Why isn't the answer to TMUA-P1-MM6-007 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM6-007 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM6-007?

No — calculators are banned in the TMUA. TMUA-P1-MM6-007 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM6-007?

TMUA-P1-MM6-007 is Paper P1 · Differentiation (specification code MM6), level 2. Drill more of the same topic from this page.

TMUA-P1-MM6-007 — Paper P1 · Differentiation · Level 2

P1MM6Level 2~210s target

Spec: MM6 · No calculator · ~210s

Find the equation of the normal to

y = x^3

at the point

(1, 1)

Options

$x + 3y = 4$
$x - 3y = -2$
$3x + y = 4$
$x + 3y = 1$
$y = 3x - 2$

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: normal-gradient, reciprocal-sign. Name the trap first, work the stem by hand, then open the solution below.

Show solution

(1, 1)

the gradient is

3

, so the normal has gradient

-\frac{1}{3}

y - 1 = -\frac{1}{3}(x - 1)

, i.e.

x + 3y = 4

. Trap:

x - 3y = -2

uses

+\frac{1}{3}

— plausible if you take the reciprocal but forget to negate.

Keep practising

Same topic · same level
P1MM6Level 2
TMUA-P1-MM6-004
Differentiate y = √x^3 (for x > 0 ) with respect to x.
Differentiation
Open TMUA-P1-MM6-004 →
Same trap: reciprocal-sign
P1MM3Level 2
TMUA-P1-MM3-009
A circle has centre O(0, 0) and the point P(6, 4) lies on it. Find the equation of the tangent to the circle at P.
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-009 →
Step up a 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 →

Browse more

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Keep practising

Same topic · same level

P1MM6Level 2

TMUA-P1-MM6-004

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

Differentiation

Open TMUA-P1-MM6-004 →

Same trap: reciprocal-sign

P1MM3Level 2

TMUA-P1-MM3-009

A circle has centre O(0, 0) and the point P(6, 4) lies on it. Find the equation of the tangent to the circle at P.

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-009 →

Step up a 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 →

TMUA-P1-MM6-007 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation

TMUA-P1-MM6-007 — Paper P1 · Differentiation · Level 2

Options

Keep practising

Master Differentiation