ESAT ESAT Mathematics 2 — Questions and Answers
Question 1: What is the determinant of the matrix [[2, 3], [1, 4]]?
- 5 (Correct answer)
- 8
- 11
- 2
Correct answer: 5
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?
- The limit as x→a equals f(a) (Correct answer)
- The function is differentiable at a
- f(a) = 0
- The function is periodic
Correct answer: The limit as x→a equals f(a)
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).
- y = -x/2 + 3 (Correct answer)
- y = 2x - 7
- y = -x/2 - 3
- y = x/2 + 3
Correct answer: y = -x/2 + 3
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?
- 1 + 4x + 6x² + 4x³ + x⁴ (Correct answer)
- 1 + 4x + 4x² + x⁴
- 1 + x + x² + x³ + x⁴
- 4 + 4x + 6x² + 4x³
Correct answer: 1 + 4x + 6x² + 4x³ + x⁴
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?
- A-level Further Mathematics standard (Correct answer)
- GCSE standard
- Undergraduate university level
- Primary school level
Correct answer: A-level Further Mathematics standard
The ESAT Mathematics questions are pitched at A-level Further Mathematics standard.
Question 6: Solve: |2x - 3| < 7
- -2 < x < 5 (Correct answer)
- x > 5 or x < -2
- -2 ≤ x ≤ 5
- x > 5
Correct answer: -2 < x < 5
-7 < 2x - 3 < 7 → -4 < 2x < 10 → -2 < x < 5.
ESAT ESAT Mathematics 2
What is the determinant of the matrix [[2, 3], [1, 4]]?