Career upgrade: Learn practical AI skills for better jobs and higher pay.
Level up
All Practice Exams

100+ Free Kaoyan Mathematics III Practice Questions

Pass your Kaoyan Mathematics III (303) - National Postgraduate Entrance Examination Mathematics III exam on the first try — instant access, no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
No single official Math III pass rate applies because admission is program-specific and ranking-based across institutions, disciplines, regions, and enrollment plans. Pass Rate
100+ Questions
100% Free
1 / 100
Question 1
Score: 0/0

For f(x) = x^2 + 4x + 5, what is the minimum value?

A
B
C
D
to track
2026 Statistics

Key Facts: Kaoyan Mathematics III Exam

100

Original local practice MCQs on this page

OpenExamPrep local question bank

150 marks / 180 minutes

Live Mathematics III paper score and time

YanZhao / CHSI Mathematics III syllabus archive

303

Common subject code for Mathematics III in YanZhao program catalog entries

YanZhao master's program catalog

56 / 22 / 22

Approximate calculus, linear algebra, probability/statistics content split in CHSI Math III archive

YanZhao / CHSI Mathematics III syllabus archive

No standalone pass score

National lines and admissions-unit re-exam requirements govern advancement

MOE / YanZhao 2026 national score line notice

Kaoyan Mathematics III is a 150-mark, 180-minute national unified written math subject for programs that require 303 Math III, commonly in economics and management-oriented tracks. This page provides 100 original local MCQs across calculus, linear algebra, probability/statistics, marginal analysis, optimization, matrices, estimation, and applied quantitative modeling.

Sample Kaoyan Mathematics III Practice Questions

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

1Evaluate the limit lim_{x -> 0} (e^x - 1) / x.
A.1
B.0
C.e
D.Does not exist
Explanation: The standard exponential limit is lim_{x -> 0} (e^x - 1) / x = 1. Equivalently, it is the derivative of e^x at x = 0.
2What is d/dx ln x at x = 1?
A.0
B.1
C.e
D.-1
Explanation: The derivative of ln x is 1/x. Substituting x = 1 gives 1.
3If total revenue is R(q) = 20q - q^2, what is marginal revenue?
A.20 - q
B.20 - 2q
C.20q - 2q^2
D.q(20 - q)
Explanation: Marginal revenue is the derivative of total revenue: R'(q) = 20 - 2q.
4Compute the integral int_0^2 3x^2 dx.
A.6
B.8
C.12
D.24
Explanation: An antiderivative of 3x^2 is x^3. Evaluating from 0 to 2 gives 2^3 - 0 = 8.
5For f(x) = x^2 + 4x + 5, what is the minimum value?
A.0
B.1
C.4
D.5
Explanation: Complete the square: x^2 + 4x + 5 = (x + 2)^2 + 1. The minimum value is 1 at x = -2.
6For f(x,y) = x^2 y + y^3, what is the partial derivative with respect to x at (2,1)?
A.2
B.4
C.5
D.7
Explanation: Treat y as constant: f_x = 2xy. At (2,1), f_x = 2(2)(1) = 4.
7If demand is Q = 100 - 2P, what is the point price elasticity dQ/dP * P/Q at P = 20?
A.-2/3
B.-3/2
C.2/3
D.-40
Explanation: At P = 20, Q = 60 and dQ/dP = -2. Elasticity is (-2)(20/60) = -2/3.
8For Q(K,L) = K^0.5 L^0.5, what happens to output if both K and L are doubled?
A.Output is unchanged
B.Output doubles
C.Output quadruples
D.Output increases by sqrt(2)
Explanation: The exponents sum to 1, so the function has constant returns to scale. Doubling both inputs doubles output.
9Let A = [[1,2],[3,4]] and v = [1,0]^T. What is Av?
A.[1,3]^T
B.[2,4]^T
C.[3,7]^T
D.[1,2]^T
Explanation: Multiplying by [1,0]^T selects the first column of A, which is [1,3]^T.
10What is 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 2*4 - 1*3 = 5.

About the Kaoyan Mathematics III Exam

Kaoyan Mathematics III is the economics and management-oriented mathematics paper used in China's National Postgraduate Entrance Examination when the target program requires subject code 303. It tests calculus, linear algebra, probability, and mathematical statistics with an emphasis on economic and management applications such as marginal functions, elasticity, constrained optimization, matrix models, random variables, distributions, estimation, and quantitative decision models. The broader postgraduate admissions process is governed by MOE rules and combines a nationally organized preliminary exam with admissions-unit re-examination and final selection.

Assessment

Mathematics III is a national unified mathematics subject used in the National Postgraduate Entrance Examination when a candidate's target admissions unit and program list subject code 303 Mathematics III. Official CHSI syllabus archive information identifies Mathematics III as a 150-mark, 180-minute closed-book written paper covering calculus, linear algebra, and probability/statistics, with calculus carrying the largest share. The subject is associated with economics and management-oriented programs and emphasizes mathematical tools for demand, marginal analysis, optimization, matrices, random variables, estimation, and quantitative modeling. Candidates must verify the current subject code in the YanZhao master's program catalog and the target university's admissions brochure because requirements are program-specific.

