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標題: Exam Paper Discuss(G.Maths.) [打印本頁]

作者: 細薯 時間: 10/3/2005 07:05 PM
標題: Exam Paper Discuss(G.Maths.)
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G.Maths.

Firstly,i will post some extracted part(especially those i don't understand) of the G.Maths. Paper I and Paper II.
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>>color=LimeGreen<<我ng識ge part~~

我ng識ge part total :
1) 14(b)(iii)
2) the whole question 15(containing 11 marks)[E-Ah][E-Ah]
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G.Math. Paper I

Section A(1)(31 marks)

1.Solve the equation (x+5)^2=x-5.
                                                                  (3 marks)

2.Solve 4^x=1/square root of 8 .
                                                                  (3 marks)

3.Let f(x)=1-x^2.Find the value od f[f(1)].
                                                                  (3 marks)

4.If the equation x^2 + 8x - k =1 has real roots,find the range of values of k.
                                                                  (4 marks)
5.Find the vertex and axis of symmetry of the graph y = x^2 - 6x +7 .
                                                                  (4 marks)
6.Solve the equation log(1-x) + log(1-8x)=2
                                                                  (4 marks)
7.If a=log3,b=log5,express the following in terms of a and b.
(a) log 45
(b) log 2
                                                                     (5 marks)
8.  (graph involved question)                            (5 marks)

Section A(2)(36 marks)

9.  (graph involved question)                               (6 marks)

10.  (graph involved question)                            (6 marks)

11.  (graph involved question)                            (7 marks)

12.  (graph involved question)                            (8 marks)

13.  (graph involved question)                            (9 marks)

Section B(33 marks)

14.(a)If the length and the area of a rectangle are l and A respectively,find the width of the rectangle in terms of l and A.
                                                                     (1 mark)
   (b)
         ____x____                                  ____x+10____
      |             |                                  |                   |
      |             | x             --------->>    |                   |       Figure 7
      |             |                                  |___________ |
      | _______ |
In Figure 7,a square of side x is changed into a rectangle of length x+10,keeping the area constant.

(i)Express the width of the rectangle in terms of x.

(ii)If the perimeter increases 5% when the square is changed to the rectangle,show that x^2 + 10x - 1000 = 0.

(iii)Write down all the steps to find the value of x,by making use of the graph y= x^2 +5x.

                                                                     (10 marks)

15.In a report,a student quoted the maximum amplitude(A)of the seismic wave and the magnitude (M)in four different earthquakes,as shown in Table 1.

      Place                A(mm)                      M
Country A                0.10                      3.5
Country B                   0.31                      4.2                Table 1
Country C                   1.19                      5
Country D                   27.95                   7

The student state that if the magnitude of the earthquake increases by x units,then the maximum ampitude will be y times the original earthquake,where y=a b^x ,a and b are constants.

(a) By comparing the earthquake in country A with the others,complete Table 2.
  (The first one has been filled in as an example.)

            |    x    |    0.7 |    1.5    | 3.5 |          Table 2
            |    y    |    3.1 |             |          |
                                                                     (1 mark)
(b)Use logarithmic transformation to show the relation between x and y by a graph of straight line .Hence find the values of a and b from the graph,correct your answer to the nearest unit.
                                                                     (7 marks)
(c)Are the data in line with the formula M= log A + K where K is a constant?Explain your answer.
                                                                     (3 marks)

16.  (graph involved question)                            (12 marks)

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Paper II 太多 graph involved question,所餘無幾~~

(to be continued)

[ Last edited by smallpotato226 on 2005-3-11 at 03:28 PM ]

作者: 抹茶可樂 時間: 10/3/2005 08:23 PM
x^2 + 10x - 1000 = 0
x^2 + 5x = -5x + 1000
Let y = x^2 + 5x = -5x + 1000
We have
y = x^2 + 5x
y = -5x + 1000
Draw the graph of y = -5x + 1000 in the same diagram with y = x^2 + 5x
Find the intersect points of two lines.
The x-coordinate of point is solution. (Reject one negative solution)

