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真二第張七第日八十月二年酉己屦夏 WAF KIU YAT PO
報日僑茶
五期星日四月四年九六九一公年八十五國民菱中育教僾華
文中學會考試題預習」
1969AFUNZ
生物科
(廿二)
MEX
現代數學科
(1=)
BIOLOGY (22)
MODERN MATHEMATICS (22)
Answer to the questions of last week:
1.
What ia digestion and why is it necessary? (b) On a large scale mate a fully labelled drawing to show the structure of the alimentary canal, and the associated glands in a Named mammal, and explain, how the structure of the alimentary canal of this illustrated mammal enables it to carry out its physical functions.
And.
(a) The complex carbohydrates, proteins and fats are
insoluble in water, and cannot be absorbed and assimilated by living cells of the body until they are converted into simple substances.
Digestion may be described as the changes that the foods normally undergo preparatory to absorption; these changes are physical and chemical and occur in the alimentary canal of an animal or in the cells of the body of a plant,
As in animals, food is utilized by the body. to obtain materials for growth and maintenance, for replacement or repair of parts, for energy to move, and for producing sex cells.
Plants synthesis the food they need for life, growth, and for building up the protoplasm of now cell..
"Gall bladder
Bile- duct
Solution of the exercise assigned last week,
(1) Given
-10
then
A+B
B+
13
(A+B)+C= |
( ).
(3
526 36/2x3
AXB2
3).
3x1+0+0 5+0+0 2+0+0
(2-22) ( 2 )
(2) No, it is because the 2 matrices are not con-
formable for addition.
(3)
Desophagus -Diaphragm
6
If A and B are conformable for addition, then „A*+B'= (A+B)'.
"Liver
-Stomach pylori hincter
Smal
intestine)
Proof:
Let A A = (a1j)mxn • B = (bij)mxn•
B1 (bji)nxm
Then A
A+B
= (aji+Þja?xm
(Cij)mxn where Ci ja
Then (A+B)» (Ch)nem
Therefore (A+B)'= A••
ices (continued)
Multiplication of matrices
There are two types of multiplication of matrices, namely the scalar multiplication: of matrices and the matrix multiplication of matrices.
pancreas
Ducdenum
ancreatic duct
Ileum
Vermiform Caecum appendix
If A
Definition: 11 A is any matrix and k any scalar quantity (real number), we define kå tobe the matrix which is formed by multiplic- ating each element of A by k. Example:
-15.
ЗА
9-12 48 24 21
then
AXB
3
3x3
3x3
0+1+0+0+0+5)
·0+3+0 0+0+7
·0+6+00+0+4/
3x3
x = ( 2 ¦ 392x4
0+2 0+6 0+3
1+0 4+0 2+0 8+0/2x4
- 12 6 3 3) 2x+
Remarks!
a. The multiplication of A and B is possible
ans makes sense if and only if the number
• of columns in A is the same as the number
of rows in B. If so, A and B are said to be conformable for multiplication..
If the order of A is mxn and that of B ja axp, then the order of AB is mxp, That is the number of rows in AB is the same as thɩ. number of rows in A, and the number of zAŽÍ. columns in AB is the number of columns in B. If A and B are conformable, B and A are not nesessarily conformable for multiplica-; tion.
In general if AB and B are both defined AB A BA. In AB we say B is premultiplied by A and in BA we say a ia prenultiplied by B.
Properties of matrix multiplication:
Matrix multiplication is not commutative: One counter example is sufficient to show the truth of the fact,
Assume Azz and B32 to be two conformable. matrices. Then
A2x3* Bxx2 C2x2
B3x2 x 42x3
C2x2 3x3
D3x3.
If A, B and C are conformable for multipli- cation, then A(BC) = (AB)C. That is matrix multiplication is associative.
In proving the property, we need a new notation, which is a symbol for sum.
