Genny maths

Question 1

What is an annuity?

Answer 1

An annuity is a form of compound interest where regular and equal payments are made periodically
OR as a single sum investment from
which regular and equal payments are received.

Question 2

What is the present value formula?

Answer 2

PV = M((1 + i)^n − 1/r(1 + i)^n)

Question 3

what is a simple network?

Answer 3

pairs of vertices are connected by max one edge

Question 4

what is a complete network?

Answer 4

every vertex is joined to every other vertex

Question 5

difference between connected and disconnected networks?

Answer 5

connected you can get to vertex by following the edges. disconnected you can’t as there disjointed

Question 6

difference between directed and undirected network?

Answer 6

directed can only move one direction on the edge but undirected can move any direction

Question 7

what is the degree of vertex?

Answer 7

no. of edges coming out of a vertex

Question 8

how do you find no. of edges other then counting?

Answer 8

0.5 x the sum of the degrees

Question 9

what are faces in networks?

Answer 9

no. of shapes in a network created by the lines +1 (for the outside)

Question 10

what is a walk?

Answer 10

Any route, can repeat edges and vertices

Question 11

what is a trail?

Answer 11

no edges are repeated (e.g. ABCB, OR ABCDAC

Question 12

what is a path?

Answer 12

no vertices are repeated and end on different vertices

Question 13

what is a cycle?

Answer 13

no vertices are repeated however the first and last one must

Question 14

what is opened or closed…? which does it apply for?

Answer 14

open starts and stops at different vertices, closed finishes as same vertex. Applies to walks and trails

Question 15

Name the 4 movements?

Answer 15

Walk, trail, path, cycle and closed walk/trail

Question 16

what is a eulerian trail

Answer 16

a closed trail (no repeated edges and start/finish on same vertex) and degree of all vertices are even

Question 17

what is a semi-eulerian trail

Answer 17

a open trail (no repeated edges and start/finish on different vertex) and degree of ONLY 2 vertices are odd

Question 18

what is a hamiltonian cycle?

Answer 18

a closed path (includes every vertex once and start/finish on same vertex)

Question 19

what is a semi-hamiltonian cycle/ hamiltonian path?

Answer 19

a open path (includes every vertex once and start/finish on different vertex)

Question 20

what is the shortest path?

Answer 20

shortest path goes to all vertices ONCE

Question 21

whats a tree?

Answer 21

simple connected network with no circuit

Question 22

how to find no. of vertices on a tree?

Answer 22

= no. of edges + 1

Question 23

whats prims algorithm 3 steps?

Answer 23

1. draw vertices only
2. start with small edges
3. continue until all vertices are connected (but not complete a curcuit)

Question 24

whats an immediate predecessor?

Answer 24

it must be complete before next activity can commence (the one before it)

Question 25

whats an earliest start time?

Answer 25

write on left of vertex and use forward scanning of longest time.

Question 26

whats critical path?

Answer 26

activities that cant be delayed without delaying the entire project

Question 27

what is earliest completion time?

Answer 27

minimum time to taken to complete all activities (basically critical path time)

Question 28

whats float time?

Answer 28

max time an activity not on critical path can be delayed

Question 29

how do you find the latest start time?

Answer 29

backward scanning on the right side of the vertex

Question 30

float time formula?

Answer 30

= latest finish time (LFT the rightest right) - earliest start time (EST the leftiest left) - activity time

Question 31

what is a planar graph?

Answer 31

no edges cross over (can be drawn on a plane)

Question 32

what is the hungarian algorithm steps (5)?

Answer 32

1. subtract smallest value in row from every element in the row
2. min lines to cover ‘0s’
3. if column doesnt contain 0, subtract lowest value from column
4. min lines to cover ‘0s’
5. add smallest uncovered value to elements that covered by 2 lines. then subtract it from all uncovered elements
6. continue until 4 lines drawn