Why isn't the answer to TMUA-P2-ERR2-005 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ERR2-005 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ERR2-005?

No — calculators are banned in the TMUA. TMUA-P2-ERR2-005 is set for a no-calculator target of about 170 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ERR2-005?

TMUA-P2-ERR2-005 is Paper P2 · Common fallacies (specification code ERR2), level 2. Drill more of the same topic from this page.

TMUA-P2-ERR2-005 — Paper P2 · Common fallacies · Level 2

P2ERR2Level 2~170s target

Spec: ERR2 · No calculator · ~170s

A student expands

(x + y)^2

x^2 + y^2

, then “cancels” squares against roots elsewhere in the problem. Which pair exposes the fallacy?

Options

The expansion is correct for all $x, y$ .
$(1 + 2)^2 = 9$ but $1^2 + 2^2 = 5$ : the missing cross term is $2xy$ .
The expansion fails only for negative numbers.
$(x+y)^2 = x^2 + y^2$ holds whenever $x = y$ .
The fallacy is that $9 \ne 9$ .

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: single-counterexample. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The correct expansion is

x^2 + 2xy + y^2

;

x = 1

y = 2

gives

9 \ne 5

. Trap: “distributing” the square over addition as if it were multiplication by

2

— powers are not linear.

Keep practising

Same topic · same level
P2ERR2Level 2
TMUA-P2-ERR2-004
A student solves -2x > 6 by dividing both sides by -2 to get x > -3. What is the error?
Common fallacies
Open TMUA-P2-ERR2-004 →
Same trap: single-counterexample
P2ARG1Level 3
TMUA-P2-ARG1-009
A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…
Statements and connectives
Open TMUA-P2-ARG1-009 →
Step up a level
P2ERR2Level 3
TMUA-P2-ERR2-009
A sixth-former optimises a profit function P(x) and argues as follows: Fermat's theorem says that if P has a local maxim…
Common fallacies
Open TMUA-P2-ERR2-009 →

Browse more

Loading…

Options

The expansion is correct for all

x, y

(1 + 2)^2 = 9

but

1^2 + 2^2 = 5

: the missing cross term is

2xy

The expansion fails only for negative numbers.

(x+y)^2 = x^2 + y^2

holds whenever

x = y

The fallacy is that

9 \ne 9

Letters only — the answer key is hidden. Work it out, then check the solution below.

Keep practising

Same topic · same level

P2ERR2Level 2

TMUA-P2-ERR2-004

A student solves -2x > 6 by dividing both sides by -2 to get x > -3. What is the error?

Common fallacies

Open TMUA-P2-ERR2-004 →

Same trap: single-counterexample

P2ARG1Level 3

TMUA-P2-ARG1-009

A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…

Statements and connectives

Open TMUA-P2-ARG1-009 →

Step up a level

P2ERR2Level 3

TMUA-P2-ERR2-009

A sixth-former optimises a profit function P(x) and argues as follows: Fermat's theorem says that if P has a local maxim…

Common fallacies

Open TMUA-P2-ERR2-009 →

TMUA-P2-ERR2-005 — Paper P2 · Common fallacies · Level 2

Options

Keep practising

Master Common fallacies

TMUA-P2-ERR2-005 — Paper P2 · Common fallacies · Level 2

Options

Keep practising

Master Common fallacies