Why isn't the answer to TMUA-P1-MM1-005 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-005 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-005?

No — calculators are banned in the TMUA. TMUA-P1-MM1-005 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM1-005?

TMUA-P1-MM1-005 is Paper P1 · Algebra and functions (specification code MM1), level 1. Drill more of the same topic from this page.

TMUA-P1-MM1-005 — Paper P1 · Algebra and functions · Level 1

P1MM1Level 1~150s target

Spec: MM1 · No calculator · ~150s

Write

x^2 + 6x + 5

in the form

(x + a)^2 + b

. What is the value of

b

Options

$b = 5$
$b = 9$
$b = 4$
$b = -4$
$b = -9$

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

Show solution

Halve the

x

-coefficient:

(x + 3)^2 = x^2 + 6x + 9

, so subtract

4

to recover

+5

. Hence

b = -4

Keep practising

Same topic · same level
P1MM1Level 1
TMUA-P1-MM1-002
Simplify 2^3 × 2^5/2^4.
Algebra and functions
Open TMUA-P1-MM1-002 →
Same trap: completing-the-square
P1MM8Level 2
TMUA-P1-MM8-019
What is the vertex of y = x^2 - 6x + 8?
Graphs of functions
Open TMUA-P1-MM8-019 →
Step up a 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 →

Browse more

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Keep practising

Same topic · same level

P1MM1Level 1

TMUA-P1-MM1-002

Simplify 2^3 × 2^5/2^4.

Algebra and functions

Open TMUA-P1-MM1-002 →

Same trap: completing-the-square

P1MM8Level 2

TMUA-P1-MM8-019

What is the vertex of y = x^2 - 6x + 8?

Graphs of functions

Open TMUA-P1-MM8-019 →

Step up a 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 →

TMUA-P1-MM1-005 — Paper P1 · Algebra and functions · Level 1

Options

Keep practising

Master Algebra and functions

TMUA-P1-MM1-005 — Paper P1 · Algebra and functions · Level 1

Options

Keep practising

Master Algebra and functions