CFA Level 1 - Quantitative Methods Review for CFA Level 1 Prep

Now that you have finished studying Quantitative methods for CFA Level 1, you need to spend a session to review important areas. It could be an additional day or extra time depending on you time availability. 

Global Formula & Concept Review

Quick tour of all Quant LOS

Time Value of Money (TVM): discounting/compounding, annuities, perpetuities, NPV/IRR.

Descriptive statistics: mean/median, variance/Standard deviation (SD), coefficient of variation, skewness, etc.

Probability: basic rules, conditional probability, Bayes, expected value and variance of random variables.

Sampling & estimation: standard error, point vs interval estimate.

Hypothesis testing & Confidence Interval: what you did Days 10–12.

Correlation & simple regression: slope, intercept, R², limitations.

• For each area, write down 3–5 key formulas 
• Do Topic‑wise Mixed Question Sets (VImp)
• Do it “slow but correct”, speed issue to revisit later in the full‑curriculum phase.

Simulate a compact Quant exam:

• Take 35–40 Quant questions from across topics, mixed and not in order, under a time cap (~60 minutes).
• No pausing to check; just mark guesses.

Review (at least another 45–60 min):

• Build a final Quant error sheet:for review later
• Spend a short block doing 5–10 questions on the single area that still feels worst after the mini‑mock

Here are some Quant review resources. The official CFA curriculum is always by far the best resource for preparation. These are additional helpful materials.

Level 1 Quant Cheat Sheet

CFA Level 1 Quantitative Methods Cheat Sheet 2026

Sample Questions

CFA® Level 1 Quantitative Methods (2025) questions and answers

CFA Level I Crash Course | Session 4: Quantitative Methods - Day 4

Day 12 - Hypothesis Testing and Cofidence Interval - Review and Practice - CFA Level 1 Prep

 Goal: Today's goal  is to turn Day 10–11 concepts into automatic exam‑style problem solving across all the testing ascpects covered so far like mean, variance, CI, p‑value/critical value, Type I/II, etc.

Make it a day for mixed concept drill

Make a single sheet that forces you to recall definitions and decision rules

• From Day 10: null vs alternative, one‑ vs two‑tailed, significance level, Type I and II errors, decision rule, test statistic idea.

• From Day 11: CI construction, when to use z vs t, single mean test, single variance test, p‑value vs critical value, power.

Questions

Do a set of 15–20 questions that mix:

• Constructing CIs (mostly 95%, with a few 90%/99%).
• Testing hypotheses about a single mean (both one‑ and two‑tailed).
• Using both critical value and p‑value approaches.

For each question, explicitly answer:

1. What are H₀ and H₁?
2. What distribution (z or t) and why?
3. Test statistic value.
4. Decision by p‑value, decision by critical value.
5. If applicable, check: does the CI include the hypothesized value?

Variance Tests + Power Interpretation

Do 5–8 questions on tests of a single variance using chi‑square. Focus on:

1. Correct df, correct tail(s), and reading chi‑square critical values.

Then add 3–5 conceptual questions (or create them for yourself) on:

1. How increasing sample size affects power.
2. How changing α changes Type I vs Type II trade‑off.

End Day 12 Quant session with a mini Quant block (20–25 questions) just on testing/CI:

• Time yourself at ~1.5 min/question.
• Then review and mark each as: “Concept error”, “Formula error”, or “Careless”.
• Anything that is a concept or formula error becomes priority for Day 13.

Daily Ethics block: 30–45 min

Try this pattern each day:

1. 10–15 min reading / notes
• Pick one small chunk: one Standard (e.g., Standard II(A)–Material Nonpublic Information) or a short section of GIPS.
• Make 2–3 bullet notes in your own words: “What is prohibited? What is allowed?”
2. 15–20 min questions
• Do 8–12 vignette‑style or stand‑alone Ethics questions from your Q‑bank or CFAI practice.
• Aim for careful reading, not speed. Ethics is about nuance and wording.

