Download This is an English translation of the original Japanese version of the

This is an English translation of the original Japanese version of the question papers set
for the 2012 Entrance Examination.
Biology
Question 1: Read the following sentences and answer the questions.
The cell cycle has four distinct phases: the M phase, during which cells divide; the [ A ] phase,
during which DNA replication occurs; the [ B ] phase from the M to [ A ] phases; and the [ C ] phase
from the [ A ] to M phases. As cyclins bind to [ D ] and are activated during the cell cycle, target
proteins are phosphorylated and specific events in each phase proceed. In addition, the cell cycle has
(1) certain checkpoints that monitor whether the processes at each phase of the cell cycle have been
properly completed before progression into the next phase.
Cell proliferation is controlled by the external cues, and the availability of nutrients is an important
component of the external cues for single-celled organisms. Multicellular organisms exert a higher
level of control over cell proliferation to maintain themselves. All the cells in multicellular
organisms have the same genetic composition, which is transmitted to daughter cells through cell
division; however, not all genes function in each cell. Each gene functions at a certain time and in a
certain cell, which leads to organ differentiation and the exercise of specific functions by individual
cells. Meanwhile, (2) mutations occur to DNA at a certain frequency. Mutations are caused both by
external factors, such as ultraviolet rays, radiation, and chemical substances, and internal factors,
such as transposons.
(1) Answer the appropriate terms for [ A ] to [ D ].
(2) In regard to underlined section (1), explain the checkpoints in approximately 50 words.
(3) In regard to underlined section (2), explain the influence of base mutations in DNA sequences on
gene functions in approximately 70 words.
Question 2: Read the following sentences and answer the questions.
Centrifuging at 1000×g for five minutes makes healthy mammal blood separate into two layers:
[ A ], which is a transparent upper layer; and a lower layer of cellular components. Cellular
components include leukocytes, such as lymphocytes, neutrophils, eosinophils, basophils, and
monocytes. In addition, it is also possible to isolate lymphocytes utilizing the gradient centrifugation
method.
(1) Answer the appropriate term for [ A ]. When drawn, the blood sample is red. What color is after
centrifugation? Choose the most appropriate answer from (a) to (c) below, and describe the reason in
approximately 20 words.
(a) Both [ A ] and the cellular components will be red.
(b) Only [ A ] will be red.
(c) Neither (a) nor (b).
(2) In regard to the proteins listed in (a) N (e) below, write “I” for those included in [ A ], write “II”
for those included in blood cellular components, and write “III” for those included in both [ A ] and
blood cellular components. Then, describe the individual functions of (a) – (e) in approximately 10
words each.
(a) Hemoglobin
(b) Histone
(c) Immunoglobulin
(d) Tubulin
(e) Insulin
(3) It is possible to create clone animals utilizing somatic cells. However, the clone animals created
utilizing lymphocytes may experience serious problems for survival. Describe the problems and the
reasons they occur in approximately 40 words.
Question 3: Read the following sentences and answer the questions.
The major source of carbon in living organisms is carbon dioxide in the atmosphere and oceans,
which is fixed in the form of organic compounds by producers. Carbon in organic compounds is
moved to each trophic level through the food chain, and returned to the environment through
respiration and the decomposition of decaying matter in each tropic level.
Primary production rate varies according to producers. (1) In the terrestrial ecosystem, primary
production rate is the fastest in tropical rainforests and wetlands, and slow in savanna and boreal
forest. In the oceans, the rate is fast in coastal and upwelling areas, and low in open ocean.
(1) How does carbon dioxide concentration in the air change according to season? Describe this and
include the factors that cause the seasonal changes in approximately 20 words.
(2) Food chains can be classified into two types; one based on plants and one based on decaying
matter and waste. Answer the name of each food chain, and using the names, explain the
characteristics of the secondary production rate in the forest ecosystem in approximately 40 words.
(3) In reference to underlined section (1), answer the important factors that control the primary
production rate in terrestrial and marine ecosystems respectively .
(4) Explain the significant differences between phosphorus cycle in ecosystems and the carbon and
nitrogen cycles in approximately 40 words.
Question 4: Read the following sentences and answer the questions.
In the process of appearingon land, plants developed stomata and epidermis covered with [ A ] to
control the release of water. When the water level in plants decreases, the stomata close to reduce
water loss. Meanwhile, when the stomata are open, plants absorb and release carbon dioxide and
oxygen as well as (1) release water. Stomata consist of a pair of [ B ] cells. (2) Along with reducing
of carbon dioxide concentration and exposure to light, potassium channel is activated in [ B ] cells.
As a result, potassium ion(K+) concentration in [ B ] cells increases, influx of water occurs, [ C ]
inside the cells increases, and stomata open. When plants lack water, the outward potassium channel
in [ B ] cells is activated, K+ ions are released from the cells, [ C ] reduces, and stomata close.
(1) Answer appropriate terms for [ A ] to [ C ].
(2) What is the phenomenon described in underlined section (1) called?
(3) In regard to underlined section (2), explain the reason that stomata open when [ C ] inside [ B ]
cells increases in reference to the structural characteristics of [ B ] cells in approximately 30 words.
