EJU Mathematics Course 2 study guide
EJU Mathematics Course 2 · Work through your exam, one topic at a time.
EJU Mathematics Course 2 is the more demanding of the two mathematics papers in the Examination for Japanese University Admission for International Students, the standardized test used by Japanese universities to assess international applicants whose schooling was largely outside Japan. Course 2 is aimed at students heading into science, engineering, or mathematics-heavy programmes, and it assumes a fuller high-school mathematics background than Course 1, including calculus, vectors, and the wider treatment of probability. The EJU Mathematics Course 2 study guide has 11 sections and about 2,399 words.
01Numbers and Expressions
Numbers and Expressions tests fluency with real numbers, powers and roots, polynomial manipulation, factoring, and rational expressions. EJU Course 2 items often combine these ideas rather than ask for a single mechanical step.
223 words, about 1 min02Quadratic Functions
Quadratic Functions covers graphs of y=ax^2+bx+c, vertex form, maxima/minima, quadratic equations and inequalities, and the discriminant's link to the number of real roots. Complete the square: y=a(x-h)^2+k gives vertex (h,k).
234 words, about 1 min03Sets, Logic and Counting
Sets, Logic and Counting tests set operations, propositional reasoning, permutations and combinations, and the binomial theorem. Questions often require choosing the correct counting model before calculating.
215 words, about 1 min04Probability
Probability examines classical probability, independent and dependent events, conditional probability, and expected value. EJU Course 2 problems often use draws without replacement or two-stage experiments.
212 words, about 1 min05Number of Integers and Integer Properties
Number of Integers and Integer Properties covers divisibility, the Euclidean algorithm, integer solutions, and base representation. These topics reward systematic division and careful handling of remainders.
226 words, about 1 min06Plane Geometry
Plane Geometry tests triangle and circle properties, angles, lengths, areas, similarity, the power of a point, and inscribed figures. Diagrams are usually described in text, so translate each condition into an equation.
255 words, about 1 min07Trigonometry
Trigonometry covers trigonometric ratios, identities, graphs, and equations and inequalities. Course 2 questions often mix radian measure with identities and periodic solutions.
194 words, under 1 min08Exponential and Logarithmic Functions
Exponential and Logarithmic Functions tests exponent laws, logarithm laws, equations and inequalities, and common and natural logarithms. Domain restrictions are central because logarithms accept only positive arguments.
208 words, about 1 min09Differentiation and Integration
Differentiation and Integration covers limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, and areas. EJU Course 2 problems often connect a derivative sign table to a graph and then to an area.
213 words, about 1 min10Sequences
Sequences covers arithmetic and geometric sequences, sums, recurrence relations, and mathematical induction. The exam tests both direct formulas and the ability to transform a recurrence into a familiar sequence.
210 words, about 1 min11Vectors
Vectors covers vector operations, position vectors, inner products, equations of lines and planes, and geometric applications. Course 2 questions often require translating perpendicularity or parallelism into dot-product or scalar-multiple equations.
209 words, about 1 min