MEXT Undergrad Syllabus
a.
Math A, B
Sets
① n(A ∪ B) = n(A) + n(B) −
n(A ∩ B)
Math A: 1 ~ 17
b.
Math B: 1 ~ 24, except 5
Permutation
①
1. Numbers and expressions
a.
Exponent rules
b.
Factorization / expansion
① (a + b)(a − ab + b ) = a + b
c.
Real numbers
d.
First-degree inequality
e.
Absolute values
②
c.
a.
Sufficient and necessary conditions
!
)!
(Usually
n
outside Japan)
r
C = C
Properties of probability
( )
( )
① y = ax + bx + c
③ P(A ∪ B) = P(A) + P(B) − P(A ∩
B)
−
b.
Minima, maxima
c.
② sin(90° − θ) = cos θ
=
Probability with constraints
① P (B) =
a.
Trigonometric ratios
=
C p (1 − p)
( ∩ )
( )
8. Properties of figures
① 1 + tan θ =
①
Independent trials
①
a. Sin, cos, tan
Ceva’s theorem
① For ∆ABC with points R, P,
and Q on AB, BC, and CA
= 2R
respectively,
② a = b + c − 2bc cos A
5. Data analysis
Deviation
① s = x − (x)
b.
= !(
!
② P(A) + P(A) = 1
4. Figures and measurements
a.
C =
① P(A) =
③ D = b − 4ac
b.
for circular permutation
Quadratic functions
② y= a x+
b.
)!
7. Probability
3. Quadratic equations
a.
(
written as
②
① A ∩ B, A ∪ B, A ⊂ B, x ∈ A
b.
(Usually written as
Combination
①
2. Sets
Sets
)!
P(n, r) outside Japan)
① When |x| = c, x = ± c
a.
!
P =(
Tendency
6. Number of possible outcomes
∙
∙
b.
Menelaus’s theorem
c.
Power of a point theorem
=1
9. Properties of integers
a.
Number of divisors
① If a natural number N = p ∙
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MEXT Undergrad Syllabus
q ∙ r ∙ ⋯, then the number of
αβ + βγ + γα = , and αβγ = −
positive divisors = (a + 1)(b +
1)(c + 1) ⋯ and the sum of all
positive divisors = (1 + p +
11. Figures and equations
a.
① For ∆ABO with O(0,0),
⋯ p )(1 + q + ⋯ q )(1 + r +
A(x , y ), and A(x , y ),
⋯r )⋯
b.
Triangles
GCD, LCM
S = |x y − x y |
① If a = ga′ and b = gb′, then a′
b.
Circles
and b′ are relative primes of
① x +y =r
each other, l = ga′b′, and
② For a circle C x + y = r , the
ab = gl
equation of the tangent line is
c.
Remainder rules
x x + y y = r for P(x , y ) on
d.
Euclidean algorithm
C
① If ax + by = c and ap + bq = c,
then x = bk + p and y =
c.
12. Trigonometry
a.
−ak + q
e.
Recurring decimal
f.
Positional notation (base 2, 3, 4, …)
sin α cos β + sin β cos α,
b.
cos(α + β) =
Binomial theorem
①
!
! ! !
Trigonometric formulas
① sin(α + β) =
10. Miscellaneous expressions
a.
Optimization problems
cos α cos β − sin α sin β,
a b c
Arithmetic mean
② sin θ =
① If a > 0 and b > 0, then
a + b ≥ 2√ab is true and
Roots
①
d.
③ sin α cos β = {sin(α + β) +
sin(α − β)}, etc.
a + b ± 2√ab = √a ± √b
Properties of complex numbers
④ sin A + cos B = 2 sin
① i = −1
e.
, cos θ =
, 2 sin θ cos θ = sin 2θ
a + b = 2√ab when a = b
c.
, etc.
tan(α + β) =
Solutions of functions
,
etc.
① If α and β are the two
⑤ sin 3θ = 3 sin θ − 4 sin θ,
solutions of ax + bx + c = 0,
then α + β = −
cos
cos 3θ = −3 cos θ + 4 cos θ
⑥ Note: sec, csc, and cot are not
and αβ =
included in the syllabus
② If α, β, and γ are the three
solutions of ax + bx + cx +
d = 0, then α + β + γ = −
and
13. Exponential and logarithmic function
a.
Exponential and logarithmic rules
① Note: In Japan, log(x) = log
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MEXT Undergrad Syllabus
base e (ln(x)) and log (x) =
log base 10
Limit definitions
b.
Basic differentiation
c.
Optimization problems
a.
b.
c.
not contain integration by
parts
a.
Curves
① y = 4px
Dot product (cross product is not
②
included)
Vector geometry (2D and 3D)
③
∆ABC and a point P, AP⃗ =
⃗
k
② For p⃗ on AB⃗, p⃗ = (1 − t)a⃗ + tb⃗
③ For h⃗ on ∆ABC, h⃗ = sOA⃗ +
b.
