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

Voronoi diagrams: exam review Exam review: second paper Answers

Section A: short questions

    1. (a) A: 5.83, B: 5.39, C: 4.47
    2. (b) C
    3. (c) On the edge between the cells of B and C
    4. (d) bus routes and walking routes (the model uses only the straight-line distance)
    1. (a) \((1, 2)\)
    2. (b) \(y=-\frac{4}{3}x+\frac{10}{3}\)
    3. (c) \(4x-5y=-7\)
    1. (a) 3 edges; the point is a vertex
    2. (b) \(3x+2y=24\)
    3. (c) B: P is in the cell of B
    1. (a) 14 units
    2. (b) 17.6%
    3. (c) Y to F: 2.00; Y to C: 2.24; estimate 26 units
    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) \(y=-\frac{2}{3}x+8\)
    2. (b) \((6, 4)\)
    3. (c) \((3, 6)\)
    4. (d) \((10, 10)\)
    5. (e) 8.06 km

Section B: long questions

    1. (a) \(y=x-1\)
    2. (b) \((\frac{11}{2}, \frac{9}{2})\)
    3. (c) V is 0.707 from E but 1.58 from A, B, C
    4. (d) A, B, C; 3 edges
    1. (a) P: 3.01, Q: 2.00, R: 1.58
    2. (b) \(P(5, \frac{3}{4})\)
    3. (c) (0, 0): 4.24, (9, 0): 1.41, (9, 7): 2.24, (0, 7): 5.00
    4. (d) At the corner (0, 7), 5.00 units from the nearest centre
    5. (e) No. 5.00 is less than 5.5.
    1. (a) \(y=-\frac{1}{3}x+\frac{28}{3}\)
    2. (b) \(y=3x-14\)
    3. (c) \((7, 7)\)
    4. (d) All three distances are \(\sqrt{20}\)
    5. (e) 89.4 km
    1. (a) \(3.00\) km\(^2\)
    2. (b) 3.75%
    3. (c) \(y=2x-\frac{15}{2}\)
    4. (d) \((\frac{11}{2}, \frac{7}{2})\)
    5. (e) 3

jmaths.xyz · AI HL · 12.8.7 Unit review