ESAT ESAT Mathematics 1 — Questions and Answers
Question 1: In the ESAT Mathematics section, if f(x) = 3x² - 2x + 1, what is f'(x)?
- 6x - 2 (Correct answer)
- 3x - 2
- 6x + 1
- 3x² - 2
Correct answer: 6x - 2
Differentiating 3x² - 2x + 1 term by term gives 6x - 2.
Question 2: Which of the following is tested in the ESAT Mathematics component?
- Calculus and algebra (Correct answer)
- Essay writing
- Data interpretation only
- Programming logic
Correct answer: Calculus and algebra
The ESAT Mathematics component assesses calculus, algebra, geometry, and other core mathematical skills.
Question 3: Solve for x: log₂(x) + log₂(4) = 5
- 8 (Correct answer)
- 16
- 32
- 4
Correct answer: 8
log₂(4x) = 5 means 4x = 32, so x = 8.
Question 4: In an ESAT-style problem, how many radians is 270°?
- 3π/2 (Correct answer)
- π/2
- 2π/3
- π
Correct answer: 3π/2
270° × (π/180) = 3π/2 radians.
Question 5: What is the sum of the infinite geometric series 1 + 1/3 + 1/9 + ...?
- 3/2 (Correct answer)
- 2/3
- 1/2
- 3
Correct answer: 3/2
For |r| < 1, the sum is a/(1-r) = 1/(1 - 1/3) = 3/2.
Question 6: Which integration technique would best solve ∫ x·eˣ dx in an ESAT question?
- Integration by parts (Correct answer)
- Substitution
- Partial fractions
- Trigonometric substitution
Correct answer: Integration by parts
Integration by parts (∫u dv = uv - ∫v du) is used for products of a polynomial and exponential.
ESAT ESAT Mathematics 1
In the ESAT Mathematics section, if f(x) = 3x² - 2x + 1, what is f'(x)?