FAD1014 Exam Scope 2025-2026 — Lecturer Slides

Exam scope breakdown by topic area with Part A (compulsory) and Part B (choose 4 of 6) distribution.

[!note] Source Images Original lecturer slides archived in wiki/assets/:

  • Slide 1: Integration (advanced topics) — fad1014-scope-slide-01.jpg
  • Slide 2: Integration (applications) — fad1014-scope-slide-02.jpg
  • Slide 3: Integration (basic methods) — fad1014-scope-slide-03.jpg
  • Slide 4: Sequence & Series (1) — fad1014-scope-slide-04.jpg
  • Slide 5: Sequence & Series (2) — fad1014-scope-slide-05.jpg
  • Slide 6: Differential Equations — fad1014-scope-slide-06.jpg
  • Slide 7: Geometry (conics) — fad1014-scope-slide-07.jpg
  • Slide 8: Geometry (parametric) — fad1014-scope-slide-08.jpg

1. INTEGRATION

Basic Integration Methods

Topic Part A Part B Notes
Integration as antiderivative ✓ ✗ Basic concept only
Indefinite integral and standard integration ✓ ✓ Both sections
Integration by substitution ✓ ✗ u-substitution
Integration by Parts ✗ ✓ Part B only

Advanced Integration Topics

Topic Part A Part B Notes
Integration of powers of trigonometric functions ✗ ✗ NOT TESTED
Integration by trigonometric substitution ✗ ✓ Part B only
Integration by partial fraction ✗ ✗ NOT TESTED
Definite Integrals ✓ ✗ Part A only

Applications of Integration

Topic Part A Part B Notes
Area under the Curve ✓ ✗ Part A only
Area between Curves ✗ ✗ NOT TESTED
Volume Revolved around x or y-axis ✗ ✗ NOT TESTED
Volume Revolved around any axis rotation ✗ ✗ NOT TESTED

[!warning] Major Scope Reduction Volume of revolution and area between curves are excluded from the exam. Only basic area under curve (Part A) is tested.

2. SEQUENCE & SERIES

Topic Part A Part B Notes
Introduction to series: Diverge and converge ✓ ✓ Both sections
Summation of Finite Series: Method of Differences ✓ ✓ Both sections
Binomial expansion I: $(a+b)^n$ ; $n \in \mathbb{Z}^+$ ✓ ✗ Positive integer n
Binomial expansion II: $(1+x)^n$ ; $n$ non-positive integer ✗ ✗ NOT TESTED
Taylor series ✗ ✗ NOT TESTED
Maclaurin series ✗ ✓ Part B only

[!tip] Binomial Focus Only Binomial I (positive integer powers) is tested. Negative/fractional powers and Taylor series are excluded.

3. DIFFERENTIAL EQUATIONS

Topic Part A Part B Notes
Introduction to first order differential equation ✓ ✗ Basic concepts
Differential Equation I: Separable ✓ ✓ Both sections
Differential Equation II: Homogeneous ✗ ✓ Part B only
Differential Equation III: Linear ✗ ✗ NOT TESTED

[!warning] Linear DEs Excluded Linear differential equations (integrating factor method) are not tested.

4. GEOMETRY: CONICAL SECTIONS

Topic Part A Part B Notes
Geometry I: Circle ✗ ✗ NOT TESTED
Geometry II: Parabola ✓ ✓ Both sections
Geometry III: Ellipse ✓ ✓ Both sections
Geometry IV: Hyperbola ✓ ✓ Both sections
Parametric Equation ✗ ✓ Part B only

[!tip] Circle Excluded Circle geometry is not tested. Focus on Parabola, Ellipse, and Hyperbola.

Summary: High-Yield Topics

Part A Focus (Compulsory — must answer all)

  1. Indefinite/Standard Integration — appears in both parts
  2. Integration by substitution — Part A only
  3. Definite Integrals — Part A only
  4. Area under Curve — Part A only
  5. Sequences & Series — convergence, method of differences, Binomial I
  6. Separable DEs — appears in both parts
  7. Parabola, Ellipse, Hyperbola — all three conics

Part B Focus (Choose 4 of 6)

  1. Integration by Parts — high priority
  2. Trigonometric substitution — Part B only
  3. Maclaurin series — Part B only
  4. Homogeneous DEs — Part B only
  5. Separable DEs — backup option
  6. Parametric Equations — Part B only

Topics to Skip (Not Tested)

  • Integration: powers of trig, partial fractions
  • Applications: area between curves, all volume of revolution
  • Series: Binomial II (negative powers), Taylor series
  • DEs: Linear DEs
  • Geometry: Circle

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