Why isn't the answer to TMUA-P1-MM4-011 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM4-011 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM4-011?

No — calculators are banned in the TMUA. TMUA-P1-MM4-011 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-MM4-011?

TMUA-P1-MM4-011 is Paper P1 · Trigonometry (specification code MM4), level 3. Drill more of the same topic from this page.

TMUA-P1-MM4-011 — Paper P1 · Trigonometry · Level 3

P1MM4Level 3~240s target

Spec: MM4 · No calculator · ~240s

A triangle has sides of length

4

5

and

6

. What is the cosine of its largest angle?

Options

$\dfrac{1}{8}$
$-\dfrac{1}{8}$
$\dfrac{5}{9}$
$\dfrac{1}{4}$
$\dfrac{3}{8}$

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: cosine-rule-angle, numerator-order. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The largest angle is opposite the side

6

\cos\theta = \frac{4^2 + 5^2 - 6^2}{2(4)(5)} = \frac{5}{40} = \frac{1}{8}

. Trap:

-\frac{1}{8}

comes from computing

36 - 41

in the numerator — plausible if you put the longest side first.

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Keep practising

Same topic · same level

P1MM4Level 3

TMUA-P1-MM4-012

The equation 2^2 x = 1 has four solutions in 0 x < 2π. What is their sum?

Trigonometry

Open TMUA-P1-MM4-012 →

TMUA-P1-MM4-011 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry

TMUA-P1-MM4-011 — Paper P1 · Trigonometry · Level 3

Options

Keep practising

Master Trigonometry