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

Worked solution for TMUA-P1-MM7-007 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM7-007 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM7-007 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM7-007?

No — calculators are banned in the TMUA. TMUA-P1-MM7-007 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-MM7-007?

TMUA-P1-MM7-007 is Paper P1 · Integration (specification code MM7), level 3. Drill more of the same topic from this page.

TMUA-P1-MM7-007 — Paper P1 · Integration · Level 3

P1MM7Level 3~240s target

Spec: MM7 · No calculator · ~240s

A curve satisfies

\frac{dy}{dx} = 6x^2 - 4x + 1

and passes through

(1, 3)

. What is its equation?

Options

$y = 2x^3 - 2x^2 + x + 2$
$y = 2x^3 - 2x^2 + x$
$y = 2x^3 - 2x^2 + x + 3$
$y = 6x^3 - 4x^2 + x + 2$
$y = 2x^3 - 4x^2 + x + 2$

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

Show solution

Integrate:

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

. Through

(1, 3)

2 - 2 + 1 + C = 3

, so

C = 2

. Trap: omitting

C

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

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The trapezium rule with 4 strips is used to estimate _0^2 x^2\,dx. Which statement is correct?
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Same trap: plus-C
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Options

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

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

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

y = 6x^3 - 4x^2 + x + 2

y = 2x^3 - 4x^2 + x + 2

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-MM7-008

The trapezium rule with 4 strips is used to estimate _0^2 x^2\,dx. Which statement is correct?

Integration

Open TMUA-P1-MM7-008 →

Same trap: plus-C

P1MM7Level 3

TMUA-P1X-MM7-06

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

Integration

Open TMUA-P1X-MM7-06 →

TMUA-P1-MM7-007 — Paper P1 · Integration · Level 3

Options

Keep practising

Master Integration

TMUA-P1-MM7-007 — Paper P1 · Integration · Level 3

Options

Keep practising

Master Integration