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100+ Free CAA Associate Actuary (China) Practice Questions

Prepare for the China Association of Actuaries Associate Actuary Examination (中国准精算师职业资格考试) exam with instant access — no signup required.

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2026 Statistics

Key Facts: CAA Associate Actuary (China) Exam

Administering Body

Regulatory Charter

Credential Level

Examination Structure

Testing Format & Time

Passing Standard

Exam Fee

The CAA offered the Associate examinations in two 2026 sittings. Candidates complete five closed-book computer papers totaling 18 hours, and the 2026 first-half passing standard was 60/100 per paper. Passed subject scores have long-term validity. Certificate issuance also requires prescribed education and applicable work experience. This bank is an English single-answer MCQ study adaptation, not an official translation, official item bank, or computer-exam simulation.

Sample CAA Associate Actuary (China) Practice Questions

Try these sample questions to test your CAA Associate Actuary (China) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In an actuarial driver risk classification model, 20% of insured drivers are classified as high-risk ($H$) and 80% as low-risk ($L$). The annual probability of having at least one accident is 0.30 for high-risk drivers and 0.05 for low-risk drivers. If a newly insured policyholder has an accident in their first year, what is the posterior probability that they belong to the high-risk class under Bayes' Theorem?
A.0.600
B.0.300
C.0.200
D.0.750
Explanation: By Bayes' Theorem, $P(H|A) = \frac{P(A|H)P(H)}{P(A|H)P(H) + P(A|L)P(L)} = \frac{0.30 \times 0.20}{(0.30 \times 0.20) + (0.05 \times 0.80)} = \frac{0.06}{0.06 + 0.04} = \frac{0.06}{0.10} = 0.600$.
2Let $X_1, X_2, \dots, X_n$ be independent Poisson random variables representing claim counts from $n$ independent policy groups, where $X_i \sim \text{Poisson}(\lambda_i)$. What is the exact distribution of the total claim count $S = \sum_{i=1}^n X_i$?
A.$\text{Poisson}(\sum_{i=1}^n \lambda_i)$
B.$\text{Gamma}(\sum_{i=1}^n \lambda_i, 1)$
C.$\text{Negative Binomial}(\sum_{i=1}^n \lambda_i, 0.5)$
D.$\text{Normal}(\sum \lambda_i, \sum \lambda_i^2)$
Explanation: The sum of independent Poisson random variables is itself a Poisson random variable whose parameter is the sum of the individual Poisson intensity parameters: $S \sim \text{Poisson}(\sum_{i=1}^n \lambda_i)$, as verified by multiplying their moment generating functions $M_S(t) = \prod M_{X_i}(t) = \exp((\sum \lambda_i)(e^t - 1))$.
3A life annuity or equipment warranty model assumes time-to-failure $T$ follows an exponential distribution with mean 10 years (rate $\lambda = 0.10$). Given that the component has already survived 6 years without failure, what is the expected total lifetime $E[T | T > 6]$?
A.16 years
B.10 years
C.4 years
D.12 years
Explanation: Due to the memoryless property of the exponential distribution, the remaining lifetime $T - 6$ given $T > 6$ is exponentially distributed with the original mean of 10 years: $E[T - 6 | T > 6] = 10$. Therefore, the expected total lifetime is $E[T | T > 6] = 6 + 10 = 16$ years.
4Let $X$ follow a Gamma distribution $\Gamma(\alpha, \beta)$ with probability density function $f(x) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x}$ for $x > 0$. What is the moment generating function $M_X(t) = E[e^{tX}]$ for $t < \beta$?
A.$(1 - \frac{t}{\beta})^{-\alpha}$
B.$(1 - \beta t)^{-\alpha}$
C.$\exp(\alpha \beta t)$
D.$(1 + \frac{t}{\beta})^\alpha$
Explanation: For $X \sim \Gamma(\alpha, \beta)$, $M_X(t) = \int_0^\infty e^{tx} \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-\beta x} dx = \frac{\beta^\alpha}{(\beta - t)^\alpha} \int_0^\infty \frac{(\beta - t)^\alpha}{\Gamma(\alpha)} x^{\alpha-1} e^{-(\beta-t)x} dx = (1 - \frac{t}{\beta})^{-\alpha}$ for $t < \beta$.
5An insurance portfolio has annual aggregate claim payouts with mean $\mu = 50$ million RMB and standard deviation $\sigma = 10$ million RMB. Using Chebyshev's Inequality, what is the minimum probability that the aggregate claim payout will fall strictly between 30 million RMB and 70 million RMB?
