Term 2 Exam Revision

GPs

100

A geometric sequence is one whereby the first term is multiplied by a number, known as the common ratio, to create the second term which is multiplied by the common ratio to create the third term and so on…

True or False?

True

200

Name both of the acronym of the first term and the common ratio in a geometric sequence.

Need to get both correct to get any points

First term "a"

Common Ratio "r"

300

What is "r" of this sequence?

2, 10, 50, 250, 1250

5

400

Write down the formula of Explicit Form of a geometric sequence. (again, you will need to get the exact form right in order to get any point)

T_n = ar_n-1

500

Write down the formula of the sum of a geometric sequence when r>1 (you know it, have to be the exact one in order to get any point)

S_n = T₁(rⁿ -1) / (r-1)

FOLRR

100

A recurrence relation, also called a difference equation, is a rule (or formula) that is used to find any term of a sequence.

True or False

False.

A recurrence relation, also called a difference equation, is a rule (or formula) that specifies (or gives)

a particular term in a sequence using the previous term or terms.

200

Consider the following sequence4,−28,224,−1372,…4,−28,224,−1372,…

Is the sequence arithmetic, geometric or neither?

neither

300

Consider the sequence defined by a₁=5 and a_n=−2a_n−1−3 

Find the 2nd term of the sequence 

-13

400

A trout farm currently has 10 000 trout in a pond. In one month, breeding has caused the trout population to increase by 10%. After one month, 3000 trout are caught and sold.

How many trout will be in the pond after one month?

8000

500

A sequence is defined by the recurrence relation 

T_n-1 =0.4T_n +18, T₁ =4

What value do the terms in this sequence approach in the long run?

Answer on my screen, I can't upload it here.

Network

100

The term we use to describe a group or system of interconnected people or things is?

NETWORK

200

Does all the vertices have to be connected to form a network?

No. Not all vertices need to have an edge.

300

What is a degree of a vertex?

The number of edges that are connected to it.

400

How many edges would a complete graph have if it contains 10 vertices?

(10x(10-1))/2

=45

500

State the Euler's formula

Number of Vertices – Number of Edges + Number of Faces = 2

Matrices and Walks

100

For a graph that has 3 vertices, it can be represented using an [what x what] matrix?

[3x3]

200

How to find a degree sum?

Degree Sum = 2 x number of edges

300

What is the key difference between Euler's graph and Hamiltonian graph?

Eulerian and semi-Eulerian graphs are interested in edges, meaning the trail must use every edge no more than once.

Hamiltonian and semi-Hamiltonian graphs are interested in vertices, meaning the path must use the same vertex no more than once.

400

A semi-Eulerian graph will have all even degree.

True or False?

False. Two vertices are of odd degree

500

Answer Q7a from you Practice Test

V = 5

E = 7

F = 4

Solving problems

100

What is "r", common ratio, for this sequence?

2, -2, 2, -2, 2

-1

200

The fourth term of a geometric sequence is 16. r, common ratio, is 2.

State the first term of the sequence.

2

300

In a geometric progression, T₄ = −192 and T₇ = 12288.

Find the value of r, the common ratio in the sequence.

-192r³ = 12288

r³= -64 (divide both sides by -192)

r = -4

400

Consider the series 4 − 8 + 16 − . . . − 2048.

Solve for n, the number of terms in the series.

n=10

500

Find the sum of the first 9 terms of the sequence 0.25, 0.5, 1, 2, 4, . . .

127.75