Why isn't the answer to TMUA-P1X-MM7-03 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM7-03 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM7-03?

No — calculators are banned in the TMUA. TMUA-P1X-MM7-03 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1X-MM7-03?

TMUA-P1X-MM7-03 is Paper P1 · Integration (specification code MM7), level 2. Drill more of the same topic from this page.

TMUA-P1X-MM7-03 — Paper P1 · Integration · Level 2

P1MM7Level 2~180s target

Spec: MM7 · No calculator · ~180s

The curve

y = x^2 - 4

lies below the

x

-axis between

x = 0

and

x = 2

. What is the area enclosed by the curve, the

x

-axis,

x = 0

and

x = 2

Options

$-\frac{16}{3}$
$\frac{16}{3}$
$\frac{8}{3}$
$4$
$0$

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: area-vs-integral, sign-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The signed integral is

[x^3/3 - 4x]_0^2 = \frac{8}{3} - 8 = -\frac{16}{3}

, but the curve is below the axis on

[0, 2]

, so the enclosed area is

|-16/3| = \frac{16}{3}

. Trap:

-\frac{16}{3}

reports the signed integral — plausible if you forget that area must be positive.

Keep practising

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Step up a level
P1MM7Level 3
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Browse more

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Keep practising

Same topic · same level

P1MM7Level 2

TMUA-P1-MM7-003

The curve y = 2x - 6 lies below the x -axis between x = 1 and x = 3. What is the area enclosed by the curve, the x -axis…

Integration

Open TMUA-P1-MM7-003 →

Same trap: sign-trap

P1MM4Level 2

TMUA-P1-MM4-005

A triangle has sides of length 5 and 7 with included angle 60^°. What is the length of the third side?

Trigonometry

Open TMUA-P1-MM4-005 →

Step up a level

P1MM7Level 3

TMUA-P1-MM7-007

A curve satisfies dy/dx = 6x^2 - 4x + 1 and passes through (1, 3). What is its equation?

Integration

Open TMUA-P1-MM7-007 →

TMUA-P1X-MM7-03 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration

TMUA-P1X-MM7-03 — Paper P1 · Integration · Level 2

Options

Keep practising

Master Integration