Examples:
1. If 1+2+3+4+.5
n(n+1)
we can express the su
Anus
Colon
Sacculas rotundus
The omitted portion of Rectum Pertum containing the pettat like facces
The Alimentary Canal and Its Associated Glands
OF Rabbit
The following parts of the alimentary canal are considered as the structures which enable the canal to carry out its physical functions:
(1) Vesophagus:
A tube with well developed muscular walls. It passes between the lungs and penetrates through the diaphragm to the stomach. At the junction of the oesophagus, and the stomach, a muscular ring is Called the cardiac sphincter. When this ring opens, the food is passed through the oesophagus to the stomach.
(11) Stomach
A greatly dilated portion of the otherwise marrow digestive tube. The opening. into the duodenum is called the pyloric sphincter. The musculature of the stomach is arranged not only in the usual circular and longitudinal fashion, but also some of the fibres take on a oblique course," The most important function of this part is the storing of food. By discharging its contents very slowly, the stomach protects the intestine from receiving too much of food at one time. When the rhythmic contraction of the stomach wall is set up, it will churn up the food to mix it with enzymes. The stomach leads to the duodenum through the pyloric sphincter which opens at intervals to force. some amount of chyme to the duodenum. (111) The small intestine
Concerning about the digestive process, the small intestine performs two distinct sorts of movements, the rhythmic segmentation and the peristalsis. In the rhythmic segmentation, the food mass is forced along the gut and is thoroughly mixed with the digestive Juice for further digestion. As in the peristalsis, the characteristic wave movement of the alimentary caral thus carries the food mass from the anterior to the posterior end of the gut..
During absorption, the presence of villi enable the small intestine to have a large absorptive surface area for the great absorption of food.
(iv) The large intestine:
The important movement of the large
Propertities of scalar multiplication of matrices :
1. Closure property: Given A, any matrix,
and k any scalar, ka is a matrix of the same order.
Associative property::
a. (A) = (a,b).A, where A is any matrix and a,b any scalars.
Distributive properties:
a.(A+B) = a.A a.B and
(a+b).A a...A + þ‚Ã where A and B are matrices of the same order and a.bare scalars.
4.Zero property::
O.A0, where A is any matriz, O the zero scalar and ◊ a zero matrix. Definition: If A be an mxn matrix and B ar pxn matrix, then the product AB is defined to be mxn patrix C in which any element Cij is obtained by multipying together the corresponding ith row of A and 1 th column of B and adding the products.
Examplest
1. IT A
then
AXB
3x44
1+4x5 2x-1)+ 1x5+4x7 2x2+1x0+
··4x6
-2x3+5x7 3x24-2
5x6
intestine is masa peristalais, quite comparable to the peristalsis of the smil intestine. This powerful waves movements pass from the cascun over the entire length of the colon. By this the contents are forced forward to.
the rectum.
The another essential function of the large intestine is considered as the absorption of water and mineral salts from the residues, so that they are changed into a semi-solid state before they can be discharged from the body.
2.) State as fully as you can, the functions of the
liver of a manial,
Axis.
) Explain briefly, how do the salivary glands
the stomach and the pancreas help in the digestion i of food in the body of a osmaal.,
The liver is the largest gland in the body of a mammal. Its function my be defined as follows:
Õ་▪ fa+1)
3=1
We can express.
1°';
Similarly the sum a1181448.
by
AST
In general
$1k
Proof of property 2 Let A = (aij)mxp,
(Ckh3nxq
and C =
BC
bjk okh pxq
A(BC)
bgk/ D
mxq
3(n+1)
which is the product in the left hand side.
Bij bjk ma
(AB)C
which is the product in the right hand side. We know that the multiplication of real numbers is associative. Therefore
A(BC) = (AB)C
(1) For production of bile - Although bile contains no digestive enzymes, but its alkaline bile salts emulsify fats, breaking them up into smaller globules and thereby providing more surfaces on which lipases can act.
- All materials absorbed from the intestins are carried to the liver by the hepatic portal vein. The liver exercises a selective action upon the materials seeking entrance into the body. When putrefactive compounds arrive at the liver, they are taken out of the circulation and transformed into less toxic substances, (111) For conversion of excess glucose into
(11) The detoxifying function
glycogen to be stored - The glucose absorbed from the sma11 intestine is carried by the hepatic portal vein to liver, where the exceas glucose is converted into glycogen and stored. When the sugar concentration the body is low, the glycogen my be
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