Why isn't the answer to TMUA-P1-MM2-020 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM2-020 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM2-020?

No — calculators are banned in the TMUA. TMUA-P1-MM2-020 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-MM2-020?

TMUA-P1-MM2-020 is Paper P1 · Sequences and series (specification code MM2), level 3. Drill more of the same topic from this page.

TMUA-P1-MM2-020 — Paper P1 · Sequences and series · Level 3

P1MM2Level 3~150s target

Spec: MM2 · No calculator · ~150s

What is the coefficient of

x^3

in the expansion of

(2+x)^5

Options

$10$
$20$
$80$
$40$

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: binomial-coefficients, general-term. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The

x^3

term is

\binom{5}{3}2^2x^3 = 10 \times 4 x^3 = 40x^3

, so the coefficient is

40

and the correct is D. Trap:

10

\binom{5}{3}

alone, forgetting the powers of

2

Keep practising

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Same topic · same level

P1MM2Level 3

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An arithmetic series has first term 7 and common difference 4. What is the smallest n such that the sum of the first n t…

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Open TMUA-P1-MM2-012 →

Same trap: binomial-coefficients

P1MM2Level 2

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What is the coefficient of x^2 in the expansion of (1+x)^4?

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Open TMUA-P1-MM2-017 →

TMUA-P1-MM2-020 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series

TMUA-P1-MM2-020 — Paper P1 · Sequences and series · Level 3

Options

Keep practising

Master Sequences and series