ྩ࿨ 5 ೥౓ɹೖֶऀબൈֶྗࢼ‫ݧ‬ʢલ‫ظ‬ʣ਺ֶ஫ ҙ ࣄ ߲1ɽࢼ‫ݧ‬։࢝ͷ߹ਤ͕͋Δ·Ͱɼ͜ͷ໰୊࡭ࢠͱղ౴࡭ࢠΛ։͔ͳ͍Ͱ͍ͩ͘͞ɽ2ɽ໰୊͸ඞਢ໰୊ͱબ୒໰୊ʹ෼͔Ε͍ͯ·͢ɽ3ɽඞਢ໰୊͸ 2 ໰͋ΓɼͦΕΒ͸ 1 ϖʔδʹ͋Γ·͢ɽબ୒໰୊͸໰୊ൣғ͝ͱʹͦΕͧΕ 2 ໰ͣͭ͋Γ·͢ɽ਺ֶ Iɾ਺ֶ IIɾ਺ֶ Aɾ਺ֶ B ͷ໰୊͸ 2 ϖʔδʹɼ਺
ֶ III ͷ໰୊͸ 3 ϖʔδʹ͋Γ·͢ɽ4ɽղ౴࡭ࢠ͸ɼඞਢ໰୊༻ͱબ୒໰୊༻ͷ 2 ࡭ʹ෼͔Ε͍ͯ·͢ɽͦΕͧΕͷղ౴࡭ࢠͷදࢴͷॴఆཝʹࢯ໊ͱड‫ݧ‬൪߸Λ͸͖ͬΓͱ‫ه‬ೖ͍ͯͩ͘͠͞ɽ

5ɽબ୒໰୊͸ղ౴͢Δ໰୊ൣғΛબͼɼબ୒໰୊༻ղ౴࡭ࢠͷදࢴͷղ౴໰୊ཝͷબ୒ཝʹ˓ҹΛ‫ه‬ೖ͍ͯͩ͘͠͞ɽ˓ҹΛ‫ه‬ೖ͍ͯ͠ͳ͍৔߹ɼ·ͨ͸ෳ਺ͷબ୒ཝʹ˓ҹΛ‫ه‬ೖͨ͠৔߹͸ɼ0 ఺ͱͳΓ·͢ɽ6ɽ‫ࢴ༻ࢉܭ‬͸ɼղ౴࡭ࢠͷதʹͱͯ͋͡Γ·͢ɽ7ɽࢼ‫ݧ‬தʹ໰୊࡭ࢠ΍ղ౴࡭ࢠͷҹ࡮ෆ໌ྎɼϖʔδͷམஸɾཚஸɼԚΕ౳ʹ‫͕ͭؾ‬͍ͨ৔߹͸ɼ੩͔ʹखΛ‫؂ͯ͛ڍ‬ಜһʹ஌Β͍ͤͯͩ͘͞ɽ8ɽࢼ‫ݧ‬ऴྃ‫ޙ‬ɼ໰୊࡭ࢠ͸࣋ͪ‫͍ͩͯͬ͘͞ؼ‬ɽ
9ɽղ౴࣌ؒ͸ 120 ෼Ͱ͢ɽ10ɽ໰୊͝ͱʹ഑఺͕‫͞ه‬Ε͍ͯ·͢ɽඞਢ໰୊I େখ 2 ‫ݸ‬ͷ͍͜͞ΖΛಉ࣌ʹ౤͛Δͱ͖ɼग़Δ໨ΛͦΕͧΕ aɼb ͱ͢Δɽ͜ͷͱ͖ɼ࠲ඪฏ໘্ͷ௚ઢ ax + by = 1 Λ  ͱ͠ɼ ͱ x ࣠ͷަ఺Λ Aɼ ͱ y ࣠ͷަ఺Λ Bͱ͢Δɽ͞Βʹ‫఺ݪ‬Λ O ͱ͠ɼOAB ͷ  OAB Λ θ ͱ͢ΔɽҎԼͷ໰͍ʹ౴͑Αɽ
ʢ഑఺ 75 ఺ʣ1ͱͳΔ֬཰Λ‫ٻ‬ΊΑɽ
3