A.0.75
B.0.50
C.0.89
D.0.95
Explanation: The interval $(30, 70)$ corresponds to $(\mu - 2\sigma, \mu + 2\sigma)$, so $k = 2$. By Chebyshev's Inequality, $P(|X - \mu| < k\sigma) \ge 1 - \frac{1}{k^2} = 1 - \frac{1}{2^2} = 1 - 0.25 = 0.75$.
6An insurer covers 10,000 independent policies. Each policy produces a claim with probability $p = 0.01$ and severity exactly 50,000 RMB. Using the Central Limit Theorem with continuity correction, what is the approximate probability that total claim payouts exceed 5,500,000 RMB? (Given standard normal CDF $\Phi(1.06) \approx 0.8554$)
A.0.1446
B.0.8554
C.0.0500
D.0.3085
Explanation: Let $N$ be the number of claims. $N \sim \text{Binomial}(10000, 0.01)$ with $\mu_N = 100$ and $\sigma_N = \sqrt{10000 \times 0.01 \times 0.99} = \sqrt{99} \approx 9.9499$. Total payout exceeds 5,500,000 RMB when $N > 110$. With continuity correction, $P(N \ge 111) = P(N > 110.5) \approx 1 - \Phi(\frac{110.5 - 100}{9.9499}) = 1 - \Phi(1.055) \approx 1 - \Phi(1.06) = 1 - 0.8554 = 0.1446$.
7Two continuous random variables $X$ (property damage loss) and $Y$ (bodily injury loss) have joint probability density function $f(x, y) = 3(x + y)$ on the unit simplex $0 \le x \le 1, 0 \le y \le 1, x + y \le 1$. What is the marginal probability density function $f_X(x)$ for $0 \le x \le 1$?
A.$\frac{3}{2}(1 - x^2)$
B.$3x(1 - x)$
C.$3(1 - x)^2$
D.$\frac{1}{2}(1 - x)$
Explanation: The coefficient 3 normalizes the joint density because the integral of $x+y$ over the unit simplex is $1/3$. Integrating over $y$ from $0$ to $1-x$ gives $f_X(x)=\int_0^{1-x}3(x+y)dy=3x(1-x)+\frac{3}{2}(1-x)^2=\frac{3}{2}(1-x^2)$ for $0\le x\le1$.
8In extreme value modeling, loss amounts exceed a statutory deductible $x_0 = 100$ thousand RMB following a single-parameter Pareto distribution with CDF $F(x) = 1 - (\frac{x_0}{x})^\alpha$ for $x \ge x_0$. Given a sample of $n$ observed losses $x_1, x_2, \dots, x_n$, what is the Maximum Likelihood Estimator (MLE) $\hat{\alpha}$?
A.$\frac{n}{\sum_{i=1}^n \ln(x_i / x_0)}$
B.$\frac{\sum_{i=1}^n \ln(x_i / x_0)}{n}$
C.$\frac{n}{\sum_{i=1}^n (x_i - x_0)}$
D.$\frac{\bar{x}}{\bar{x} - x_0}$
Explanation: The likelihood is $L(\alpha) = \prod_{i=1}^n \frac{\alpha x_0^\alpha}{x_i^{\alpha+1}} = \alpha^n x_0^{n\alpha} \prod x_i^{-(\alpha+1)}$. The log-likelihood is $\ell(\alpha) = n \ln \alpha + n\alpha \ln x_0 - (\alpha+1)\sum \ln x_i$. Setting $\frac{\partial \ell}{\partial \alpha} = \frac{n}{\alpha} + n\ln x_0 - \sum \ln x_i = 0$ yields $\hat{\alpha} = \frac{n}{\sum_{i=1}^n \ln(x_i / x_0)}$.
9A sample of $n$ independent observations $X_1, \dots, X_n$ is drawn from a continuous uniform distribution $U(0, \theta)$. What is the Method of Moments estimator $\hat{\theta}_{MM}$ and is it unbiased?
A.$\hat{\theta}_{MM} = 2\bar{X}$, and it is an unbiased estimator of $\theta$
B.$\hat{\theta}_{MM} = \bar{X}$, and it is a biased estimator of $\theta$
C.$\hat{\theta}_{MM} = X_{(n)}$, and it is an unbiased estimator of $\theta$
D.$\hat{\theta}_{MM} = \frac{n+1}{n} X_{(n)}$, and it is a biased estimator of $\theta$
Explanation: For $U(0, \theta)$, the theoretical first moment is $E[X] = \frac{\theta}{2}$. Equating to the sample mean $\bar{X} = \frac{\theta}{2}$ gives $\hat{\theta}_{MM} = 2\bar{X}$. Since $E[2\bar{X}] = 2E[\bar{X}] = 2(\frac{\theta}{2}) = \theta$, $\hat{\theta}_{MM}$ is strictly unbiased.
10For a random sample of size $n$ drawn from an exponential distribution with rate parameter $\lambda$ ($f(x) = \lambda e^{-\lambda x}, x > 0$), what is the Cramér-Rao Lower Bound (CRLB) for the variance of any unbiased estimator of $\lambda$?
A.$\frac{\lambda^2}{n}$
B.$\frac{\lambda}{n}$
C.$\frac{1}{n\lambda^2}$
D.$\frac{\lambda^2}{n^2}$
Explanation: The log-likelihood for a single observation is $\ln f(x; \lambda) = \ln \lambda - \lambda x$. The second derivative is $\frac{\partial^2 \ln f}{\partial \lambda^2} = -\frac{1}{\lambda^2}$. The Fisher Information for a sample of size $n$ is $I_n(\lambda) = -n E[\frac{\partial^2 \ln f}{\partial \lambda^2}] = \frac{n}{\lambda^2}$. Thus, the Cramér-Rao Lower Bound is $\frac{1}{I_n(\lambda)} = \frac{\lambda^2}{n}$.

