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
Maximum at $(3, 34)$, minimum at $(5, -68)$
C
Stationary point of inflection at $(4, 32)$
D
Minimum at $(3, 34)$, maximum at $(5, - 68)$
E
Maximum at $(0, -20)$
Question 2
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
$\frac{200}{\pi}$
C
$40,000\pi$
D
$200\pi$
E
$\frac{40,000}{\pi}$
Hint:
The largest possible shape with a fixed perimeter is a circle! It turns out that $l = 0$.
Find the area enclosed by the curve $ y = (x+3)(x-2)(x-5)$ and the $x$-axis.
A
$-\frac{200}{3}$
B
$106$
C
$64$
D
$\frac{200}{3}$
E
$\frac{1355}{6}$
Question 5
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
$81$
B
$\frac{729}{4}$
C
$9$
D
$-\frac{81}{2}$
E
$\frac{81}{4}$
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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