໰1cos θ <

໰22 sin θ cos θ ͕੔਺ͱͳΔ֬཰Λ‫ٻ‬ΊΑɽ

໰3

OAB ͷ಺઀ԁͷ൒‫͕ܘ‬༗ཧ਺ͱͳΔ֬཰Λ‫ٻ‬ΊΑɽII ࠲ඪฏ໘্ͷ‫ۂ‬ઢ y = x |x − 2| Λ C ͱ͠ɼ௚ઢ y = mx Λ  ͱ͢Δɽͨͩ͠ɼ
0 < m < 2 ͱ͢Δɽ·ͨɼ‫ۂ‬ઢ C ͱ௚ઢ  Ͱғ·Εͨ෦෼ͷ໘ੵΛ S ͱ͢ΔɽҎԼͷ໰͍ʹ౴͑Αɽʢ഑఺ 75 ఺ʣ໰1‫ۂ‬ઢ C ͱ௚ઢ  ΛಉҰͷ࠲ඪฏ໘্ʹਤࣔͤΑɽ

໰2໘ੵ S Λ m Λ༻͍ͯදͤɽ

໰3໘ੵ S ͕࠷খͱͳΔͱ͖ͷ m ͷ஋Λ‫ٻ‬ΊΑɽͨͩ͠ɼͦͷͱ͖ͷ S ͷ஋Λ‫ٻ‬ΊΔඞཁ͸ͳ͍ɽඞਢ໰୊͸ɼ͜ͷϖʔδͰऴΓͰ͋Δɽ
— 1 —બ୒໰୊ (਺ֶ Iɾ਺ֶ IIɾ਺ֶ Aɾ਺ֶ B)√√

I n Λࣗવ਺ͱ͢Δɽਖ਼ͷ࣮਺ a = 2 + 5, b = −2 + 5 Λ༻͍ͯɼ਺ྻ {cn } Λ33cn = an − bn ͱఆΊΔɽҎԼͷ໰͍ʹ౴͑Αɽʢ഑఺ 75 ఺ʣ໰1ab, c3 , c1 ͕ͦΕͧΕ੔਺Ͱ͋Δ͜ͱΛࣔͤɽ໰2cc√2 , √4 ͕ͦΕͧΕ੔਺Ͱ͋Δ͜ͱΛࣔͤɽ
55

໰3f (a) = f (b) = 0 ͱͳΔΑ͏ͳɼ੔਺܎਺ͷ 4 ࣍ଟ߲ࣜ f (x) Λ 1 ͭ‫ٻ‬ΊΑɽ
·ͨɼ઴Խࣜ cn+4 = Acn+2 + Bcn Λຬͨ͢Α͏ͳఆ਺ A ͓Αͼ B ͷ஋ΛͦΕͧΕ‫ٻ‬ΊΑɽ

໰4c2nc2n−1 ͓Αͼ √ ͕ͦΕͧΕਖ਼ͷ੔਺Ͱ͋Δ͜ͱΛࣔͤɽ͞Βʹɼc2n−1 ͕5(c2n )2 − 1 ͷ໿਺Ͱ͋Δ͜ͱΛࣔͤɽII x ͷൣғΛ 0 < x <q ΛఆΊΔɽπɼa Λਖ਼ͷఆ਺ͱ͢Δɽ·ͨɼ࣍ͷΑ͏ʹ x ʹؔ͢Δ৚݅ p,2



1>
=0a
৚݅ q : −1 < log(cos x) 8 cos3 x − 8 cos x +৚݅ p : (x − a)2x−1cos x<0ҎԼͷ໰͍ʹ౴͑Αɽʢ഑఺ 75 ఺ʣ໰1

cos 4x − cos x Λ 2 ͭͷࡾ֯ؔ਺ͷੵͷ‫ʹܗ‬ม‫͠ܗ‬ɼcos 4x <= cos x Λຬͨ͢x ͷ஋ͷൣғΛ‫ٻ‬ΊΑɽ

໰2৚݅ p Λຬͨ͢ x ͷൣғΛ a Λ༻͍ͯදͤɽ

໰3cos 4x Λ cos x Λ༻͍ͯදͤɽ·ͨɼ৚݅ q Λຬͨ͢ x ͷ஋ͷൣғΛ‫ٻ‬ΊΑɽ໰4໋୊ʮq ⇒ pʯ͕ɼ0 < x <ͷൣғΛ‫ٻ‬ΊΑɽπͷ͢΂ͯͷ x ʹରͯ͠੒ΓཱͭΑ͏ͳ a ͷ஋2਺ֶ Iɾ਺ֶ IIɾ਺ֶ Aɾ਺ֶ B ͷ໰୊͸ɼ͜ͷϖʔδͰऴΓͰ͋Δɽ
— 2 —બ୒໰୊ (਺ֶ III)
I ఆ਺ p Λ 3 Ҏ্ͷ‫਺ح‬ɼi Λ‫਺ڏ‬୯Ґͱ͠ɼα = cos

