Why isn't the answer to TMUA-P1-MM8-009 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-009 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-009?

No — calculators are banned in the TMUA. TMUA-P1-MM8-009 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-MM8-009?

TMUA-P1-MM8-009 is Paper P1 · Graphs of functions (specification code MM8), level 3. Drill more of the same topic from this page.

TMUA-P1-MM8-009 — Paper P1 · Graphs of functions · Level 3

P1MM8Level 3~240s target

Spec: MM8 · No calculator · ~240s

Which statement correctly describes the stationary points of

y = x^3 - 3x^2

Options

local minimum $0$ at $x = 0$ , local maximum $-4$ at $x = 2$
local maximum $0$ at $x = 0$ , local minimum $-4$ at $x = 2$
local maximum $0$ at $x = 2$ , local minimum $-4$ at $x = 0$
a point of inflection at $x = 0$ only
no stationary points

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: calculus-to-graph, max-min-swap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

y' = 3x^2 - 6x = 3x(x-2)

, stationary at

0

and

2

;

y'' = 6x - 6

is negative at

0

(maximum, value

0

) and positive at

2

(minimum, value

-4

). Trap: swapping them is plausible if you classify by position rather than testing the second derivative.

Keep practising

Same topic · same level
P1MM8Level 3
TMUA-P1-MM8-010
Which of the following statements about the curve y = 2^x - 3 is FALSE?
Graphs of functions
Open TMUA-P1-MM8-010 →
Same trap: max-min-swap
P1MM4Level 2
TMUA-P1-MM4-010
What is the maximum value of y = 3 - 2 x?
Trigonometry
Open TMUA-P1-MM4-010 →
More in this topic
P1MM8Level 3
TMUA-P1-MM8-022
The cubic y = (x-1)^2(x+2) touches the x -axis at one point. Where?
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Open TMUA-P1-MM8-022 →

Browse more

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Options

local minimum

0

x = 0

, local maximum

-4

x = 2

local maximum

0

x = 0

, local minimum

-4

x = 2

local maximum

0

x = 2

, local minimum

-4

x = 0

a point of inflection at

x = 0

only

no stationary points

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

Keep practising

Same topic · same level

P1MM8Level 3

TMUA-P1-MM8-010

Which of the following statements about the curve y = 2^x - 3 is FALSE?

Graphs of functions

Open TMUA-P1-MM8-010 →

Same trap: max-min-swap

P1MM4Level 2

TMUA-P1-MM4-010

What is the maximum value of y = 3 - 2 x?

Trigonometry

Open TMUA-P1-MM4-010 →

TMUA-P1-MM8-009 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-009 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions