0001-BASIC-MATHEMATICS-F2-SUMMARY

Objectives: 0001-BASIC-MATHEMATICS-F2-SUMMARY

Table of Contents
Table of Contents

Acknowledgments v

Preface vi

Chapter One   Exponents and Radicals 1
Exponents 1
Radicals 21
Rationalising the denominator 34
Transposition of formulae 41
Chapter summary 46
Revision exercise 1 47
Chapter Two   Algebra 49
Binary operations 49
Brackets in computations 53
Quadratic expressions 72
Chapter summary 72
Revision exercise 2 73
Chapter Three   Quadratic equations 75
Solving quadratic equations 75
General formula for solving quadratic equations 96
Chapter summary 106
Revision exercise 3 107
Chapter Four   Logarithms 109
Standard form 109
Laws of logarithms 118
Table of common logarithms 128
Chapter summary 147
Revision exercise 4 148
Chapter Five   Congruence 152
Congruence of triangles 152
Postulates, proofs and theorems 153
Postulates for congruence 161
Chapter summary 180
Revision exercise 5 181
Chapter Six   Similarity 186
Similar figures 186
Similar triangles 191
Properties of similar triangles 206
Chapter summary 211
Revision exercise 6 213
Chapter Seven   Geometrical transformations 215
Reflection 215
Rotation 220
Translation 226
Enlargement 240
Combined transformation 252
Chapter summary 254
Revision exercise 7 254
Chapter Eight   Pythagoras’ theorem 256
Pythagoras’ theorem 256
Application of Pythagoras’ theorem 266
Chapter summary 270
Revision exercise 8 271
Chapter Nine   Trigonometry 273
Trigonometric ratios 273
Trigonometric ratios of special angles 282
Trigonometric tables 287
Angle of elevation and angle of depression 294
Chapter summary 298
Revision exercise 9 299
Chapter Ten   Sets 301
Description of sets 301
Types of sets 302
Operations with sets 307
Venn diagrams 314
Chapter summary 316
Revision exercise 10 327
Chapter Eleven   Statistics 330
Pictograms 330
Bar charts 332
Line graphs 336
Pie chart 339
Frequency distribution tables 343
Histograms 349
Frequency polygons 353
Cumulative frequency curves or Ogive 360
Chapter summary 367
Revision exercise 11 368

Answers to odd-numbered questions 371

Mathematical tables 424

Glossary 453

Bibliography 459

Index 460

Master Notes – Part 1 (No LaTeX)

Complete Secondary Math Notes – Part 1

English explanations • Swahili insights for complex ideas • Real-life examples • Practice checks

Chapter 1 — Exponents & Radicals
Exponents (Indices)

Core rules (for a ≠ 0):

  • Product rule: a^m * a^n = a^(m+n)
  • Quotient rule: a^m / a^n = a^(m-n)
  • Power to a power: (a^m)^n = a^(m*n)
  • Power of a product: (ab)^n = a^n * b^n
  • Zero exponent: a^0 = 1
  • Negative exponent: a^(-n) = 1 / a^n
  • Fractional exponent: a^(p/q) = qth-root(a^p) = (qth-root(a))^p, a ≥ 0 when q is even
Quick examples:
2^3 * 2^5 = 2^8 = 256
(3^2)^4 = 3^8 = 6561
10^(-3) = 1/1000 = 0.001
Swahili Insight: Kielezi (exponent) kinaonyesha mara ngapi namba inajizidisha. Mfano 5^3 = 5*5*5. Ukiona kielezi hasi kama 5^(-2), geuza kuwa 1/(5^2).
Scientific notation (standard form)

Write numbers as a × 10^n with 1 ≤ a < 10. Examples: 540000 = 5.4 × 10^5, 0.00054 = 5.4 × 10^(-4).

Radicals (Roots)

nth-root(a) is the number r such that r^n = a. Notation: sqrt(a) for square root, cbrt(a) for cube root.

Key facts
  • sqrt(ab) = sqrt(a) * sqrt(b) for a,b ≥ 0
  • sqrt(a/b) = sqrt(a) / sqrt(b), b ≠ 0
  • Simplify by factoring out perfect squares: sqrt(72) = sqrt(36*2) = 6*sqrt(2)
Rationalising denominators

Remove roots from denominators by multiplying by a helpful form.

