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100+ Free IFoA CS1 Practice Questions

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2026 Statistics

Key Facts: IFoA CS1 Exam

2 papers

Paper A and Paper B

IFoA CS1 page

3h 20m

Paper A Time

IFoA CS1 page

1h 50m

Paper B Time

IFoA CS1 page

30%

Regression and GLMs Weight

IFoA CS1 syllabus

200 hrs

Recommended Study

IFoA CS1 page

70/30

Paper A vs B Weight

IFoA CS1 page

IFoA Subject CS1 Actuarial Statistics is examined through two computer-based papers sat together: Paper A (3 hours 20 minutes) tests theory in Word, and Paper B (1 hour 50 minutes) tests data analysis in Word and R, with Paper A weighted 70% and Paper B 30%. The 2026 syllabus weights Regression Theory and Applications (including GLMs) most heavily at 30%, followed by Statistical Inference at 25% and Random Variables and Distributions at 20%, with Bayesian Statistics at 15% and Data Analysis at 10%. The pass mark is set by the IFoA Board of Examiners each session rather than published as a fixed percentage. These 100 MCQs are knowledge-prep over the same body of statistics.

Sample IFoA CS1 Practice Questions

Try these sample questions to test your IFoA CS1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A random variable X follows a Poisson distribution with mean 4. What is the variance of X?
A.4
B.2
C.8
D.16
Explanation: For a Poisson distribution, the mean and variance are both equal to the parameter lambda. With lambda = 4, the variance equals 4.
2The moment generating function (MGF) of a random variable X is M(t) = exp(2t + 3t^2). What are the mean and variance of X?
A.Mean 2, variance 3
B.Mean 2, variance 6
C.Mean 3, variance 2
D.Mean 4, variance 6
Explanation: This is the MGF of a normal distribution exp(mu*t + sigma^2*t^2/2). Matching mu = 2 and sigma^2/2 = 3 gives variance sigma^2 = 6. So mean is 2 and variance is 6.
3Which discrete distribution models the number of failures before the first success in a sequence of independent Bernoulli trials?
A.Binomial
B.Hypergeometric
C.Geometric
D.Negative binomial with r = 2
Explanation: The geometric distribution models the number of trials (or failures) until the first success. It is a special case of the negative binomial with r = 1.
4If X follows an exponential distribution with rate parameter lambda = 0.5, what is P(X > 4)?
A.e^(-8)
B.e^(-0.5)
C.1 - e^(-2)
D.e^(-2)
Explanation: For an exponential distribution, P(X > x) = e^(-lambda*x). With lambda = 0.5 and x = 4, this is e^(-0.5*4) = e^(-2).
5The gamma distribution with shape parameter alpha and rate parameter beta has mean alpha/beta. What is its variance?
A.alpha/beta^2
B.alpha/beta
C.alpha^2/beta
D.1/beta^2
Explanation: The gamma distribution with rate beta has mean alpha/beta and variance alpha/beta^2. The variance is the shape parameter divided by the square of the rate parameter.
6A continuous random variable X has probability density function f(x) = 3x^2 for 0 <= x <= 1. What is E(X)?
A.1/2
B.3/4
C.2/3
D.3/5
Explanation: E(X) = integral of x * 3x^2 dx from 0 to 1 = integral of 3x^3 dx = [3x^4/4] from 0 to 1 = 3/4.
7If X follows a lognormal distribution such that ln(X) ~ N(mu, sigma^2), which statement is true?
A.X can take negative values
B.ln(X) is lognormally distributed
C.X is always positive and right-skewed
D.The mean of X equals e^mu
Explanation: Because X = e^Y where Y is normal, X is strictly positive and the distribution is right-skewed. The mean of X is exp(mu + sigma^2/2), not e^mu.
8For a binomial distribution with n = 20 and p = 0.3, what is the variance?
A.6
B.14
C.2.05
D.4.2
Explanation: The variance of a binomial distribution is np(1-p) = 20 * 0.3 * 0.7 = 4.2.
9The coefficient of skewness of a symmetric distribution such as the normal distribution is equal to what value?
A.0
B.1
C.3
D.Undefined
Explanation: The coefficient of skewness measures asymmetry. For any symmetric distribution, including the normal, the third central moment and hence the skewness coefficient is 0.
10If X and Y are independent random variables with Var(X) = 4 and Var(Y) = 9, what is Var(X - Y)?
A.5
B.13
C.-5
D.36
Explanation: For independent variables, Var(X - Y) = Var(X) + Var(Y) = 4 + 9 = 13. Variances add even when subtracting because the coefficient is squared.