About the CAA Associate Actuary (China) Exam

The China Associate Actuary Qualification Examination (中国准精算师职业资格考试) is a national level-evaluation professional qualification (水平评价类职业资格), not a statutory license to practise. Under 金规〔2023〕3号, the China Association of Actuaries administers five compulsory subjects: Probability and Mathematical Statistics; Integrated Economics and Finance; Actuarial Mathematics; Actuarial Models and Data Analysis; and Actuarial Risk Management. The official outline spans probability and statistics, microeconomics, macroeconomics, finance, insurance, accounting, interest theory, life and non-life actuarial mathematics, risk theory, survival analysis, simulation, regression, time series, machine learning, enterprise risk management, and capital management. Passing the papers is not by itself sufficient for the certificate: candidates must also complete the prescribed legal/regulatory and ethics education and meet the applicable actuarial or financial work-experience condition.

Assessment

Closed-book computer examination (闭卷机考) consisting of A1 《概率论与数理统计》(3 hours, 100 points), A2 《经济金融综合》(3 hours, 100 points), A3 《精算数学》(4 hours, 100 points), A4 《精算模型与数据分析》(4 hours, 100 points), and A5 《精算风险管理》(4 hours, 100 points). No separate oral, practical, case-study, or assignment component is listed for the examination itself; legal/regulatory and ethics education are separate certificate conditions.

Time Limit

18 hours total: A1 and A2 are 3 hours each; A3, A4, and A5 are 4 hours each.

Passing Score

60/100 points per subject paper in the CAA's 2026 first-half results notice; passed subjects have long-term validity.

Exam Fee

The CAA's 2025 public fee consultation proposed continuing ¥100 RMB per Associate paper; the public 2026 registration notice does not restate the fee, so confirm the live amount during registration. (China Association of Actuaries (中国精算师协会 / CAA), under the qualification framework issued by NFRA and MOHRSS)

CAA Associate Actuary (China) Exam Content Outline

20%

Probability and Mathematical Statistics (概率论与数理统计)

Probability foundations, univariate and multivariate random variables, probability mass/density functions, cumulative distribution functions, marginal and conditional distributions, expectation, variance, covariance, moment generating functions, characteristic functions, probability inequalities (Markov, Chebyshev, Jensen), Law of Large Numbers (Weak and Strong), Central Limit Theorem (Lindeberg-Lévy, Liapunov), point estimation (Maximum Likelihood Estimation MLE, Method of Moments, unbiasedness, consistency, sufficiency, Fisher information, Cramér-Rao inequality), interval estimation, hypothesis testing (Neyman-Pearson lemma, likelihood ratio tests, t-tests, chi-square goodness-of-fit tests, F-tests), and single/two-way Analysis of Variance (ANOVA).

20%

Integrated Economics and Finance (经济金融综合)

The official A2 outline divides the paper equally among microeconomics (20%), macroeconomics (20%), finance (20%), insurance (20%), and accounting and financial management (20%). The 20 questions in this bank use the same four-question-per-cluster allocation.

20%

Actuarial Mathematics (精算数学)

The official A3 outline allocates 20% to compound-interest theory, 40% to life actuarial mathematics, and 40% to non-life actuarial mathematics. The 20 questions in this bank use four interest-theory, eight life, and eight non-life questions.

20%

Actuarial Models and Data Analysis (精算模型与数据分析)

The official A4 outline allocates 30% to risk theory, 15% to survival analysis, 10% to simulation, 15% to regression, 10% to time series, and 20% to machine learning. The 20 questions in this bank use six, three, two, three, two, and four questions across those clusters. Machine-learning coverage includes classification, model evaluation and selection, decision trees, and dimensionality reduction.

20%

Actuarial Risk Management and Solvency (精算风险管理与偿付能力)

The official A5 outline allocates 15% to foundations, 10% to risk identification and classification, 15% to risk modeling, 20% to risk measurement, 20% to risk-management tools, and 20% to capital management. The 20 questions in this bank use three, two, three, four, four, and four questions across those clusters. Regulatory items use current C-ROSS Phase II solvency, liquidity, risk-management assessment, and capital-planning provisions.