5 / sqrt(3) = (5*sqrt(3)) / 3
1 / (2 + sqrt(3)) → multiply by (2 − sqrt(3)) top and bottom:
(2 − sqrt(3)) / ( (2+sqrt(3))*(2−sqrt(3)) ) = (2 − sqrt(3)) / (4 − 3) = 2 − sqrt(3)
Swahili Insight: “Kurationalisha” ni kuondoa mzizi chini ya mstari wa mgawanyiko. Tumia kiambatanishi (conjugate) kama (a + sqrt(b)) na (a − sqrt(b)).
Common mistakes: (a+b)^2 ≠ a^2 + b^2. Correct: a^2 + 2ab + b^2. Pia, sqrt(a+b) ≠ sqrt(a) + sqrt(b).
Practice: (i) Simplify sqrt(50). (ii) Rewrite 3/sqrt(5) with no root in the denominator. (iii) Evaluate (2^3 * 2^(-5))^2.
Chapter 2 — Algebra
Binary operations

A binary operation combines two items from a set to produce one item (e.g., a ★ b = a + 2b on integers).

  • Closure: result stays in the set (integers → integer?).
  • Associative: (a★b)★c = a★(b★c).
  • Identity e: a★e = a for all a.
  • Inverse: for each a, find a⁻¹ so that a★a⁻¹ = e.
Swahili Insight: Fikiria “sheria mpya ya kujumlisha.” Uliza: je, matokeo bado yako ndani ya kundi? Je, kuna kitambulishi (identity) na kinyume (inverse)?
Brackets, expansion, and simplification
  • (a + b)^2 = a^2 + 2ab + b^2
  • (a − b)^2 = a^2 − 2ab + b^2
  • (a + b)(a − b) = a^2 − b^2
  • Distribute carefully: k(a + b) = ka + kb
Example: (3x − 2)(x + 5) = 3x^2 + 15x − 2x − 10 = 3x^2 + 13x − 10.
Factorisation
  • Common factor: 6x^2 + 9x = 3x(2x + 3)
  • Perfect square: a^2 + 2ab + b^2 = (a + b)^2
  • Difference of squares: a^2 − b^2 = (a − b)(a + b)
  • Quadratic trinomials (ax^2 + bx + c): find p and q so that p*q = a*c and p + q = b; then regroup.
Factorise: (i) x^2 + 5x + 6 (ii) 4x^2 − 9 (iii) 6x^2 + 11x + 4.
Chapter 3 — Quadratic Equations
Standard form

ax^2 + bx + c = 0 where a ≠ 0.

3 main solving methods
  1. Factor & solve: if ax^2+bx+c factors, set each bracket = 0.
  2. Complete the square: move c, make the left side a perfect square by adding (b/2a)^2 to both sides, then take square roots.
  3. Quadratic formula: x = [−b ± sqrt(b^2 − 4ac)] / (2a).
Discriminant
  • D = b^2 − 4ac
  • D > 0 → two distinct real roots
  • D = 0 → one repeated real root
  • D < 0 → no real roots (complex)
Real-life: Height of a ball, h(t) = −5t^2 + 20t + 1 (meters). When does it hit the ground? Solve −5t^2 + 20t + 1 = 0 and keep the positive time.
Swahili Insight: “Kukamilisha mraba” hutumia kuongeza na kutoa (b/2a)^2 ili upande wa kushoto uwe kama (x + k)^2. Kisha chukua mizizi na kumbuka ishara ±.
Common traps: forgetting to divide by 2a in the formula; taking only the + root; or mixing signs when moving terms.
Solve: 2x^2 − 7x + 3 = 0. Decide the nature of roots of x^2 − 4x + 7 = 0 using D = b^2 − 4ac.
Chapter 4 — Logarithms
What a logarithm means

log_b(a) = c means “raise base b to power c to get a.” So b^c = a. Valid when b > 0 and b ≠ 1; a > 0.