About the IFoA CS1 Exam

IFoA Subject CS1 Actuarial Statistics is a Core Principles actuarial exam covering probability distributions, data analysis, statistical inference, regression and generalised linear models, and Bayesian statistics and credibility theory, with applied data work in R.

Assessment

Paper A theory exam in Word plus Paper B data analysis in Word and R, taken in the same sitting

Time Limit

Paper A: 3 hours 20 minutes; Paper B: 1 hour 50 minutes

Passing Score

Pass mark is set by the IFoA Board of Examiners each session and is not published as a fixed percentage

Exam Fee

Approximately GBP 290 student fee per session (Institute and Faculty of Actuaries (IFoA))

IFoA CS1 Exam Content Outline

20%

Random Variables and Distributions

Work with discrete and continuous distributions, expectations, variances, moment and probability generating functions, conditional and compound distributions, sums of random variables, and the central limit theorem.

10%

Data Analysis

Summarise data using measures of location and dispersion, build histograms and boxplots, interpret skewness and outliers, and use exploratory graphics including Q-Q plots in R.

25%

Statistical Inference

Estimate parameters by maximum likelihood and the method of moments, assess estimator properties, build confidence intervals, and carry out hypothesis tests including chi-square and likelihood ratio tests.

30%

Regression Theory and Applications

Fit simple and multiple linear regression, interpret correlation and copulas, and apply generalised linear models with appropriate link functions, deviance and model selection criteria.

15%

Bayesian Statistics and Credibility

Apply Bayes theorem, conjugate priors, loss functions and posterior summaries, and use credibility theory including Buhlmann, Buhlmann-Straub and empirical Bayes methods.

How to Pass the IFoA CS1 Exam

What You Need to Know

  • Passing score: Pass mark is set by the IFoA Board of Examiners each session and is not published as a fixed percentage
  • Assessment: Paper A theory exam in Word plus Paper B data analysis in Word and R, taken in the same sitting
  • Time limit: Paper A: 3 hours 20 minutes; Paper B: 1 hour 50 minutes
  • Exam fee: Approximately GBP 290 student fee per session

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

IFoA CS1 Study Tips from Top Performers

1Learn the standard distributions cold, including their means, variances and generating functions, so you can recognise the right model quickly under exam time pressure.
2Practise maximum likelihood and method of moments derivations until setting up and solving the score equations becomes routine rather than something you reconstruct each time.
3Treat generalised linear models as the highest-value topic: be fluent with link functions, the exponential family, deviance and interpreting exponentiated coefficients on the mean.
4For Bayesian and credibility questions, memorise the common conjugate pairs and the Buhlmann credibility formula Z = n/(n + k) so you can apply them without re-deriving.
5Build genuine R fluency for Paper B by repeatedly fitting models with lm and glm, simulating data, and reading output, because exam pace depends on comfort with the software.

Frequently Asked Questions

How is the IFoA CS1 exam structured?

CS1 is assessed by two computer-based papers taken in the same sitting. Paper A is a theory paper completed in Word lasting 3 hours 20 minutes, and Paper B is a data analysis paper completed in Word and R lasting 1 hour 50 minutes.

How long is the IFoA CS1 exam?

Paper A lasts 3 hours 20 minutes and Paper B lasts 1 hour 50 minutes, and both must be sat in the same exam session. Paper A is weighted at 70% and Paper B at 30% of the overall mark.

What is the passing score for IFoA CS1?

The pass mark is set by the IFoA Board of Examiners for each session and is not published as a single fixed percentage. It is typically in the region of 55 to 60% of the available marks.

Which topics carry the most weight in CS1?

Regression Theory and Applications, which includes generalised linear models, is the largest area at about 30%. Statistical Inference is around 25% and Random Variables and Distributions about 20%, with Bayesian Statistics 15% and Data Analysis 10%.

Do I need to know R for CS1?

Yes. Paper B is a practical, software-based assessment that tests your ability to apply the statistical methods from Paper A using R programming, so working R skills are essential for that paper.

How much study time does CS1 require?

The IFoA recommends around 200 hours of study for CS1. Most candidates spread this over several months alongside work, balancing theory practice for Paper A with data analysis practice for Paper B.