Скачать или смотреть The Modulus Function (Q12 A2 P2 Edexcel 2025)

In this video, Lee Guffick (former Head of Maths and A-Level Examiner) works through Question 12 from A-Level Maths Paper 2 (Edexcel 2025) — a classic modulus graph and composite function question that frequently appears in the final few marks of the paper.

Lee explains how to handle modulus expressions such as
𝑓
(
𝑥
)
=
4
∣
𝑥
−
3
∣
−
5
f(x)=4∣x−3∣−5, find
𝑓
(
𝑎
)
f(a) given
∣
𝑎
∣
=
1
∣a∣=1, determine the range of composite functions like
𝑔
(
𝑓
(
𝑥
)
)
=
2
𝑥
+
17
g(f(x))=2x+17, and explore conditions under which no solutions exist for equations involving gradients (e.g.
𝑓
(
𝑥
)
=
ℎ
(
𝑥
)
f(x)=h(x)).

If you’re preparing for the A2 Edexcel Maths exam, this video is ideal for mastering graph transformations, modulus inequalities, and intersection logic — all common areas where students lose marks.

⏱️ TIMESTAMPS:
00:00 Introduction & question setup
00:30 Evaluating
𝑓
(
𝑎
)
f(a) for
𝑎
=
1
a=1 and
𝑎
=
−
1
a=−1
01:10 Sketching
𝑦
=
4
∣
𝑥
−
3
∣
−
5
y=4∣x−3∣−5 and finding the vertex
01:50 Determining the minimum value of
𝑓
(
𝑥
)
f(x)
02:20 Substituting into
𝑔
(
𝑓
(
𝑥
)
)
=
2
𝑥
+
17
g(f(x))=2x+17 to find the range
03:00 Understanding composite function transformations
03:40 Setting up
𝑓
(
𝑥
)
=
ℎ
(
𝑥
)
=
𝑘
𝑥
f(x)=h(x)=kx and interpreting intersection conditions
05:00 Linking gradient values (
𝑘
k) to solution existence
06:10 Finding the range of
𝑘
k for which there are no solutions
07:10 Examiner insights & how to avoid common errors

✏️ TOPICS COVERED:

Modulus graphs and vertex identification

Evaluating modulus expressions at positive and negative values

Composite functions and range determination

Gradient and intersection analysis

Range of
𝑘
k for no solutions to
𝑓
(
𝑥
)
=
ℎ
(
𝑥
)
f(x)=h(x)

Visual reasoning with transformations of straight lines

💯 EXAM TIPS:

For
𝑓
(
𝑥
)
=
𝑎
∣
𝑥
−
𝑏
∣
+
𝑐
f(x)=a∣x−b∣+c, the vertex is at
(
𝑏
,
𝑐
)
(b,c).

Remember that
∣
𝑎
∣
=
1
∣a∣=1 gives two possible inputs,
𝑎
=
1
a=1 and
𝑎
=
−
1
a=−1.

When working with
𝑔
(
𝑓
(
𝑥
)
)
g(f(x)), always find the range of
𝑓
(
𝑥
)
f(x) first.

The modulus graph has two linear sections: gradients
+
𝑎
+a and
−
𝑎
−a. Use these when comparing to
ℎ
(
𝑥
)
=
𝑘
𝑥
h(x)=kx.

Watch for exam traps involving "no solutions" — this often relates to gradient boundaries.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner who helps ambitious students achieve A/A grades* and secure places at top universities including Oxford, Cambridge and the Ivy League. His channel features full Edexcel paper walkthroughs, topic tutorials, and expert revision strategies designed for top-grade success.

📅 JOIN OUR PROGRAMME:
→ Personalised 1:1 tutoring: https://www.gufficktuition.com/tutoring

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📱 CONNECT WITH US:
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→ Email: [email protected]

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