}\)
    3. (c) \(2x-3y=-6\)
    1. (a) 3 edges; the point is a vertex
    2. (b) \(3x+y=18\)
    3. (c) C: P is in the cell of C
    1. (a) 19%
    2. (b) 20.8%
    3. (c) Y to F: 2.00; Y to A: 2.24; estimate 19%
    4. (d) Y is almost the same distance from two sites, so a small move changes the estimate; X is well inside one cell.
    1. (a) \(y=-\frac{2}{3}x+\frac{31}{3}\)
    2. (b) \((5, 7)\)
    3. (c) \((8, 5)\)
    4. (d) \((3, 4)\)
    5. (e) 5.10 km

Section B: long questions

    1. (a) \(y=2x-\frac{13}{2}\)
    2. (b) \((6, \frac{11}{2})\)
    3. (c) V is 1.00 from E but 2.00 from A, B, C
    4. (d) A, B, C; 3 edges
    1. (a) P: 2.00, Q: 1.58, R: 2.24
    2. (b) \(R(6, 2)\)
    3. (c) (0, 0): 3.61, (9, 0): 3.16, (9, 7): 4.12, (0, 7): 3.16
    4. (d) At the corner (9, 7), 4.12 units from the nearest village
    5. (e) Yes. 4.12 is at least 4.
    1. (a) \(y=\frac{1}{3}x+4\)
    2. (b) \(y=x-2\)
    3. (c) \((9, 7)\)
    4. (d) All three distances are \(\sqrt{20}\)
    5. (e) 44.7 km
    1. (a) \(\frac{25}{2}\) km\(^2\)
    2. (b) 13.0%
    3. (c) \(y=-\frac{1}{2}x+7\)
    4. (d) \((6, 4)\)
    5. (e) 3

jmaths.xyz · AI HL · 12.8.7 Unit review