Why isn't the answer to TMUA-P1-MM8-024 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-024 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-024?

No — calculators are banned in the TMUA. TMUA-P1-MM8-024 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-MM8-024?

TMUA-P1-MM8-024 is Paper P1 · Graphs of functions (specification code MM8), level 3. Drill more of the same topic from this page.

TMUA-P1-MM8-024 — Paper P1 · Graphs of functions · Level 3

P1MM8Level 3~150s target

Spec: MM8 · No calculator · ~150s

How many real solutions does

|x^2 - 4| = 3

have?

Options

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: modulus-graphs, intersections-count. Name the trap first, work the stem by hand, then open the solution below.

Show solution

|x^2-4| = 3

gives

x^2 = 7

x^2 = 1

, i.e.

x = \pm\sqrt{7}, \pm 1

: four solutions, so the correct is C. Trap:

2

solves only

x^2 - 4 = 3

and ignores the reflected branch.

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: modulus-graphs
P1MM8Level 2
TMUA-P1-MM8-020
Where does y = |x| - 2 meet the x -axis?
Graphs of functions
Open TMUA-P1-MM8-020 →
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: modulus-graphs

P1MM8Level 2

TMUA-P1-MM8-020

Where does y = |x| - 2 meet the x -axis?

Graphs of functions

Open TMUA-P1-MM8-020 →

TMUA-P1-MM8-024 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-024 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions