【纪念当年的帖子（2008）】高級數學纲要笔记

_囧_

哇 謝謝你哦樓主

长今

真的！！我这个老师，在这里，为这篇文章做品质保证！！

harry_lim

原帖由 长今 于 19-10-2009 08:08 PM 发表
真的！！我这个老师，在这里，为这篇文章做品质保证！！

原来你是老师啊！
失敬失敬

乙劍真人

原帖由 ~HeBe~_@ 于 6-10-2009 02:21 AM 发表
其实这个题目有问题。

谢谢你的意见..

原帖由 kurukawa 于 10-10-2009 01:25 PM 发表
呃。。。不好意思哦。。。
这课是不是有一个部分是叫
Normal Distribution
要用到那个table的。。。
我想问问谁人有那个table。。。
可以给我吗 不好意思。。。谢谢

请教你老师教你按计算机，方便快捷又省时间..

原帖由 _囧_ 于 10-10-2009 02:16 PM 发表
哇 謝謝你哦樓主

不必客气..

原帖由 长今 于 19-10-2009 08:08 PM 发表
真的！！我这个老师，在这里，为这篇文章做品质保证！！

谢谢老师的赞赏..

Boys_like_girls

大家好，我是新来的
又一题关于Differentiation的题目不会做，想请教各位
Find the minimum value of
A= x^2+y^2 if x + y=10

乙劍真人

原帖由 Boys_like_girls 于 25-10-2009 09:45 PM 发表
Find the minimum value of A= x^2+y^2 if x + y=10

            A= x² + y²   ---(1)
x + y=10     ---(2)

From (2), let y = 10 - x

Therefore, A = x² + (10 - x)²
                       = x² + 100 - 20x + x²
                       = 2x² - 20x + 100 ---(3)
            dA/dx = 4x - 20 ---(*)
Let dA/dx = 0
          4x - 20 = 0
                    x = 5

From (*), d²A/dx² = 4>0
Since d²A/dx² >0, A is a minimum value.

Substitute x = 5 into (3),
Minimum value of A = 2(5)² - 20(5) + 100
                                   = 50

Boys_like_girls

ok...
get it
真实感激不尽啊

Boys_like_girls

还有一个问题想要问高人的
就是在做solution of triangle的时候啊
有时使用sine rule和 cos rule做同一个题目阿
会拿到不一样的答案的
必须怎样做才确保答案没有错呢

_囧_

function 2004 年的可以show step 出来吗？
太久没动忘记怎样做了

乙劍真人

原帖由 Boys_like_girls 于 26-10-2009 12:53 PM 发表
还有一个问题想要问高人的
就是在做solution of triangle的时候啊
有时使用sine rule和 cos rule做同一个题目阿
会拿到不一样的答案的
必须怎样做才确保答案没有错呢

不可能..
答案一定一样..

Example:
Identify the length of AB for the diagram below by using:
(a) Sine Rule
(b) Cosine Rule

SOLUTIONS:

(a) Sine Rule
AB/sin 35° = 8.2/sin 50°
AB = 6.14 cm

(b) Cosine Rule
AB² = 10.66² + 8.2² - 2(10.66)(8.2) cos 35°
        = 37.67
AB = 6.14 cm

Boys_like_girls

Given 3 sides : a=10cm b=5.3cm c=8, angle C=70°
找B
b² = a² + c² - 2(a)(c) cos B°
5.3²=10²+8²-2(10)(8)cosB°
28.09=100+64-160cosB°
160cosB°=135.91
cos B°=0.849
B°=31.84°

(a) Sine Rule
c/sin C° = b/sin B
8/sin 70° =5.3/sin B
8.513 =5.3/sin B
sin B=5.3/8.513
sin B=0.6222
B°=38.5°
问题出在哪里呢？

乙劍真人

原帖由 Boys_like_girls 于 27-10-2009 09:42 PM 发表
Given 3 sides : a=10cm b=5.3cm c=8, angle C=70°
找B
b² = a² + c² - 2(a)(c) cos B°
5.3²=10²+8²-2(10)(8)cosB°
28.09=100+64-160cosB°
160cosB°=135.91
cos B°=0.849
B°=31.84°