Day 11: CFA Level I Quantitative Methods Study Plan - Hypothesis Testing, Correlation, Regression | CFA Level 1 90 Days Prep

This is a study plan, not official CFA Institute curriculum material. Use it to guide your preparation, then rely on your CFA notes, curriculum, or question bank for the actual readings and practice questions.

Day 11 builds on yesterday's hypothesis testing foundations by connecting test statistics to confidence intervals and working through full hypothesis test examples. Today you'll move from understanding the theory to applying the decision framework across different test types.

Prep Checklist

10-15 minutes :

• Workspace: Open a new notebook page titled "Confidence Intervals & Hypothesis Test Applications"
• Formula sheet: Add formulas for confidence interval construction, critical values for t-tests and z-tests, and the relationship between confidence level and significance level
• Calculator: Clear memory and review how to find t-statistics and z-statistics using your calculator's distribution functions
• Question bank setup: Create or filter a set called "Day 11 CI and Hypothesis Applications"
• Flash Cards: Filled or ready to be filled up
• Log Book: To log concepts, errors as we have been doing

Today's goal is connecting yesterday's concepts to real applications. You should be able to construct a confidence interval, perform a complete hypothesis test, and explain what both tell you about the population parameter.

Daily Ethics reading and prep

Spend 10-15 minutes on Ethics before the Quant block.

Today's Ethics focus: selective reporting and cherry-picking results.

Read or create one short scenario where an analyst reports only statistically significant findings while hiding non-significant tests. Then ask:

• Did the analyst disclose all tests performed?
• Were negative or null findings suppressed?
• Does the presentation create false confidence?
• Are limitations and uncertainty clearly stated?
• Could this selective disclosure mislead stakeholders?

Then complete 5 Ethics warm-up questions focusing on misrepresentation, disclosure obligations, and fair dealing. For any missed Ethics question, classify it as Concept gap or Reading error.

Main study block

Today's Quantitative Methods focus is confidence intervals and hypothesis testing applications.

Study these subtopics:

• Confidence interval construction: Using sample statistics to create a range estimate for the population parameter
• Relationship between CI and hypothesis tests: A two-tailed test at α = 0.05 corresponds to a 95% confidence interval
• t-test versus z-test: When to use t-distribution (small sample, unknown population variance) versus z-distribution (large sample or known variance)
• Test of a single mean: Performing a complete hypothesis test for a population mean
• Test of a single variance: Testing claims about population variance using chi-square distribution
• Interpreting confidence intervals: What it means when a hypothesized value falls inside or outside the interval
• Critical value approach: Comparing test statistic to critical value
• p-value approach: Comparing p-value to significance level
• Power of a test: The probability of correctly rejecting a false null (1 - Type II error probability)

Key insight for today: A confidence interval gives you a range of plausible values, while a hypothesis test gives you a yes/no decision about a specific claim. Both use the same underlying statistics but answer different questions.

25-question practice target

Complete 25 questions today using this breakdown:

• 5 questions: Confidence interval construction and interpretation
• 4 questions: Relationship between confidence intervals and hypothesis tests
• 3 questions: Choosing between t-test and z-test
• 4 questions: Complete hypothesis test of a mean (all steps)
• 3 questions: Critical value approach versus p-value approach
• 2 questions: Test of variance or other parameters
• 4 questions: Mixed review from Days 9-10 (sampling, hypothesis foundations)
• 5 questions: Ethics warm-up on selective reporting and disclosure

For every complete hypothesis test question, write out all five steps in order: (1) state hypotheses, (2) identify test statistic and distribution, (3) state decision rule, (4) calculate test statistic, (5) make decision and interpret in context.

Mistake-log prompt

Log every missed or guessed question using exactly one of these labels:

• Concept gap: I did not understand when to use t versus z, or how CI relates to hypothesis tests
• Formula gap: I understood the concept but used the wrong formula or forgot degrees of freedom
• Calculator error: I made an arithmetic error, used wrong distribution function, or misread a table
• Reading error: I misunderstood the question stem, mixed up one-tailed and two-tailed, or misinterpreted the confidence level

For Ethics mistakes, use mainly Concept gap or Reading error.

Five-question review checkpoint

Answer these without notes at the end of the session:

1. How do you construct a 95% confidence interval for a population mean when population variance is unknown?
2. What is the relationship between a 95% confidence interval and a two-tailed test at α = 0.05?
3. When should you use a t-test instead of a z-test?
4. What are the five steps of a complete hypothesis test?
5. If a 90% confidence interval for the mean is [12.5, 18.3], would you reject H₀: μ = 20 at α = 0.10 using a two-tailed test? Why?

This completes your Day 11 study plan. Tomorrow you'll likely move into comparing two populations or advance to other hypothesis test applications, building on the confidence interval and testing framework you've solidified today.

Can you comment on how many LOS you have covered so far and if this study plan has been helpful?

CFA Level 1 Hypotheses Testing - Additional Study Resources | Sample Questions

 Here are some study resources for CFA Level 1 Hypotheses testing. The CFA official material is the best way to prepare for any paper. These resources help in refining and revising concepts.

Hypothesis Testing | CFA Level 1 - AnalystPrep

https://youtu.be/qwiEHnEXmz8?si=K_Bh6oD1PLDbUvYJ

https://youtu.be/iz1sfne1cNA?si=rnYJPVJEu7Z1atMX

CFA Level 1 Quantitative Methods Cheat Sheet 2026

Hypothesis Testing - Quantitative Methods | CFA® Level 1 Guide | PrepBuddy

Check out these resources for more understanding on CFA Level 1 Hypotheses testing

Day 10: CFA Level I Hypothesis Testing Foundations Study Plan

Today’s CFA Level I study focuses on hypothesis testing.  Today’s goal is to understand how analysts use sample evidence to make careful decisions without overstating certainty. Understand the basic structure of a hypothesis test: null hypothesis, alternative hypothesis, test statistic, significance level, p-value, and decision rule. The focus should be on interpretation first, then calculation.

This is a study plan and blog draft, not official CFA Institute curriculum material. Use it to guide your preparation, then rely on your CFA notes, curriculum, or question bank for the actual readings and practice questions.

Checklist pre - study

Spend 10-15 minutes setting up before you begin.

• Workspace: Prep a clean workspace with notebook ready
• Formula sheet: Mark formulas for test statistic, standard error, confidence interval, and p-value interpretation.
• Flash cards: Keep flash cards ready to fill or filled
• Calculator: Clear previous statistics entries and keep your normal distribution or z-table reference ready if you use one.
• Question bank setup: Create or filter a set called “Day 10 Hypothesis Testing.”
• Time block: Plan 90 minutes total: 15 minutes prep, 60 minutes study and practice, 15 minutes review.

Today’s goal is not to memorize every test immediately. The first goal is to understand the logic: claim, evidence, decision, and interpretation.

Daily Ethics reading and prep

Spend 10-15 minutes on Ethics before the Quant block.

Today’s Ethics focus: misleading conclusions from weak evidence.

Read or create one short scenario where an analyst makes a strong recommendation based on limited data. Then ask:

• Is the sample large enough to support the conclusion?
• Has the analyst explained uncertainty?
• Are assumptions disclosed?
• Is the language too certain?
• Could a client be misled by the conclusion?

Then complete 5 Ethics warm-up questions or scenario checks. For any missed Ethics question, classify it mainly as Concept gap or Reading error.

Main study block

Today’s Quantitative Methods focus is hypothesis testing foundations.

Study these subtopics:

• Null hypothesis: The default claim or status quo being tested.
• Alternative hypothesis: The claim you are looking for evidence to support.
• One-tailed test: Used when the alternative points in one direction.
• Two-tailed test: Used when the alternative allows movement in either direction.
• Test statistic: A standardized measure of how far the sample result is from the hypothesized value.
• Significance level: The threshold for rejecting the null hypothesis.
• p-value: The probability of observing evidence as extreme as the sample result, assuming the null is true.
• Type I error: Rejecting a true null hypothesis.
• Type II error: Failing to reject a false null hypothesis.
• Decision rule: The process for deciding whether to reject or fail to reject the null.

A useful rule for today: do not say “accept the null.” Say fail to reject the null. This wording matters because a test may not prove the null is true; it may only show that the evidence is not strong enough to reject it.

25-question practice target

Complete 25 questions today.

Use this breakdown:

• 4 questions: Identify null and alternative hypotheses
• 4 questions: One-tailed versus two-tailed tests
• 4 questions: Test statistic interpretation
• 3 questions: Significance level and rejection rules
• 3 questions: p-value interpretation
• 2 questions: Type I and Type II errors
• 5 questions: Ethics warm-up on evidence, disclosure, and misleading conclusions

For every Quant question, write the decision in plain English after solving. For example: “There is enough evidence to reject the null,” or “There is not enough evidence to reject the null.”

Mistake-log prompt

Log every missed or guessed question using exactly one of these labels:

• Concept gap: I did not understand the testing idea or decision logic.
• Formula gap: I understood the logic but forgot the formula or used the wrong setup.
• Calculator error: I made an arithmetic, table, or input error.
• Reading error: I misunderstood the wording, tail direction, significance level, or conclusion.

For Ethics mistakes, use mainly Concept gap or Reading error.

Five-question review checkpoint

Answer these without notes at the end of the session:

1. What is the difference between the null hypothesis and the alternative hypothesis?
2. When should a test be one-tailed instead of two-tailed?
3. What does a p-value tell you in plain language?
4. What is the difference between Type I and Type II error?
5. Why should you say “fail to reject the null” instead of “accept the null”?

The main lesson from Day 10 is that hypothesis testing is not just math. It is a discipline for making claims carefully. A good analyst does not just calculate a result; they explain what the evidence does and does not support.

Tomorrow preview

Day 11 will continue hypothesis testing with confidence intervals, test statistics, rejection regions, and more practice in translating numerical results into clear conclusions.

 

Central Limit Theorem - Probability Distribution - Concept

 CLT means Central Limit Theorem.  

It says that if you take many random samples from a population and calculate the mean of each sample, the distribution of those sample means will become approximately normal as the sample size gets larger, even if the original population is not normal.  

In simple CFA terms:  

Population distribution: The original data may be skewed or messy.  

Sample mean: The average from one sample. 

 Sampling distribution of the mean: The pattern you get if you take many samples and calculate many sample means.  

CLT idea: As sample size increases, those sample means tend to form a normal-shaped distribution.  

Why it matters: It allows analysts to use normal-distribution tools for inference, confidence intervals, and hypothesis testing. 

CLT does not mean the original data becomes normal. It means the distribution of sample means becomes approximately normal.

Day 9: CFA Level I - Probability Distributions & Sampling Study Plan | 90 Days to CFA Level 1

Today is about probability distributions and sampling—two ideas that show up everywhere in Quant (and later in Fixed Income and Portfolio concepts). 

Disclaimer - This is a study plan and practice guide, not official CFA Institute curriculum material.

Checklist before Studying

• Workspace: one clean page for formulas + one for “common traps.”
• Calculator check: clear TVM registers; confirm STAT functions are working; set decimals to a comfortable default (often 4–6).
• Materials: formula sheet/flashcards, one short notes source, question bank.
• Question bank setup: create a mini-quiz tag set: Normal, Lognormal, t, Chi-square, F, CLT, Sampling distributions.

Daily Ethics reading + prep (15–20 minutes)

• Micro-reading: Professionalism—what it means to act with integrity even when no one is watching.
• Do this: Write a 3–4 line reflection: A friend asks for “inside” exam questions or leaked mocks. How do you respond?
• 5 Ethics warm-up checks:
1. Is it acceptable to use “shared memory dumps” from past candidates?
2. What is the clean alternative when you feel underprepared?
3. What would you do if a study group circulates suspicious material?
4. What is the most professional way to say no?
5. Who could be harmed by unethical shortcuts?

Main study block (75–120 minutes): Distributions & sampling

1) Common distributions (recognition + use cases)

• Normal distribution: symmetry, mean = median = mode, role in z-scores.
• Lognormal distribution: log of variable is normal; why prices/wealth-like variables can be skewed.
• Student’s t-distribution: fatter tails; small samples, unknown variance.
• Chi-square distribution: relates to variance.
• F-distribution: ratio of variances.

