Why isn't the answer to TMUA-P1-MM6-003 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-003 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-003?

No — calculators are banned in the TMUA. TMUA-P1-MM6-003 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-MM6-003?

TMUA-P1-MM6-003 is Paper P1 · Differentiation (specification code MM6), level 1. Drill more of the same topic from this page.

TMUA-P1-MM6-003 — Paper P1 · Differentiation · Level 1

P1MM6Level 1~150s target

Spec: MM6 · No calculator · ~150s

Let

f(x) = x^3

. What is the value of

f''(2)

Options

$3x^2$
$6x$
$6$
$3x$
$12$

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: second-derivative. Name the trap first, work the stem by hand, then open the solution below.

Show solution

f'(x) = 3x^2

and

f''(x) = 6x

, so

f''(2) = 12

Keep practising

Same topic · same level
P1MM6Level 1
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Differentiate y = x^5 with respect to x.
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Open TMUA-P1-MM6-001 →
Same trap: second-derivative
P1MM6Level 2
TMUA-P1-MM6-021
Given y = x^4, find d^2y/dx^2.
Differentiation
Open TMUA-P1-MM6-021 →
Step up a level
P1MM6Level 2
TMUA-P1-MM6-004
Differentiate y = √x^3 (for x > 0 ) with respect to x.
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Open TMUA-P1-MM6-004 →

Browse more

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Keep practising

Same topic · same level

P1MM6Level 1

TMUA-P1-MM6-001

Differentiate y = x^5 with respect to x.

Differentiation

Open TMUA-P1-MM6-001 →

Same trap: second-derivative

P1MM6Level 2

TMUA-P1-MM6-021

Given y = x^4, find d^2y/dx^2.

Differentiation

Open TMUA-P1-MM6-021 →

Step up a level

P1MM6Level 2

TMUA-P1-MM6-004

Differentiate y = √x^3 (for x > 0 ) with respect to x.

Differentiation

Open TMUA-P1-MM6-004 →

TMUA-P1-MM6-003 — Paper P1 · Differentiation · Level 1

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-003 — Paper P1 · Differentiation · Level 1

Options

Keep practising

Master Differentiation