(a) Sine Rule
c/sin C° = b/sin B
8/sin 70° =5.3/sin B
8.513 =5.3/sin B
sin B=5.3/8.513
sin B=0.6222
B°=38.5°
问题出在哪里呢？

haha..
问题出在小数点..

sin B = 0.6
      B = 36.87°

cos B = 0.8
       B = 36.87°

乙劍真人

SPM FORECAST 2009:

(1) Functions
- Determination the Relations, Images and Objects of a functions.
- Inverse Functions (find unknown and value that undefined).

(2) Quadratic Equations
- Solution of Quadratic Equations.
- Types of Roots and applications of b² - 4ac.

(3) Quadratic Functions
- Maximum Point vs Minimum Point.
- Applications of b² - 4ac and Inequalities.

(5) Indices and Logarithms
- Laws of Indices vs Laws of logarithms.
- Changing the base of logarithms.

(6) Coordinate Geometry
- Equation of Tangent vs Equation of Normal.
- Parallel Lines vs Perpendicular Lines.

(7) Statistics
- Interquatile Ranges.
- Effects on Mode, Median and Mean when measurement Changed.

(8) Circular Measure
- Length of Arc or circles.
- Area of Sector and Triangles.

(9) Differentiation
- Applications in Maximum and Minimum values.
- Rate of Changes vs Small Changes & Approximation.

(10) Solution of Triangles
- Problem Solving involving Sine Rule & Cosine Rule.
- Refer Past Year Questions for SPM format.

(11) Index Number
- Price Index vs Composite Indices.
- Refer Past Year Questions for SPM format.

(12) Progressions
- The n term of AP vs GP.
- Sum of first n terms and Sum to Infinity.

(13) Linear Law
- Reduction of Non-linear Relations (Log) to Linear Form, Y = mX + c.
- Identify the values of X and Y from Graph.

(14) Integration
- Determination of Integral by Substitution and Definite Integrals.
- Area under a graph vs Volume of Revolutions.

(15) Vector
- Vectors in the Cartesian Plane.
- Magnitude of Vector vs Unit Vector.

(16) Trigonometric Functions
- Proving Basic Identity vs Double angle Formulae.
- Solving Trigonometric Equations for given Domain.

(17) Permutations and Combinations
- How many 4-digit even numbers > 5000 can be formed with digits 4, 5, 6, 7 or 8 without repetition.
- Find the number of committees for more men than women.

(18) Probability
- Probability of an Event, n(S) / n(A).
- Identify the probability for same colour balls if balls drawn randomly twice.

(19) Probability Distributions
- Identify Mean vs Standard Deviation by using Binomial Distributions.
- Identify Standardised Score (Z) and applications for Normal Distributions.

(20) Motion Along a Straight Line
- Velocity Displacement vs Acceleration Velocity.
- Refer Past Year Questions for SPM format.

(21) Linear Programming
- Region that satisfies several Linear Inequalities.
- Refer Past Year Questions for SPM format.

至于完整的预测考题将会迟些再上载，敬请留意。
祝大家考试顺利！

Boys_like_girls

哦！谢谢你哦！
那最好要用多少个小数点呢？
我看一本参考书说小数点要留到最后才round off的，
是吗？

harry_lim

除非question是有注明要correct到几个decimal places/signidiciant figures才用
那么linear law的最好是correct to 3 decimal places好了！

Boys_like_girls

哦！是这样哦！

天空之道

the first term of an arithmetic progression is -10 . Given that the sum of the first n term of the progression is -12 and the next n term of the progression is 42 , calculate the value of n.

天空之道

没大错哦
我会再接再厉看有没办法做的出
老师讲这不会出在spm的

~搞怪男孩~

新来的。。中4罢了~add math还算可以~希望可以在这里学到更多~~

GeForceKAS

高级数学不会很难啦。。。。。哈哈