Bookvise — Read deeply. Recall confidently.

Read with depth.
Recall with confidence.

Bookvise pairs beautifully structured eBooks with the practice that makes them stick — section notes, visual guides, flashcards, quizzes, and timed mock tests, all in one focused study space.

Notes

Section-by-section, ready to re-read.

Hierarchical, annotated notes with definitions, key insights, and pull-out diagrams. Highlighted phrases mark exactly what to recall.

Concept-by-concept structure
Key terms ready to revisit
Quick Revision Sheets for the night before

Illustrations

Diagrams that respond.

Subject-tuned figures live next to the lesson. Many are interactive — morph a graph between functions, drop a ball under gravity, fire α-particles at a gold foil, peel a virus down to bare RNA.

Inline, captioned, citable
Interactive figures where it matters
Step-by-step callout layers

Questions

Practice that sits next to the lesson.

Multiple-choice questions live inside each section, with explained answers. Wrong picks feed straight into your revision deck.

In-section MCQs with full approach
Curated practice sets, by topic
Printable papers for offline study

Flashcards

Cloze recall, on a steady schedule.

Bookvise flashcards aren't front-and-back trivia. They're cloze cards — a sentence with the key phrase blurred out. Tap to recall.

Tap any blurred phrase, in context
Spaced repetition across all books
Streaks & due-today nudges

1 Function as a special relation

A function f: A → B is a relation that pairs every input with exactly one output — no input skipped, none mapped twice. The allowed inputs form its domain; the values it actually produces form its range. When both live inside the reals ℝ, it's a real function — the workhorse of all calculus.

Key insight

A relation breaks the function rule in only two ways — an input with more than one image, or an input with no image at all.

Real function

A function whose domain and range both lie inside ℝ. If only the range sits in ℝ, it is merely real-valued.

Image / preimage — if f(a) = b, then b is the image of a, and a a preimage of b.
Domain rule — every element of A must be paired; the domain is all of A.
Range ⊆ codomain — f(x) = x² maps ℝ → ℝ but only reaches [0, ∞).

2 Domain, range & codomain

For f: A → B, the domain is A (every input), the codomain is the declared target set B, and the range is what f actually hits — { f(x) : x ∈ A }. The range can be a strict subset of the codomain.

Range vs codomain

The codomain is the set outputs are promised to land in; the range is the set they actually reach — always range ⊆ codomain.

Domain — every allowed input; for 1/x it is ℝ−{0}.
Range — for f(x) = x² it is [0, ∞), not all of ℝ.
Real function — domain and range both ⊆ ℝ.

3 Standard real functions

A handful of named functions recur everywhere, each with a signature graph you learn to read at a glance — try morphing between them in Illustrations.

Five to know by shape

Identity f(x) = x — a line through the origin · Square f(x) = x² — an upward parabola · Modulus f(x) = |x| — a V at the origin · Reciprocal f(x) = 1/x — a two-branch hyperbola · Greatest integer [x] — a staircase.

1 Acceleration & motion under gravity

Velocity rarely stays fixed — acceleration is how fast it changes, a = Δv/Δt. Galileo saw that in free fall every object gains the same velocity each second (≈ 9.8 m/s), not per metre. Fix a sign convention and gravity becomes one constant acceleration a = −g — on the way up, at the peak, and on the way down.

Key insight

Whether you speed up or slow down depends on the directions of v and a — same sign speeds up, opposite slows down. The sign of a alone tells you nothing.

Acceleration

The rate of change of velocity with time — the slope of the velocity–time graph.

SI unit — m/s² (metre per second, per second).
Constant a — makes v = u + at and s = ut + ½at² valid.
Free fall — a = −g ≈ −9.8 m/s², independent of mass.

2 Equations of uniformly accelerated motion

When acceleration is constant, three equations tie together initial velocity u, final velocity v, acceleration a, time t and displacement s — no calculus required.

v = u + at

s = ut + ½at²

v² = u² + 2as

When they apply

Only while a stays uniform along a straight line. The moment acceleration changes, split the motion into intervals where a is constant.

