ESAT ESAT Further Mathematics 2

Question 1

Which of the following is the general solution to the differential equation dy/dx = 2y?

Accepted Answer

y = Ce^(2x)

Answer

y = Ce^(-2x)

Answer

y = 2x + C

Answer

y = x² + C

Question 2

What is the polar form of the complex number -1 + i?

Accepted Answer

√2 exp(i·3π/4)

Answer

√2 exp(iπ/4)

Answer

2 exp(i·3π/4)

Answer

√2 exp(-iπ/4)

Question 3

How many distinct real roots does x⁴ - 5x² + 4 = 0 have?

Accepted Answer

4

Answer

2

Answer

0

Answer

3

Question 4

For f(x) = x³ - 3x, which statement correctly describes its turning points?

Accepted Answer

Local max at x = -1, local min at x = 1

Answer

Local max at x = 1, local min at x = -1

Answer

No turning points

Answer

Local max at x = 0

Question 5

What is the product of the complex numbers (2 + i) and (1 - 3i)?

Accepted Answer

5 - 5i

Answer

2 - 6i

Answer

5 + 5i

Answer

-1 - 5i

Question 6

What is the volume of the solid formed when y = √x (0 ≤ x ≤ 4) is rotated 360° about the x-axis?

Accepted Answer

8π

Answer

4π

Answer

16π

Answer

32π

Question 7

Which technique is most appropriate for evaluating ∫x·e^x dx?

Accepted Answer

Integration by parts

Answer

Substitution

Answer

Partial fractions

Answer

Trigonometric substitution