How to Pass the CAA Associate Actuary (China) Exam

What You Need to Know

  • Passing score: 60/100 points per subject paper in the CAA's 2026 first-half results notice; passed subjects have long-term validity.
  • Assessment: Closed-book computer examination (闭卷机考) consisting of A1 《概率论与数理统计》(3 hours, 100 points), A2 《经济金融综合》(3 hours, 100 points), A3 《精算数学》(4 hours, 100 points), A4 《精算模型与数据分析》(4 hours, 100 points), and A5 《精算风险管理》(4 hours, 100 points). No separate oral, practical, case-study, or assignment component is listed for the examination itself; legal/regulatory and ethics education are separate certificate conditions.
  • Time limit: 18 hours total: A1 and A2 are 3 hours each; A3, A4, and A5 are 4 hours each.
  • Exam fee: The CAA's 2025 public fee consultation proposed continuing ¥100 RMB per Associate paper; the public 2026 registration notice does not restate the fee, so confirm the live amount during registration.

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

CAA Associate Actuary (China) Study Tips from Top Performers

1Master Mathematical Derivations: In Subject A1, memorize the properties of common parametric distributions (Poisson, Gamma, Normal, Beta) and practice Maximum Likelihood Estimator (MLE) and Fisher Information derivations.
2Drill Actuarial Math Formulas: In Subject A3, be proficient in converting between effective interest rates, nominal interest rates, and force of interest, and master equivalence principle premium calculations and prospective reserve formulas.
3Understand Non-Life Reserving Methods: Know the exact step-by-step algorithms for Chain Ladder development factors, Bornhuetter-Ferguson expected losses, and Cape Cod premium weightings.
4Master GLMs and Stochastic Processes: In Subject A4, understand how link functions connect linear predictors to exponential dispersion family means (log link for Poisson frequency, log/reciprocal link for Gamma severity).
5Apply Current C-ROSS Rules: In Subject A5, remember that the two solvency-ratio thresholds must be met together with an integrated risk rating of Category B or better, and distinguish quantifiable-risk, control-risk, and additional capital.
6Practice Timed Quantitative Problems: Allocate time to work through multi-step computational problems under exam-like conditions to build speed and calculation accuracy.

Frequently Asked Questions

What is the China Association of Actuaries Associate Actuary Examination (中国准精算师职业资格考试)?

The CAA Associate Actuary Examination is the five-subject examination tier of China's national level-evaluation actuarial professional qualification (水平评价类职业资格). NFRA and MOHRSS established the framework in 金规〔2023〕3号, and the China Association of Actuaries administers the examinations. It is not a statutory licence to practise.

What is the structure, duration, and passing standard of the official examination?

The examination comprises five closed-book computer papers: A1 概率论与数理统计 and A2 经济金融综合 are 3 hours each; A3 精算数学, A4 精算模型与数据分析, and A5 精算风险管理 are 4 hours each. Each paper is scored out of 100, and the CAA's 2026 first-half passing standard was 60. Passed subject scores have long-term validity. The public 2026 notices do not publish a fixed question count or item-type mix.

What are the eligibility requirements to sit for the CAA Associate Actuary exams?

To sit, candidates must meet the conduct requirements and hold a recognized bachelor's degree or be currently enrolled as an undergraduate (大学本科在读及以上学历或学位). Earning the Associate certificate after passing all five papers also requires the prescribed legal/regulatory and ethics education plus the applicable actuarial or financial work experience; the requirement varies by degree level.

How is China's C-ROSS Phase II solvency framework tested in the exam?

C-ROSS Phase II is applied within A5's risk-measurement, risk-management-tool, and capital-management clusters. This bank covers current core and comprehensive solvency thresholds, the integrated risk-rating condition, quantifiable and control-risk capital, risk-management assessment scoring, insurer liquidity ratios, and three-year capital planning.

What is the difference between China Associate Actuary (准精算师) and Fellow Actuary (正精算师)?

The Associate tier has one common five-paper foundation. The Fellow tier is divided into seven distinct professional categories—Life, Non-Life, Health, Social Insurance and Pensions, Financial Risk, Asset Management, and Data Science—each with one common, three specialty, and one elective paper. Holding the Associate certificate is a condition for the Fellow certificate; it is not described here as a prerequisite merely to sit a Fellow paper.

Why is this OpenExamPrep question bank presented in English?

The CAA's public outline, candidate instructions, schedules, and exam-system materials are published in Chinese, but the public 2026 notices reviewed for this bank do not expressly enumerate official delivery languages. This bank therefore omits an official-language code. Its English single-answer questions preserve official Chinese names and necessary local terms, but they are a study adaptation—not an official translation, official item bank, format simulation, or substitute for practice in the CAA computer system.