Why isn't the answer to TMUA-P1-MM1-019 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-019 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-019?

No — calculators are banned in the TMUA. TMUA-P1-MM1-019 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-MM1-019?

TMUA-P1-MM1-019 is Paper P1 · Algebra and functions (specification code MM1), level 3. Drill more of the same topic from this page.

TMUA-P1-MM1-019 — Paper P1 · Algebra and functions · Level 3

P1MM1Level 3~240s target

Spec: MM1 · No calculator · ~240s

What is the product of all real solutions of

|2x + 1| = |x + 4|

Options

$3$
$-5$
$-\dfrac{5}{3}$
$\dfrac{4}{3}$
$-15$

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-squaring, missing-sign-case. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Square both sides:

(2x+1)^2 = (x+4)^2

gives

3x^2 - 4x - 15 = 0

, i.e.

(3x+5)(x-3) = 0

. Roots

3

and

-\frac{5}{3}

multiply to

-5

. Trap:

3

alone comes from only solving

2x + 1 = x + 4

and missing the sign-flipped case.

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: missing-sign-case
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 →
More in this topic
P1MM1Level 3
TMUA-P1-MM1-017
The line y = 3x + k is tangent to the curve y = x^2 + 2x + 1. What is the value of k?
Algebra and functions
Open TMUA-P1-MM1-017 →

Browse more

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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: missing-sign-case

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 →

TMUA-P1-MM1-019 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

Master Algebra and functions

TMUA-P1-MM1-019 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

Master Algebra and functions