作者: 細薯 時間: 10/3/2005 08:27 PM

Originally posted by 落雷 at 2005-3-10 08:23 PM:
x^2 + 10x - 1000 = 0
x^2 + 5x = -5x + 1000
Let y = x^2 + 5x = -5x + 1000
We have
y = x^2 + 5x
y = -5x + 1000
Draw the graph of y = -5x + 1000 in the same diagram with y = x^2 + 5x
Find the ...

thx~this one i understand la~
i lost 11 marks in Q.15......

作者: SusanCrystal 時間: 10/3/2005 08:38 PM
做下先:

1.
(x+5)²=x-5
x²+10x+25=x-5
x²+9x+30=0
x=[-9±√(81-120)]/2
x=[-9±(√39) i]/2

2.
4^x=1/(√8)
x=log [1/(√8)]/log 4
x=[log1-log(√8)]/log 4
x=-1.5log2/2log2
x=-3/4

3.
f(x)=1-x²
f(1)=1-1=0
f[f(1)]=1-0=1

4.
x²+8x-k=1
x²+8k-(k+1)=0
∵It has real roots.
∴ Δ=0
64+4k+4=0
68+4k=0
4k=-68
k=-17

5.
y=x²-6x+7
=[x²-2(3)x+3²]-9+7
=(x-3)²-2
∴vertex=(3,-2), axis: x=3

作者: 抹茶可樂 時間: 11/3/2005 12:02 AM
y1=ab^x1
y2=ab^x2

y1/y2=ab^x1-x2

|    x    |    0.7 |    1.5    | 3.5 |       Table 2
|    y    |    3.1 | 11.9    | 279.5 |

y=ab^x
logy=log(ab^x)
logy=loga+logb^x
logy=xlogb+loga

|    x    |    0.7 |    1.5    | 3.5 |       Table 3
| logy    |    0.49 | 1.08    | 2.45 |

Use this data to draw a straight line
Find the slope and y-intercept of the line
By comparing with logy=xlogb+loga
logb=slope
loga=y-intercept

No.
From logy=xlogb+loga,
logA=Mlogb+loga
M=logA/logb-loga/logb
Although -loga/logb is a constant
logA is with the coefficient 1/logb
which does not match the formula

作者: dolphin_ice 時間: 11/3/2005 12:25 AM
er...唔好笑我...不過呢份係cal 定non-cal paper來ga? >.<"

作者: 細薯 時間: 11/3/2005 02:37 PM

Originally posted by 紅唇娃 at 2005-3-11 12:25 AM:
er...唔好笑我...不過呢份係cal 定non-cal paper來ga? >.<"

可以用calculater

(係咪問這個?)

| x | 0.7 | 1.5 | 3.5 | Table 2
| y | 3.1 | 11.9 | 279.5 |

really??
then i have one more mark la~~YEAH!!

[ Last edited by smallpotato226 on 2005-3-11 at 02:48 PM ]

作者: 細薯 時間: 11/3/2005 03:01 PM

2.
4^x=1/(√8)
x=log [1/(√8)]/log 4
x=[log1-log(√8)]/log 4
x=-1.5log2/2log2
x=-3/4

my calculation:

2.
4^x=1/(√8)
(2^2)^x = 1/[2^(3/2)]
2^(2x) = 2^(-3/2)
2x = -3/2
x = -3/4

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我頂ng順啦!!!!!!
o岩o岩睇返書
第15題一 D 都ng難..........
只係ar Sir果教時ng明
之後Exam前冇睇到

點解天要玩我
我只係冇溫兩part(Graph of Exponential and Logarithmic Function & Application of Logarithms)
佢份卷就出左11分..........><

[ Last edited by smallpotato226 on 2005-3-11 at 03:09 PM ]

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