Why isn't the answer to TMUA-P1-MM2-010 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM2-010 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM2-010?

No — calculators are banned in the TMUA. TMUA-P1-MM2-010 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM2-010?

TMUA-P1-MM2-010 is Paper P1 · Sequences and series (specification code MM2), level 2. Drill more of the same topic from this page.

TMUA-P1-MM2-010 — Paper P1 · Sequences and series · Level 2

P1MM2Level 2~210s target

Spec: MM2 · No calculator · ~210s

What is the coefficient of

x^2

in the expansion of

(1 + 3x)^5

Options

$10$
$30$
$90$
$135$
$270$

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-coefficient, inner-power-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The

x^2

term is

\binom{5}{2}(3x)^2 = 10 \cdot 9x^2

, so the coefficient is

90

. Trap:

10

is just

\binom{5}{2}

— plausible if you forget to square the

3

Keep practising

Same topic · same level
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A sequence is defined by u_1 = 5 and u_n+1 = 2u_n - 3. What is the value of u_3?
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Same trap: inner-power-trap
P1MM2Level 3
TMUA-P1-MM2-013
The expansion of (1 + 4x)^6 begins 1 + 24x + cx^2 +. What is the value of c?
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Open TMUA-P1-MM2-013 →
Step up a level
P1MM2Level 3
TMUA-P1-MM2-012
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 →

Browse more

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Keep practising

Same topic · same level

P1MM2Level 2

TMUA-P1-MM2-006

A sequence is defined by u_1 = 5 and u_n+1 = 2u_n - 3. What is the value of u_3?

Sequences and series

Open TMUA-P1-MM2-006 →

Same trap: inner-power-trap

P1MM2Level 3

TMUA-P1-MM2-013

The expansion of (1 + 4x)^6 begins 1 + 24x + cx^2 +. What is the value of c?

Sequences and series

Open TMUA-P1-MM2-013 →

Step up a level

P1MM2Level 3

TMUA-P1-MM2-012

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…

Sequences and series

Open TMUA-P1-MM2-012 →

TMUA-P1-MM2-010 — Paper P1 · Sequences and series · Level 2

Options

Keep practising

Master Sequences and series

TMUA-P1-MM2-010 — Paper P1 · Sequences and series · Level 2

Options

Keep practising

Master Sequences and series