Why isn't the answer to TMUA-P1-MM3-007 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM3-007 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM3-007?

No — calculators are banned in the TMUA. TMUA-P1-MM3-007 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM3-007?

TMUA-P1-MM3-007 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-MM3-007 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

P1MM3Level 2~180s target

Spec: MM3 · No calculator · ~180s

AB

is a diameter of a circle with centre

O

, and

C

lies on the circle. If angle

CAB = 34^\circ

, what is angle

CBA

Options

$34$
$46$
$56$
$68$
$90$

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: angle-in-semicircle. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The angle in a semicircle is

90^\circ

, so the triangle's angles sum:

180 - 90 - 34 = 56

. Trap:

34^\circ

assumes the triangle is isosceles — plausible from the symmetric-looking diagram.

Keep practising

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

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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 →

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-MM3-007 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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

TMUA-P1-MM3-007 — Paper P1 · Coordinate geometry in the (x,y)-plane · Level 2

Options

Keep practising

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