University Entrance Common Test (共通テスト): Comprehensive Practice

reliable means “able to be depended on”, so trustworthy is the synonym. Vocabulary on the Common Test is always asked in the form of a paraphrase. Being pulled by the similar-looking relief or rely and picking another word is the usual way points are lost.

rise-rose-risen means “went up”. sharply (suddenly, steeply) reinforces the upward direction. Confusing the past form rose with the flower rose, or choosing the opposite direction, decreased, is the standard mistake.

The two sentences stand in contrast (rain, and yet we go out), so However is correct. For discourse-marker questions, decide the logical relation first (cause, contrast, addition) and the answer comes in a moment. Therefore marks a cause-and-result link, so it is wrong.

postpone = put off, “move to a later date”. The Common Test often asks for paraphrases of phrasal verbs. The preposition after put changes the meaning completely, so aim straight for off. Mixing it up with put on is the typical error.

get one free means “the second one costs nothing”. When reading materials, take the numbers and the condition words (free / half / off) exactly as written. Stretching the meaning to half (half price) or all (everything) is the pitfall that costs points.

sufficient = enough, “as much as is needed”. Check an abstract word by replacing it with an easy synonym. Confusing it with the similar-looking efficient (working without waste) is the standard mistake.

a quarter to seven means “15 minutes before 7”, so 6:45. to = before, past = after. Reading “a quarter to” as “15 minutes after 7” is the biggest source of lost points when catching numbers. Fix the direction of to and past and answer instantly.

annual means “happening once a year, every year”; the root annu- means year. Taking annual for monthly or daily makes you lose a whole set of points when you read how often something happens in a notice or a chart.

fall through means that a plan “collapses, comes to nothing”. Unfortunately points in a negative direction. Narrowing down the direction of the answer from the evaluative word at the head of the sentence is a time-saving technique.

“Hurry up, or you will miss the bus”, so otherwise. An imperative + ( ) + a result is the standard pattern for otherwise, meaning “if you do not do so”. Putting in therefore, which marks a cause-and-result link, breaks the meaning.

under 6 means “younger than 6”, so a 6-year-old is not included and has to pay. In reading materials, under / over / and up are traps right at the boundary. Reading a 6-year-old as free makes you lose the fee-calculation question that follows as well.

half past eight means “30 minutes after 8”, so 8:30. past means after. Taking half past the other way round, as “half an hour before 8”, is the typical mistake when catching numbers.

far from + an adjective is a strong negative, “not … at all”. Translating far literally as “distant” and reading the sentence as positive is the biggest trap. Memorize far from = not at all and you can decide immediately.

would rather A than B means “want to do A rather than B”, and here A is stay home. Misreading the part after than (B = go out) as what the speaker prefers is the standard mistake. Fix it as: the one in front is the one you want.

3 students×1000＋2 adults×1500＝6000 yen; there are 5 people, so the group discount is 200×5＝1000 yen off → 5000 yen. Two checks are needed: whether the “5 or more people” condition is met, and then subtracting the discount once for each person. Forgetting the discount gives 6000 yen (the standard way points are lost).

In the standard form y=(x-p)^2+q the vertex is (p, q). Since the term is (x-2)^2, the x-coordinate is +2. Flipping the sign and answering (-2,3) is the most common mistake. Remember that p is the value inside the parentheses with its sign reversed.

The even numbers are 2, 4 and 6, that is 3 cases divided by all 6 cases ＝1/2. Forgetting to put the number of cases (6) in the denominator and answering 1/3 is the mistake. Count the whole sample space first.

3!＝3×2×1＝6 ways. An “arrangement”, in which the order matters, uses the factorial. Answering 3 ways, the number of people itself, is the standard mistake. Decide first whether the question is about permutations or combinations.

Lining the 5 values up in increasing order, the middle one is the 3rd ＝3. The mean is (20)/5＝4, so confusing it with the mean 4 is the trap. The difference between the mean, which is dragged along by the outlier 10, and the median, which is hardly affected, comes up often.

