Why isn't the answer to TMUA-P1-MM1-017 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-017 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-017?

No — calculators are banned in the TMUA. TMUA-P1-MM1-017 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-MM1-017?

TMUA-P1-MM1-017 is Paper P1 · Algebra and functions (specification code MM1), level 3. Drill more of the same topic from this page.

TMUA-P1-MM1-017 — Paper P1 · Algebra and functions · Level 3

P1MM1Level 3~240s target

Spec: MM1 · No calculator · ~240s

The line

y = 3x + k

is tangent to the curve

y = x^2 + 2x + 1

. What is the value of

k

Options

$0$
$1$
$\dfrac{3}{4}$
$3$
$-\dfrac{3}{4}$

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: tangency-discriminant, coefficient-matching. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Tangency means

x^2 + 2x + 1 = 3x + k

has a repeated root:

x^2 - x + (1 - k) = 0

with discriminant

1 - 4(1-k) = 0

, so

k = \frac{3}{4}

. Trap:

1

is just the constant term of the curve — plausible if you equate coefficients instead of using the discriminant.

Keep practising

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Keep practising

Same topic · same level

P1MM1Level 3

TMUA-P1-MM1-016

The polynomial P(x) = x^3 + px^2 + qx - 12 is divisible by both (x - 1) and (x + 3). What is the value of p?

Algebra and functions

Open TMUA-P1-MM1-016 →

Same trap: tangency-discriminant

P1MM3Level 3

TMUA-P1X-MM3-05

The line y = 2x + k with k > 0 is tangent to the circle x^2 + y^2 = 20. What is k?

Coordinate geometry in the (x,y)-plane

Open TMUA-P1X-MM3-05 →

TMUA-P1-MM1-017 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

Master Algebra and functions

TMUA-P1-MM1-017 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

Master Algebra and functions