FAST-NU Advanced Mathematics — Differentiation
Differentiation is part of the Advanced Mathematics section of FAST's BS CS/Engineering admission test (usually 50 of the 120 MCQs, 50% of the marks). It breaks into 6 subtopics, and we hold 111 FAST-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (6)
How Differentiation is tested
Across the 7 FAST-pattern papers on ParhaiKrlo, Differentiation accounts for 37 questions. It appears in all 7, about 5.3 questions a paper. The heaviest was FAST Past Paper 07, with 6 questions.
| Paper | Questions |
|---|---|
| FAST Past Paper 07 | 6 |
| FAST Past Paper 06 | 5 |
| FAST Past Paper 05 | 5 |
| FAST Past Paper 04 | 5 |
| FAST Past Paper 03 | 6 |
| FAST Past Paper 02 | 5 |
| FAST Past Paper 01 | 5 |
Differentiation MCQs from the FAST-pattern papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · FAST Past Paper 07 · Differentiation
If x = t² and y = t³, then the value of d²y/dx² at t = 1 is:
- A.3/4
- B.3/2
- C.3
- D.6
Show answer
Answer: A. 3/4 — dy/dx = 3t²/(2t) = 3t/2. Then d²y/dx² = d/dt(3t/2) ÷ dx/dt = (3/2)/(2t) = 3/(4t) = 3/4 at t = 1.
- Q2 · FAST Past Paper 06 · Differentiation
The derivative of a constant function f(x) = c is:
- A.1
- B.0
- C.c
- D.undefined
Show answer
Answer: B. 0 — A constant does not change, so its rate of change is 0.
- Q3 · FAST Past Paper 05 · Differentiation
If f(x) = x² ln x, then f′(e) is:
- A.3e
- B.2e
- C.e
- D.e²
Show answer
Answer: A. 3e — Product rule: f′(x) = 2x ln x + x² · (1/x) = 2x ln x + x. At x = e: 2e + e = 3e.