Comprehensive Revision Notes on General Mathematics, Literature-in-English, and Visual Arts

Number Bases and Modular Arithmetic

• Number Base System: Represents numbers using specific sets of digits; a base must always be strictly greater than every digit appearing in the number.

  • Base 2 (Binary): Uses digits $0$ and $1$.

  • Base 5 (Quinary): Uses digits $0, 1, 2, 3, 4$.

  • Base 8 (Octal): Uses digits $0$ through $7$.

  • Base 10 (Decimal): Uses digits $0$ through $9$.

• Base Conversions:

  • Other Bases to Base 10: Multiply each digit by its place value ($\text{base}^n$) and sum the terms.

  • Base 10 to Another Base: Divide repeatedly by the new base and read remainders from bottom to top.

  • Fractions to Another Base: Multiply the fractional part repeatedly by the target base and record whole-number parts from top to bottom.

• Base Operations: Carry when digits sum to or exceed the base value; borrow units valued at the base itself rather than $10$.

• Modular Arithmetic: Evaluates remainders following division by a modulus $n$.

  • Addition and Subtraction: Perform the standard arithmetic operation, then compute the non-negative remainder modulo $n$.

  • Modular Division: Multiply the numerator by the modular multiplicative inverse of the denominator ($a \times a^{-1} \ne 0 \text{ mod } n$ where a \times a^{-1} \buildrel n \to \bmod \buildrel \to 1).

Approximation and Indices

• Rounding Off: Inspect the checking digit directly to the right of the target place value; round up if $5$-$9$, or round down (keep unchanged and replace subsequent digits with zeros) if $0$-$4$.

• Error Calculations:

  • Absolute Error: $|\text{Actual value} - \text{Approximate value}|$

  • Percentage Error: $\frac{|\text{Actual value} - \text{Approximate value}|}{\text{Actual value}} \times 100\%$

• Laws of Indices:

  • Multiplication: $a^m \times a^n = a^{m+n}$

  • Division: $a^m \div a^n = a^{m-n}$

  • Power of a Power: $(a^m)^n = a^{mn}$

  • Power of a Product: $(ab)^n = a^n b^n$

  • Zero Index: $a^0 = 1$ where $a \neq 0$

  • Negative Index: $a^{-n} = \frac{1}{a^n}$

  • Fractional Indices: $a^{1/n} = \sqrt[n]{a}$ and $a^{m/n} = (\sqrt[n]{a})^m$

Fundamentals of Literature and Literary Genres

• Definition and Scope: Literature is the artistic expression of human experiences, ideas, feelings, and imagination through spoken or written words across culture, politics, religion, society, conflict, and human behaviour.

• Categories: Oral (passed by word of mouth), written (recorded text), and traditional (inherited communal works).

• Core Literary Genres:

  • Prose: Written in continuous sentences and paragraphs (e.g., novels, novellas, short stories, biographies).

  • Drama: Composed primarily of dialogue and stage directions for performance by actors before an audience (e.g., tragedy, comedy, tragicomedy).

  • Poetry: Formatted into lines and stanzas using concentrated language, rhythm, sound devices, and imagery (e.g., sonnets, odes, elegies, ballads).

• Oral Literature: Transmitted intergenerationally by spoken word; includes folktales, myths, legends, proverbs, riddles, praise poetry, and traditional songs.

• Functions of Literature: Entertainment, education, instruction, reflection of society, cultural preservation, moral correction, social awareness, inspiration, and catharsis (the purging or release of strong emotions in drama/tragedy).

Poetic Forms, Stanzas, and Devices

• Stanza Classification by Line Count:

  • Monostich: $1$ line

  • Couplet: $2$ lines

  • Tercet: $3$ lines

  • Quatrain: $4$ lines

  • Quintain: $5$ lines

  • Sestet: $6$ lines

  • Septet: $7$ lines

  • Octave: $8$ lines

• Poetic Forms:

  • Sonnet: $14$-line poem with regular metre.

  • Shakespearean Sonnet: Consists of $3$ quatrains and $1$ final couplet with the rhyme scheme $\text{ABAB CDCD EFEF GG}$.

  • Ode: Expresses praise or deep emotion toward a subject.

  • Elegy: Mournful poem lamenting death or loss.

  • Epic: Extended narrative poem depicting heroic exploits.

  • Ballad: Song-like narrative poem.

  • Lyric: Expresses individual thoughts and emotions.

  • Limerick: Five-line humorous poem.

• Figurative Language & Devices:

  • Simile: Comparison using "like" or "as".

  • Metaphor: Direct figurative equation of one thing with another.

  • Personification: Attributing human traits to inanimate objects or non-human entities.

  • Hyperbole: Purposeful exaggeration for effect.

  • Onomatopoeia: Words that imitate sound.

  • Oxymoron: Combination of contradictory terms side by side.

  • Irony: Contrast between expectations and reality.

  • Euphemism: Substituting a mild term for a harsh one.

  • Pun: Wordplay exploiting multiple meanings or homophones.

  • Sound Devices: Alliteration (initial consonant sounds), Assonance (vowel sounds), Consonance (consonant sounds within words), and Rhyme.

  • Narrative Devices: Foreshadowing, Flashback, Imagery, Diction, Tone, and Mood.

Visual Arts Elements, Principles, and Challenges

• Visual Arts: Art forms appreciated predominantly through vision (e.g., drawing, painting, sculpture, ceramics, textiles, printmaking, photography, graphics).

• Elements of Art: Line, Shape (2D), Form (3D), Colour, Texture (tactile/visual surface quality), Space, and Value (lightness or darkness).

• Principles of Design: Balance, Contrast, Emphasis, Rhythm, Pattern, Unity, Proportion, and Movement.

• Systemic Challenges: High cost or scarcity of materials, inadequate funding, substandard studio facilities, deficient professional training, weak market patronage, copyright infringement, poor conservation/preservation, limited exhibition exposure, and low public appreciation.

Colour Theory and Nigerian Art Evolution

• Colour Classifications (RYB Model):

  • Primary Colours: Red, yellow, blue.

  • Secondary Colours: Formed by mixing two primaries: Orange ($\text{Red} + \text{Yellow}$), Green ($\text{Yellow} + \text{Blue}$), Violet/Purple ($\text{Blue} + \text{Red}$).

  • Tertiary Colours: Mixture of an adjacent primary and secondary colour.

  • Temperature: Warm colours (red, orange, yellow) evoke excitement/energy; cool colours (blue, green, violet) evoke calmness/distance.

  • Complementary Colours: Pairs located opposite each other on the colour wheel (Red/Green, Blue/Orange, Yellow/Violet).

  • Colour Properties: Hue (colour name), Tint (hue + white), Shade (hue + black), Tone (hue + grey), Intensity (brightness/saturation).

• Traditional Nigerian Art: Deeply tied to religion, rulership, ceremonies, and utility; utilizes indigenous media.

  • Nok: Terracotta sculptures.

  • Benin: Bronze and brass castings.

  • Ife: Naturalistic sculptures.

  • Igbo: Mask traditions and wood carvings.

• Modern Nigerian Art: Integrates ancestral traditions with Western academic methods and contemporary techniques.

  • Aina Onabolu: Pioneer of modern Nigerian painting and Western-style portraiture.

  • Ben Enwonwu: Prominent modernist painter and sculptor addressing cultural identity.

  • Uche Okeke: Pioneer who integrated traditional Igbo aesthetics into modern art.

  • Bruce Onobrakpeya: Pioneer of printmaking and experimental mixed-media techniques.