Why isn't the answer to TMUA-P1-MM8-012 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-012 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-012?

No — calculators are banned in the TMUA. TMUA-P1-MM8-012 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-MM8-012?

TMUA-P1-MM8-012 is Paper P1 · Graphs of functions (specification code MM8), level 1. Drill more of the same topic from this page.

TMUA-P1-MM8-012 — Paper P1 · Graphs of functions · Level 1

P1MM8Level 1~150s target

Spec: MM8 · No calculator · ~150s

What is the vertex of the graph

y = x^2 + 3

Options

$(0, 3)$
$(3, 0)$
$(0, -3)$
$(-3, 0)$

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: quadratic-vertex, graph-translation. Name the trap first, work the stem by hand, then open the solution below.

Show solution

x^2 \geq 0

with equality at

x = 0

, so the lowest point is

(0, 3)

and the correct is A. Trap:

(3, 0)

swaps the roles of

x

and

y

Keep practising

Same topic · same level
P1MM8Level 1
TMUA-P1-MM8-001
The line y = 2x + 3 crosses the y -axis at which point?
Graphs of functions
Open TMUA-P1-MM8-001 →
Same trap: graph-translation
P1MM8Level 2
TMUA-P1-MM8-004
How is the graph of y = f(x) + 2 obtained from the graph of y = f(x)?
Graphs of functions
Open TMUA-P1-MM8-004 →
Step up a level
P1MM8Level 2
TMUA-P1-MM8-005
Let f(x) = 2x + 1 and g(x) = x^2. What is the value of f(g(3))?
Graphs of functions
Open TMUA-P1-MM8-005 →

Browse more

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Keep practising

Same topic · same level

P1MM8Level 1

TMUA-P1-MM8-001

The line y = 2x + 3 crosses the y -axis at which point?

Graphs of functions

Open TMUA-P1-MM8-001 →

Same trap: graph-translation

P1MM8Level 2

TMUA-P1-MM8-004

How is the graph of y = f(x) + 2 obtained from the graph of y = f(x)?

Graphs of functions

Open TMUA-P1-MM8-004 →

Step up a level

P1MM8Level 2

TMUA-P1-MM8-005

Let f(x) = 2x + 1 and g(x) = x^2. What is the value of f(g(3))?

Graphs of functions

Open TMUA-P1-MM8-005 →

TMUA-P1-MM8-012 — Paper P1 · Graphs of functions · Level 1

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-012 — Paper P1 · Graphs of functions · Level 1

Options

Keep practising

Master Graphs of functions