3 Free fall & sign conventions

In free fall the only acceleration is gravity, g ≈ 9.8 m/s² — the same for a feather and a hammer in vacuum. Pick "up" as positive and gravity reads a = −g for the whole flight.

Free fall

Motion under gravity alone, air resistance neglected — independent of the object's mass.

At release — u = 0, then speed v = gt downward.
At the top of a throw — v = 0, yet a is still −g.
Galileo's odd-number rule — distances in equal times go 1 : 3 : 5 : 7 …

1 Rutherford's nuclear model

In 1911 Geiger and Marsden fired α-particles at a thin gold foil (~100 nm). Almost all passed straight through, a few bent slightly, and about 1 in 20,000 bounced back near 180°. Rutherford concluded the atom is mostly empty space with a tiny, dense, positive nucleus — ending Thomson's uniform "plum-pudding" sphere.

Key insight

Most α-particles sail straight through, so the atom is overwhelmingly empty space — only the rare back-scatter reveals the tiny nucleus.

Nucleus

The tiny central core (radius ~10⁻¹⁵ m) holding all the positive charge and nearly all the mass of the atom.

Tiny — ~10⁻⁵ of the atom's radius: a cricket ball in a 5 km stadium.
Dense & massive — carries almost the entire atomic mass.
Positive — electrons are held in orbit by Coulomb attraction.

2 The gold-foil experiment

A radium source fires α-particles through a collimator at a foil only a few hundred atoms thick; a movable ZnS screen flashes wherever each particle lands, so every scattering angle can be counted.

Three observations

Most pass straight through → the atom is mostly empty · Some deflect at small angles → a concentrated positive charge · ~1 in 20,000 rebound near 180° → that charge sits in a tiny, massive core.

3 From Thomson to Rutherford

Thomson pictured the atom as a "plum pudding" — electrons dotted through a uniform sphere of positive charge. That model predicts only gentle deflections, so the rare back-scatter disproved it outright.

What replaced it

A planetary atom — a tiny, dense, positive nucleus at the centre with electrons revolving around it, held by electrostatic (Coulomb) attraction.

1 Viruses, viroids & prions

Some infectious agents refuse the five-kingdom system. A virus is a non-cellular particle — a protein coat around either RNA or DNA, never both — inert and crystallisable outside a host, yet able to hijack a cell inside. Strip the coat and you get a viroid (naked RNA); keep only a misfolded protein and you get a prion.

Key insight

A virus carries RNA or DNA — never both. It sits right on the boundary between living and non-living.

Virus

An acellular, obligate intracellular parasite — a capsid (protein coat of capsomere subunits) enclosing one core of RNA or DNA.

Outside a host — an inert, crystallisable particle with no metabolism.
Capsid shape — helical (TMV) or polyhedral (bacteriophage).
Classification — excluded from all five kingdoms.

2 Structure of a virus

A virus is a nucleoprotein particle: a genome of RNA or DNA wrapped in a capsid built from repeating protein subunits called capsomeres. The capsid's geometry gives the virus its shape.

Capsid

The protein coat of a virus, assembled from capsomere subunits, that protects and packages the nucleic acid.

Helical — rod-shaped, as in tobacco mosaic virus (TMV).
Polyhedral — many-sided, as in a bacteriophage head.
Genome — RNA or DNA, single- or double-stranded, but never both.

3 Viroids, prions & lichens

Below viruses sit even simpler agents: a viroid is free, low-molecular-weight RNA with no coat, and a prion is an infectious misfolded protein with no genome at all. Lichens go the other way — a partnership of two organisms.

Lichen — a symbiosis

An intimate association of an alga and a fungus: the alga photosynthesises food while the fungus supplies shelter, water and minerals — together they pioneer bare rock and signal clean air.