ESAT ESAT Further Mathematics

Question 1

What is the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ...?

Accepted Answer

3/2

Answer

2

Answer

4/3

Answer

3

Question 2

Which is the correct binomial expansion of (1+x)^(-2) for |x| < 1, up to the x² term?

Accepted Answer

1 - 2x + 3x²

Answer

1 + 2x + 3x²

Answer

1 - 2x - 3x²

Answer

1 - x + x²

Question 3

Find the value of d²y/dx² at x = 0 for y = sin(3x).

Accepted Answer

0

Answer

-9

Answer

9

Answer

3

Question 4

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

Accepted Answer

5

Answer

8

Answer

11

Answer

2

Question 5

If z = 3 + 4i, what is |z|, the modulus of z?

Accepted Answer

5

Answer

7

Answer

25

Answer

√7

Question 6

Evaluate the definite integral ∫₀^π sin(x) dx.

Accepted Answer

2

Answer

0

Answer

1

Answer

π

Question 7

What are the eigenvalues of the upper triangular matrix with rows [3, 1] and [0, 2]?

Accepted Answer

3 and 2

Answer

1 and 0

Answer

5 and 1

Answer

2 only (repeated)