Why isn't the answer to TMUA-P1-MM6-022 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-022 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-022?

No — calculators are banned in the TMUA. TMUA-P1-MM6-022 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM6-022?

TMUA-P1-MM6-022 is Paper P1 · Differentiation (specification code MM6), level 3. Drill more of the same topic from this page.

TMUA-P1-MM6-022 — Paper P1 · Differentiation · Level 3

P1MM6Level 3~150s target

Spec: MM6 · No calculator · ~150s

A rectangle has perimeter

40

. What is its maximum possible area?

Options

$200$
$100$
$50$
$400$

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: optimisation, stationary-points. Name the trap first, work the stem by hand, then open the solution below.

Show solution

With sides

x

and

20 - x

, area

A = 20x - x^2

and

A\' = 20 - 2x = 0

gives

x = 10

, so

A = 100

and the correct is B. Trap:

200

doubles the true maximum by using perimeter as area.

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Keep practising

Same topic · same level

P1MM6Level 3

TMUA-P1-MM6-009

The area of a circle is A = π r^2. The radius increases at 2 cm/s. At what rate is the area increasing when r = 5 cm?

Differentiation

Open TMUA-P1-MM6-009 →

Same trap: stationary-points

P1MM6Level 2

TMUA-P1-MM6-008

The curve y = x^3 - 3x has a local maximum. What is its y -value?

Differentiation

Open TMUA-P1-MM6-008 →

TMUA-P1-MM6-022 — Paper P1 · Differentiation · Level 3

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-022 — Paper P1 · Differentiation · Level 3

Options

Keep practising

Master Differentiation