The inscribed angle is 1/2 of the central angle, so 120÷2＝60°. Answering 120°, the same as the central angle, is the most common mistake. Apply “the inscribed angle is half the central angle” at once.

Completing the square gives y=(x-2)^2-3, so the minimum at the vertex is -3. Mistaking the constant term 1 for the minimum is the trap. If the parabola opens upward, the y-coordinate of the vertex is the minimum.

(1/2)×(1/2)＝1/4. It is 1 case out of all 4 (heads-heads, heads-tails, tails-heads, tails-tails). Answering 1/2 or 1/3 comes from miscounting the sample space. For independent events, take the product of the probabilities.

C(5,2)＝(5×4)/(2×1)＝10 ways. Confusing it with the permutation P(5,2)＝20, in which the order matters, is the standard mistake. If you only “choose”, it is a combination (divide by the factorial).

sin30°＝1/2 and cos60°＝1/2, so the sum is 1. Mixing up the values of sin30° and sin60° (＝√3/2) is the most common mistake. Keep the table of the basic trigonometric ratios fixed in your head.

Substituting x=1 into f'(x)=2x gives 2. Leaving the answer as the derivative 2x is the trap (a “coefficient” is a number). Keep the order: differentiate first, then substitute.

From a_n=a_1+(n-1)d we get 2+3×(5-1)＝2+12＝14. Using n instead of (n-1) and getting 2+3×5＝17 is the most common mistake. The common difference is added (term number - 1) times.

The dot product is the sum of the products of the components: 1×3+2×(-1)＝3-2＝1. A slip in multiplying the signed component (-1) easily gives 5 or -1. Do it mechanically: x-components together plus y-components together.

An antiderivative of 3x^2 is x^3, and [x^3](0→1)＝1-0＝1. Leaving the 3 in as a coefficient and answering 3, or dividing by 3 and answering 1/3, are the sources of lost points. It is quick once you notice that in 3x^2→x^3 the coefficient and the exponent cancel each other out.

The vertex at x=1 gives the minimum -1, and the maximum is found by comparing the endpoints: x=0→0 and x=3→9-6＝3, so the maximum is 3. Taking the vertex value -1 as the maximum, or ignoring the domain and letting the value grow without limit, are the mistakes. When an interval is given, always compare the endpoints with the vertex.

From f'(x)=3x^2-3＝0 we get x=±1. The table of increase and decrease shows a local maximum at x=-1, and f(-1)=-1+3＝2 is the local maximum value. Mixing it up with the local minimum -2 at x=1 is the trap that separates students. The point where the function changes from increasing to decreasing, seen from the left, is the local maximum.

演繹 (en'eki, deduction) runs “general → individual” (for example: all people die, therefore he too will die). It is the exact opposite of 帰納 (kinou, induction), which runs “individual → general”, so learning the direction backwards makes you misread a whole essay. Memorize it by the direction of the arrow.

帰納 (kinou, induction) runs “individual → general” (many observations are turned into a law). It is a frequently asked pair with 演繹 (en'eki, deduction: general → individual). Getting the direction the wrong way round is the most common mistake.

A paradox, like the saying 「急がば回れ」 (isogaba maware, “if you are in a hurry, take the long way round”), looks contradictory and yet hits on a truth. It is easily confused with a plain mistake or with a contradiction itself. Judge it by two elements: “looks contradictory” plus “contains a truth”.

「をかし」 expresses a bright, intellectual sense of beauty: “it has charm, it is amusing”. The contrast with 「あはれ」 (aware), a quiet and deeply felt emotion, is asked very often. Always keep the two feelings apart (bright → をかし / deep → あはれ).

「ありがたし」 ＝ 有り難し ＝ “hard to exist, therefore rarely found”. Taking it in the modern sense of “thanks” leads to a misreading; it is a typical word whose old and modern meanings differ. Judge it from its origin, “it is difficult for such a thing to exist”.

The double negative 「不…不…」 is a strong affirmative: “one absolutely must do …”. Jumping to the conclusion that a row of negatives means a negative is the trap. Process it mechanically: negative × negative ＝ strong affirmative.

