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Mathematics - SS 1 - SS 1 Mathematics Revision : First & Second Term
This comprehensive revision covers all the key topics from both First and Second Terms. Use this to:
| Week | Topic | Key Concepts |
|---|---|---|
| 1 | Number Bases I | Definition, binary, octal, decimal, hexadecimal; place value; conversion to base 10 |
| 2 | Number Bases II | Conversion from base 10; addition, subtraction, multiplication in bases |
| 3 | Modular Arithmetic | Modulo, congruence, addition, subtraction, multiplication |
| 4 | Indices I | Laws of indices (multiplication, division, power of power, zero index) |
| 5 | Indices II | Negative indices, fractional indices, solving equations with indices |
| 6 | Logarithms I | Definition, laws of logarithms (product, quotient, power, change of base) |
| 7 | Logarithms II | Characteristic and mantissa, calculations with logarithms, antilogarithms |
| 8 | Surds I | Definition, simplification, addition and subtraction |
| 9 | Surds II | Multiplication, division, rationalising the denominator, surd equations |
| Week | Topic | Key Concepts |
|---|---|---|
| 1 | Revision of First Term | Review of First Term concepts |
| 2 | Sets I | Definition, elements, methods, types, cardinality, subsets |
| 3 | Sets II | Union, intersection, difference, complement |
| 4 | Sets III – Venn Diagrams | Two-set and three-set diagrams, word problems, inclusion-exclusion |
| 5 | Algebraic Expressions | Variables, coefficients, constants, like terms, expansion, substitution |
| 6 | Linear Equations | Solving equations with variables, brackets, fractions, word problems |
| 7 | Simultaneous Equations | Elimination, substitution, graphical methods; word problems |
| 8 | Quadratic Equations I | Factorization method, difference of two squares |
| 9 | Quadratic Equations II | Completing the square, quadratic formula, discriminant |
| Topic | Formula | Variables |
|---|---|---|
| Number Bases | N = dₙ×bⁿ + ... + d₀×b⁰ | b = base |
| Modular Arithmetic | a ≡ b (mod m) if m|(a−b) | m = modulus |
| Indices | aᵐ × aⁿ = aᵐ⁺ⁿ | a = base |
| Negative Index | a⁻ⁿ = 1/aⁿ | n = positive integer |
| Fractional Index | a¹/ⁿ = ⁿ√a | n = root |
| Logarithms | logₐ b = c ⇔ aᶜ = b | a = base |
| Log Product | logₐ (xy) = logₐ x + logₐ y | a = base |
| Surds | √(a×b) = √a × √b | a, b ≥ 0 |
| Topic | Formula | Variables |
|---|---|---|
| Sets – Subsets | Number of subsets = 2ⁿ | n = number of elements |
| Sets – Union | n(A∪B) = n(A) + n(B) − n(A∩B) | A, B = sets |
| Sets – Inclusion-Exclusion (3) | n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(A∩C) − n(B∩C) + n(A∩B∩C) | A, B, C = sets |
| Algebra – Expansion | a(b + c) = ab + ac | a, b, c = constants/variables |
| Algebra – Double Brackets | (a + b)(c + d) = ac + ad + bc + bd | a, b, c, d = constants/variables |
| Algebra – Difference of Squares | (a + b)(a − b) = a² − b² | a, b = constants/variables |
| Algebra – Perfect Square | (a + b)² = a² + 2ab + b² | a, b = constants/variables |
| Quadratic – Formula | x = [−b ± √(b² − 4ac)] / 2a | a, b, c from ax² + bx + c = 0 |
| Quadratic – Discriminant | Δ = b² − 4ac | a, b, c from ax² + bx + c = 0 |
Test your understanding of all topics from First and Second Term:
Answers: 1-B, 2-A, 3-A, 4-C, 5-A, 6-B, 7-A, 8-B, 9-A, 10-C
1. 25₁₀ = 11001₂
2. 4 − 9 = −5; −5 + 5 = 0
3. (2³ × 2⁵) ÷ 2⁴ = 2⁸ ÷ 2⁴ = 2⁴
4. 27²/³ = (³√27)² = 3² = 9
5. log₂ 16 + log₂ 4 = 4 + 2 = 6
6. √27 = 3√3, √12 = 2√3, sum = 5√3
7. 1/√3 × √3/√3 = √3/3
8. 64 = 2⁶ → x = 6
9. (x + 3)(x + 2) = x² + 5x + 6
10. 3x + 2 = 2x + 7 → 3x − 2x = 7 − 2 → x = 5
1. 101₂ + 111₂ = 1100₂
2. 1101₂ − 101₂ = 1000₂
3. (a) {1,2,3,4,5,6,7,8} (b) {4,5} (c) {1,2,3}
4. 3x − 6 = 15 → 3x = 21 → x = 7
5. Add: 4x = 16 → x = 4, 3(4) + 2y = 12 → 12 + 2y = 12 → y = 0 → x = 4, y = 0
6. x² − 9 = 0 → (x − 3)(x + 3) = 0 → x = 3 or −3
7. x = [5 ± √(25−16)]/4 = [5 ± 3]/4 → x = 2 or 1/2
8. 2⁵ = x → x = 32
9. √12 × √3 = √36 = 6
10. Δ = 36 − 36 = 0 → Two real and equal roots