IB MYP Year 9 Maths Surds – Criterion A Higher Level Practice Workbook
IB MYP Year 9 Maths Surds – Criterion A Higher Level Practice Workbook
IB MYP MYP 3 • Criterion A: Knowing & Understanding • Higher Level • 82 Marks • 75 Minutes
📘 Digital Maths Practice Workbook
Build confidence with surds through structured revision, worked examples, familiar practice and challenging Level 7–8 problems designed around IB MYP Mathematics Criterion A.
Learn Surds. Understand the Methods. Then Challenge Yourself.
Surds can begin with simple skills such as simplifying square roots, but higher-level mathematics requires students to understand which method to use, apply it accurately and solve unfamiliar problems.
This IB MYP Year 9 Maths Surds Criterion A Practice Workbook has been designed to develop exactly those skills.
Created for IB MYP Year 9 / MYP 3 Higher Level Mathematics, the workbook combines Criterion A guidance, a complete surds revision toolkit, worked examples, differentiated practice and challenging unfamiliar problems.
Students progress from familiar surd techniques towards more demanding applications involving rationalising denominators, surd equations, nested surds, geometry and indices.
🎯 Criterion A Focus
Practise Knowing & Understanding through familiar and unfamiliar mathematical situations.
📈 Levels 3–8
Progress from foundational practice to challenging Level 7–8 surd problems.
🧠 Higher-Level Thinking
Develop the ability to recognise and select an appropriate mathematical method.
✏️ 82 Marks
Complete 82 marks of structured surds practice across two sections.
Created Specifically Around IB MYP Criterion A
This workbook does not simply place the words “Criterion A” on the cover. Criterion A is built into the structure of the resource.
Students are introduced to the three key strands of Knowing & Understanding:
- Select appropriate mathematics when solving problems in familiar and unfamiliar situations.
- Apply the selected mathematics successfully when solving problems.
- Solve problems correctly in a variety of contexts.
The workbook then shows students what increasing levels of mathematical sophistication can look like specifically when working with surds.
Understand the Difference Between Familiar and Unfamiliar Problems
A major feature of this workbook is the progression from routine mathematical skills to unfamiliar problem-solving.
Section 1
Familiar Problems
Levels 3–6
42 marks
Build fluency with the core surd techniques students are expected to know and apply accurately.
Section 2
Unfamiliar & Challenging Problems
Levels 5–8
40 marks
Students must decide which mathematical method is appropriate rather than simply following a familiar pattern.
Total: 82 marks
This structure helps students identify whether their difficulty comes from basic technique, multi-step application or selecting a method for an unfamiliar problem.
What's Inside the Surds Workbook?
1. Criterion A Guidance
Understand what Knowing & Understanding means and how mathematical work develops across MYP achievement levels.
2. Surds Toolkit
Review the essential rules and techniques needed to work confidently with surds.
3. Worked Examples
Study higher-level examples showing how to select, apply and check an appropriate method.
4. Familiar Practice
Strengthen core skills through structured Levels 3–6 questions.
5. Unfamiliar Challenges
Apply surd knowledge to challenging Level 7–8 problems where the method is not immediately obvious.
6. Self-Assessment
Use the final revision checklist to identify skills that need further practice.
Complete Surds Revision Toolkit
The workbook includes a dedicated reference section covering the key techniques students need for Year 9 surds.
- Simplifying surds using the largest square factor
- Adding and subtracting like surds
- Multiplying surds
- Dividing surds
- Working with coefficients and surds
- Squares of surds
- Rationalising single-term denominators
- Using conjugate pairs
- Rationalising binomial denominators
- Working with perfect-square expressions
- Connecting surds with index notation
The resource also emphasises fully simplifying a surd by looking for the largest square factor, rather than stopping after a partial simplification.
Master the Core Surd Skills
Simplifying Surds
Students practise reducing irrational roots into their simplest exact form and learn to continue simplifying until no square factor remains.
Adding, Subtracting, Multiplying & Dividing
Students develop fluency with operations involving surds, coefficients and powers, while learning to simplify expressions completely.
Expanding Brackets with Surds
The workbook progresses into algebraic manipulation involving single brackets, double brackets and more advanced expressions involving surds.
Rationalising Denominators
Students learn how to rationalise denominators involving:
- √a
- a ± √b
- √a ± √b
- Binomial denominators
- More challenging multi-term denominators
The workbook explains the role of conjugates and why the technique removes the surd from the denominator.
