Let a = (2, 5) and b = (-1, 3). What is |2a - b|?

Worked solution for TMUA-P1-MGEO-015 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MGEO-015 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MGEO-015 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MGEO-015?

No — calculators are banned in the TMUA. TMUA-P1-MGEO-015 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-MGEO-015?

TMUA-P1-MGEO-015 is Paper P1 · Geometry (specification code M-Geo), level 3. Drill more of the same topic from this page.

TMUA-P1-MGEO-015 — Paper P1 · Geometry · Level 3

P1M-GeoLevel 3~210s target

Spec: M-Geo · No calculator · ~210s

Let

\mathbf{a} = (2, 5)

and

\mathbf{b} = (-1, 3)

. What is

|2\mathbf{a} - \mathbf{b}|

Options

$12$
$74$
$\sqrt{24}$
$5$
$\sqrt{74}$

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: mgeo-vectors, vector-magnitude. Name the trap first, work the stem by hand, then open the solution below.

Show solution

2\mathbf{a} - \mathbf{b} = (4 - (-1), 10 - 3) = (5, 7)

, so

|2\mathbf{a} - \mathbf{b}| = \sqrt{5^2 + 7^2} = \sqrt{74}

.
Trap:

12

adds the components (

5 + 7

) instead of applying Pythagoras.

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Same topic · same level

P1M-GeoLevel 3

TMUA-P1-MGEO-009

A right circular cone has base radius 5 cm and slant height 13 cm. What is its volume in cm ^3?

Geometry

Open TMUA-P1-MGEO-009 →

Same trap: mgeo-vectors

P1M-GeoLevel 2

TMUA-P1-MGEO-014

Let a = (3, 1) and b = (1, 4). What is a + b?

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Open TMUA-P1-MGEO-014 →

TMUA-P1-MGEO-015 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry

TMUA-P1-MGEO-015 — Paper P1 · Geometry · Level 3

Options

Keep practising

Master Geometry