Why isn't the answer to TMUA-P1-MM8-022 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-022 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-022?

No — calculators are banned in the TMUA. TMUA-P1-MM8-022 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-MM8-022?

TMUA-P1-MM8-022 is Paper P1 · Graphs of functions (specification code MM8), level 3. Drill more of the same topic from this page.

TMUA-P1-MM8-022 — Paper P1 · Graphs of functions · Level 3

P1MM8Level 3~150s target

Spec: MM8 · No calculator · ~150s

The cubic

y = (x-1)^2(x+2)

touches the

x

-axis at one point. Where?

Options

$x = -2$
$x = 1$
$x = -1$
$x = 2$

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: repeated-roots, cubic-shape. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The squared factor

(x-1)^2

is zero at

x = 1

without changing sign, so the graph touches there and the correct is B. Trap:

x = -2

is a single root where the graph crosses.

Keep practising

Same topic · same level
P1MM8Level 3
TMUA-P1-MM8-009
Which statement correctly describes the stationary points of y = x^3 - 3x^2?
Graphs of functions
Open TMUA-P1-MM8-009 →
Same trap: cubic-shape
P1MM8Level 2
TMUA-P1-MM8-006
A cubic y = ax^3 + with a > 0 has three distinct real roots. Which best describes its graph?
Graphs of functions
Open TMUA-P1-MM8-006 →
More in this topic
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 →

Browse more

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Keep practising

Same topic · same level

P1MM8Level 3

TMUA-P1-MM8-009

Which statement correctly describes the stationary points of y = x^3 - 3x^2?

Graphs of functions

Open TMUA-P1-MM8-009 →

Same trap: cubic-shape

P1MM8Level 2

TMUA-P1-MM8-006

A cubic y = ax^3 + with a > 0 has three distinct real roots. Which best describes its graph?

Graphs of functions

Open TMUA-P1-MM8-006 →

TMUA-P1-MM8-022 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-022 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions