Hong Kong Secondary School STEM Specialist

Hi, I'm Gary.

I am a F4 student passionate about pure & applied mathematics and empirical natural sciences.

Hover over "I am a F4 student" above to see continuous color shift!

Welcome to my portfolio! I specialize in Mathematics Extended Part 2 (M2)—focusing on calculus and algebra—while actively pursuing rigorous study in Physics, Biology, and Chemistry.

Explore M2 Mathematics View Sciences (Phys/Bio/Chem)

∫dx

Focus

Math M2

Science 1

Physics

Science 2

Biology

Science 3

Chemistry

HKDSE Module Spotlight

Mathematics Extended Part 2 (M2)

Advanced HKDSE Mathematics syllabus combining rigorous differential & integral calculus, matrix transformations, spatial 3D vectors, and mathematical induction.

Syllabus: Calculus & Algebra

$\frac{d}{dx}$

Calculus

Limits, derivative first principles, product/quotient/chain rules, implicit differentiation, curve sketching, and integration by substitution.

$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$

$\mathbf{A}^{-1}$

Matrices & Determinants

Matrix multiplication, determinant calculation, matrix inversion via adjugate, and solving systems of linear equations using Cramer's Rule.

$$\det(\mathbf{A}) = ad - bc$$

$\vec{u} \cdot \vec{v}$

3D Vectors

Scalar dot products, vector cross products, projections, vector equations of lines and planes in 3D space.

$$\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \, \hat{n}$$

$\sum k^2$

Induction & Binomial

Proving mathematical propositions for $n \in \mathbb{N}$ via inductive steps, alongside general binomial series expansion.

$$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$

Interactive M2 Calculus Canvas

Live Function & Tangent Line Explorer

Select a function $f(x)$ and drag the slider to observe the moving tangent line, instantaneous slope $f'(x)$, and derivative curve in real time.

Select M2 Target Function $f(x)$:

Tangent Point Evaluation ($x_0$): x₀ = 1.00

Position $x_0$:

1.000

Function Value $f(x_0)$:

0.841

Tangent Slope $f'(x_0)$:

0.540

Gary's Natural Sciences Portfolio

Physics, Biology & Chemistry

Beyond mathematics, Gary actively explores physical mechanics, cellular biology, and chemical thermodynamics. Click any card below to launch interactive lab drawers!

Physics

Investigating Newton's laws of motion, wave optics, energy transformations, and electromagnetism with mathematical rigor.

Kinematics & Projectile Motion

Refraction, Diffraction & Wave Mechanics

Circuits, Voltage & Magnetic Induction

$$F = ma \quad | \quad v = f\lambda \quad | \quad E = mc^2$$

Biology

Diving into molecular genetics, enzyme kinetics, cellular respiration, human physiology, and ecosystems.

DNA Transcription & Translation

Enzyme Catalysis & Substrate Binding

Cellular ATP Synthesis & Photosynthesis

$$\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{ATP}$$

Chemistry

Understanding atomic structures, chemical equilibrium, acid-base stoichiometry, redox, and organic functional groups.

Ideal Gas State ($PV = nRT$)

Thermodynamics & Enthalpy ($\Delta G$)

Organic Reactions & Functional Groups

$$PV = nRT \quad | \quad \Delta G = \Delta H - T\Delta S$$

Get in Touch with Gary

Have questions about Form 4 M2 Mathematics, physics problem-solving, or STEM collaboration? Send me a message!