ECAT Mathematics — Differentiation
Differentiation is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 7 subtopics, and we hold 60 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (7)
How Differentiation is tested
Across the 7 ECAT past papers on ParhaiKrlo, Differentiation accounts for 25 questions. It appears in all 7, about 3.6 questions a paper. The heaviest was ECAT Past Paper 07, with 6 questions.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 6 |
| ECAT Past Paper 06 | 3 |
| ECAT Past Paper 05 | 4 |
| ECAT Past Paper 04 | 3 |
| ECAT Past Paper 03 | 3 |
| ECAT Past Paper 02 | 3 |
| ECAT Past Paper 01 | 3 |
Differentiation MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Differentiation
Using f(x₀ + δx) ≈ f(x₀) + f′(x₀)δx, the approximate value of sin(9π/10) is:
- A.π/10
- B.0
- C.−π/10
- D.9π/10
Show answer
Answer: A. π/10 — Take x₀ = π, δx = −π/10: sin π + cos π × (−π/10) = 0 + π/10.
- Q2 · ECAT Past Paper 06 · Differentiation
Differentiating (x − 1)(x + 2)² with respect to x gives:
- A.2x(x + 2)
- B.2(x − 1)(x + 2)
- C.2(x − 1)
- D.3x(x + 2)
Show answer
Answer: D. 3x(x + 2) — (x + 2)² + 2(x − 1)(x + 2) = (x + 2)(3x) = 3x(x + 2).
- Q3 · ECAT Past Paper 05 · Differentiation
Differentiating (x − 1)(x + 2)² with respect to x gives:
- A.2x(x + 2)
- B.2(x − 1)(x + 2)
- C.2(x − 1)
- D.3x(x + 2)
Show answer
Answer: D. 3x(x + 2) — (x + 2)² + 2(x − 1)(x + 2) = (x + 2)(x + 2 + 2x − 2) = 3x(x + 2).