FAD1015 Exam Leaks 2025-2026

Comprehensive exam focus tips compiled from multiple student sources for the 2025-2026 academic year final examination.

Exam Information

  • Course: FAD1015 — Mathematics III
  • Academic Year: 2025-2026
  • Format: Two parts (Part A and Part B)
  • Confirmed by: YX tutorial teacher (matrix teacher), Adian Sani

Part A — Confirmed Question Breakdown

Q1: Binomial Distribution

From Adian Sani:

Sub-question Topic
(a) Definition of binomial distribution
(b) Determine if binomial or not
(c) Determine parameter and statistic
(d) Characteristics of binomial distribution
(e) Determine type of distribution
(f) Identify parameter or statistics

Key Concepts:

  • Binomial distribution formula and conditions
  • Parameters: n (trials), p (probability)
  • Statistics vs parameters distinction

Q2: Poisson Approximation & Uniform/Exponential

From Adian Sani:

Sub-question Topic
(a) Poisson approximation
(b) Law for binomial to switch to Poisson
(c) Uniform/Exponential distribution
(d) Matrices — refer to TUTO 13 Q1

Key Concepts:

  • When to approximate binomial with Poisson (n large, p small)
  • np = λ (Poisson parameter)
  • Uniform distribution properties
  • Exponential distribution properties
  • Matrix operations

Part B — Confirmed Question Breakdown

Q3: Cumulative Distribution & Poisson Calculations

From Adian Sani:

Sub-question Topic
(a) Cumulative distribution function (CDF)
(b) Poisson distribution calculations

Key Concepts:

  • CDF: F(x) = P(X ≤ x)
  • Poisson probability mass function
  • Cumulative Poisson probabilities

Q4: Continuous/Discrete & Probability

From Adian Sani:

Sub-question Topic
(a) Continuous or discrete — determine type
(b) Smallest or biggest value of n
(c) Calculate P(a < X < b)
(d) Mean and standard deviation

Key Concepts:

  • Identifying distribution type
  • Finding range boundaries
  • Interval probability calculations
  • Expected value and variance formulas

Q5: Hypothesis Testing

From Adian Sani:

Sub-question Topic
(a) Critical value — find it
(b) Find p-value
(c) Compare with α (alpha/significance level)
(d) Make a conclusion
(e) Confidence interval then conclusion

Key Concepts:

  • One-tailed vs two-tailed tests
  • Z-test vs T-test selection
  • p-value interpretation
  • Decision rule: reject H₀ if p < α
  • Confidence interval construction

[!warning] Hypothesis Testing in R NOT Tested Chen Jing confirmed: Hypothesis testing IN R is NOT coming out. All hypothesis testing questions are by-hand only — use Z-table, t-table, formulas, and manual calculations. No t.test() R code.

Manual hypothesis testing (critical values, p-values, conclusions, CIs) is still in Q5.

Q6: Matrices in R ⭐ HIGHEST PRIORITY

From Adian Sani:

Sub-question Topic
(a) Matrix inverse and transpose
(b) System using Cramer's rule
(c) Given R coding, find output
(d) Detect errors: transpose, multiplication, inverse
(e) Plot scatterplot and find descriptive summary

Key Concepts:

  • Matrix inversion methods
  • Transpose operation
  • Cramer's rule for solving systems
  • R syntax and output prediction
  • Error identification in matrix operations
  • R plotting functions
  • Descriptive statistics in R

[!warning] Most Questions in R Most matrix questions will be in R programming format. Know R syntax cold.

General Tips from Multiple Sources

Normal Distribution Questions

From Anthonny's Maths Tips:

  • Questions will give a lot of numbers
  • Case study given will be in long sentences
  • They will give irrelevant information that is not needed
  • Don't be tricked — identify what's actually needed for Normal distribution

Statistical Analysis

  • Students usually struggle with statistical analysis part
  • Check back tutorial questions for practice

Matrices

  • Matrix questions are easy conceptually
  • Most will be in R programming format
  • Focus areas:
    • CRV (Tutorial 5/6)
    • Matrices in R — paling banyak (most questions)
    • cbind/rbind
    • Create matrix, row matrix

R Programming Focus

From Anthonny:

  1. CRV — Tutorial 5/6
  2. Matrices in R — highest volume
  3. cbind/rbind
  4. Create matrix, row matrix

Key Topics Summary by Priority

Priority Topic Question Source
⭐⭐⭐ Matrices in R Q6 Adian Sani
⭐⭐⭐ Hypothesis Testing Q5 Adian Sani
⭐⭐⭐ CDF & Poisson Q3 Adian Sani
⭐⭐ Continuous/Discrete & Probability Q4 Adian Sani
⭐⭐ Binomial Definition Q1 Adian Sani
⭐⭐ Poisson Approximation Q2 Adian Sani
⭐ Normal Distribution General Anthonny

Tutorial References

Tutorial Question Topic Priority
Tuto 13 Q1 Matrices ⭐⭐⭐
Tuto 5/6 All CRV ⭐⭐

R Programming Commands to Know

Matrix Creation

matrix(data, nrow, ncol)
cbind(vector1, vector2)  # column bind
rbind(vector1, vector2)  # row bind

Matrix Operations

t(A)           # transpose
solve(A)       # inverse
det(A)         # determinant
A %*% B        # matrix multiplication

Descriptive Statistics

mean(x)
sd(x)
var(x)
summary(x)

Plotting

plot(x, y)           # scatterplot
hist(x)              # histogram
boxplot(x)           # box plot

Pre-Exam Checklist

Part A Preparation

  • [ ] Binomial distribution definition memorized
  • [ ] Can identify if scenario is binomial or not
  • [ ] Know parameters (n, p) vs statistics distinction
  • [ ] Poisson approximation conditions (n large, p small)
  • [ ] Law: λ = np
  • [ ] Uniform distribution properties
  • [ ] Exponential distribution properties
  • [ ] Tutorial 13 Q1 — matrix problem solved

Part B Preparation

  • [ ] CDF calculations — F(x) = P(X ≤ x)
  • [ ] Poisson calculations — PMF and cumulative
  • [ ] Identify continuous vs discrete distributions
  • [ ] Find smallest/biggest n values
  • [ ] Calculate P(a < X < b) for various distributions
  • [ ] Mean and SD formulas for all distributions

Hypothesis Testing

  • [ ] Find critical values (z-table, t-table)
  • [ ] Calculate p-values
  • [ ] Compare p-value with α
  • [ ] Write proper conclusions
  • [ ] Construct confidence intervals
  • [ ] Know when to use z-test vs t-test

Matrices in R (Critical)

  • [ ] Matrix transpose in R
  • [ ] Matrix inverse in R
  • [ ] Cramer's rule by hand and in R
  • [ ] Predict R code output
  • [ ] Detect errors in R code
  • [ ] Scatterplot commands
  • [ ] Descriptive summary commands
  • [ ] cbind and rbind usage

Normal Distribution

  • [ ] Filter irrelevant information in long questions
  • [ ] Identify which numbers are actually needed
  • [ ] Long sentence case study practice

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