Worked Examples for Higher-Level Thinking
The workbook includes Level 7–8 worked examples designed to model the thinking expected in Criterion A.
Students are encouraged to:
Select
Identify which mathematical method is appropriate for the problem.
Apply
Carry out the mathematical process accurately and systematically.
Check
Use estimation or another method to check whether the exact answer is reasonable.
Examples include rationalising a binomial denominator using its conjugate and solving an equation involving a surd coefficient.
Challenge Yourself with Level 7–8 Surds
The second section moves beyond typical textbook-style exercises.
Students are told that these problems are unfamiliar and challenging and must determine the method themselves.
Challenge problems include:
- Showing that a complicated surd expression is an integer
- Using reciprocal relationships involving surds
- Solving equations with surd coefficients
- Simplifying nested surds
- Rationalising more challenging denominators
- Applying surds to geometry
- Comparing surds without a calculator
- Connecting surds with indices
Nested Surds – Higher-Level Challenge
The workbook goes beyond routine surd manipulation with problems involving expressions such as √(p + q√r).
Students investigate how perfect-square structures can be used to simplify nested radicals and must recognise the underlying algebraic relationship rather than simply apply a memorised rule.
This helps develop the transition from knowing a technique to recognising when that technique is useful.
Surds Applied to Geometry
Surds are also connected to geometry through an unfamiliar right-angled triangle problem.
The shorter sides are given as (2 + √3) cm and (2 − √3) cm, requiring students to determine an exact hypotenuse and show that the area is exactly ½ cm².
This is an excellent example of applying surd knowledge in a context where the question is not simply labelled as a surd exercise.
Surds and Indices
The workbook also connects surds with index notation.
Students practise moving between surd and index forms and apply this relationship to exact calculations and equations.
The higher-level section includes problems involving powers of 2 and 3, exponential equations and exact evaluation of expressions containing roots.
Self-Assessment & Revision Checklist
The workbook finishes with a dedicated checklist so students can identify which skills they have mastered and which areas need further revision.
Students can check whether they can:
- Simplify any surd using the largest square factor.
- Collect like surds after simplifying them.
- Multiply and divide surds, including coefficients and powers.
- Expand brackets containing surds.
- Rationalise different types of denominators.
- Rationalise a three-term denominator in two steps.
- Solve linear equations involving surd coefficients.
- Simplify nested surds.
- Convert between surd form and index form.
- Check exact answers using a decimal estimate.
This creates a practical revision cycle:
Learn → Practise → Assess → Identify Gaps → Revise → Reattempt
Who Is This Workbook For?
IB MYP Year 9 / MYP 3 Students
Designed specifically for students studying Year 9 Higher Level Mathematics within the IB MYP framework.
Students Preparing for Criterion A
Useful for practising Knowing & Understanding through both familiar and unfamiliar mathematical situations.
Students Targeting Levels 7–8
Includes challenging problems requiring students to select and apply methods independently.
Parents & Tutors
A structured resource combining explanation, examples, practice and self-assessment in one workbook.
Workbook Details
| Curriculum | IB MYP Mathematics |
|---|---|
| Year Level | Year 9 / MYP 3 |
| Level | Higher Level |
| Criterion | A – Knowing & Understanding |
| Unit | Game Graphics — Indices, Roots & Surds |
| Subject Area | Number / Algebra |
| Total Marks | 82 |
| Suggested Time | 75 minutes |
| Calculator | No calculator unless instructed otherwise |
| Format | Digital PDF Workbook |
What's Included?
✓ Criterion A Guidance
Student-friendly explanation of Knowing & Understanding and the progression towards higher achievement levels.
✓ Surds Toolkit
Essential rules, formulae and techniques for Year 9 surds.
✓ Worked Examples
Higher-level examples demonstrating method selection, application and checking.
✓ 82 Marks of Practice
Familiar and unfamiliar questions covering Levels 3–8.
✓ Level 7–8 Challenges
Nested surds, equations, rationalisation, geometry and indices.
✓ Self-Assessment Checklist
A practical revision tool for identifying strengths and areas for improvement.
Important Note
This resource is designed for IB MYP Mathematics Year 9 / MYP 3 and focuses specifically on Criterion A: Knowing & Understanding. The student-friendly Criterion A descriptions are paraphrased within the workbook; teachers should use the official IB MYP descriptors when making formal achievement judgements.
This is a practice and revision workbook, not an official IB assessment paper.