Tangent lines
c.
Parametric curves
①
tOB⃗ + uOC⃗ (s + t + u = 1)
17. Sequences
d.
Arithmetic and geometric
a.
① S = n(a + l), S = n(2a +
n(n + 1)(2n + 1), ∑
k =
=a +d
② a
= n(a )
= −1 when
|r| < 1, = 0 when r = 1, and
k =
① a
Limits of r
① Ex. lim →
=a
k = n(n + 1), ∑
Recurrence
Polar coordinates
20. Limits
Sum of sequences
n(n + 1) , etc.
x = a sin θ
etc.
y = bcos θ
① (r, θ)
sequences
② ∑
= 1 with
−
F √a + b , 0 , F′(−√a + b , 0)
⃗
(n − 1)d), S = a
= 1 with
+
F √a − b , 0 , F′(−√a − b , 0)
① If aPA⃗ + bPB⃗ + cPC⃗ = 0 for a
c.
Geometry on complex plane
19. Curves on a plane
16. Vectors
b.
+ i sin
① ∠βαγ = arg
② Note: Integral calculus 1 does
a.
Nth root of 1
① z = cos
Basic integration
− (β − α)
b.
De Moivre’s theorem
i sin nθ
① ∫ a(x − α)(x − β)dx =
a.
+ ra = 0
① (cos θ + i sin θ) = cos nθ +
15. Integral calculus 1
a.
+ qa
18. Complex plane
14. Differential calculus 1
a.
③ pa
= 1 when |r| > 1
b.
Limits of sequences
① Ex. a
② Ex.
√
, lim → a
=
√
√
√
+
√
√
+ ⋯+
+⋯
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MEXT Undergrad Syllabus
c.
③ Ex. Fractals
a.
Integration by parts
Trigonometric limits
b.
Trigonometric integration
c.
Volume
d.
Integration of parametric functions
e.
Length of a curve
① lim →
=1
21. Differential calculus 2
a.
Chain rule
b.
Limits of e
① lim → (1 + h) = e
① L=∫
1 + y′
② L=∫
+
dt for a
c.
Implicit differenciation
d.
Mean-value theorem
e.
L’Hospital’s rule
f.
Optimization problems
*Note 1: The “matrix” section was removed
g.
Differentiation of parametric
from the syllabus a few years ago, but there
functions
is a chance it will come back in the next
Approximation
years (2024~25 or so).
h.
parametric function
① If h ≈ 0, then f(a + h) ≈ f(a) +
f′(a)h
② If x ≈ 0, then f(x) ≈ f(0) +
f (0)x
*Note 2: I did not add much detail for
obvious contents such as for exponential and
logarithmic functions and calculus.
22. Integral calculus 2
4
MEXT Undergrad Syllabus
Japanese
1. Section A
a.
JLPT N5 ~ N4
2. Section B
a.
JLPT N3 ~ N2
3. Section C
a.
JLPT N2 ~ N1
b.
Additional proverbs and expressions not covered in JLPT
JLPT N5 →
30/300 ≈ 10%
JLPT N4 →
60/300 ≈ 20%
JLPT N3 →
120/300 ≈ 40%
JLPT N2 →
190/300 ≈ 60%
JLPT N1 (100/180 ~ 130/180) →
220/300 ≈ 70%
JLPT N1 (130/180 ~ 150/180) →
220/300 ≈ 80%
JLPT N1 (160/180+) →
270/300 ≈ 90%+
(Including lucky guesses)
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MEXT Undergrad Syllabus
d.
Chemistry
5. Solution
*Note: Numbers or formulas with a ✤ sign
must be memorized.
a.
Henry’s law
b.
Concentration
① Mass percent concentration (%)
② Mole-concentration (mol/L)
1. Constituent particles of matter
a.
Simple substances
b.
Compounds
c.
Allotropes
③ Molar concentration (mol/kg)
c.
d.
10 ~10 m ✤
(First) ionization energy
② Tyndall effect
2. Chemical formulas
a.
Molecular weight / formula weight
b.
Avogadro’s number
c.
③ Brownian movement
④ Electrophoresis
e.
✤
① Coagulation
① The volume of any (ideal) gas is
② Salting out
22.4L ✤ at standard state,
③ Dialysis
and standard state always
means 101 kPa at 0C°✤
a.
1
Ion, covalent, metallic bonds and
④ Sol, gel
6. Chemical reactions and energy
a.
② Enthalpy of dissolution
Waals force, hydrogen bond)
Electronegativity
c.
Molecular polarity
d.
