Just a handful of questions to make sure you're doing integration and differentiation more or less right...

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Question 1

Where is/are the turning point(s) of $y = x^3 - 12x^2 + 45x - 20$?

A

Minimum at $(0, -20)$

B

Stationary point of inflection at $(4, 32)$

C

Maximum at $(0, -20)$

D

Maximum at $(3, 34)$, minimum at $(5, -68)$

E

Minimum at $(3, 34)$, maximum at $(5, - 68)$

Question 2

The curve $C$ has the equation $y = x^2 - 3x - 18$, and crosses the $x$-axis at points $P$ and $Q$. The lines $l_1$ and $l_2$ are tangent to the curve at $P$ and $Q$, and meet at the point $R$. What is the area of triangle $PQR$?

A

$9$

B

$-\frac{81}{2}$

C

$\frac{81}{4}$

D

$\frac{729}{4}$

E

$81$

Question 3

Find the area enclosed by the curve $ y = (x+3)(x-2)(x-5)$ and the $x$-axis.

A

$\frac{1355}{6}$

B

$-\frac{200}{3}$

C

$64$

D

$106$

E

$\frac{200}{3}$

Question 4

The perimeter of a running track is 400 metres, and consists of two semi-circles of radius $r$ connected by two straights of length $l$. What is the maximum area enclosed by the running track, in m$^2$?

A

$400$

B

$40,000\pi$

C

$\frac{200}{\pi}$

D

$200\pi$

E

$\frac{40,000}{\pi}$

Hint:

The largest possible shape with a fixed perimeter is a circle! It turns out that $l = 0$.

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Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

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Quick calculus quiz http://t.co/zusG4MyTUX