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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 determinant of the matrix [[2, 3], [1, 4]]?

    Answer: 5

    det = (2×4) - (3×1) = 8 - 3 = 5.

  2. In ESAT Mathematics, what does it mean for a function to be continuous at a point x = a?

    Answer: The limit as x→a equals f(a)

    Continuity at x = a requires that lim(x→a) f(x) = f(a).

  3. Find the equation of the line perpendicular to y = 2x + 5 passing through (4, 1).

    Answer: y = -x/2 + 3

    Perpendicular slope is -1/2; using point-slope form: y - 1 = -1/2(x - 4) → y = -x/2 + 3.

  4. What is the binomial expansion of (1 + x)⁴?

    Answer: 1 + 4x + 6x² + 4x³ + x⁴

    Using Pascal's triangle or binomial coefficients: (1+x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴.

  5. Which of the following best represents the ESAT Mathematics difficulty level?

    Answer: A-level Further Mathematics standard

    The ESAT Mathematics questions are pitched at A-level Further Mathematics standard.

  6. Solve: |2x - 3| < 7

    Answer: -2 < x < 5

    -7 < 2x - 3 < 7 → -4 < 2x < 10 → -2 < x < 5.