2πp





+i sin2πpͱ͢Δɽ·1ͱ͠ɼෳૉ਺ z ͷภ֯ arg z Λ 0 <= arg z < 2πz+1ͷൣғͰߟ͑Δɽn Λ p ҎԼͷࣗવ਺ͱ͢Δͱ͖ɼҎԼͷ໰͍ʹ౴͑Αɽͨɼෳૉ਺ z ʹରͯ͠ f (z) =ʢ഑఺ 75 ఺ʣ໰1αn ͷ࣮෦͓Αͼ‫ڏ‬෦Λɼp ͱ n Λ༻͍ͯͦΕͧΕදͤɽ

໰2f (αn ) ͸࣮෦໰3tan (arg f (αn )) ͷ࠷େ஋ͱͦͷͱ͖ͷ n Λɼp Λ༻͍ͯͦΕͧΕදͤɽ1ͷෳૉ਺Ͱ͋Δ͜ͱΛࣔͤɽ
2II n Λࣗવ਺ͱ͠ɼఆੵ෼ In Λ
In = n1

1x(x2 + 1)dxͱఆΊΔɽҎԼͷ໰͍ʹ౴͑Αɽʢ഑఺ 75 ఺ʣ
໰122x>= 1 ͷͱ͖ɼx + 1 <= x +1 <= 2x Ͱ͋Δ͜ͱΛ༻͍ͯɼ࣍ͷෆ౳ࣜΛূ໌ͤΑɽ

14
໰2

໰3



1
1− 2n



<= In <
= log



2nn+1



1abx + c͕ x ʹ͍ͭͯͷ߃౳ࣜͱͳΔΑ͏ʹɼఆ਺ a, b, c=+x(x2 + 1)
xx2 + 1ͷ஋ΛఆΊΑɽ͞Βʹɼఆੵ෼ In Λ‫ٻ‬ΊΑɽ‫ ݶۃ‬lim In Λ‫ٻ‬ΊΑɽn→∞਺ֶ III ͷ໰୊͸ɼ͜ͷϖʔδͰऴΓͰ͋Δɽ
— 3 —௧࿴ 㻡 ᖺᗘ㻌 ධᏛ⪅㑅ᢤᏛຊヨ㦂㻌 䠄๓ᮇ䠅㻌㻌㻌እᅜㄒ䠄ⱥㄒ䠅㻌ὀព஦㡯㻝㻚 ヨ㦂㛤ጞ䛾ྜᅗ䛜䛒䜛䜎䛷䠈䛣䛾ၥ㢟෉Ꮚ䛸ゎ⟅෉Ꮚ䜢㛤䛛䛺䛔䛷䛟䛰䛥䛔䠊㻌㻞㻚 ၥ㢟䛿㻝䝨䞊䝆䛛䜙㻝㻜䝨䞊䝆䛻䛒䜚䜎䛩䠊㻌㻟㻚 ゎ⟅෉Ꮚ䛾⾲⣬䛾ᡤᐃḍ䛻Ặྡ䛸ཷ㦂␒ྕ䜢䛿䛳䛝䜚䛸グධ䛧䛶䛟䛰䛥䛔䠊㻌㻠㻚 ୗ᭩䛝⏝⣬䛿䠈ゎ⟅෉Ꮚ䛾୰䛻⥛䛨䛶䛒䜚䜎䛩䠊㻌㻡㻚 ヨ㦂୰䛻ၥ㢟෉Ꮚ䜔ゎ⟅෉Ꮚ䛾༳ๅ୙᫂░䠈䝨䞊䝆䛾ⴠ୎䞉஘୎㻘㻌ở䜜➼䛻Ẽ䛵䛔䛯ሙྜ䛿䠈㟼䛛䛻ᡭ䜢ᣲ䛢䛶┘╩ဨ䛻▱䜙䛫䛶䛟䛰䛥䛔䠊㻌㻢㻚 ヨ㦂⤊஢ᚋ䠈ၥ㢟෉Ꮚ䛿ᣢ䛱ᖐ䛳䛶䛟䛰䛥䛔䠊㻌㻣㻚 ゎ⟅᫬㛫䛿㻥㻜ศ䛷䛩䠊㻌㻤㻚 㻼㼍㼞㼠䛤䛸䛻㓄Ⅼ䛜グ䛥䜜䛶䛔䜎䛩䠊㻌㻥㻚 ⱥㄒ㎡᭩䜢౑⏝䛩䜛䛣䛸䛜䛷䛝䜎䛩䠊㻌㻌

Part 1: Reading Comprehension I

䠄㓄Ⅼ 80㻌Ⅼ䠅

Use the information in the article to answer questions (1) – (8). For each question, choose one answer(A, B, C or D).
Sustainable aviation fuel taking off worldwide
The move toward sustainable aviation fuel (SAF) derived from cooking oil, household garbage andother materials is gaining momentum in the airline industry, which has been the target of criticism
overseas because of the high carbon dioxide emissions associated with flying.
In late March, aircraft manufacturer Airbus SE flew an A380 jumbo jet for about three hours powered
solely by SAF for a test flight in Toulouse in southwestern France, indicating the safety of SAF andsignaling a wave of change in the aviation industry.
The term “flight shaming” was popularized by environmental activist Greta Thunberg. In 2019, theSwedish teenager crossed the Atlantic Ocean by yacht when she traveled to the U.N. headquarters in
New York for a climate summit, instead of traveling by plane.
Jet fuel derived from crude oil is responsible for most of the carbon dioxide emissions produced by theairline industry, which has come under increased scrutiny amid a global push for decarbonization.
The sense of urgency is particularly strong in Europe, where environmental issues attract moreattention. European countries have started setting goals for the introduction of SAFs, which currently
account for less than 1% of the total global supply of aviation fuels.
In Norway, it has been mandatory for airlines to use SAF mixed with other fuels since 2020, andBritain wants 75% of aviation fuel to be powered by SAFs by 2050.
A shift has also been seen among Japanese airlines. In March, All Nippon Airways, Japan Airlines and14 other companies established an organization called Act For Sky to promote the use of domestically
produced SAFs.
The organization, whose members include Nissin Foods Holdings Co., Odakyu Electric Railway Co.
and a manufacturer of fuels derived from cooking oil, is working to secure raw materials and establish
distribution networks.
ANA and JAL, competitors in the aviation industry, have already joined hands to promote the use ofSAFs. In June, both airlines flew regular flights using fuel mixed with sustainable aviation fuel derived
from microalgae and wood chips.
-1-The government wants 10% of the aviation fuel used by domestic airlines to be SAFs by 2030.
The International Civil Aviation Organization, a United Nations agency, aims to adopt this year atarget of net-zero carbon dioxide emissions among international airliners by 2050. As a result, efforts
by the world’s airlines are likely to accelerate.
“European and North American airlines might cut trips to Japan if planes cannot refuel with SAFs atJapanese airports,” said a senior official of the Land, Infrastructure, Transport and Tourism Ministry.
Securing raw materials is one of many challenges that lie ahead.
Euglena Co. produces health foods made from a type of algae called euglena, and also manufactures
fuel derived from the aquatic organism and used cooking oil.
Last year, Honda Aircraft Co. flew a HondaJet private plane using an SAF manufactured by Euglena,
which plans to build a mass production site in the future so that it can supply fuel to major airlines.
[...]
Keeping costs down will be a challenge, too. SAFs are three to four times the price of conventional
aviation fuels. ANA wants companies to shoulder part of the burden in return for certificates to use thefuel.

Source:The Japan News (2022, April 12). Sustainable aviation fuel taking off worldwide. The Yomiuri
Shimbun. Retrieved from https://japannews.yomiuri.co.jp/science-nature/climate-change/2022041219729/

-2-

(1)

What is the main idea of the article?

(A) People should stop travelling by plane to reduce carbon dioxide emissions.
(B) SAFs are less economical than jet fuel made from crude oil.
(C) European countries require their airlines to use SAFs.
(D) There are increased efforts to use SAFs.

(2)

According to the article, why is the airline industry using SAFs?

(A) to reduce the cost of flying(B) to reduce the environmental impact of flying(C) to reduce the production of household garbage(D) to improve the performance of aircraft engines(3)

According to the article, what did Airbus SE do in late March?

(A) It manufactured an A380 aircraft.
(B) It conducted a test flight.
(C) It released a new type of SAF.
(D) It transferred its headquarters to New York.

(4)

According to the article, what did Greta Thunberg do in 2019?

(A) She promoted the use of cooking oil and household garbage in the aviation industry.
(B) She travelled to New York on a plane powered by SAF.
(C) She encouraged people to fly on planes powered by SAFs.
(D) She went to a climate summit at the U.N. headquarters.

