This is an English translation of the original Japanese version of the question papers set

for the 2013 Entrance Examination.

Biology

Question 1: Read the following passage and answer the questions.

Genes A, B, C, a, b, and c of a plant are located on the same chromosome and linked to one another.

Genes A, B, and C are dominant over Genes a, b, and c, respectively. An individual with genotype

AABBCC and an individual with genotype aabbcc were crossed to produce F1 individuals, which were

self-fertilized to produce F2 individual seeds. The phenotype segregation ratios of 1000 F2 individuals

are shown below. As a result, recombination values between A and B, A and C, and B and C were 21%,

18%, and 9%, respectively.

ABC: ABc: AbC: aBC: Abc: aBc: abC: abc

376: 19: 33: [i]: 73: [ii]: 11: 384

(1) Provide the appropriate number for [i] and [ii]. However, double recombination is not an option.

(2) A diagram of a chromosome including gene A is shown below. Each number shows the distance

between two genes. Genes B and C are located somewhere along the chromosome from position [iii]

to [viii]. Choose the most appropriate answer from among [iii] to [viii] below to indicate the locations

of genes B and C.

[iii] Gene A [iv] [v] [vi] [vii] [viii]

(3) Gene A (a) and gene D (d), which is located on a different chromosome, affect the flower color of

the plant. The flower of an individual with both dominant genes A and D becomes yellow, and others

become white. The individual with both recessive genes a and d in a homozygous condition dies.

Under such circumstances, provide the ratio of yellow to white flowers in F1 individuals that were

produced by self-fertilizing of an individual with genotype AaDd.

(4) When choosing an individual randomly from F2 individuals produced by (3) to produce F3

individuals, provide the probability that any F3 individuals would not die due to a recessive

homozygous condition.

Question 2: Read the following passage and answer the questions.

Photosynthesis involves electron transfer which produces [ i ] by using light energy,

photophosphorylation coupled with the electron transfer which synthesizes [ ii ], and carbon

assimilation which fixes carbon dioxide to organic substances utilizing the energy of [ ii ] and the

reducing power of [ i ]. The rate of plant photosynthesis is affected by a wide range of environmental

factors. The graph below shows the relationship between light intensity and apparent photosynthetic

rate. Light intensity at point A and B differs according to the plant involved.

Flower bud formation is controlled by internal factors such as growth state and age, and external

factors such as length of day and temperature. Plants are classified into three types depending on the

photoperiods that promote flower bud formation, long-day plants, short-day plants, and day-neutral

plants.

見かけの光合成速度：Apparent photosynthetic rate

光強度：Light intensity

(1) Provide the appropriate terms for [i] and [ii].

(2) What do A, B, and C in the graph express? Provide the most appropriate term for each.

(3) Plants are classified into heliophytes and sciophytes according to their light requirements. Describe

the differences between heliophytes and sciophytes in approximately 30 words. Include the differences

in the values of A, B, and C.

(4) One of the environmental factors that affect the rate of photosynthesis is light intensity. Provide

two other major environmental factors.

(5) There are two kinds of chromoproteins that function when plants detect photoperiods and form

見かけの光合成速度

0 光強度 A B

C

flower buds. One is a cryptochrome. What is the other one?

(6) Explain short-day plants using the two terms, light period and dark period, in approximately 30

words.

Question 3: Read the following passage and answer the questions.

Animals developed osmotic adjustment systems appropriate to their living environments to

maintain body fluid homeostasis. For example, in order to control the osmotic pressure of body fluids,

saltwater fish eliminate salt from their gills and also eliminate small amounts of [ i ] urine from their

kidneys, while freshwater fish, which are Osteichthyes same as saltwater fish, absorb salt through their

gills and eliminate large amounts of [ ii ] urine from their kidneys. In mammals, including human

beings, kidneys play the same role. The kidney’s cortex contains renal corpuscles. Blood flowing

through the renal artery passes through [ iii ] and is filtered into [ iv ], which allows everything in the

blood plasma except proteins through. Most of the glucose, approximately 95% of the water, and

necessary inorganic salt in the filtrate, which is primitive urine is reabsorbed in blood capillaries in the

renal tubule. Furthermore, approximately 4% of water is reabsorbed in the collecting duct, (1) which

controls the osmotic pressure of body fluids. In addition, mammal kidneys also play an important role

in eliminating (2) unnecessary nitrogen compounds produced in the body as [ v ] through the ornithine

cycle.

(1) Provide the appropriate terms for [i] to [v].

(2) In regard to underlined section (1), list two hormones that have a direct bearing on osmotic control

in human kidneys, provide where the hormones are produced, and describe the function of the

hormones in approximately 50 words.

(3) In regard to underlined section (2), nitrogen compounds produced as a result of amino-acid

degradation inside the body are harmful and need to be eliminated. Mammals usually eliminate these

as [ v ]. How do Osteichthyes and Aves eliminate nitrogen compounds? How is their elimination of

the nitrogen compounds adapted to their living environments? Explain about Osteichthyes and Aves

separately in approximately 50 words for each.

Question 4: Read the following passage and answer the questions.

The process of eukaryotic gene expression on chromosomes is as follows: Gene sequences are first

transcribed as (1) pre-mRNA. The transcribed pre-mRNA then goes through (2) 5’-terminal and 3’-

terminal modification and (3) splicing to become a mature mRNA. Next, the mature mRNA is

transported from the nucleus to the cytoplasm. At this point, (4) nucleic acids cannot pass through the

nuclear membrane; therefore, mRNA is transported through [ i ] formed in the nuclear membrane. The

proteins coded by the mRNA are then synthesized in [ ii ].

(1) Provide the appropriate terms for [i] and [ii].

(2) In regard to underlined section (1), describe the pre-mRNA sequences transcribed when the sense-

strand of the DNA sequence is ATGGGCTTC.

(3) In regard to underlined section (2), describe the 5’- and 3’- terminal modifications separately within

30 words for each.

(4) In regard to underlined section (3), alternative splicing may occur in some genes. Explain the

alternative splicing phenomenon and its effect in approximately 50 words.

(5) In regard to underlined section (4), explain why nucleic acids cannot pass through the nuclear

membrane with reference to the chemical properties of nucleic acids, the major constituents of the

nuclear membrane, and their structural characteristics in approximately 50 words.

Chemistry

Question 1: The gases H2, CH4, and O2 were placed in three 1-L containers (A, B, and C, respectively),

which were connected by stopcocks. At a temperature of 27°C, the gas pressures inside containers A,

B, and C were 60, 90, and 300 kPa, respectively. The stopcocks were then opened and the gases were

allowed to mix. Answer the following questions.

Numerical values should be given to 2 significant figures. Show your calculations. The volume of

each stopcock can be ignored. Treat the gases as ideal gases. The solubilities of the gases in water and

the volume of liquid water can be ignored.

(1) Calculate the pressure of the mixed gas.

(2) This mixed gas was ignited and the H2 and CH4 were completely combusted. Calculate the pressure

of the gas when maintained at 27°C following the combustion. The vapor pressure of water at 27°C

can be ignored.

(3) The temperature was then increased from the state described in (2) to 67°C. When the system

reached equilibrium after this operation, the pressure inside the containers was 95.3 kPa. Calculate the

vapor pressure of water under this condition.

Question 2: Answer the following questions relating to aqueous solutions. Numerical values of your

answers should be given to 2 significant figures. Show your calculations. If necessary, log2 = 0.30,

log3 = 0.48, and log7 = 0.85.

(1) In order to prepare 100 mL of a 0.30 M aqueous solution of acetic acid (referred to as aqueous

acetic acid solution A), how many mL of 99% acetic acid (molecular weight = 60.05, specific gravity

= 1.05) are required?

(2) Write the equilibrium for acetic acid in water, and calculate the pH of the aqueous acetic acid

solution A on the basis that the pKa value of acetic acid is 4.7 (Ka: acid dissociation constant) and the

degree of ionization (α) of acetic acid is significantly lower than 1.

(3) Calculate the pH of a mixed solution B, which is obtained by adding 30 mL of a 0.60 M aqueous

sodium hydroxide solution to the aqueous acetic acid solution A. The pH of an aqueous solution of a

weak acid and its salt of a strong base can be represented by the equation shown below, where Ca

denotes the concentration of the weak acid, Cs denotes the concentration of the salt of the weak acid

and the strong base, and Ka denotes the acid dissociation constant of the weak acid.

(4) Calculate the pH of an aqueous solution obtained by diluting the mixed solution B 10 times with

water.

(5) Calculate the pH when 1.0 mL of 3.0 M hydrochloric acid is added to the mixed solution B.

(6) Calculate the pH when 3.0 mL of a 1.0 M aqueous sodium hydroxide solution is added to the mixed

solution B.

Question 3: Read the passage below and then answer the questions. Numerical values of your answers

should be given to 2 significant figures. Atomic weights are as follows. C: 12, H: 1.0, O: 16.

