Why isn't the answer to TMUA-P1-MM1-014 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-014 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-014?

No — calculators are banned in the TMUA. TMUA-P1-MM1-014 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-MM1-014?

TMUA-P1-MM1-014 is Paper P1 · Algebra and functions (specification code MM1), level 2. Drill more of the same topic from this page.

TMUA-P1-MM1-014 — Paper P1 · Algebra and functions · Level 2

P1MM1Level 2~210s target

Spec: MM1 · No calculator · ~210s

Find the sum of all real solutions of

|3x - 4| = 11

Options

$5$
$\dfrac{8}{3}$
$\dfrac{4}{3}$
$-\dfrac{7}{3}$
$\dfrac{22}{3}$

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: modulus-two-cases, dropped-branch. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Split into

3x - 4 = 11

(so

x = 5

) and

3x - 4 = -11

(so

x = -\frac{7}{3}

). Their sum is

5 - \frac{7}{3} = \frac{8}{3}

. Trap:

5

is only the positive-branch root — plausible if you forget the modulus has two cases.

Keep practising

Same topic · same level
P1MM1Level 2
TMUA-P1-MM1-001
The equation x^2 + kx + 9 = 0 has two equal real roots. What is the sum of all possible values of k?
Algebra and functions
Open TMUA-P1-MM1-001 →
Same trap: modulus-two-cases
P2PRF2Level 2
TMUA-P2Z-PRF2-003
To prove |xy| = |x||y| for all real x and y by cases, which splitting of the cases is exhaustive, with each case correct…
Proof by cases
Open TMUA-P2Z-PRF2-003 →
Step up a 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 →

Browse more

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Keep practising

Same topic · same level

P1MM1Level 2

TMUA-P1-MM1-001

The equation x^2 + kx + 9 = 0 has two equal real roots. What is the sum of all possible values of k?

Algebra and functions

Open TMUA-P1-MM1-001 →

Same trap: modulus-two-cases

P2PRF2Level 2

TMUA-P2Z-PRF2-003

To prove |xy| = |x||y| for all real x and y by cases, which splitting of the cases is exhaustive, with each case correct…

Proof by cases

Open TMUA-P2Z-PRF2-003 →

Step up a 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 →

TMUA-P1-MM1-014 — Paper P1 · Algebra and functions · Level 2

Options

Keep practising

Master Algebra and functions

TMUA-P1-MM1-014 — Paper P1 · Algebra and functions · Level 2

Options

Keep practising

Master Algebra and functions