-3-(5)

According to the article, what proportion of the worldwide supply of aviation fuels are SAFs?

(A) less than 1%(B) 10%(C) 75%(D) More than 99%(6)

According to the article, why was Act For Sky established?

(A) to encourage the use of Japanese-made SAFs
(B) to research SAF manufacturing technology(C) to manufacture SAFs from microalgae(D) to increase competition within the aviation industry(7)

According to the article, from which one of the following can SAFs be made?

(A) crude oil(B) hydrogen(C) wood chips(D) industrial waste(8)

According to the article, why is adopting SAFs difficult?

(A) Governments have limited the amount of SAFs that can be made.
(B) The process of manufacturing SAFs is dangerous.
(C) Environmental activists oppose the use of SAFs.
(D) SAFs are more expensive than conventional aviation fuels.

-4-Part 2: Writing I

䠄㓄Ⅼ 50 Ⅼ䠅

In your opinion, what are some of the advantages and disadvantages of air travel? Write about 100
words in English.

-5-㸦ࡇࡢ࣮࣌ࢪࡣⓑ⣬࡛࠶ࡿ㸧

-6-

Part 3: Reading Comprehension II䠄㓄Ⅼ 㻠㻜 Ⅼ䠅

Use the information in the article to answer questions (1) – (4). For each question, choose one answer(A, B, C or D).
Care robot a 'night shift work friend' at Japanese nursing home
OTSU -- A self-navigating artificial intelligence-equipped robot is doing its bit as part of the night shiftcrew at a nursing home in this west Japan city, helping to improve care while assisting in infection
countermeasures.
A robot with faint blue lights quietly opens the door of a room at the Activa Biwa nursing home in thecity of Otsu just past 9 p.m., when the lights are turned off for residents. After making sure that theresident in need of care is in bed, the robot silently closes the door.
The Aeolus robot became part of the Activa Biwa staff in November 2021. Using UV-C lights, it
disinfects commonly touched places in the building including handrails and doorknobs. It can also
detect abnormalities in residents as they sleep based on their posture or movements, and notify humancoworkers by sharing images it has taken of the residents.
Its sensors allow the robot to self-navigate around the building, avoiding obstacles. It can operate anelevator on its own using arms with seven joints each. It was even able to prevent one resident fromfalling after detecting them trying to get into their wheelchair from their bed.
It makes the rounds on one floor of the facility's care ward, which has about 30 rooms, in about 45
minutes. The nursing home operator plans to add more Aeolus robots and increase the number offloors they look after.
Kayo Kojima, 60, the central Japan area manager for Activa Biwa's operating firm Trust Garden, told
the Mainichi Shimbun, "The nursing care business will be even more short-staffed as Japan's
population ages. To secure good service qualities, we've introduced a robot now, and we want toexpand the things we can do."Care unit leader Yuta Minamisawa, 26, who often works with the Aeolus robot on night shifts, said of
his robotic coworker, "I was worried at first that it might create more work, but it's helped reduce workby making the rounds and disinfecting appliances. It's become my night shift work friend that I can relyon."-7-Source:Mainichi Japan (2022, February 28). Care robot a 'night shift work friend' at Japanese nursing home.
The Mainichi. Retrieved from https://mainichi.jp/english/articles/20220226/p2a/00m/0sc/019000c

-8-

(1)

According to the article, what does the robot at Activa Biwa currently do?

(A) It socializes with the residents.
(B) It helps the residents change their clothes.
(C) It provides the residents with medicine.
(D) It sanitizes surfaces people frequently touch.

(2)

According to the article, what did Kayo Kojima say about the nursing care business?

(A) Care robots will become more skilled than human workers.
(B) There will not be enough people to work in nursing homes.
(C) Residents will prefer robots to humans.
(D) The quality of nursing home staff will increase.

(3)

According to the article, why does the robot at Activa Biwa share images?

(A) to promote friendship among residents of the nursing home(B) to let staff know of possible problems with residents(C) to inform staff of surfaces that need disinfecting(D) to show coworkers that it is doing its job(4)

According to the article, what is Trust Garden’s plan for care robots?

(A) increase the number of floors that robots monitor(B) improve the robots' ability to avoid obstacles(C) have the robots work during the day shift(D) add speech functionality to the robots-9-Part 4: Writing II䠄㓄Ⅼ 30 Ⅼ䠅

If you were a resident in a nursing home, would you prefer a human or robot caregiver? Write about 60
words in English.

- 10 -