「ぞ・なむ・や・か」 are closed with the 連体形 (attributive form), while 「こそ」 is closed with the 已然形 (realis form). Closing なむ with the 已然形 is the standard mistake. Memorize each particle together with the form that closes the sentence.

When we abstract, throwing away the unnecessary aspects is 捨象 (shashou), and pulling out the necessary common points is 抽象 (chuushou, abstraction). The two are asked as a pair. Understanding it as “throwing everything away” is the trap.

In the old language 「うつくし」 means “cute, dear” toward small things. Translating it with the modern meaning “beautiful” costs marks; it is a representative word whose meaning has changed over time. If the object is an infant or a small animal, take it as “cute”.

「使・令・遣」 + a person + a verb is the causative, “make someone do”. Taking the same shape as a passive is the standard mistake. When you see a causative character (使, 令), settle on “make … do”.

「けり」 expresses the past (“did …”) and exclamation (“how … it is!”). At the end of a waka it is usually exclamation. Confusing it with the perfective 「たり・り」 is the mistake. Tell past from exclamation by the context: narrative prose, or speech and waka.

敷衍 (fuen) means “to spread out and explain at length”. It is the exact opposite of summarizing (making shorter), so be careful not to swap them. 「つまり／要するに」 (in short) is the signal for a summary, and 「言い換えれば／例えば」 (in other words / for example) is the signal for 敷衍.

「のたまふ」 is the respectful form of 「言ふ」 (iu, to say), and it raises the person who speaks, that is the doer of the action. Its role is the reverse of the humble 「申す」 (mousu). Judge by the direction of the respect: respectful language raises the doer, humble language raises the receiver.

「未」 is read 「いまだ…ず」 and means “not yet …” (with a partly negative nuance). Its reading is easily confused with 「将・且」 (masani … su, be about to) and 「当」 (masani … beshi, ought to). Memorize each twice-read character together with its okurigana, as a word that is read twice.

A noun (体言, taigen) + 「なり」 gives the assertion “is …”. Here the word just before it, 「人」 (hito, person), is a noun, so it is assertion. If it were attached to a 終止形 (conclusive form) it would be hearsay or inference, but here it is attached to a noun. Telling assertion from hearsay by what the word attaches to (a noun or a conclusive form) is the point that makes the difference.

H2O＝1×2＋16＝18, so 1mol is 18g (this is the molar mass). Answering 16 for O alone or 2 for H alone means you have missed some atoms. Add each atomic mass as many times as the subscript in the formula tells you.

v＝v0＋at＝0＋2×3＝6 m/s. Confusing it with the formula for distance (½at^2＝9) and answering 9 is the standard mistake. Store “velocity is at, distance is ½at^2” as two separate things.

Antibodies (immunoglobulins) are made by plasma cells, which are differentiated B cells. T cells attack infected cells and give commands, but they do not make antibodies. Confusing this division of roles is the most common mistake.

The weight is W＝mg＝2×9.8＝19.6 N. Writing the mass 2kg straight as 2N, or answering 9.8N, which is only g, are the mistakes. It is mass × gravitational acceleration, and the unit is N.

The basic wave equation gives v＝fλ＝2×3＝6 m/s. Dividing (f÷λ or λ÷f) gives 1.5 or 0.67. Fix it as: speed is the product of frequency and wavelength.

Hydrochloric acid is a strong acid, so there are many hydrogen ions and pH<7. Confusing it with neutral (7) or basic (>7) is the mistake. Note as well that the pH value changes with concentration and is not always 0.

In DNA the pairs are A-T and G-C (complementarity). Uracil (U) is the partner of A in RNA, so it is wrong for DNA. Memorize the pairs A-T / G-C firmly.

Ohm's law gives V＝IR＝3×2＝6 V. Dividing gives 1.5 or 0.67. Confirm that V＝IR is a product by checking the units (V=A×Ω).

11.2÷22.4＝0.5 mol. Multiplying by 22.4 makes the value too large. Fix the direction: “volume ÷22.4 ＝ mol”. You can also check it intuitively: half the volume means half the number of moles.

x＝½at^2＝½×2×2^2＝½×2×4＝4 m. The value happens to come out the same as the one from the velocity formula (at＝4), but forgetting to square t gives 2, and dropping the ½ gives 8.

DNA→RNA is transcription, and RNA→protein is translation. Reversing the order (transcription → translation) is a frequent mistake. DNA→DNA is replication. Distinguish the three terms by following the flow.

An exothermic reaction releases heat and its enthalpy decreases, so ΔH<0 (negative). Going by the feel of the old curriculum, where the heat of reaction was Q>0, and choosing the positive sign is the typical mistake under the new curriculum. Update it to: exothermic ＝ ΔH is minus.

By Le Chatelier's principle the equilibrium shifts in the direction that eases the applied change, that is toward the endothermic side, which for an exothermic reaction is the reverse reaction (to the left). Guessing intuitively that it goes to the right, where the products increase, is the trap. Judge it by “the direction that cancels the change you made”.

From x＝½gt^2 we have x∝t^2, that is t∝√x. If the distance is doubled, the time becomes √2 times. Making it 2 times, the same as the distance, is the most common mistake. Undoing a squared relation with a square root is the key idea in this kind of thinking question.

U＝½kx^2＝½×100×(0.1)^2＝½×100×0.01＝0.5 J. Dropping the square on x or the ½ gives 5 or 1. Work out 0.1 squared ＝0.01 first and do not forget the ½ — that is what makes the difference.

The three principles are popular sovereignty, respect for fundamental human rights, and pacifism. Sovereignty rests with the people, and “sovereignty of the Emperor” is the idea of the Constitution of the Empire of Japan, so it is not included. The difference in where sovereignty lies under the old and the new constitution is asked often.

The three duties are paying taxes, working, and having one's children receive education. Voting is a right, not a duty. Confusing rights with duties is the trap.

Hot with heavy rain all year round is the tropical rainforest climate (Af). The Mediterranean climate is the exact opposite, with dry summers and rainy winters. Tell them apart by how the rainfall is spread over the seasons, and do not mix them up with the dry or the polar zones.

The transformation of 1868 (the first year of Meiji) is the Meiji Restoration. It is easy to confuse with the Taika Reform of 645 because the strings of digits look alike. Tie it to the year: “1868 ＝ the Meiji Restoration”.

The UN headquarters is in New York. Geneva, home of the UN Office at Geneva and of the WHO, and Paris, home of UNESCO, are the traps. Organize which major international organization goes with which city.

Contour lines packed close together mean the height changes a lot over a short horizontal distance, that is a steep slope. The wider the spacing, the gentler the slope. Learning it the other way round, close together ＝ gentle, is a source of lost points when reading topographic maps.

The total of value added ＝ GDP. The CPI is an indicator of the price level and means something different. Separate them by their roles: “the size of production ＝ GDP”, “prices ＝ CPI”.

The First World War began in 1914 and ended in 1918. The figures are easily confused with 1939, the start of the Second World War, and with 1904, the Russo-Japanese War. Memorize them as a pair: “first 14-18 / second 39-45”.

Legislation ＝ the Diet, administration ＝ the Cabinet, justice ＝ the courts. The body that “makes laws” is the Diet. Confusing it with the Cabinet, which carries the laws out, is the mistake. Fix each of the three powers together with its function.

When demand > supply (many people want the goods and the goods are scarce), the price rises. Conversely, when supply is excessive it falls. Mixing up which of demand and supply is the larger with the direction of the price is the standard mistake.

The meridian of Japan Standard Time is 135 degrees east and passes through Akashi. It is easy to confuse with the capital, Tokyo, but Tokyo lies at about 140 degrees east. Memorize “Akashi ＝ 135 degrees” firmly.

The Berlin Wall came down in 1989 and became the symbol of the end of the East-West Cold War. The Soviet Union was dissolved in 1991, a different year (this is the trap). Keep the order straight: the fall of the Wall (1989) → the dissolution of the USSR (1991).

The court of last resort, which holds the final power of constitutional review, is the Supreme Court (the power of judicial review). Its role differs from that of the Diet, which legislates, and the Cabinet, which administers. Fix it as “the guardian of the Constitution ＝ the Supreme Court”.

Real GDP ≒ nominal GDP ÷ the price level. If the whole of the nominal increase comes from rising prices, real GDP, which measures quantity, stays flat. Reading a rise in nominal terms straight as growth is the pitfall. “Real” means with price changes taken out.

More yen are needed to obtain 1 dollar, which means the value of the yen has fallen: a weaker yen. A weaker yen makes Japanese products cheaper abroad, so it favors exports, while imports become more expensive. Intuitively taking a larger number as a stronger yen is the biggest trap. Judge it by “the more yen per 1 dollar, the weaker the yen”.

With place weights 8, 4, 2 and 1: 8+0+2+1＝11. Getting the weights wrong gives 13 or 7. Line the powers of 2 up from the right as 1, 2, 4, 8 … and add them together.

6＝4+2＝110 (a 1 in the 4s place, a 1 in the 2s place, a 0 in the 1s place). Confusing it with 5 (101) or 4 (100) is the mistake. Dividing by 2 repeatedly and reading the remainders from the bottom also gives 110.

AND means “and”, and the output is 1 only when every input is 1. “At least one is 1” is the condition for OR (logical disjunction) and is the trap. Learn them as a pair: AND ＝ all 1, OR ＝ any 1.

In hexadecimal, A, B, C, D, E and F are 10, 11, 12, 13, 14 and 15, so A is 10. Mixing it up with F as 15 or B as 11 is the mistake. Start from “A=10” and count up in order.

Browsing the web uses HTTP/HTTPS. SMTP is for sending mail, POP for receiving mail, and FTP for transferring files. Mixing up which protocol goes with which purpose is where points are lost.

The three basic structures are sequence, branching and iteration, and repeating is iteration. Its role is different from that of branching, which chooses the processing according to a condition. Distinguish them as “repeating ＝ iteration (a loop)” and “choosing by a condition ＝ branching”.

An upward slope, where one quantity increases as the other increases, is a positive correlation; a downward slope is a negative correlation. The point that a correlation does not necessarily mean causation is also a frequent trap.

What determines a row uniquely is the primary key, and what links the table to another table is the foreign key. Confusing the two roles is the standard mistake. Identify it by “no duplicates, never empty ＝ the primary key”.

101(=5)+11(=3)＝8＝1000 in binary. Adding as though the numbers were decimal gives 112, and forgetting the carry gives 110. Converting to decimal once to check is the safe way.

IPv4 uses 32 bits (8 bits × 4 groups, for example 192.168.0.1). 128 bits is IPv6. Confusing the 8 bits of one group with the 32 bits of the whole address is the mistake.

2^8＝256. Taking the bit count 8 itself as the number of values, or shifting the exponent by one and answering 2^7＝128 or 2^9＝512, is the most common mistake. Fix “n bits ＝ 2 to the power of n possibilities”.

Choosing which processing to run according to a condition is branching (selection). It is different from iteration, which repeats the same processing. Judge at once that “if … then / otherwise” is the sign of branching.

Adding 1+2+3+4+5 one after another gives 15. Displaying only the last kazu (5) gives 5, and mistaking the range for 1 to 4 gives 10. For a loop, check the initial value, the final value and the step, and actually follow the numbers through (trace it).

The correlation coefficient runs from -1 to 1, and 0.9, which is close to +1, means a strong positive correlation. However, a correlation does not imply causation (a third factor may be at work). Jumping to “correlation ＝ causation” is the typical way points are lost in the data-use section that is strengthened from 2026.

x is doubled again and again: 1→2→4→8→16→32. When x=16, the condition 16<20 is true, so the body runs once more and x=32, kaisu=5; then with x=32 the condition is false and the loop ends. Therefore kaisu=5. Stopping at x=16 and answering 4 is the trap that separates students. Follow the timing of the test (it is made at the top of the loop) carefully.