Time Limit

180 minutes for the live Mathematics III written preliminary-exam paper

Passing Score

No standalone Math III pass score. MOE publishes annual national preliminary-exam score requirements by discipline/category and region, including single-subject thresholds for subjects with full mark greater than 100; admissions units set their own re-exam requirements on that basis.

Exam Fee

No separate fee for Mathematics III alone. Candidates pay the national postgraduate entrance exam registration/exam fee set by the relevant provincial education admissions/examination agency and report point. (Ministry of Education of the People's Republic of China; National Education Examinations Authority; China Graduate Admissions Information Network (YanZhao/CHSI); provincial education admissions examination institutions; and admissions units)

Kaoyan Mathematics III Exam Content Outline

About 56%

Calculus

Functions, limits, continuity, derivatives, differentials, integrals, multivariable calculus, series, differential equations, marginal functions, elasticity, extrema, constrained optimization, and economic applications.

About 22%

Linear Algebra

Determinants, matrix operations, inverse matrices, rank, vector groups, linear systems, eigenvalues, eigenvectors, diagonalization, quadratic forms, and matrix-based economic or management models.

About 22%

Probability and Mathematical Statistics

Random events, conditional probability, independence, discrete and continuous random variables, common distributions, expectation, variance, covariance, transformations, large-sample ideas, sampling distributions, point estimation, method of moments, and maximum likelihood.

Integrated throughout

Economics and Management Modeling

Demand and revenue models, marginal cost and profit, consumer and producer optimization, production functions, input-output models, Markov transitions, regression equations, price indexes, expected profit, and decision analysis.

How to Pass the Kaoyan Mathematics III Exam

What You Need to Know

  • Passing score: No standalone Math III pass score. MOE publishes annual national preliminary-exam score requirements by discipline/category and region, including single-subject thresholds for subjects with full mark greater than 100; admissions units set their own re-exam requirements on that basis.
  • Assessment: Mathematics III is a national unified mathematics subject used in the National Postgraduate Entrance Examination when a candidate's target admissions unit and program list subject code 303 Mathematics III. Official CHSI syllabus archive information identifies Mathematics III as a 150-mark, 180-minute closed-book written paper covering calculus, linear algebra, and probability/statistics, with calculus carrying the largest share. The subject is associated with economics and management-oriented programs and emphasizes mathematical tools for demand, marginal analysis, optimization, matrices, random variables, estimation, and quantitative modeling. Candidates must verify the current subject code in the YanZhao master's program catalog and the target university's admissions brochure because requirements are program-specific.
  • Time limit: 180 minutes for the live Mathematics III written preliminary-exam paper
  • Exam fee: No separate fee for Mathematics III alone. Candidates pay the national postgraduate entrance exam registration/exam fee set by the relevant provincial education admissions/examination agency and report point.

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 III Study Tips from Top Performers

1Confirm subject code 303 in the current admissions catalog before committing to a Math III plan.
2Treat calculus as the highest-volume area, but do not neglect linear algebra and probability/statistics because they often produce compact high-value problems.
3Practice marginal analysis, elasticity, constrained optimization, and expected-value modeling in addition to pure symbolic calculation.
4For linear algebra, connect row reduction, rank, determinant, inverse, eigenvalue, and quadratic-form criteria instead of memorizing them as separate tricks.
5For probability and statistics, keep a formula sheet organized by distribution, expectation/variance identities, transformations, CLT, and estimation methods.
6Use timed mixed sets and write out full solution steps for longer problems; Math III rewards both speed on objective items and clean reasoning on constructed-response work.

Frequently Asked Questions

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

This OpenExamPrep bank contains exactly 100 original multiple-choice questions for cn-kaoyan-mathematics-3. The live Mathematics III paper is a 150-mark, 180-minute written paper and is not a 100-question MCQ exam.

Who takes Kaoyan Mathematics III?

Candidates take Mathematics III only when their target admissions unit and program list subject code 303 Mathematics III. It is commonly associated with economics and management-oriented programs, but candidates must confirm requirements in the current YanZhao catalog and university admissions materials.

What does Mathematics III cover?

The subject covers calculus, linear algebra, probability, and mathematical statistics. Compared with engineering-oriented math papers, Math III practice should emphasize economic and management applications such as marginal analysis, elasticity, optimization, matrices, distributions, estimation, and modeling.

Is there a separate passing score for Math III?

No. MOE publishes annual national preliminary-exam basic score requirements by discipline/category and region, including single-subject thresholds for full-mark-greater-than-100 subjects. Admissions units may set higher re-exam requirements.

Does this bank reproduce official questions?

No. The questions are original practice items written to cover the Mathematics III skill set and economics/management emphasis without copying official exam questions.

Where should I verify current Math III requirements?

Start with YanZhao/CHSI, the current master's program catalog, the MOE admissions rules, and the target university or research institute's official graduate admissions brochure.