(4) It is known that a phytohormone, which mediates signal transduction in response to water stress,
is involved in the closure of stomata. Answer the name of this phytohormone and describe its
functions in the process of seed maturation in approximately 40 words.
Question 5: Explain the following terms in approximately 40 words each.
(1) Competitive exclusion
(2) Genome imprinting
(3) Phytochrome
(4) Proteasome
Chemistry
Question 1: Aqueous solutions of copper (II) sulfate and sodium chloride were separately placed in
two electrolytic baths (X and Y, respectively) and connected using platinum electrodes (A, B, C, and
D), as shown in the diagram. When a current of 1.00 A was passed through the parallel-connected
electrolytic baths (X and Y) for 600 seconds using the battery shown in the diagram, the mass of the
electrode (B) increased by 0.127 g.
Assuming that the experiment was conducted in an ideal manner, answer questions (1) to (4) below.
Show your calculations. Faraday's constant is 9.65 × 104 C/mol-1 and the atomic weight of Cu is 63.5.
In addition, 1 mol of gas occupies a volume of 22.4 L under standard conditions.
(1) The following reaction occurs at the surface of the electrode (A) due to electron transfer.
2H2O → O2 + 4H+ + 4e–
In the same way, describe the reactions that occur at the electrodes (B, C and, D).
(2) Under standard conditions, how many liters of gas(es) are produced in the electrolytic bath (X)?
(3) How many Amperes of current flow through the electrolytic bath (X)?
(4) How many moles of gas(es) are produced from the electrolytic bath (Y)?
Text in diagram (top to bottom)
Electrolytic bath (X)
Aqueous solution of copper (II) sulfate
Electrolytic bath (Y)
Aqueous solution of sodium chloride
Battery
Question 2: Answer questions (1) to (3) below.
(1) For an aqueous solution of a weak monoprotic acid (HA) having a concentration (c), express the
acid dissociation constant (Ka) of HA by using c and the degree of ionization (α). In addition,
assuming that α << 1, express the H+ concentration [H+] by using c and Ka.
(2) Using the equations determined in (1), calculate the pH of a 0.16 M aqueous solution of a weak
acid (HA) having a pKa of 6.0 (solution X).
(3) Calculate the pH of a mixed solution obtained by adding 20 ml of a 0.30 M aqueous solution of
NaOH to 100 ml of solution X.
Assume that precipitation does not occur. In addition, the concentrations of HA and A– and the acid
dissociation constant (Ka) are linked by the equation below:
_
[A ]
pH = pK a + log
[H A]
(equation)
Table of logarithms
Use the table of logarithms on the right if necessary.
Show your calculations.
Question 3: A linear hexapeptide (X) was isolated by partially hydrolyzing a natural protein. When
the amino acids composition of this peptide was analyzed, it was found that the peptide comprised
amino acids having the planar structures (a) to (e) below. Read statements 1 to 4 below, which relate
to this hexapeptide (X), and then answer the following questions (1) to (3).
1.Both amino acids that constitute the N- and C-terminus of X do not exhibit optical rotation.
2. Two kind of tripeptides were obtained by digestion of X with an enzyme trypsin that specifically
cleaves the peptide bond on the carboxyl group side of a basic amino acid residue.
3. A tetrapeptide (Z1) and a dipeptide (Z2) were obtained by digestion of X with an enzyme
chymotrypsin that specifically cleaves the peptide bond on the carboxyl group side of an aromatic
amino acid residue. An aqueous solution of Z1 had an absorption wavelength of approximately 280
nm, but an aqueous solution of Z2 did not.
4. When amino acids obtained by completely hydrolyzing the tetrapeptide Z1 were separated by
paper chromatography, followed by spraying with a ninhydrin solution and heating, several purple
spots and one yellow spot were detected.
(1) The 20 main amino acids constituting proteins can be represented by three-letter or single-letter
codes, and (a) to (e) are also represented by some of the single-letter codes shown below.
A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y
Using the same style as the example of methionine below, give the names, three-letter codes and
single-letter codes of the amino acids (a) to (e).
Example: Methionine, Met, M
(2) Express the amino acid sequence in the peptide X in order from the N-terminus using the
symbols (a) to (e).
(3) With reference to the structures of (a) to (e), describe the planar structure of the tetrapeptide Z1.
Question 4: In the reactions (1) to (10) shown below, fill in the blank sections
by selecting
the appropriate structural formula or term from the list of answers shown below and draw the
appropriate structural formula in the blank section
in questions.
Text in reactions:
(1) Acid catalyst
(2) Base
(4) Acid catalyst
(10) Radical initiator
[List of answers]
CH3SH
CH3OH
CH3I
CH3OCH3
CH3COOH
CH2N2
CH2=CH2
CH3SOCH3
Acid catalyst
R1-N=C=O
Light
R1-NH-COOH
CH3COOOH
Base
Heat
Question 5: Read the following sentences and then answer questions (1) to (4) below.
