A-Level Mathematics Core

Question 1

What is the derivative of sin(3x) with respect to x?

Accepted Answer

3cos(3x)

Answer

cos(3x)

Answer

-3cos(3x)

Answer

3sin(3x)

Question 2

The equation x² + 6x + k = 0 has no real roots. Which inequality must k satisfy?

Accepted Answer

k > 9

Answer

k < 9

Answer

k > 6

Answer

k < -9

Question 3

What is the integral of (2x + 1)⁴ with respect to x?

Accepted Answer

(2x + 1)⁵ / 10 + C

Answer

(2x + 1)⁵ / 5 + C

Answer

4(2x + 1)³ + C

Answer

(2x + 1)⁵ / 2 + C

Question 4

A geometric series has first term 8 and common ratio 0.5. What is the sum to infinity?

Accepted Answer

16

Answer

8

Answer

12

Answer

24

Question 5

What is the equation of the normal to the curve y = x³ at the point (2, 8)?

Accepted Answer

y = -x/12 + 49/6

Answer

y = 12x - 16

Answer

y = -12x + 32

Answer

y = x/12 + 47/6

Question 6

If log₂(x) + log₂(x - 2) = 3, what is the value of x?

Accepted Answer

4

Answer

2

Answer

6

Answer

8