Why isn't the answer to TMUA-P1-MM6-009 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-009 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-009?

No — calculators are banned in the TMUA. TMUA-P1-MM6-009 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM6-009?

TMUA-P1-MM6-009 is Paper P1 · Differentiation (specification code MM6), level 3. Drill more of the same topic from this page.

TMUA-P1-MM6-009 — Paper P1 · Differentiation · Level 3

P1MM6Level 3~240s target

Spec: MM6 · No calculator · ~240s

The area of a circle is

A = \pi r^2

. The radius increases at

2

cm/s. At what rate is the area increasing when

r = 5

cm?

Options

$2\pi$
$5\pi$
$10\pi$
$25\pi$
$20\pi$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: related-rates, chain-rule-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

By the chain rule

\frac{dA}{dt} = 2\pi r\frac{dr}{dt} = 2\pi(5)(2) = 20\pi

. Trap:

10\pi

uses

\frac{dr}{dt} = 1

— plausible if you differentiate

\pi r^2

and stop before applying the chain rule.

Keep practising

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Keep practising

Same topic · same level

P1MM6Level 3

TMUA-P1-MM6-010

For which values of x is f(x) = x^3 - 6x^2 + 9x + 1 strictly increasing?

Differentiation

Open TMUA-P1-MM6-010 →

TMUA-P1-MM6-009 — Paper P1 · Differentiation · Level 3

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-009 — Paper P1 · Differentiation · Level 3

Options

Keep practising

Master Differentiation