Why isn't the answer to TMUA-P1-MM3-006 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM3-006 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM3-006?

No — calculators are banned in the TMUA. TMUA-P1-MM3-006 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-MM3-006?

TMUA-P1-MM3-006 is Paper P1 · Coordinate geometry in the (x,y)-plane (specification code MM3), level 2. Drill more of the same topic from this page.

TMUA-P1-MM3-006 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

P1MM3Level 2~210s target

Spec: MM3 · No calculator · ~210s

The circle

x^2 + y^2 - 6x + 4y - 3 = 0

has radius

r

. What is

r

Options

$3$
$4$
$9$
$16$
$\sqrt{3}$

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: completing-square-circle, radius-squared-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Complete both squares:

(x-3)^2 + (y+2)^2 = 9 + 4 + 3 = 16

, so

r = \sqrt{16} = 4

. Trap:

16

r^2

, not

r

— plausible if you stop before the final square root.

Keep practising

Same topic · same level
P1MM3Level 2
TMUA-P1-MM3-001
In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-001 →
Same trap: completing-square-circle
P1MM3Level 2
TMUA-P1X-MM3-02
The circle x^2 + y^2 + 8x - 6y + 9 = 0 has radius r. What is r?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1X-MM3-02 →
Step up a level
P1MM3Level 3
TMUA-P1-MM3-010
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?
Coordinate geometry in the (x,y)-plane
Open TMUA-P1-MM3-010 →

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Keep practising

Same topic · same level

P1MM3Level 2

TMUA-P1-MM3-001

In an arithmetic sequence the 3rd term is 11 and the 8th term is 31. What is the first term?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-001 →

Same trap: completing-square-circle

P1MM3Level 2

TMUA-P1X-MM3-02

The circle x^2 + y^2 + 8x - 6y + 9 = 0 has radius r. What is r?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1X-MM3-02 →

Step up a level

P1MM3Level 3

TMUA-P1-MM3-010

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?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1-MM3-010 →

TMUA-P1-MM3-006 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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

TMUA-P1-MM3-006 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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