0代表错误或遗漏的答案。没有负面的标记。

2。

6an 1 + 9an 2 = 3n; n 2：

an = 1
2 n2
3n 3n
an = 1
2n3n
an = 2n2
3n
an = 1
2n2
+ 3n
an = 3n + 1
3。

an + 2nan 1 = 1; n 1；

（a）有一个独特的解决方案，其中a0 = 0。
（b）对于a0 = 0和a2 = 2没有解决方案。
（c）一个特定的解决方案是由= n！（2）n + 1给出的。
（d）如果（an）和（bn）是解，则（an + bn）也是。
（a）和（b）都为假
（b）和（c）都为真
（c）和（d）都为假
（a）和（d）都为真

4，

（A）所有顶点均具有偶数度的连通图

（B）最多具有两个奇数个顶点的连通图具有

（B）来自（A）？
（a）在适当的顶点处添加一个循环
（b）在两个合适的顶点之间添加一条边（c）使用自变量

（d）使用有关顶点着色和最大顶点的参数

（a）和（b）
（a）和（c）
（b）和（c）
（b）和（d）
（c）和（d）

Students will be given 3 hours to complete this multiple choice exam.
Calculators are permitted.
All questions should be answered. Each question (Q2-Q21) carries 5 marks
for a fully correct answer, 1 for a partially correct answer (if appropriate),
and 0 for an incorrect or missing answer. There are no negative marks.
You are not permitted to give or receive any unauthorized help on
this exam and all work should be your own.
1.
I arm that I will not give or receive any unauthorized help on this
exam, and that all work will be my own:
 true
 false

2.
Consider the recurrence relation
an 6an 1 + 9an 2 = 3n; n  2:
Say which of the following is a valid solution of this equation.
 an = 1
2 n2
3n 3n
 an = 1
2n3n
 an = 2n2
3n
 an = 1
2n2
+ 3n
 an = 3n+1
3.
Consider the rst-order recurrence relation
an + 2nan 1 = 1; n  1;
and the following statements referring to this equation:
(a) There is a unique solution for which a0 = 0.
(b) There is no solution for which a0 = 0 and a2 = 2.
(c) One particular solution is given by an = n!( 2)n + 1.
(d) If (an) and (bn) are solutions then so is (an + bn).
 both (a) and (b) are false
 both (b) and (c) are true
 both (c) and (d) are false
 both (a) and (d) are true

4.
The following two propositions are known to be true:
(A) A connected graph all of whose vertices have even degree possesses
a closed Eulerian trail.
(B) A connected graph with at most two vertices of odd degree possesses
an Eulerian trail.
Which two strategies, taken together, best describe how one can deduce
(B) from (A)?
(a) adding a loop at a suitable vertex
(b) adding an edge between two suitable vertices (c) using an argument
about the sum of vertex degrees
(d) using an argument about vertex colouring and maximum vertex
degree
 (a) and (b)
 (a) and (c)
 (b) and (c)
 (b) and (d)
 (c) and (d)