Why isn't the answer to TMUA-P1-MM1-016 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-016 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-016?

No — calculators are banned in the TMUA. TMUA-P1-MM1-016 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-MM1-016?

TMUA-P1-MM1-016 is Paper P1 · Algebra and functions (specification code MM1), level 3. Drill more of the same topic from this page.

TMUA-P1-MM1-016 — Paper P1 · Algebra and functions · Level 3

P1MM1Level 3~240s target

Spec: MM1 · No calculator · ~240s

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

Options

$5$
$6$
$11$
$-6$
$13$

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: remainder-theorem-system, variable-swap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

P(1) = 0

gives

p + q = 11

and

P(-3) = 0

gives

3p - q = 13

. Adding yields

4p = 24

, so

p = 6

. Trap:

5

is the value of

q

, found if you stop one step early or swap the unknowns.

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The line y = 3x + k is tangent to the curve y = x^2 + 2x + 1. What is the value of k?

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Open TMUA-P1-MM1-017 →

TMUA-P1-MM1-016 — Paper P1 · Algebra and functions · Level 3

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TMUA-P1-MM1-016 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

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