Practices By Topics (Grade 5 to 12, IB / AP)

We are currently testing our new practices! Notice a mistake? Let Gordon know at Virtuoso Studio (WhatsApp: 437-248-0882).

練習內容更新中,目前正進行測試。若有發現錯誤,請傳 WhatsApp 給 Virtuoso Studio 的 Gordon (437-248-0882)。

练习内容更新中,目前正进行测试。若有发现错误,请传 WhatsApp 给 Virtuoso Studio 的 Gordon (437-248-0882)。


These drills target the core quantitative skills necessary for any technical field. 

這些練習針對任何技術領域所需的核心技能。

这些练习针对任何技术领域所需的核心技能。


These drills emphasize quality over quantity, focusing on the core, essential skills learners will need for the rest of their lives. In fact, the word 'math' originally stems from the Greek root meaning 'basic knowledge' or 'learning'—it isn't just about arithmetic and counting, but about mastering the fundamental thinking skills everyone needs to thrive.

這些訓練強調質大於量,專注於學習者終生受核心與關鍵技能。事實上,『數學』一詞最初源於希臘語詞根,意指『基礎知識』或『學習』——它不僅僅關乎算術和計數,更是關於掌握每個人在人生中茁壯成長所需的根本思維能力。

这些训练强调质大于量,专注于学习者终生受益的核心与关键技能。事实上,‘数学’一词最初源于希腊语词根,意指‘基础知识’或‘学习’——它不仅限于算术和计数,更是关于掌握每个人在人生中茁壮成长所需的根本思维能力。


Level 1 - Computational Skill   計算能力.   计算能力


Grade 5 - 8

Fraction ** 

Percents ** 

Ratios & Proportions ** 

Scientific Notation **

Exponents ** 

Solving Linear Equations **

Areas and Volumes **

Financial Literacy, Simple and Compound Interest** 

Angles Facts in Different Geometric Setup **

*** Problem Solving (where Algebra helps) **** VERY IMPORTANT! Its the basis of everything for life !!!!  ***


Level 2 - Mathematical Structures   數學結構.   数学结构


Grade 9 - The Function Framework is very Simple to understand but Powerful, however, not understanding it will cause a lot of confusion in all topics that follows, below are two different ways to understand the concept of a function

in terms of calculational procedure, there is very little difference between Grade 8 and Gra

*** Function - The most important mathematical model ** 

*** Function - The Machine View and the Graph View *** 


Grade 10 - Financial Mathematics

Grade 10 - Arithmetic, Geometric Sequences and Series, and Financial Mathematics (with Multiple Cashflows) *** 


Grade 10 - 

Advanced Computation Techniques: Solving System of Equations, Quadratic Models and Trigonometry (Triangle Sides - Angle Relationship)

Grade 10 - Solving System of Equations ** 

Grade 10 - Introduction to Right Triangle and Acute Triangle Trigonometry ** 

Grade 10 - Quadratic Functions and Equations **


Level 3 - Mathematical Models   數學模型   数学模型


Grade 11 - Towards a general Framework for Mathematical Models

Grade 11 - Sinusoidal Functions and Sketching It  **

Grade 11 - Transformation of Functions ** 


Grade 12 - Towards realistic mathematical models

Grade 12 - Average Rate of Change to Instantaneous Rate of Change, the Derivative and Linear Approximation (Equation of Tangent Line) **


Level 4 - Deeper Understanding   深層理解   深层理解


Concepts IB/AP Students Must Know - Connections between Concepts and Special Models

IB/AP: *** Back to Basic: Understanding the Structure behind the Graphs of Functions / Equations" *** 

IB/AP: Estimating Values of Functions (That maynot have a formula) using Taylor Series **

IB/AP: Passage from Discrete to Continuous Growth **



Level 5 - Polymathic (Interdisciplinary) Fields   跨學科範疇   跨学科范畴


Sound & Music **