2) CLT (Central Limit Theorem) intuition

• The sampling distribution of the sample mean tends toward normal as sample size grows.
• CLT does not make your data normal.
• Why standard errors shrink as sample size rises.

3) Sampling and sampling distributions

• Population vs sample.
• Sampling distribution: distribution of a statistic across many samples.
• Standard error: what it represents and why it matters.
• Pitfalls: SD vs SE; treating one sample as “the truth.”

25-question practice target (20 Quant + 5 Ethics)

Quant (20)

1. Normal distribution & z-scores (6)
2. Lognormal vs normal recognition/interpretation (4)
3. t-, chi-square, F identification/use (4)
4. CLT and sampling distribution concepts (4)
5. Standard error vs standard deviation traps (2)

Ethics (5)

• Professionalism + integrity scenarios (5)

Mistake-log prompt

• Concept gap
• Formula gap
• Calculator error
• Reading error

Five-question review checkpoint

1. In one sentence, what does the CLT tell you about the sample mean?
2. What is the difference between standard deviation and standard error?
3. Give one real-world variable often modelled as lognormal.
4. When might a t-distribution be more appropriate than a normal distribution?
5. What does “sampling distribution of the mean” mean?

• One takeaway + ethics reflection reminder.

Tomorrow preview (Day 10)

Hypothesis testing foundations: null vs alternative, test-statistic intuition, and interpreting results without overthinking the math.

Day 8: CFA Level I Probability Basics Study Plan (Quantitative Methods)

Today is a study plan (not official CFA Institute curriculum material) to help you learn probability basics in a practical, test-ready way.

Checklist

• Workspace: Clear your desk; keep only your notes, formula sheet/flashcards, and calculator.
• Materials: 1 notebook page titled “Probability – Rules + Common Traps.”
• Calculator: Set your standard defaults (keep this consistent every day). Practice entering fractions/decimals cleanly.
• Question bank setup: Create a mini-quiz set called “Day 7 Probability” with tags:
• Probability rules
• Conditional probability
• Independence
• Bayes (basic)

Daily Ethics block (15–20 minutes)

Ethics warm-up: Conflicts of interest in everyday life

Restate: Put client/employer interests first; disclose conflicts early and clearly.
Write a 4-line scenario: “A friend asks for ‘sure-shot’ stock tips.” What do you say to avoid misleading them?
Do 5 quick Ethics questions (or 5 short scenario checks). Keep answers in one sentence each.

Main study block (70–90 minutes): Probability fundamentals

Focus on understanding the rules and spotting the keywords that show up in CFA-style questions.

A) Probability language (foundation)

• Random variable vs outcome vs event
• Complement rule: 
• Mutually exclusive events (cannot both happen)

B) Addition and multiplication rules

• Addition rule (general): 
• Mutually exclusive special case: 
• Multiplication rule: 

C) Conditional probability and independence

• 
• Independence test:  (or )
• Common trap: “Independent” is not the same as “mutually exclusive.”

D) Total probability + Bayes (basic intuition)

• Think in “paths” (e.g., different groups that could produce an outcome)
• Bayes’ idea: update your belief when you receive new information
• “Given that…” usually signals conditional probability.

25-question practice target (45–60 minutes)

Timed: aim for ~90 seconds per question.

12 questions: addition/multiplication rules (union/intersection)
6 questions: conditional probability 
2 questions: independence vs mutually exclusive (identify which is which)
5 questions: Ethics warm-up set (or 5 mini scenarios)

After each set of 5 questions: pause for 60 seconds and write the one rule you forgot or misread.

5) Mistake-log prompt (write 1–2 lines per miss)

Use exactly one label per mistake:

• Concept gap
• Formula gap
• Calculator error
• Reading error

(If Ethics errors happen, classify them mainly as Concept gap or Reading error.)

6) Five-question review checkpoint (10 minutes)

Answer without notes:

1. If , what is ?
2. If events are mutually exclusive, what is ?
3. Write the general addition rule for .
4. Write the multiplication rule for .
5. In one sentence: what does “independent” mean in probability?

