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100+ Free Kaoyan Mathematics I Practice Questions

Pass your National Postgraduate Entrance Examination Mathematics I (301) exam on the first try — instant access, no signup required.

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No single official pass rate applies because Kaoyan admissions use national score lines, admissions-unit retest lines, discipline categories, recruitment plans, retest performance, and ranking. Pass Rate
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Question 1
Score: 0/0

What is integral_0^1 2x dx?

A
B
C
D
to track
2026 Statistics

Key Facts: Kaoyan Mathematics I Exam

150 points

Full mark for Mathematics I in the preliminary exam

MOE/NEEA national postgraduate exam framework and math syllabus resources

180 minutes

Exam time for preliminary subjects such as unified mathematics

MOE 2026 National Master's Graduate Admissions Work Management Regulations

2025-12-21 08:30

Scheduled 2026-cycle morning slot for business course I or professional foundation subjects

MOE 2026 National Master's Graduate Admissions Work Management Regulations

Program-specific

Admissions units decide whether Mathematics I is required for each program

MOE 2026 National Master's Graduate Admissions Work Management Regulations

100

Free local practice questions here

OpenExamPrep

Kaoyan Mathematics I is a 150-point, 180-minute closed-book preliminary subject, commonly required by many engineering and science programs but always program-specific. The real paper is not a 100-MCQ test; this local bank provides 100 original MCQs across advanced mathematics, linear algebra, probability, and statistics.

Sample Kaoyan Mathematics I Practice Questions

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

1For f(x) = x^3 - 3x^2 + 5, what is f'(2)?
A.0
B.2
C.4
D.8
Explanation: Differentiate first: f'(x) = 3x^2 - 6x. Substituting x = 2 gives 12 - 12 = 0.
2Evaluate lim as x -> 0 of sin(3x)/x.
A.0
B.1
C.3
D.1/3
Explanation: Write sin(3x)/x = 3[sin(3x)/(3x)]. Since sin u/u -> 1 as u -> 0, the limit is 3.
3What is integral_0^1 2x dx?
A.1/2
B.1
C.2
D.4
Explanation: An antiderivative of 2x is x^2. Evaluating from 0 to 1 gives 1^2 - 0^2 = 1.
4Define f(x) = (e^x - 1)/x for x != 0. What value of f(0) makes f continuous at 0?
A.0
B.1
C.e
D.Does not exist
Explanation: Continuity requires f(0) to equal lim as x -> 0 (e^x - 1)/x. This standard derivative limit equals 1.
5For f(x) = ln(1 + x^2), what is f'(1)?
A.1/2
B.1
C.2
D.ln 2
Explanation: By the chain rule, f'(x) = 2x/(1 + x^2). At x = 1, this is 2/(2) = 1.
6Find the sum of the geometric series 1 + 1/2 + 1/4 + 1/8 + ... .
A.1
B.3/2
C.2
D.The series diverges
Explanation: The first term is 1 and the common ratio is 1/2. Since |r| < 1, the sum is a/(1 - r) = 1/(1/2) = 2.
7If y' = 2x and y(0) = 1, what is y(2)?
A.3
B.4
C.5
D.6
Explanation: Integrating y' = 2x gives y = x^2 + C. Since y(0) = 1, C = 1, so y(2) = 4 + 1 = 5.
8For f(x, y) = x^2 y + y^3, what is the partial derivative f_x at (1, 2)?
A.2
B.4
C.8
D.12
Explanation: Treat y as constant. f_x = 2xy, and at (1, 2) this equals 2*1*2 = 4.
9What is the gradient of f(x, y) = x^2 + y^2 at (3, 4)?
A.(3, 4)
B.(6, 8)
C.(9, 16)
D.(12, 6)
Explanation: The gradient is (2x, 2y). At (3, 4), it is (6, 8).
10Evaluate the double integral of x + y over the unit square 0 <= x <= 1, 0 <= y <= 1.
A.1/2
B.1
C.3/2
D.2
Explanation: The integral splits as integral of x over the square plus integral of y over the square. Each part is 1/2, so the total is 1.

About the Kaoyan Mathematics I Exam

Kaoyan Mathematics I, commonly subject 301, is the broadest national unified mathematics paper used in China's master's preliminary examination system. It covers advanced mathematics, linear algebra, probability theory, and mathematical statistics at undergraduate engineering/science depth. Many engineering and science programs require Mathematics I, but candidates must verify the exact math subject in the target admissions unit's professional catalog because program requirements can differ by university, discipline, and degree type.

Assessment

Subject 301 Mathematics I is a national unified preliminary examination math subject. It is commonly used by many engineering and science master's programs, especially routes that need the broadest calculus, linear algebra, probability, and statistics coverage, but each admissions unit and program decides its required subject in the current admissions catalog. The real Math I paper is a 150-point, 180-minute closed-book written exam; published syllabus conventions use single-choice questions, fill-in questions, and solution/proof questions rather than a 100-MCQ format. This page is a local 100-question MCQ practice bank and should be paired with real-paper fill-in and written-solution practice.

