A curve satisfies dy/dx = 3x^2 + 2x - 1 and passes through (2, 5). What is its equation?

Worked solution for TMUA-P1X-MM7-06 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1X-MM7-06 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM7-06 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM7-06?

No — calculators are banned in the TMUA. TMUA-P1X-MM7-06 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-P1X-MM7-06?

TMUA-P1X-MM7-06 is Paper P1 · Integration (specification code MM7), level 3. Drill more of the same topic from this page.

TMUA-P1X-MM7-06 — Paper P1 · Integration · Level 3

P1MM7Level 3~240s target

Spec: MM7 · No calculator · ~240s

A curve satisfies

\frac{dy}{dx} = 3x^2 + 2x - 1

and passes through

(2, 5)

. What is its equation?

Options

$y = x^3 + x^2 - x - 5$
$y = x^3 + x^2 - x$
$y = x^3 + x^2 - x + 5$
$y = 6x + 2$
$y = x^3 + x^2 - x - 3$

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: plus-C, initial-condition. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Integrate:

y = x^3 + x^2 - x + C

. Through

(2, 5)

8 + 4 - 2 + C = 5

, so

C = -5

and

y = x^3 + x^2 - x - 5

. Trap: omitting

C

entirely is plausible if you integrate but forget the curve is only fixed by the given point.

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Options

y = x^3 + x^2 - x - 5

y = x^3 + x^2 - x

y = x^3 + x^2 - x + 5

y = 6x + 2

y = x^3 + x^2 - x - 3

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

Keep practising

Same topic · same 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-MM7-06 — Paper P1 · Integration · Level 3

Options

Keep practising

Master Integration

TMUA-P1X-MM7-06 — Paper P1 · Integration · Level 3

Options

Keep practising

Master Integration