NaCl, CsCl, diamond,
body-centered cubic lattice,
face-centered cubic lattice, and
hexagonal close-packed structure
① Number of atoms per unit cube,
coordination number, and
atomic packing factor ✤
4. States of matter
a.
Vapor pressure
b.
Vapor-liquid equilibrium
c.
Ideal gas law
Enthalpy
① Enthalpy of formation
intermolecular bonds (van der
b.
Hydrophobic and hydrophilic
colloids
Standard state
3. Chemical bonds and crystals
Colloids
① Size of colloid particles:
phosphorous)
① 6.02 ∙ 10
Osmotic pressure
① Π = cRT
① SCOP (sulfur, carbon, oxygen,
d.
Differences of ideal and real gas
③ Enthalpy of neutralization
b.
Binding energy
c.
Hess’s law
7. Reaction speed
a.
Activation energy
b.
Catalysis
c.
Chemical equilibrium
d.
Le Chatelier’s principle
e.
Equilibrium constant
8. Acid and base
a.
Arrhenius’s theory
b.
Bronsted-Lowry’s theory
c.
pH
6
MEXT Undergrad Syllabus
d.
Neutralization
f.
Oxoacid
① Phenolphthalein (pH ≥ 7)
12. Metals
② Methyl orange (pH ≤ 7)
a.
Alkali metals
b.
Alkaline earth metals
9. Oxidation and reduction
a.
Oxidizer, reducing agent
b.
Battery
Ra are considered alkaline
① Primary, secondary
earth metals due to their
② Voltaic battery
distinctive characteristics
① In Japan, only Ca, Sr, Ba, and
compared to Be and Mg. ✤
−Zn|H SO aq|Cu +, reaction on
each side ✤
c.
③ Daniell cell
① Production of aluminum,
bauxite, aluminum oxyde
−Zn|ZnSO aq|CuSO aq|Cu +,
reaction on each side ✤
④ Manganese battery
d.
Hydroxide
e.
Complex ions
① [Ag(NH ) ] , straight line ✤
⑤ Lead-acid battery
c.
−Pb|H SO aq|PbO +, reaction
② [Cu(NH ) ] , square ✤
on each side ✤
③ [Zn(NH ) ] , tetrahedron ✤
④ [Fe(CN) ] , octahedron ✤
Ionization tendency
① From bigger to smaller, Li K
Ca Na Mg Al Zn Fe Ni Sn Pn
13. Inorganic substances
a.
(H ) Cu Hg Ag Pt Au ✤
d.
Electrolysis
e.
Faraday’s law
AgNO , HF
b.
solubility, and other characteristic
Elements in group 1,2, 13 ~ 18
features of the following gases must
must be memorized in order (top to
be memorized
down) ✤
① H , O , Cl , HCl, HF, H S, SO ,
Transition elements and their
characteristics
c.
The production method, collecting
method, color, odor, acidity,
10. Periodic table
b.
Storage methods
① Na, K, P, CaO, CaC , NaOH,
① 96500 C/mol
a.
Aluminum
Main group elements and their
characteristics
NO , NO, CO , CO, NH ✤
c.
Precipitation
14. Aliphatic compounds
a.
11. Non-metals
Hydrocarbons
① Alkane, cycloalkane
a.
Halogens
② Alkene, cycloalkene
b.
Contact process ✤
③ Alkyne
c.
Haber bosch process ✤
d.
Ostwald process ✤
acidity, and other characteristics of
e.
Solvay or ammonia-soda process ✤
the following functional groups
b.
The formula, naming, hydrolysis,
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MEXT Undergrad Syllabus
must be memorized
① −OH, − O − , −CHO, =
CO, − COOH, − COO −
② Ribose, deoxyribose
17. Artificial polymers
a.
① Rayon
, −NH , − NO , − SO H ✤
c.
Isomers
② Acetate
① Geometric, optical,
③ Nylon (polyamide)
stereoisomer
d.
Fibers
④ Vinylon
Alcohol
⑤ Acrylic fiber
① Primary, secondary, tertiary
⑥ Polyester
② Monohydric, dihydric, trihydric
b.
Synthetic resin (plastic)
e.
Ether
① Polyethylene
f.
Ester
② Polyvinyl acetate
g.
Carboxylic acid
③ Phenolic resin
h.
Oils and fats and soap
④ Urea resin
① Detergent
⑤ Polyethylene terephthalate
② Surface active agent
15. Aromatic compounds
a.
Phenol
b.
Aromatic carboxylic acid
c.
Aniline
d.
Pharmaceuticals
c.
Rubber
① Natural rubber (latex)
② Synthetic rubber,
vulcanization
① Sulfonamides
② Antibiotics
e.
Dye, azo compounds
16. Natural polymers
a.
Sugar
① Monosaccharide
② Polysaccharide
b.
Amino acid
① Zwitterions
② Ninhydrin reaction
c.