A diethyl ether solution (A) containing cyclohexylamine, benzoic acid, and toluene was placed in a
separating funnel and extracted with a 5% aqueous solution of sodium hydrogen carbonate, thereby
resulting in an organic layer (fraction (1)) and a water layer. The pH of the obtained water layer was
adjusted to 2 with 6 M hydrochloric acid and then extracted with diethyl ether, thereby producing an
organic layer (fraction (2)) and a water layer (fraction (3)).
(1) In which of fraction (1), fraction (2), or fraction (3) is each of the benzoic acid and the toluene
mainly contained?
(2) Explain a solvent fractionation method for separating the cyclohexylamine into an organic layer
from the diethyl ether solution (A).
(3) If a diethyl ether solution (B), further incorporating phenol in the diethyl ether solution (A), is
subjected to the above-mentioned fractionation procedure, in which of fraction (1), fraction (2), or
fraction (3) is the phenol mainly contained?
(4) Explain a solvent fractionation method for separating the phenol into an organic layer from the
diethyl ether solution (B).
Physics
Question 1: Take a thin stick held horizontally with both ends at height h, with length I
= 2√3 h and a mass of 2 m, and cut it at the middle. The two halves of the stick freely
pivot on each end and fall within the vertical plane. Assume that the halves began to
fall gently from the horizontal state. What is the angular velocity ω when the tip of the
half touches the ground? Ignore friction and air resistance.
Question 2: Suppose there is an alternating-current bridge circuit as shown in the
following figure. When an alternating current of angular frequency ω [rad/s] was
impressed between the contact points B and D and the values of Cx and Rx were
adjusted, the electric potential difference between contact points A and C became 0.
Find the values of Cx and Rx at this time. Assume R1, R2 and Rx are resistance [Ω] and
C2, C3 and Cx are capacitors [F].
Question 3: Answer the following questions about a cyclic process in which a working
substance of one mole of ideal gas cycles through three states, A (p1, V1, T1), B (p2, V2,
T1), and C (p3, V2, T2), in the order A → B → C → A, as shown in the following figure.
Assume (i) A → B is the isothermal change, (ii) B → C is the constant volume change,
and (iii) C → A is the adiabatic change. Furthermore, assume volume V1 < V2, pressure
p1 > p2 > p3, and temperature T1 > T2, and for this gas assume that the molar specific
heat at constant volume is Cv [J/mol-1 K-1], the molar specific heat at constant pressure
is Cp [J/mol-1 K-1], and the specific heat ratio is γ.
(1) Find the conditions that must be satisfied by the pressure p3 at state C in order for
the working substance to return to the initial state A in the adiabatic process of C → A.
(2) Find the amount of heat absorbed in one cycle of A → B → C → A.
Question 4: Give brief explanations about the following terms.
(1) Coriolis force
(2) Fresnel lens
(3) Seebeck effect
(4) Biot-Savart law
(5) Thermal neutron
Mathematics
Question 1: Assume point P in 3-dimensional space has coordinate (1, 1, 1) in an x, y, z
orthogonal coordinate system, as shown in Figure 1. Assume that there is a straight line
L passing through the origin and point P. Answer the following questions.
(1) Assume Q is a plane that passes through point P and is perpendicular to straight
line L. Find the equation for the line of intersection between Q and the x-y plane.
(2) Rotate a straight line that passes through point P and forms a 30° angle with the
straight line L around the straight line L. When this is done, the locus of the point of
intersection of this straight line and the x-y plane traces an ellipse. Find the center of
this ellipse.
(3) Find the length of the major axis and the length of the minor axis of the ellipse in (2).
Figure 1: Point P and straight line L within a 3-dimensional space
Question 2: Figure 2 describes the one-step transition probability of the Markov chain
Xt, t = 1, 2, 3, ･･･ For example, in the case that an object is in state 2 at a given point in
time, at the next point in time the object transitions to states 1, 3, or 4 with respective
probabilities of 1/3. States 4 and 5 are the absorbing states. Answer the following
questions regarding this Markov chain.
(1) Find the probability that an object will finally reach state 5, in the case that the
object is in state 2 currently.
(2) Find the average number of steps through which an object reaches absorbing states
4 or 5, in the case that the object is in state 2 currently.
Figure 2: The one-step transition probability of Markov chain Xt
Question 3: Answer the following questions about a right cylinder that is inscribed in a
sphere with a radius of 1.0.
(1) If the height of the right cylinder is assumed to be x and the radius of the base to be y,
show the relational expression for x and y.
(2) Find the height, radius of the base, and the volume for the right cylinder with the
maximum volume.
(3) Find the height, radius of the base, and the volume for the right cylinder with the
maximum lateral area.
Question 4: Answer the following questions.
(1) Assume n is a positive constant and ln = ∫cosnx dx. Show that the following equation
is satisfied at this time:
ln =
cosn-1x sin x +
ln-2
(2) Find the area of the domain bounded by curve |x|2/3 + |y|2/3 = p2/3 as in Figure 3.
Assume p is a positive constant.
(3) Find the volume of the body bounded by the curved surface |x|2/3 + |y|2/3 + |z|2/3 =
q2/3. Assume q is a positive constant.
Figure 3: Curve |x|2/3 + |y|2/3 = p2/3