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100+ Free Kaoyan Mathematics II Practice Questions

Pass your National Postgraduate Entrance Examination Mathematics II (302) exam on the first try — instant access, no signup required.

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No single official pass rate applies because admissions depend on national lines, admissions-unit retest lines, discipline category, enrollment plan, retest performance, and ranking. Pass Rate
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If grad f = (1,2) and u = (3/5,4/5), what is the directional derivative in direction u?

A
B
C
D
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Key Facts: Kaoyan Mathematics II Exam

100 local MCQs

Original practice questions in this cn-kaoyan-mathematics-2 bank

OpenExamPrep local question bank

302

Official national unified subject code for Mathematics II

MOE 2026 admissions management regulations / CHSI YanZhao

150 marks

Full score for the business-course mathematics paper unit in the preliminary exam

MOE 2026 admissions management regulations

180 minutes

Testing window for the live preliminary mathematics/business-course paper

MOE 2026 admissions management regulations

Advanced math + linear algebra

Core Math II syllabus emphasis; no probability/statistics block

NEEA/HEP mathematics syllabus materials and CHSI mathematics subject coverage summary

Program-specific

Admissions units determine whether a major uses Math I, Math II, Math III, or another subject

MOE 2026 admissions management regulations

Kaoyan Mathematics II (302) is a 150-mark, 180-minute national unified preliminary mathematics subject used by specific programs. It focuses on advanced mathematics and linear algebra and is narrower than Math I/III because it excludes probability and mathematical statistics. This page contains 100 original local MCQs for targeted practice.

Sample Kaoyan Mathematics II Practice Questions

Try these sample questions to test your Kaoyan Mathematics II exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate lim_{x -> 0} sin(3x)/x.
A.3
B.1/3
C.0
D.Does not exist
Explanation: Use sin u/u -> 1. Rewrite sin(3x)/x as 3 sin(3x)/(3x), so the limit is 3.
2For f(x) = x^3 - 2x + 1, what is f'(2)?
A.8
B.10
C.11
D.5
Explanation: Differentiate first: f'(x) = 3x^2 - 2. Substituting x = 2 gives 12 - 2 = 10.
3Compute integral_0^1 2x dx.
A.1
B.2
C.1/2
D.0
Explanation: An antiderivative of 2x is x^2. Evaluating from 0 to 1 gives 1^2 - 0^2 = 1.
4Let f(x) = sin x / x for x != 0 and f(0) = a. Which value of a makes f continuous at x = 0?
A.0
B.1
C.-1
D.Any real number
Explanation: Continuity at 0 requires a = lim_{x -> 0} sin x/x. The standard limit is 1, so a must be 1.
5What is the second derivative of e^(2x) at x = 0?
A.2
B.4
C.1
D.0
Explanation: The first derivative is 2e^(2x), and the second derivative is 4e^(2x). At x = 0 this equals 4.
6For f(x,y) = x^2 + y^2, what is grad f at (1,-2)?
A.(2,-4)
B.(1,-2)
C.(2,4)
D.(-2,4)
Explanation: The gradient is (partial f/partial x, partial f/partial y) = (2x, 2y). At (1,-2), this is (2,-4).
7For f(x,y) = xy^2 + 3x, what is partial f/partial y at (2,1)?
A.2
B.4
C.7
D.10
Explanation: Treat x as constant when differentiating with respect to y. partial f/partial y = 2xy, so at (2,1) the value is 4.
8Solve dy/dx = 3y with y(0) = 2.
A.y = 2e^(3x)
B.y = 3e^(2x)
C.y = 2 + 3x
D.y = e^(6x)
Explanation: The equation has exponential solutions y = Ce^(3x). The initial condition y(0)=2 gives C=2, so y = 2e^(3x).
9Find det [[2,1],[3,4]].
A.5
B.8
C.11
D.-5
Explanation: For a 2 by 2 matrix [[a,b],[c,d]], the determinant is ad - bc. Here it is 2*4 - 1*3 = 5.
10For A = [[a,1],[2,3]], for which condition is A invertible?
A.a = 2/3
B.a != 2/3
C.a = 0
D.a != 3/2
Explanation: A 2 by 2 matrix is invertible exactly when its determinant is nonzero. det A = 3a - 2, so A is invertible when a != 2/3.

About the Kaoyan Mathematics II Exam

Kaoyan Mathematics II, subject code 302, is one of the national unified mathematics subjects for China's National Postgraduate Entrance Examination preliminary exam. It is used only when the selected admissions unit and program list Mathematics II in the current major directory. Compared with Mathematics I and Mathematics III, Math II has a narrower scope: it emphasizes advanced mathematics and linear algebra, with no probability and mathematical statistics section. This practice page provides 100 original MCQs for concept checks, computation, theorem-condition recognition, and engineering-style applications; it does not reproduce official questions and should be paired with written full-paper practice.

Assessment

This local practice bank contains 100 original four-option MCQs. The live Mathematics II (302) subject is a national unified preliminary-exam mathematics paper with a 150-mark full score and a 180-minute written testing window when selected by the admissions unit as the business-course mathematics subject. It is program-specific: many engineering routes use Mathematics I, some engineering and professional routes use Mathematics II, economics/management routes often use Mathematics III, and exact subject choice is set in each admissions unit's major directory. Math II is narrower than Math I and Math III because it concentrates on advanced mathematics and linear algebra and does not include the probability and mathematical statistics block used by Math I/III.