Time Limit

180 minutes. For the 2026 admissions cycle, business course I or professional foundation subjects, including unified mathematics subjects where assigned, were scheduled 2025-12-21, 08:30-11:30 Beijing time.

Passing Score

No standalone pass mark. Candidates must meet the national basic preliminary-score requirements for their discipline and any higher admissions-unit or program-specific retest requirements.

Exam Fee

Varies by province, reporting point, and admissions unit; candidates pay required registration or preliminary-exam fees through official CHSI/YanZhao or local authority channels. (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 I Exam Content Outline

Largest Math I component; commonly about 60%

Advanced Mathematics

Functions, limits, continuity, one-variable differential and integral calculus, applications of derivatives and integrals, infinite series, multivariable calculus, vector algebra and space analytic geometry, multiple integrals, line and surface integrals, and ordinary differential equations.

Core component; commonly about 20%

Linear Algebra

Determinants, matrices, elementary transformations, matrix rank, vector groups, linear independence, linear systems, eigenvalues, eigenvectors, diagonalization, quadratic forms, orthogonal transformations, and positive definiteness.

Core component; commonly about 20%

Probability Theory and Mathematical Statistics

Random events and probability, conditional probability, independence, random variables and distributions, multidimensional random variables, numerical characteristics, laws of large numbers, central limit theorem, sample statistics, parameter estimation, and basic hypothesis-testing ideas.

How to Pass the Kaoyan Mathematics I Exam

What You Need to Know

  • Passing score: No standalone pass mark. Candidates must meet the national basic preliminary-score requirements for their discipline and any higher admissions-unit or program-specific retest requirements.
  • Assessment: Subject 301 Mathematics I is a national unified preliminary examination math subject. It is commonly used by many engineering and science master's programs, especially routes that need the broadest calculus, linear algebra, probability, and statistics coverage, but each admissions unit and program decides its required subject in the current admissions catalog. The real Math I paper is a 150-point, 180-minute closed-book written exam; published syllabus conventions use single-choice questions, fill-in questions, and solution/proof questions rather than a 100-MCQ format. This page is a local 100-question MCQ practice bank and should be paired with real-paper fill-in and written-solution practice.
  • Time limit: 180 minutes. For the 2026 admissions cycle, business course I or professional foundation subjects, including unified mathematics subjects where assigned, were scheduled 2025-12-21, 08:30-11:30 Beijing time.
  • Exam fee: Varies by province, reporting point, and admissions unit; candidates pay required registration or preliminary-exam fees through official CHSI/YanZhao or local authority channels.

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 I Study Tips from Top Performers

1Confirm subject 301 in the target admissions unit's current professional catalog before committing to a Math I plan.
2Treat advanced mathematics as the backbone: limits, derivatives, integrals, series, multivariable calculus, vector calculus, and ODEs support many Math I problem types.
3For linear algebra, connect row reduction, rank, linear systems, eigenvalues, diagonalization, and quadratic forms instead of memorizing them as separate chapters.
4For probability and statistics, practice translating word problems into distributions, events, expectations, variances, joint densities, estimators, and sampling distributions.
5Maintain an error log for algebra slips, sign errors, missing domain conditions, and theorem-condition mistakes; these cost heavily on written Math I solutions.
6After MCQ drills, rehearse complete written solutions because the real paper requires fill-in, calculation, and proof-style answer formats.

Frequently Asked Questions

Is Kaoyan Mathematics I officially a 100-question MCQ exam?

No. The real 301 Mathematics I paper is a 150-point written exam with selected-response, fill-in, and written solution or proof tasks. This page contains 100 original MCQs for targeted concept and calculation practice.

How long is the Kaoyan Mathematics I exam?

The preliminary exam subject is 180 minutes. For the 2026 admissions cycle, unified mathematics subjects assigned as business course I or professional foundation subjects were scheduled in the 2025-12-21 morning session.

Does every Kaoyan candidate take Mathematics I?

No. Mathematics I is used by many engineering and science programs, but candidates must check the target school and program catalog. Some programs use Mathematics II, Mathematics III, economics comprehensive ability, another professional foundation subject, or a self-set subject.

How is Mathematics I scored?

The real paper is worth 150 points. There is no separate universal pass mark for Mathematics I; candidates must meet the national basic score-line requirements for their discipline and any admissions-unit retest line.

What topics should be prioritized?

Build a strong base in limits, derivatives, integrals, multivariable calculus, ODEs, matrices, eigenvalues, distributions, expectations, variance, sampling distributions, and parameter estimation. Math I rewards both calculation accuracy and structural reasoning.

What should I practice beyond these MCQs?

Use real-paper fill-in and written-solution drills. Mathematics I requires setting up multi-step calculations, proving or justifying results, and organizing work clearly under the 180-minute time limit.