[討論]Pure maths [復制鏈接]

打d題目出黎睇下^^

1. Suppose that the recurrence relation is a1=0, a2=1, a n+1 = 1/2 (an+a n-1) n =2,3,4.....

(a) Given that bi= 1-(3ai/2) where i=1,2,3,...,n, find b1, b2, b3.

(b) Hence, guess a formula for the general term of the sequence {ai}and prove it by induction.

(深色係term) (7marks)

2. Suppose p is a prime number not equal to 2, prove that [2*(p-1) -1] / p is an interger. (7marks)

有d唔識打,,,唔知summation個符號

3. Let f(x) = x*4 - 2x*3 - 4x*2 + 6x + 1 and g(x) = x*3 - 5x -3

(a) Show that f(x) and g(x) are relatively prime.
(b) Find the polynomials u(x) and v(x) such that u(x) f(x) + v(x) g(x) = 1.
(c) Hence, resolve 1/ [(x*4 - 2x*3 - 4x*2 + 6x + 1)(x*3 - 5x -3)] into partial fractions.

(8marks)

4. Find the equation of the image of the curve C: y*2-2(3)*(1/2)xy-x*2-2=0 under a reflection in the line through the origin making and angle 60degree with the positive x-axis. (8marks)

push

宜家教緊inequalities

下面是引用望晴天於2006-02-12 15:31發表的:
push
宜家教緊inequalities [表情]

難野wo

下面是引用望晴天於2006-02-12 15:31發表的:
push
宜家教緊inequalities [表情]

eeeee
我都係啵......

=﹏="
唔知係咪我地學校教得快...
晨咁早教晒inequalities....
剛又教晒matrix...

而家已經教左1+1/4本書...=0=

下面是引用alvin_bun於2006-02-14 06:20發表的:
=﹏="
唔知係咪我地學校教得快...
晨咁早教晒inequalities....
剛又教晒matrix...
.......

我地除complex no.之外教曬啦algebra...

開左calculus...

下面是引用望晴天於2006-02-17 17:08發表的:
我地除complex no.之外教曬啦algebra...
開左calculus... [表情]

做乜唔教complex no. ge.........

下面是引用望晴天於2006-02-17 17:08發表的:
我地除complex no.之外教曬啦algebra...
開左calculus... [表情]

我地都係喎=]"
calculus教左半本啦又=﹏="

剛教完呢個limit of function=]"

下面是引用alvin_bun於2006-02-19 19:09發表的:
我地都係喎=]"
calculus教左半本啦又=﹏="
.......

咁你下年教乜....

下面是引用傷心小sam於2006-02-19 19:25發表的:
咁你下年教乜.... [表情]

唔知=﹏="
教past paper掛

我就考p.maths ~ d 同in 果份paper 上年平均廿幾分就pass ~
建議放多d心機落去d 同 in 度~特別係in ~好難下~

下面是引用alvin_bun於2006-02-21 21:46發表的:
唔知=﹏="
教past paper掛

past paper?

我都係近呢個幾月先做咋wor(做5至10年乜都夠la...)......

仲有....past paper洗鬼教咩，又唔係冇marking scheme~~

e+ mock都考埋，估計有百六分

下面是引用Arreat Summit於2006-02-21 23:34發表的:
我就考p.maths ~ d 同in 果份paper 上年平均廿幾分就pass ~
建議放多d心機落去d 同 in 度~特別係in ~好難下~

係ar，calculus只要操多d就得ga la

algebra就比較抽象、難明...