Key log laws (b is the base)
  • log_b(xy) = log_b(x) + log_b(y)
  • log_b(x/y) = log_b(x) − log_b(y)
  • log_b(x^k) = k * log_b(x)
  • Change of base: log_b(a) = log_k(a) / log_k(b) (common choice k = 10 or e)
  • Inverse facts: b^(log_b(a)) = a and log_b(b^k) = k
Solving styles
  • Exponential equations: If numbers share a base, equate exponents. Else, take logs both sides and isolate the unknown.
  • Log equations: Combine logs using laws, convert to exponential form, solve, then check solutions keep arguments > 0.
Example 1 (exponential): 3^(2x−1) = 27 → 27 = 3^3 → 2x−1 = 3 → x = 2.
Example 2 (log): log(2x − 1) + log(3) = log(24) → log(3*(2x − 1)) = log(24) → 3(2x − 1) = 24 → x = 4 (valid since 2x − 1 > 0).
Swahili Insight: Tumia sheria “jumlisha kuwa kuzidisha” na “tofautisha kuwa kugawanya.” Ukimaliza, hakikisha kile kilicho ndani ya log kiko chanya (> 0) ili jibu liwe halali.
Mistake to avoid: log(x + y) ≠ log(x) + log(y). Hakuna sheria hiyo.
(i) Evaluate log_10(0.001). (ii) Solve 2^(x+1) = 5. (iii) Solve log_10(x−3) + log_10(2) = log_10(10).
Mastery Toolkit — Study & Problem Solving
How to master each topic
  • Summarize each rule in your own words; write two correct examples and one “trap” example.
  • Space practice: 10–20 mins daily beats 2 hours once a week.
  • Error log: record every mistake, why it happened, and the fix.
  • Teach a friend or “rubber duck” the process aloud; if you can explain, you own it.
Ushauri wa shuleni (Swahili): Fanya maswali machache kila siku. Andika “sababu ya kosa” kila mara unapokosea. Ukifundisha mwingine, utaelewa zaidi.
Answer-any-question checklist
  • Identify the form (e.g., “this is a quadratic” → pick method).
  • State the rule you will apply (out loud or in writing).
  • Show each algebra step; avoid jumping.
  • Finish with a unit or a reality check if it’s an application.
Chapter Two - Algebra

Chapter Two: Algebra

Algebra is a branch of mathematics that uses symbols (like x, y) to represent numbers. These symbols help us to form expressions and equations, making it easier to generalize mathematical rules.

Swahili: Algebra ni tawi la hisabati linalotumia alama (mfano x, y) kuwakilisha namba. Alama hizi hutumika kuunda misemo na milinganyo ili kurahisisha kanuni za hisabati.

1. Binary Operations

Binary operations are operations performed on two numbers, such as:

  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
Example: If a = 5 and b = 3, then:
  • a + b = 8
  • a - b = 2
  • a × b = 15
  • a ÷ b ≈ 1.67

Swahili: Binary operations ni kazi zinazohusisha namba mbili. Mfano: kujumlisha, kutoa, kuzidisha, kugawanya.

2. Brackets in Computations

When solving problems with brackets, we follow the order of operations (BODMAS): Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction.

Example: Solve: (2 + 3) × 4
Step 1: Inside brackets = 5
Step 2: Multiply = 5 × 4 = 20

Swahili: Katika kutumia mabano tunafuata mpangilio wa BODMAS. Yaani, mabano kwanza, halafu viwango (powers), kisha mgawanyo, kuzidisha, kujumlisha, kutoa.

3. Quadratic Expressions

A quadratic expression is an expression of the form: ax² + bx + c, where a, b, and c are numbers, and a ≠ 0.

Example: 2x² + 3x + 1
This is quadratic because the highest power of x is 2.

Swahili: Quadratic expression ni msemo wa aina ax² + bx + c. Ni quadratic kwa sababu nguvu kubwa zaidi ya x ni mraba (2).

4. Simplifying Algebraic Expressions

To simplify expressions, collect like terms (terms with the same variable and power).

Example: Simplify: 3x + 5x - 2
Step 1: Combine like terms (3x + 5x = 8x)
Step 2: Result = 8x - 2

Swahili: Ili kurahisisha misemo ya algebra, unakusanya sehemu zenye alama zinazofanana. Mfano: 3x + 5x = 8x.

5. Real-Life Example of Algebra

Imagine you are buying pens. Each pen costs 500 shillings. If you buy x pens, the total cost is:

Total Cost = 500x shillings If x = 4, then cost = 500 × 4 = 2000 shillings.

Swahili: Tuseme unanunua kalamu, kila moja ni shilingi 500. Ukiwa na kalamu x, gharama jumla = 500x.

