SS 1

Revision – First & Second Term

Mathematics SS 1 Third Term

📌 Welcome to Your Combined Revision!

This comprehensive revision covers all the key topics from both First and Second Terms. Use this to:

Review key concepts from both terms
Refresh your memory before starting Third Term
Practice with revision questions
Identify areas that need more attention

First Term Topics Overview

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

Second Term Topics Overview

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

First & Second Term Topics – Summary

Key Formulas – First Term

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

Key Formulas – Second Term

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

Revision Questions

Test your understanding of all topics from First and Second Term:

Section A: Multiple Choice (Choose the correct option)

Convert 1101₂ to base 10.
A) 11 B) 13 C) 15 D) 17
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∪ B.
A) {1,2,3,4,5,6} B) {3,4} C) {1,2,5,6} D) {1,2,3,4}
Simplify: 3x + 5x − 2x
A) 6x B) 8x C) 10x D) 4x
Evaluate: 7 + 8 (mod 6)
A) 1 B) 2 C) 3 D) 4
Simplify: 2³ × 2⁵
A) 2⁸ B) 2¹⁵ C) 2² D) 2⁷
What is log₂ 8?
A) 2 B) 3 C) 4 D) 5
Simplify: √12
A) 2√3 B) 3√2 C) 4√3 D) 2√6
Solve: 2x + 3 = 11
A) 3 B) 4 C) 5 D) 6
Solve: x² − 5x + 6 = 0
A) 2, 3 B) 1, 6 C) 2, 4 D) 3, 4
The discriminant of x² + x + 1 = 0 is:
A) 3 B) 1 C) −3 D) 0

Answers: 1-B, 2-A, 3-A, 4-C, 5-A, 6-B, 7-A, 8-B, 9-A, 10-C

Section B: Short Answer Questions

Convert 25₁₀ to binary.
Evaluate: 4 − 9 (mod 5).
Simplify: (2³ × 2⁵) ÷ 2⁴.
Evaluate: 27²/³.
Simplify: log₂ 16 + log₂ 4.
Simplify: √27 + √12.
Rationalise: 1/√3.
Solve: 2ˣ = 64.
Expand: (x + 3)(x + 2).
Solve: 3x + 2 = 2x + 7.

Section C: Calculation Questions

Add: 101₂ + 111₂.
Subtract: 1101₂ − 101₂.
If A = {1,2,3,4,5} and B = {4,5,6,7,8}, find (a) A∪B (b) A∩B (c) A−B
Solve: 3(x − 2) = 15.
Solve using elimination: 3x + 2y = 12, x − 2y = 4.
Solve: x² − 9 = 0.
Solve using the quadratic formula: 2x² − 5x + 2 = 0.
Solve: log₂ x = 5.
Simplify: √12 × √3.
Find the discriminant of x² − 6x + 9 = 0 and state the nature of roots.

Answers to Section B

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

Answers to Section C

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

Examination Preparation Tips

📌 Tips for Success:

Review all formulas – make a formula sheet and memorise them.
Understand key definitions – be able to explain concepts in your own words.
Practice calculations – work through all examples and assignment questions.
Know your number bases – binary, octal, and hexadecimal conversions.
Practice surd operations – simplification, rationalisation, and equations.
Know your set operations – union, intersection, complement, Venn diagrams.
Practice algebraic manipulation – expansion, factorization, solving equations.
Quadratic equations – be comfortable with all three methods (factorization, completing the square, formula).
Time management – allocate time for each section during the exam.
Read questions carefully – identify what is being asked before answering.

Board Summary

╔════════════════════════════════════════════════════════════════════════════╗ ║ SS1 MATHEMATICS – FIRST & SECOND TERM REVISION ║ ╠════════════════════════════════════════════════════════════════════════════╣ ║ ║ ║ FIRST TERM TOPICS: ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Number Bases: Binary, Octal, Decimal, Hex ║ ║ • Modular Arithmetic: Modulo, congruence, operations ║ ║ • Indices: Laws, negative, fractional, equations ║ ║ • Logarithms: Definition, laws, characteristic & mantissa ║ ║ • Surds: Definition, simplification, operations, rationalisation ║ ║ ║ ║ SECOND TERM TOPICS: ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • Sets: Definition, types, operations (∪, ∩, −, ′) ║ ║ • Venn Diagrams: 2-set and 3-set, word problems ║ ║ • Algebraic Expressions: Simplification, expansion, FOIL ║ ║ • Linear Equations: Variables, brackets, fractions, word problems ║ ║ • Simultaneous Equations: Elimination, substitution, graphical ║ ║ • Quadratic Equations: Factorization, formula, completing the square ║ ║ ║ ║ KEY FORMULAS: ║ ║ ───────────────────────────────────────────────────────────────────────── ║ ║ • (a+b)² = a² + 2ab + b² ║ ║ • (a−b)² = a² − 2ab + b² ║ ║ • (a+b)(a−b) = a² − b² ║ ║ • n(A∪B) = n(A) + n(B) − n(A∩B) ║ ║ • x = [−b ± √(b²−4ac)] / 2a ║ ║ ║ ╚════════════════════════════════════════════════════════════════════════════╝

✅ You're now ready for Third Term!

Remember to stay calm, read all questions carefully, and show your working clearly. You've got this! 💪