Some substances are huge molecules having molecular weights in excess of 10,000, which are

known as polymers. Polymers include [A] polymers, in which a large number of mainly carbon atoms

are linked, and [B] polymers, in which a large number of silicon atoms, oxygen atoms or other atoms

are linked. However, the term “polymer” generally refers to [A] polymers. In addition, [A] polymers

include [C] polymers and synthetic polymers. Cellulose, which is a typical example of a [C] polymer,

is molded into films, fibers, and so on by derivatization such as acetylation. Synthetic polymers include

polyethylene, polyethyleneterephthalate, and so on. Polyethylene is synthesized by [D] polymerization

of ethylene molecules, which contain double bonds, and is used in packaging films and so on.

Polyethyleneterephthalate is a polymer obtained by [E] polymerization of terephthalic acid and

ethylene glycol, and is widely used for fibers or PET bottles.

Synthetic polymers are used in a wide variety of everyday situations due to being “light, strong,

and non-degradable”, but cause environmental concerns due to remaining for long periods when

disposed of in nature. As a result, there have been advances in the development of [F] polymers that

are degraded by microorganisms in soil or water. Polylactic acid, which is an example of a [F] polymer,

is synthesized by [E] polymerization of lactic acid, but only low molecular weight poly(lactic acid)

can be obtained. It is possible to first prepare a lactide, which is a cyclic diester of lactic acid, and then

prepare a high molecular weight poly(lactic acid) by [G] polymerization of this lactide. In fact,

poly(lactic acid) is used in materials for food packaging and so on.

(1) Insert the most appropriate terms for [A] to [G] in the passage above.

(2) If a 2,3,6-O-triacetylglucose unit, which is a constituent of triacetylcellulose, comprises spheres

having diameters of 0.50 nm, what is the length (cm) of a triacetylcellulose molecular chain that is a

linear chain having a molecular weight of 5.0 × 105? Show your calculations.

(3) Crystalline polymers such as polyethylene contain crystal regions, in which molecular chains are

regularly aligned, and amorphous regions, in which molecular chains are randomly aligned. The

density of a polymer was measured and found to be 1.17 g/cm3. If the density of crystal regions was

1.20 g/cm3 and the density of amorphous regions was 1.05 g/cm3, calculate the weight percentage of

crystal regions in this polymer. Show your calculations.

(4) With regard to the underlined section in the passage above, explain why only low molecular weight

poly(lactic acid) can be obtained.

Question 4: Read the passage below and then answer the questions.

Triacylglycerols are neutral lipids and are obtained by esterifying a fatty acid to a glycerol skeleton.

Triacylglycerols are hydrolyzed by a variety of lipases to produce glycerol and a fatty acid. The

produced fatty acid forms a thioester with coenzyme A (CoA) to give an acyl-CoA, which is then

decomposed by β-oxidation, as shown in the diagram below. The produced acyl-CoA is oxidized,

thereby forming a double bond between the α-position and the β-position and producing [A]. Water is

then added, thereby forming a β-hydroxyacyl-CoA [B]. Next, the alcohol group in [B] is oxidized to

give a β-ketoacyl-CoA [C], and another CoA is added and decomposed, thereby producing acetyl-CoA

and an acyl-CoA from which a two-carbon fragment is lost. This two-carbon less acyl-CoA is then

repeatedly subjected to β-oxidation many times, thereby producing a large quantity of acetyl-CoA.

Diagram. β-oxidation pathway

Two-carbon less acyl-CoA Acetyl-CoA

(1) The chemical reaction mentioned in the underlined section above is called saponification. Write

the chemical reaction formula for a case in which tripalmitylglycerol (molecular formula: C51H98O6)

is completely saponified by potassium hydroxide.

(2) The diagram shows a β-oxidation pathway. Write suitable structural formulae for [A], [B], and [C]

in the same style as the other structural formulae.

(3) What is the maximum number of acetyl-CoA molecules able to be produced by repeated β-

oxidation of one molecule of palmitic acid.

(4) Describe the structural formula of a compound obtained by reducing a β-hydroxycarboxylic acid,

which is obtained by acid hydrolysis of the β-hydroxyacyl-CoA [B], with lithium aluminum hydride

followed by acetylation with acetic anhydride and pyridine.

Physics

Question 1: Suppose there is a thin stick of length l and weight m which has been placed at an angle

with its top end touching vertical wall A and its bottom end touching both vertical wall B and

horizontal plane P, as shown in the figure below. Knock the stick over by moving wall A upwards

away from the stick. The stick falls as its top end freely rotates within the vertical plane from height

h, with its bottom end as the pivot. Find the angular velocity ω when the tip of the stick touches the

horizontal plane P. Assume gravitational acceleration is g and take into account the moment of inertia

of the stick. Ignore friction and air resistance.