Revision Exercise 2

  1. Simplify: (4x + 3) + (2x - 5)
  2. If y = 6, find the value of 2y + 3
  3. Expand: (x + 2)(x + 3)
  4. Factorize: x² + 5x + 6
  5. Mary buys x oranges at 200 shillings each. Write an expression for the total cost.
Mathematics Notes - Quadratic Equations to Pythagoras

Chapter Three: Quadratic Equations

Solving Quadratic Equations

A quadratic equation is an equation of the form: ax² + bx + c = 0, where a ≠ 0. The highest power of x is 2.

Methods of Solving Quadratic Equations

  1. Factorization

    Express the quadratic in the form (x + p)(x + q) = 0, then solve for x.

    Example: Solve x² + 5x + 6 = 0.
    Factorization → (x + 2)(x + 3) = 0.
    Solutions: x = -2 or x = -3.
  2. Completing the Square

    Rearrange the equation into x² + bx = k, then add (b/2)² to both sides. Njia hii hutumika hata pale ambapo haitawezekana kufactorize moja kwa moja.

    Example: Solve x² + 4x + 1 = 0.
    Move constant: x² + 4x = -1.
    Add (4/2)² = 4: x² + 4x + 4 = 3.
    (x + 2)² = 3.
    x = -2 ± √3.
  3. Quadratic Formula

    For any quadratic equation ax² + bx + c = 0, the solutions are: x = [-b ± √(b² - 4ac)] / (2a). Hii ndiyo njia ya jumla ambayo inaweza kutumika kwa quadratic yoyote.

    Example: Solve 2x² + 3x - 2 = 0.
    Here a = 2, b = 3, c = -2.
    Discriminant D = b² - 4ac = 9 - (4×2×-2) = 9 + 16 = 25.
    x = [-3 ± √25] / 4.
    x = (-3 ± 5) / 4 → x = 1/2 or -2.

Chapter Summary

  • Quadratics appear in physics (e.g., projectile motion), business (profit maximization), and real life (area problems).
  • Discriminant (b² - 4ac) helps determine the type of roots: - If D > 0 → Two distinct real roots. - If D = 0 → One real root (repeated). - If D < 0 → No real root (imaginary roots).

Revision Exercise 3

  1. Solve: x² - 7x + 10 = 0.
  2. Find the roots of: 2x² + 5x + 3 = 0 using the quadratic formula.
  3. Complete the square to solve: x² + 6x + 5 = 0.
  4. If the product of two numbers is 20 and their sum is 9, form a quadratic equation and solve it.

Chapter Four: Logarithms

Standard Form

Numbers can be expressed in standard form (scientific notation) as: A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. Mfano: 23400 = 2.34 × 10⁴

Laws of Logarithms

  • log(a × b) = log a + log b
  • log(a / b) = log a - log b
  • log(aⁿ) = n log a
Example: log(1000) = 3 (since 10³ = 1000). log(2 × 5) = log 2 + log 5.

Table of Common Logarithms

Before calculators, logarithm tables were used to find logs and antilogs. Leo, tunatumia calculator, lakini kuelewa mizizi ya logarithm tables ni muhimu.

Chapter Summary

  • Standard form simplifies very large and small numbers.
  • Logarithms convert multiplication/division into addition/subtraction.
  • Very useful in growth/decay problems (e.g., population growth, half-life in physics).

Revision Exercise 4

  1. Write 0.00056 in standard form.
  2. Simplify using laws of logarithms: log(25) - log(5).
  3. Use logarithms to evaluate: 32 × 125.

Chapter Five: Congruence

Congruence of Triangles

Two figures are congruent if they have the same shape and size. Kwa maneno mengine, triangle mbili zinakuwa sawa kabisa kwenye pande na pembe zake.

Postulates and Proofs

Triangles are congruent if they satisfy ANY of these conditions:

  • SSS (Side-Side-Side): All three sides equal.
  • SAS (Side-Angle-Side): Two sides and the included angle equal.
  • ASA (Angle-Side-Angle): Two angles and the included side equal.
  • AAS (Angle-Angle-Side): Two angles and a non-included side equal.
  • RHS (Right angle-Hypotenuse-Side): Right triangle with equal hypotenuse and one side.
Real-life example: When constructing bridges or houses, congruent triangles are used for stability in trusses.

Chapter Summary

Congruence ensures equality in shapes — used in engineering, architecture, and design.

Revision Exercise 5

  1. State the five conditions of triangle congruence.
  2. In △ABC and △DEF, AB = DE, AC = DF, and ∠A = ∠D. Prove the triangles are congruent.