Tomorrow preview (Day 9) Tomorrow, we move into probability distributions (what mean/variance are telling you, and how to recognize common distribution setups fast).

Day 7: CFA Level I Quant Study Plan: Probability Foundations - 90 days Plan

 Day 7 continues the Quantitative Methods block. After working on descriptive statistics, today’s focus is probability: how to think about uncertainty, possible outcomes, and expected results.

This is a study-plan blog post, not official CFA curriculum material. Use it to organize your preparation, then rely on your CFA materials, notes, or question bank for the actual readings and practice questions.

Checklist

Spend 10-15 minutes preparing your study setup as usual.

• Workspace: Open one clean page titled “Probability Foundations.”
• Materials: Keep your formula sheet, calculator, question bank, and notebook ready.
• Formula focus: Mark formulas for probability rules, conditional probability, expected value, variance, and standard deviation.
• Flash Cards: Keep them at hand or ready to be filled up
• Visual setup: Keep space for probability trees, two-way tables, and simple outcome grids.
• Question bank filter: Select Quant questions tagged probability, expected value, conditional probability, and joint probability.
• Time block: Plan 45 minutes for study, 35 minutes for practice, and 15 minutes for review, at least. 2.5-3 hrs is a better block

Today’s goal is to understand how probabilities combine, not just memorize formulas.

Daily Ethics reading and prep

Spend 10 minutes on Ethics before the Quant block.

Today’s Ethics focus: reasonable basis and probability-based claims.

Read one short scenario where an analyst makes a forecast or probability-based recommendation. Ask yourself:

• Is the forecast supported by reasonable analysis?
• Are assumptions clearly explained?
• Is the analyst overstating certainty?
• Are risks disclosed?
• Could the client misunderstand the probability statement?

Then complete 5 quick Ethics questions or flashcards. If you miss one, classify it mainly as a Concept gap or Reading error.

Main study block

Today’s Quantitative Methods focus is probability foundations.

Study these subtopics:

• Basic probability: The chance that an event occurs.
• Mutually exclusive events: Events that cannot happen at the same time.
• Independent events: Events where one outcome does not affect the other.
• Conditional probability: The probability of one event given that another event has occurred.
• Joint probability: The probability that two events occur together.
• Addition rule: Used when combining probabilities of events.
• Multiplication rule: Used when finding joint probabilities.
• Expected value: The probability-weighted average outcome.
• Variance and standard deviation of outcomes: Measures of uncertainty around expected value.

A useful habit today: write the event labels clearly. Many probability mistakes happen because A, B, , , and  get mixed up.

25-question practice target

Complete 25 questions today.

Use this breakdown to begin with:

4 questions: Basic probability and event definitions
4 questions: Mutually exclusive versus independent events
4 questions: Conditional probability
3 questions: Joint probability and multiplication rule
3 questions: Addition rule and combined probabilities
2 questions: Expected value and probability-weighted outcomes
5 questions: Ethics warm-up on forecasts, reasonable basis, and disclosure

For each Quant question, write down what is given and what is being asked before solving. Probability is easier when the setup is clean.

Mistake-log prompt

After practice, log every missed or guessed question using these four labels:

• Concept gap: I did not understand the probability rule or event relationship.
• Formula gap: I understood the concept but used the wrong formula or setup.
• Calculator error: I made an arithmetic error or entered probability values incorrectly.
• Reading error: I misunderstood the wording, especially “given,” “and,” “or,” “at least,” or “mutually exclusive.”

For Ethics mistakes, use mainly Concept gap or Reading error.

Five-question review checkpoint

End the session by answering these five questions:

1. Can I explain the difference between mutually exclusive and independent events?
2. What does conditional probability mean in plain language?
3. Did I confuse “and” with “or” in any practice question?
4. What was my accuracy on the 20 Quant questions and 5 Ethics questions?
5. Which probability rule should I review tomorrow before moving forward?

     Day 8 will continue Quantitative Methods with probability distributions, normal distribution intuition, expected value, variance, and interpretation.