Question 2: Suppose there is a circuit connecting a resistor with resistance R, a coil with self-

inductance L, and a capacitor with an electrical capacitance C in a series, as shown in the figure below.

Supply voltage v(t) = V0 sinωt to this circuit, where V0 is a constant, ω is the angular frequency, and t

is time.

(1) Provide a differential equation to express the relationship between v(t) and the electrical current

i(t) flowing through the circuit.

(2) Assuming that i(t) = I0 sin(ωt – δ), find I0 and δ.

(3) Find the value of ω that maximizes I0 in (2).

h 𝑙

A

B P

Question 3: Suppose that there is the cycle expressed in a pressure-volume (p-V) diagram like the figure

below, whose working fluid is an ideal gas. In this cycle the state of the substance changes in the order

1 → 2 → 3 → 4 → 1. Process 1 → 2 is adiabatic compression, process 2 → 3 is the absorption of heat

from outside the system and an isometric change, process 3 → 4 is adiabatic expansion, and process 4

→ 1 is emission of heat to outside the system and an isometric change. Assume that the temperatures in

each state are T1, T2, T3, and T4, respectively. Set the molar specific heat at constant volume to Cv = 0.72

kJ kg-1 K-1, the molar specific heat at constant pressure to Cp = 1.00 kJ kg-1 K-1, and the ratio of specific

heats to γ = 1.4, and assume that these constants are not changed by temperature or pressure. Assume

that p1 = 100 kPa, V1 = 450 cm3, and T1 = 293 K, and that the density at that time is ρ = 1.2 kg m-3. Note

it is assumed that density depends only on pressure.

(1) Find the temperature T2 in state 2 when V2 = 50cm3. Do the calculation on the basis that 91.4 ≈ 21.7.

(2) Find the energy Q23 absorbed by the gas in process 2 → 3 when T3 = 4400 K.

(3) Find the external work W34 done by the gas in process 3 → 4.

Question 4: Give brief explanations of the following terms.

(1) Inertial mass

(2) Holography

(3) Heisenberg’s uncertainty principle

(4) Magic number

(5) Dulong-Petit law

1V

1

2

3

4

2V

1p

4p

2p

3p

V

p

Mathematics

Question 1: Assume matrix A = and vector b = .

The formula for converting coordinate system Γ to coordinate system Γ’ is expressed as x = Ax' + b,

where x is a coordinate in coordinate system Γ and x' is a coordinate in coordinate system Γ’ .

Answer the following questions based on these assumptions.

(1) Find A-1(c-b) when vector c = .

(2) Find the equation in the coordinate system Γ’ of a line expressed by the following equation in the

coordinate system Γ.

Question 2: Suppose you continuing rolling a die until 5 or 6 comes up. Answer the following

questions assuming that each of the numbers on the die has an equal probability of coming up.

(1) Find the probability that 5 or higher will come up for the first time when you roll the die the second

time.

(2) Find the probability that 5 or higher will come up by the time you have rolled the die for the second

time.

(3) Find the minimum value of n where the probability that 5 or higher will come up is 2/3 and over

by the time you have rolled the die for the nth time.

Question 3: Answer the following questions about the following binary function of x and y: z (x, y) =

-x4 + x2y2 – y4 + 2x2 + y2.

(1) Find the maximum and minimum values of this function and all of the points which give the

maximum and minimum values.

(2) Assuming that the vertical upward is the positive direction of the z-axis, in the case that water has

been poured on the curved surface expressed by this function find the maximum value of the z-

coordinate of the surface of the water. Assume that the water does not get through the curved surface

and ignore the surface tension of the water.

Question 4: Answer the following questions where the Laplace transform of function f(x) is defined as

ℒ [f(x)] = ∫ 𝑓(𝑥)𝑒−𝑠𝑥∝

0dx. Assume that the integral ∫ 𝑓(𝑥)𝑒−𝑠𝑥∝

0dx converges, f'(x) is piecewise

continuous for 0 < x < ∞, and f(x)e-sx → 0 (as x → ∞).

(1) Show that the following equation holds in this case.

ℒ [f'(x)] = sℒ [f(x)] – f(0)

(2) Find the Laplace transforms of the following functions. Assume that s > α > 0.

(A) g(x) = xe-αx

(B) h(x) = x2e-αx

(3) Use the Laplace transform and the inverse Laplace transform to solve the following ordinary

differential equation.

y'' + 4y' + 4y = e-2x

Assume that y = 0 and y' = 1 when x = 0.