ESAT ESAT Mathematics

Question 1

In the ESAT Mathematics section, if f(x) = 3x² - 2x + 1, what is f'(x)?

Accepted Answer

6x - 2

Answer

Differentiating 3x² - 2x + 1 term by term gives 6x - 2.

Question 2

Which of the following is tested in the ESAT Mathematics component?

Accepted Answer

Calculus and algebra

Answer

The ESAT Mathematics component assesses calculus, algebra, geometry, and other core mathematical skills.

Question 3

Solve for x: log₂(x) + log₂(4) = 5

Accepted Answer

8

Answer

log₂(4x) = 5 means 4x = 32, so x = 8.

Question 4

In an ESAT-style problem, how many radians is 270°?

Accepted Answer

3π/2

Answer

270° × (π/180) = 3π/2 radians.

Question 5

What is the sum of the infinite geometric series 1 + 1/3 + 1/9 + ...?

Accepted Answer

3/2

Answer

For |r| < 1, the sum is a/(1-r) = 1/(1 - 1/3) = 3/2.

ESAT - Engineering & Science Admissions Test Practice Test