Practice Test GeeksESAT - Engineering & Science Admissions Test Practice Test
← All ESAT Flashcard Decks

ESAT Mathematics Flashcards

6 cards from real ESAT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 ESAT Mathematics flashcards as text

  1. What is the area enclosed by y = x² and y = x between x = 0 and x = 1?

    Answer: 1/6

    ∫₀¹ (x - x²) dx = [x²/2 - x³/3]₀¹ = 1/2 - 1/3 = 1/6.

  2. What is the value of sin(π/6)?

    Answer: 1/2

    sin(30°) = sin(π/6) = 1/2 is a standard trigonometric value.

  3. If a vector a = (3, 4), what is |a|?

    Answer: 5

    |a| = √(3² + 4²) = √(9 + 16) = √25 = 5.

  4. What is the general solution to dy/dx = 2y?

    Answer: y = Ce^(2x)

    Separating variables: dy/y = 2dx → ln|y| = 2x + const → y = Ce^(2x).

  5. How many complex roots does x⁴ + 1 = 0 have?

    Answer: 4

    A degree-4 polynomial always has exactly 4 roots (counting multiplicity) in the complex numbers.

  6. What is the dot product of vectors (1, 2, 3) and (4, -1, 2)?

    Answer: 8

    (1)(4) + (2)(-1) + (3)(2) = 4 - 2 + 6 = 8.