Free GARP FRM Part I Quantitative Analysis Practice Questions

Quantitative Analysis carries 20% of GARP FRM Part I (GARP). Questions test probability and random variables, common univariate and multivariate distributions, sample moments, hypothesis testing, single and multiple linear regression with diagnostics, stationary and non-stationary time series, measuring returns, volatility, and correlation, simulation and bootstrapping, and the machine-learning readings in the current curriculum.

196 questions 54 easy 94 medium 48 hard 2026 syllabus

Sample Questions

Question 1 Easy
In classical hypothesis testing, a Type I error occurs when:
Solution
C is correct. A Type I error is the false rejection of a true null hypothesis. Its probability equals the chosen significance level α\alpha. Failing to reject a false null is a Type II error, with probability β\beta.
Question 2 Medium
In the bias-variance tradeoff, increasing model complexity most likely:
Solution
A is correct.

As model complexity increases, the model fits training data more closely, reducing bias (the error from overly simplistic assumptions). However, the model becomes more sensitive to the specific training data used, increasing variance (the error from sensitivity to small fluctuations in the training set). This is the fundamental bias-variance tradeoff.
Question 3 Hard
A simple linear regression uses 25 observations with TSS = 450 and ESS = 360. What is the F-statistic for this regression?
Solution
A is correct.

For simple linear regression: RSS=TSS−ESS=450−360=90\text{RSS} = \text{TSS} - \text{ESS} = 450 - 360 = 90. dfregression=1df_{\text{regression}} = 1 (one independent variable); dfresidual=n−2=25−2=23df_{\text{residual}} = n - 2 = 25 - 2 = 23. MSR=ESSdfregression=3601=360\text{MSR} = \frac{\text{ESS}}{df_{\text{regression}}} = \frac{360}{1} = 360. MSE=RSSdfresidual=9023=3.913\text{MSE} = \frac{\text{RSS}}{df_{\text{residual}}} = \frac{90}{23} = 3.913. F=MSRMSE=3603.913=92.0F = \frac{\text{MSR}}{\text{MSE}} = \frac{360}{3.913} = 92.0.
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