Chapter Six: Similarity

Similar Figures

Two figures are similar if they have the same shape but different sizes. Mfano mzuri ni ramani (map) na dunia halisi — ramani ni mfano mdogo wa dunia.

Similar Triangles

Conditions for similarity of triangles:

  • AAA (All three angles equal).
  • SAS (Two sides proportional and included angle equal).
  • SSS (All sides proportional).
Real-life: Photocopy machines enlarge or reduce documents — similar figures.

Chapter Summary

Similarity is applied in maps, models, scaling of drawings, and photography.

Revision Exercise 6

  1. State three conditions of similarity in triangles.
  2. A tree 12 m high casts a shadow of 8 m. A pole casts a shadow of 2 m. Find the height of the pole.

Chapter Seven: Geometrical Transformations

Types of Transformations

  • Reflection: Flipping an object over a line.
  • Rotation: Turning an object around a fixed point.
  • Translation: Sliding an object from one place to another.
  • Enlargement: Resizing while maintaining proportions.
  • Combined Transformation: Applying more than one transformation.
Real-life: Computer graphics use transformations in animations and video games.

Chapter Summary

Transformations are key in design, robotics, and computer vision.

Revision Exercise 7

  1. Describe a reflection in the line y = x.
  2. Find the image of (2,3) after a rotation of 90° about the origin.

Chapter Eight: Pythagoras’ Theorem

The Theorem

In a right-angled triangle, the square of the hypotenuse = sum of squares of other two sides. c² = a² + b². Hii ni theorem maarufu sana inayotumika sana maishani.

Example: If a right-angled triangle has legs 3 cm and 4 cm, then hypotenuse = √(3²+4²) = √25 = 5 cm.

Applications

  • Construction: Finding lengths of diagonals.
  • Navigation: Determining shortest paths.
  • Surveying: Measuring inaccessible distances.

Chapter Summary

Pythagoras’ theorem connects geometry with real-life applications in building, maps, and physics.

Revision Exercise 8

  1. Find the diagonal of a rectangle with sides 6 m and 8 m.
  2. A ladder 10 m long rests against a wall. If the foot of the ladder is 6 m from the wall, how high does the ladder reach?
Math Notes - Trigonometry, Sets, and Statistics

Chapter Nine: Trigonometry

Trigonometric Ratios

Trigonometry is the study of the relationships between the angles and sides of triangles. The three main trigonometric ratios are:

  • Sine (sin) = Opposite / Hypotenuse
  • Cosine (cos) = Adjacent / Hypotenuse
  • Tangent (tan) = Opposite / Adjacent
Example (English): In a right triangle, if the angle is 30° and the hypotenuse is 10 cm, the opposite side = sin(30°) × 10 = 5 cm.
Mfano (Swahili): Ikiwa pembetatu ina pembe ya 30° na upande wa hypotenuse ni 10 cm, basi upande ulio kinyume = sin(30°) × 10 = 5 cm.

Trigonometric Ratios of Special Angles

Special angles such as 30°, 45°, and 60° have exact values for sine, cosine, and tangent.

Table:
sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) = 1/√3
sin(45°) = √2/2, cos(45°) = √2/2, tan(45°) = 1
sin(60°) = √3/2, cos(60°) = 1/2, tan(60°) = √3

Trigonometric Tables

Before calculators, trigonometric tables were used to find approximate values of sine, cosine, and tangent for given angles.

Mfano wa maisha halisi: Wakati wa kujenga paa, fundi anaweza kutumia meza za trigonometria kupata pembe zinazohitajika ili paa litoshe vizuri.

Angle of Elevation and Depression

- Angle of elevation: The angle formed when looking up at an object.
- Angle of depression: The angle formed when looking down at an object.

Real-life example: If you stand 50 m away from a tree and look up at the top at an angle of 30°, you can calculate the height of the tree using tan(30°).

Chapter Summary

Trigonometry helps in solving right triangles, measuring heights and distances, and has applications in navigation, construction, and physics.

Revision Exercise 9

  1. Find the height of a building if you stand 40 m away and the angle of elevation is 45°.
  2. Calculate sin(60°), cos(45°), and tan(30°).

Chapter Ten: Sets

Description of Sets

A set is a collection of distinct objects. Sets are usually written with curly brackets, e.g., A = {2, 4, 6, 8}.

Types of Sets

  • Finite set: A set with a countable number of elements.
  • Infinite set: A set with unlimited elements.
  • Empty set: A set with no elements (∅).
  • Universal set: A set containing all possible elements in a given context.

