ESAT ESAT Mathematics 2

Question 1

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

Accepted Answer

5

Answer

det = (2×4) - (3×1) = 8 - 3 = 5.

Question 2

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

Accepted Answer

The limit as x→a equals f(a)

Answer

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

Question 3

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

Accepted Answer

y = -x/2 + 3

Answer

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

Question 4

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

Accepted Answer

1 + 4x + 6x² + 4x³ + x⁴

Answer

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

Question 5

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

Accepted Answer

A-level Further Mathematics standard

Answer

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

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