Protein
① Peptide bond
② Biuret test
③ Xanthoprotein reaction
④ Enzyme
d.
Nucleic acid
① DNA, RNA
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MEXT Undergrad Syllabus
② F⃗ ∙ ∆t
Physics
b.
collision
1. Constant acceleration motion
a.
① V − v = −e(V − v)
V-t graph
6. Circular motion and universal
① v = v + at
gravitation
② x = v t + at
③ v −v
b.
Coefficient of restitution and
a.
= 2ax
Circular motion
Potential energy
① T=
=
①
② a=
= rω
mv
② Mgh
c.
Relative velocity
③ F=m
2. Equilibrium of forces
b.
= mrω
Universal gravitation
a.
Action-reaction law
b.
Friction
① f=G
c.
Forces
② U = −G
c.
① mg
①
② kx
e.
d.
Spring
①
=
+
⋯
a.
Newtonian equation of motion
② W = Fl
b.
c.
5. Conservation of momentum
Momentum and impulse
① mv⃗
Pendulum
① T = 2π
② g = g + a in an elevator
① μ′N
① kv
Spring pendulum
① T = 2π
Friction
Air resistance
= Aω
③ T=
4. Movements with resistance
a.
≥0
Simple harmonic motion
② v = Aω cos ωt, v
Conservation of energy and work
① U = kx
b.
+ −G
① x = A sin ωt
⋯
① F⃗ = ma⃗
a.
mv
7. Harmonic motion and pendulum
3. Laws of motion
b.
Escape velocity
①
, k=k +k
Center of mass
① x =
a.
rv = constant
② T = ka
③ ρVg
d.
Kepler’s law
③ g =
g + a in a car
8. Temperature and heat
a.
Heat capacity
① Q = mc∆t
② Q = C∆t
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MEXT Undergrad Syllabus
b.
Thermal efficiency
① e=
a.
=
① n=
<1
② n
9. Motion of particles and change in state
a.
Equation of state and laws of gas
Movement of particles
mv =
T = nRT
c.
Change in state
d.
① C = R, C = C + R
a.
10. Properties of waves
Fixed end and free end reflection
c.
Interference
① |l − l | = mλ or =
③ V = k| |
④ N = 4πkQ =
+m λ
Sound waves
⑤ U = qV
13. Capacitor
, f =
a.
(m = 1,2,3, ⋯)
② Open pipe: f =
③ Closed pipe: f =
Capacitor laws
① Note: In Japan, capacitors are
(m =
called “condensers”
② Q = CV
1,2,3, ⋯)
(m =
③ C=ε
1,3,5, ⋯)
f.
Formulas and laws
② E=k
−
b.
e.
Newton’s rings
① F=k
Y-t and y-x graphs
① String: v =
Young’s experiment
12. Electrostatic force and electric field
③ Q = ∆U + W
d.
= +
① d=
② pV = constant, γ =
① y = A sin 2π
Doppler effect
④ U = QV
① f =
⑤ F=
Beat
11. Light waves
=
① λm =
③ W = p∆V = nR∆T
a.
=
② m=
② ∆U = nC ∆T
c.
=
Lenses
①
② pS = p S + Mg
①
=
③ n sin θ = n sin θ
b.
① PV = nRT
b.
Properties of light
f
b.
Conservation of electric power
14. DC circuit
10
MEXT Undergrad Syllabus
a.
Current laws
②
① I = Senv
③ a=
② V = RI
④ f = evB
b.
③ V = E − rl
15. Electric current and magnetic field
a.
, H =
+ eV = mv
Wave-particle duality of light
① E = hv
Magnetic field
① H=
mv
② hv = W + mv
, H = nI
③ λ=
c.
② B = μH
X-rays
① λ=
③ eE = evB
④ E = vB
d.
Compton effect
16. Electromagnetic induction
e.
Bragg’s law
a.
Induction laws
19. Atoms and nuclei
∆
① V = −N
① 2d sin θ = nλ (n = 1,2,3, ⋯)
∆
a.
② V = Blv = Blv cos θ
b.
① m
Self and mutual induction
① V = −L
∆
∆
b.
17. AC circuit
Generator of AC
② Balmer series
① V = V sin ωt
③ Paschen series
④
AC circuit
c.
① V = RI
② V = ωLI
c.
Release of light
① Lyman series
② φ = BS cos ωt
b.
(n = 1,2,3, ⋯)
③ E=−
∆
③ U = LI
a.
=k
② 2πr = n
∆
② V = −M
Hydrogen atom
③ V=
I
④ Z=
R + ωL −
−
Radioactive decay
①
d.
=R
=
Properties of atoms and energy
① E = mc
Resonance circuit
① T = 2π√LC
②
LI = CV
18. Electrons and lights
a.
Electron in a magnetic field
① F = eE
11