Why isn't the answer to TMUA-P1-MM3-010 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM3-010 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM3-010?

No — calculators are banned in the TMUA. TMUA-P1-MM3-010 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-MM3-010?

TMUA-P1-MM3-010 is Paper P1 · Coordinate geometry in the (x,y)-plane (specification code MM3), level 3. Drill more of the same topic from this page.

TMUA-P1-MM3-010 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

P1MM3Level 3~240s target

Spec: MM3 · No calculator · ~240s

The line

y = x + 1

crosses the circle

x^2 + y^2 = 25

at two points. What is the length of the chord joining them?

Options

$7$
$7\sqrt{2}$
$14$
$5\sqrt{2}$
$10$

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: line-circle-intersection, chord-length. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Substituting gives

2x^2 + 2x - 24 = 0

, i.e.

x = 3

x = -4

, with points

(3, 4)

and

(-4, -3)

. The distance is

\sqrt{7^2 + 7^2} = 7\sqrt{2}

. Trap:

7

is just the

x

-difference — plausible if you forget the

y

-coordinates differ too.

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Keep practising

Same topic · same level

P1MM3Level 3

TMUA-P1-MM3-011

A cyclic quadrilateral has two opposite angles (3x + 20)^° and (x + 40)^°. What is the larger of these two angles?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-011 →

TMUA-P1-MM3-010 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane

TMUA-P1-MM3-010 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 3

Options

Keep practising

Master Coordinate geometry in the (x,y)-plane