Why isn't the answer to TMUA-P2-ERR1-001 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ERR1-001 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ERR1-001?

No — calculators are banned in the TMUA. TMUA-P2-ERR1-001 is set for a no-calculator target of about 160 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ERR1-001?

TMUA-P2-ERR1-001 is Paper P2 · Identifying errors in proofs (specification code ERR1), level 1. Drill more of the same topic from this page.

TMUA-P2-ERR1-001 — Paper P2 · Identifying errors in proofs · Level 1

P2ERR1Level 1~160s target

Spec: ERR1 · No calculator · ~160s

A “proof” that

1 = 2

reads: (1) Let

a = b

. (2) Then

a^2 = ab

. (3) So

a^2 - b^2 = ab - b^2

. (4) Factorising gives

(a-b)(a+b) = b(a-b)

. (5) Dividing both sides by

(a - b)

gives

a + b = b

. (6) Since

a = b

2b = b

, so

2 = 1

. Which line is the first unjustified step?

Options

Line (6): substituting $a = b$ is invalid.
Every line is valid, so $1 = 2$ .
Line (2): $a^2 = ab$ does not follow from $a = b$ .
Line (4): the factorisation is incorrect.
Line (5): it divides by $(a - b)$ , which equals $0$ .

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: line-number-fault, division-by-zero-variable. Name the trap first, work the stem by hand, then open the solution below.

Show solution

From

a = b

we have

a - b = 0

, and division by zero is never allowed — line (5) is the first bad step; all lines before it are fine. Trap: blaming the algebra (factorisation is correct) instead of the illegal cancellation of a zero factor.

Keep practising

Same topic · same level
P2ERR1Level 1
TMUA-P2-ERR1-002
A proof claims √(-4)^2 = -4: (1) √(-4)^2 = √16. (2) √16 = 4. (3) Hence √(-4)^2 = -4. It cites the rule √x^2 = x for all…
Identifying errors in proofs
Open TMUA-P2-ERR1-002 →
Same trap: line-number-fault
P2ERR1Level 1
TMUA-P2-ERR1-003
A student claims: (1) ab/a = b for all numbers a, b. (2) Put a = 0, b = 5. (3) Hence 0/0 = 5. Which is the first unjusti…
Identifying errors in proofs
Open TMUA-P2-ERR1-003 →
Step up a level
P2ERR1Level 2
TMUA-P2-ERR1-004
A “proof” for acute A, B reads: (1) Suppose A = B. (2) “Cancel” to get A = B. (3) Hence equal sines imply equal angles.…
Identifying errors in proofs
Open TMUA-P2-ERR1-004 →

Browse more

Loading…

Options

Line (6): substituting

a = b

is invalid.

Every line is valid, so

1 = 2

Line (2):

a^2 = ab

does not follow from

a = b

Line (4): the factorisation is incorrect.

Line (5): it divides by

(a - b)

, which equals

0

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

Keep practising

Same topic · same level

P2ERR1Level 1

TMUA-P2-ERR1-002

A proof claims √(-4)^2 = -4: (1) √(-4)^2 = √16. (2) √16 = 4. (3) Hence √(-4)^2 = -4. It cites the rule √x^2 = x for all…

Identifying errors in proofs

Open TMUA-P2-ERR1-002 →

Same trap: line-number-fault

P2ERR1Level 1

TMUA-P2-ERR1-003

A student claims: (1) ab/a = b for all numbers a, b. (2) Put a = 0, b = 5. (3) Hence 0/0 = 5. Which is the first unjusti…

Identifying errors in proofs

Open TMUA-P2-ERR1-003 →

Step up a level

P2ERR1Level 2

TMUA-P2-ERR1-004

A “proof” for acute A, B reads: (1) Suppose A = B. (2) “Cancel” to get A = B. (3) Hence equal sines imply equal angles.…

Identifying errors in proofs

Open TMUA-P2-ERR1-004 →

TMUA-P2-ERR1-001 — Paper P2 · Identifying errors in proofs · Level 1

Options

Keep practising

Master Identifying errors in proofs

TMUA-P2-ERR1-001 — Paper P2 · Identifying errors in proofs · Level 1

Options

Keep practising

Master Identifying errors in proofs