Find the area of the region bounded by \(y = {x^3}\) and \(y = {x^2} + 2x\), correcting to two decimal place.

Correct

Incorrect

Question 6 of 10

6. Question

Find \(a\) and \(b\), if the volume of the solid formed when \(y = {x^2} \) for \(2 \le x \le 4\) is revolved through \(2\pi \) or \(360^\circ \) about the \(y\)-axis is \(a\pi \) where \(a\) and \(b\) have no common factors.

\(a = \)

Correct

Incorrect

Question 7 of 10

7. Question

A binomial random variable has a mean of 8 and a variance of 6.4. Find \(\Pr \left( {X = 10} \right)\), correcting to four significant figures.

Correct

Incorrect

Question 8 of 10

8. Question

A fair coin is tossed five times. Find the probability of obtaining two Heads and three Tails.

Correct

Incorrect

Question 9 of 10

9. Question

Find the positive value of \(k\), correcting to three significant figures, if the length of \( \begin{pmatrix} k \\ – 3 \end{pmatrix} \) is 7.2.

Correct

Incorrect

Question 10 of 10

10. Question

Find the first two values of \(t\) when \(h = 5\) given \(y = 3 + 4\cos \dfrac{\pi }{3}\left( {t – 4} \right)\).