Operations with Sets

  • Union ( ∪ ): Combines all elements.
  • Intersection ( ∩ ): Common elements.
  • Difference ( - ): Elements in one set but not in the other.
  • Complement ( A' ): Elements not in set A.

Venn Diagrams

Venn diagrams are used to visually represent sets and their relationships.

Mfano wa maisha halisi: Wanafunzi wanaocheza mpira (set A) na wanaocheza muziki (set B). Venn diagramu inaweza kuonyesha wanafunzi wanaoshiriki shughuli zote mbili.

Revision Exercise 10

  1. List all elements in A ∪ B where A = {2,4,6}, B = {4,6,8}.
  2. Draw a Venn diagram to show students who like football and basketball.

Chapter Eleven: Statistics

Pictograms

A pictogram uses pictures or symbols to represent data.

Bar Charts

Bar charts use rectangular bars to show comparisons among categories.

Line Graphs

Line graphs show data that changes over time, connected by straight lines.

Pie Chart

A circular chart divided into sectors, showing proportions.

Frequency Distribution Tables

Organizes data into classes and shows how often each class occurs.

Histograms

A graphical representation of grouped data using adjacent bars.

Frequency Polygons

Formed by joining the midpoints of histogram bars with straight lines.

Cumulative Frequency Curves (Ogive)

Shows the running total of frequencies. Useful for estimating medians and percentiles.

Mfano wa maisha halisi: Mwalimu anaweza kutumia ogive kujua ni wanafunzi wangapi wamepata alama chini ya 50% katika mtihani.

Revision Exercise 11

  1. Draw a bar chart showing the number of cars sold in 5 months: 20, 35, 25, 40, 30.
  2. Construct a cumulative frequency curve for the data: 5, 10, 15, 20, 25 with frequencies 3, 6, 10, 8, 5.
Maths Notes - Advanced Sections

Answers to Odd-numbered Questions

This section provides worked-out solutions for odd-numbered questions across all chapters. Note: Even-numbered questions are left for self-practice.

Example (Exponents & Radicals):

Q1: Simplify \(2³ × 2⁴\).

Answer: Since bases are the same, add exponents: 2³ × 2⁴ = 2⁷ = 128.

Swahili: Hapa tunaongeza viashiria kwa sababu msingi ni sawa.

Example (Quadratic Equations):

Q3: Solve x² - 5x + 6 = 0.

Answer: Factorize → (x - 2)(x - 3) = 0. ∴ x = 2 or x = 3.

Real Life Example: Quadratics are used in profit maximization (e.g., when revenue depends on the square of production units).

Mathematical Tables

Mathematical tables are reference tools for quick calculations before calculators were common. They include logarithm tables, square roots, trigonometric values, etc.

Sample Logarithm Table (Base 10)
Number Log Value
20.3010
30.4771
50.6990
101.0000

Swahili: Jedwali la logarithm liliwasaidia wanafunzi na wahandisi kufanya mahesabu haraka bila kutumia kalkuleta.

Sample Trigonometric Table
Angle (°) sin θ cos θ tan θ
300.50.8660.577
450.7070.7071.000
600.8660.51.732

Glossary

A glossary of key mathematical terms.

  • Algebra: A branch of mathematics dealing with symbols and rules for manipulating them.
  • Coefficient: A number multiplying a variable (e.g., in 5x, 5 is the coefficient).
  • Histogram: A graphical representation of frequency distribution.
  • Logarithm: The power to which a base must be raised to obtain a number (log₁₀ 100 = 2).
  • Trigonometry: The study of relationships between angles and sides of triangles.

Bibliography

Reference books and sources used in preparing the notes:

  1. New General Mathematics (NGM) Series – Oxford University Press.
  2. Essential Mathematics for Secondary Schools – Longman.
  3. Core Mathematics for O-Level – Cambridge.
  4. Additional real-life examples sourced from engineering, business, and economics applications.

Index

An alphabetical list of topics covered in these notes:

  • Algebra – Page 49
  • Congruence – Page 152
  • Cumulative Frequency – Page 353
  • Exponents – Page 1
  • Logarithms – Page 109
  • Pythagoras Theorem – Page 256
  • Quadratic Equations – Page 75
  • Statistics – Page 330
  • Trigonometry – Page 273

Reference Book: N/A

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