Time Limit

180 minutes for the live preliminary mathematics/business-course paper; in the 2026 admissions rules, business course (1) or professional foundation comprehensive was scheduled 2025-12-21, 08:30-11:30 Beijing time.

Passing Score

No standalone pass/fail mark for Mathematics II. Candidates must meet MOE annual national preliminary-exam score requirements, including applicable single-subject thresholds for 150-mark subjects, and any higher admissions-unit retest requirement.

Exam Fee

No separate fee for Mathematics II alone. Candidates pay the postgraduate entrance exam registration/test fee through provincial education admissions/examination agency channels; amounts and refund rules vary by province, test site, and registration category. (Ministry of Education of the People's Republic of China / National Education Examinations Authority, with CHSI/YanZhao, provincial education admissions examination institutions, and admissions units)

Kaoyan Mathematics II Exam Content Outline

About 78%

Advanced Mathematics / Calculus

Functions, limits, continuity, derivatives, differentials, one-variable integration, applications of derivatives and integrals, multivariable functions, partial derivatives, double integrals, ordinary differential equations, and calculus-based engineering modeling.

About 22%

Linear Algebra

Determinants, matrices, rank, vectors and vector spaces, linear systems, eigenvalues, eigenvectors, diagonalization, and quadratic forms, with attention to theorem conditions and computation accuracy.

Not included in Mathematics II

Probability and Mathematical Statistics

Unlike Mathematics I and Mathematics III, Mathematics II does not test the probability and mathematical statistics block. Candidates should still verify the selected program's subject code because some programs require Math I, Math III, 396 economic comprehensive ability, or a self-designed mathematics subject instead.

How to Pass the Kaoyan Mathematics II Exam

What You Need to Know

  • Passing score: No standalone pass/fail mark for Mathematics II. Candidates must meet MOE annual national preliminary-exam score requirements, including applicable single-subject thresholds for 150-mark subjects, and any higher admissions-unit retest requirement.
  • Assessment: This local practice bank contains 100 original four-option MCQs. The live Mathematics II (302) subject is a national unified preliminary-exam mathematics paper with a 150-mark full score and a 180-minute written testing window when selected by the admissions unit as the business-course mathematics subject. It is program-specific: many engineering routes use Mathematics I, some engineering and professional routes use Mathematics II, economics/management routes often use Mathematics III, and exact subject choice is set in each admissions unit's major directory. Math II is narrower than Math I and Math III because it concentrates on advanced mathematics and linear algebra and does not include the probability and mathematical statistics block used by Math I/III.
  • Time limit: 180 minutes for the live preliminary mathematics/business-course paper; in the 2026 admissions rules, business course (1) or professional foundation comprehensive was scheduled 2025-12-21, 08:30-11:30 Beijing time.
  • Exam fee: No separate fee for Mathematics II alone. Candidates pay the postgraduate entrance exam registration/test fee through provincial education admissions/examination agency channels; amounts and refund rules vary by province, test site, and registration category.

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

Kaoyan Mathematics II Study Tips from Top Performers

1Confirm subject code 302 in the current admissions-unit major directory before committing to a Math II plan.
2Prioritize calculus depth: limits, derivatives, integrals, multivariable functions, differential equations, and applications carry most of the Math II workload.
3Study linear algebra as a connected system: determinants, rank, systems, vector spaces, eigenvalues, diagonalization, and quadratic forms often combine in one problem.
4Do not spend Math II review time on probability and mathematical statistics unless another subject in your program requires it.
5After MCQ drilling, practice fill-in and full written solution/proof tasks under the 180-minute paper rhythm.
6Keep a formula-condition notebook for common traps such as differentiability versus continuity, positive definite tests, diagonalization conditions, and convergence tests.

Frequently Asked Questions

How many questions are in this local Kaoyan Mathematics II bank?

This OpenExamPrep bank contains exactly 100 original four-option MCQs for cn-kaoyan-mathematics-2. The live 302 Mathematics II paper is a 150-mark written paper and is not a 100-MCQ format.

How long is the real Mathematics II exam?

The live national unified mathematics/business-course paper has a 180-minute testing window when Mathematics II is selected by the admissions unit. For the 2026 admissions cycle, the business course (1) session was scheduled for December 21, 2025, 08:30-11:30 Beijing time.

What is the main difference between Mathematics II and Mathematics I or III?

Mathematics II focuses on advanced mathematics and linear algebra and excludes probability and mathematical statistics. Mathematics I and Mathematics III have broader syllabus structures that include probability/statistics blocks, and they are used for different discipline and program requirements.

Which candidates take Mathematics II?

Only candidates whose selected admissions unit and major directory list subject 302 Mathematics II take it. Program requirements are not guessed from the exam name; candidates must verify the current major directory on YanZhao or the university graduate admissions site.

Is there a universal passing score for Mathematics II?

No. Candidates must meet the MOE national basic preliminary-exam score requirements for their discipline/region, including applicable single-subject thresholds for 150-mark subjects, and any higher retest line set by the admissions unit.

Does this practice bank copy official Kaoyan questions?

No. The items are original MCQs written to practice Math II concepts, calculations, and reasoning patterns. Candidates should also practice full written papers because the live exam includes non-MCQ tasks.