Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Chapter 1 — Set Language
| Formula | Expression |
|---|---|
| Union count | n(A ∪ B) = n(A) + n(B) − n(A ∩ B) |
| Three-set union | n(A ∪ B ∪ C) = n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C) |
| Power set | n(P(A)) = 2^n(A) |
| Proper subsets | 2^n(A) − 1 |
| De Morgan's Law 1 | (A ∪ B)' = A' ∩ B' |
| De Morgan's Law 2 | (A ∩ B)' = A' ∪ B' |
Chapter 2 — Real Numbers
| Formula | Expression |
|---|---|
| Surd multiplication | √a × √b = √(ab) |
| Surd division | √a / √b = √(a/b) |
| Conjugate rationalisation | (a+√b)(a−√b) = a² − b |
| Exponent product | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Exponent power | (aᵐ)ⁿ = aᵐⁿ |
| Fractional exponent | a^(1/n) = ⁿ√a |
| Negative exponent | a⁻ⁿ = 1/aⁿ |
Chapter 3 — Algebra
| Identity | Expression |
|---|---|
| Cube expansion + | (a+b)³ = a³ + 3a²b + 3ab² + b³ |
| Cube expansion − | (a−b)³ = a³ − 3a²b + 3ab² − b³ |
| Sum of cubes | a³+b³ = (a+b)(a²−ab+b²) |
| Difference of cubes | a³−b³ = (a−b)(a²+ab+b²) |
| Three variable square | (a+b+c)² = a²+b²+c²+2ab+2bc+2ca |
| Three variable cubes | a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca) |
| Remainder Theorem | Remainder of p(x)÷(x−a) = p(a) |
| Factor Theorem | (x−a) is factor ↔ p(a) = 0 |
Chapter 5 — Coordinate Geometry
| Formula | Expression |
|---|---|
| Distance formula | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Midpoint | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Section (internal) | P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) |
| Centroid | G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3) |
Chapter 6 — Trigonometry
| Identity | Expression |
|---|---|
| Pythagorean 1 | sin²θ + cos²θ = 1 |
| Pythagorean 2 | 1 + tan²θ = sec²θ |
| Pythagorean 3 | 1 + cot²θ = cosec²θ |
| Complementary sin/cos | sin(90°−θ) = cosθ; cos(90°−θ) = sinθ |
| Complementary tan/cot | tan(90°−θ) = cotθ; cot(90°−θ) = tanθ |
Chapter 7 — Mensuration
| Shape | LSA | TSA | Volume |
|---|---|---|---|
| Cuboid | 2h(l+b) | 2(lb+bh+lh) | lbh |
| Cube | 4a² | 6a² | a³ |
| Cylinder | 2πrh | 2πr(r+h) | πr²h |
| Cone | πrl | πr(r+l) | (1/3)πr²h |
| Sphere | — | 4πr² | (4/3)πr³ |
| Hemisphere | 2πr² | 3πr² | (2/3)πr³ |
Slant height: l = √(r² + h²)
Chapters 8–9 — Statistics and Probability
| Formula | Expression |
|---|---|
| Mean (grouped) | Σfx / Σf |
| Median (grouped) | L + [(N/2−cf)/f] × h |
| Mode (grouped) | L + [(f₁−f₀)/(2f₁−f₀−f₂)] × h |
| Empirical relationship | Mode = 3 Median − 2 Mean |
| Probability | P(E) = n(E)/n(S) |
| Complement | P(E') = 1 − P(E) |
Frequently Asked Questions
Print or copy this page into your notebook. Before each revision session, read through it. In the final week, test yourself by covering the right column and trying to recall each formula from memory.