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SS 1 Mathematics Revision: First Term
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Mathematics - SS 1 - SS 1 Mathematics Revision: First Term

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Home β€Ί SS β€Ί Mathematics β€Ί Revision – First Term
SS 1

Revision – First Term

Mathematics SS 1 First Term
πŸ“Œ Welcome to Your First Term Revision!

This comprehensive revision covers all the topics from the First Term. Use this to:

  • Review key concepts from each topic
  • Practice with revision questions
  • Prepare for your end-of-term examination
  • Identify areas that need more attention

Topics Covered in First Term

Week Topic Key Concepts
1 Number Bases I Definition of number bases, binary, octal, decimal, hexadecimal; place value; conversion to base 10
2 Number Bases II Conversion from base 10 to other bases; addition, subtraction, multiplication in bases
3 Modular Arithmetic Concept of modulo; congruence; addition, subtraction, multiplication in modulo
4 Indices I Definition; 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; conversion between exponential and logarithmic forms; laws of logarithms
7 Logarithms II Characteristic and mantissa; calculations with logarithms; antilogarithms; solving equations
8 Surds I Definition of surds; simplification; addition and subtraction of surds
9 Surds II Multiplication and division of surds; rationalising the denominator; surd equations
First Term Topics – Summary

Topic 1: Number Bases I – Summary

πŸ”‘ Key Points:
  • Number Base: A system for representing numbers using a set of digits.
  • Common Bases: Binary (2), Octal (8), Decimal (10), Hexadecimal (16).
  • Expanded Form: N = dβ‚™Γ—bⁿ + ... + dβ‚‚Γ—bΒ² + d₁×bΒΉ + dβ‚€Γ—b⁰
  • Conversion to Base 10: Use the expanded form method.

Topic 2: Number Bases II – Summary

πŸ”‘ Key Points:
  • Conversion from Base 10: Use the division method (read remainders bottom to top).
  • Addition: Carry when sum β‰₯ base.
  • Subtraction: Borrow when top digit < bottom digit.
  • Multiplication: Use the base's multiplication table; carry when product β‰₯ base.

Topic 3: Modular Arithmetic – Summary

πŸ”‘ Key Points:
  • Modulus (m): The number that defines the range of values.
  • Congruence: a ≑ b (mod m) if m divides (a βˆ’ b).
  • Addition: (a + b) mod m
  • Subtraction: (a βˆ’ b) mod m (if negative, add m).
  • Multiplication: (a Γ— b) mod m

Topic 4: Indices I – Summary

πŸ”‘ Key Points:
  • Definition: aⁿ = a Γ— a Γ— ... (n times).
  • Law 1: aᡐ Γ— aⁿ = aᡐ⁺ⁿ
  • Law 2: aᡐ Γ· aⁿ = aᡐ⁻ⁿ
  • Law 3: (aᡐ)ⁿ = aᡐⁿ
  • Law 4: a⁰ = 1 (a β‰  0)

Topic 5: Indices II – Summary

πŸ”‘ Key Points:
  • Negative Index: a⁻ⁿ = 1/aⁿ
  • Fractional Index: aΒΉ/ⁿ = ⁿ√a
  • General Fractional: aᡐ/ⁿ = ⁿ√(aᡐ) = (ⁿ√a)ᡐ
  • Solving Equations: Express both sides as powers of the same base, then equate indices.

Topic 6: Logarithms I – Summary

πŸ”‘ Key Points:
  • Definition: logₐ b = c ⇔ aᢜ = b
  • Product Law: logₐ (xy) = logₐ x + logₐ y
  • Quotient Law: logₐ (x/y) = logₐ x βˆ’ logₐ y
  • Power Law: logₐ (xⁿ) = n logₐ x
  • Change of Base: logₐ x = log_b x / log_b a

Topic 7: Logarithms II – Summary

πŸ”‘ Key Points:
  • Characteristic: Integer part of log (digits βˆ’ 1 for N β‰₯ 1; negative for N < 1).
  • Mantissa: Decimal part (found from log tables).
  • Calculations: Add logs for multiplication; subtract for division; multiply by power for powers; divide by root for roots.
  • Antilog: antilog y = 10ΚΈ

Topic 8: Surds I – Summary

πŸ”‘ Key Points:
  • Definition: Irrational numbers expressed as roots (e.g., √2, √3).
  • Simplification: √(aΓ—b) = √a Γ— √b; find perfect square factors.
  • Addition/Subtraction: Only similar surds can be added/subtracted.
  • Conjugate: a + √b and a βˆ’ √b

Topic 9: Surds II – Summary

πŸ”‘ Key Points:
  • Multiplication: √a Γ— √b = √(ab)
  • Division: √a Γ· √b = √(a/b)
  • Rationalising: Multiply numerator and denominator by the conjugate.
  • Solving Equations: Isolate the surd, square both sides, solve, check for extraneous solutions.

Key Formulas Summary

Topic Formula Variables
Number Bases N = dβ‚™Γ—bⁿ + ... + dβ‚€Γ—b⁰ b = base
Modular Arithmetic a ≑ b (mod m) if m|(aβˆ’b) m = modulus
Indices aᡐ Γ— aⁿ = aᡐ⁺ⁿ a = base
Negative Index a⁻ⁿ = 1/aⁿ n = positive integer
Fractional Index a¹/ⁿ = ⁿ√a n = root
Logarithms logₐ b = c ⇔ aᢜ = b a = base
Log Product logₐ (xy) = logₐ x + logₐ y a = base
Surds √(aΓ—b) = √a Γ— √b a, b β‰₯ 0

Revision Questions

Test your understanding of all First Term topics:

Section A: Multiple Choice (Choose the correct option)

  1. Convert 1101β‚‚ to base 10.
    A) 11 B) 13 C) 15 D) 17
  2. Evaluate: 7 + 8 (mod 6)
    A) 1 B) 2 C) 3 D) 4
  3. Simplify: 2Β³ Γ— 2⁡
    A) 2⁸ B) 2¹⁡ C) 2² D) 2⁷
  4. What is logβ‚‚ 8?
    A) 2 B) 3 C) 4 D) 5
  5. Simplify: √12
    A) 2√3 B) 3√2 C) 4√3 D) 2√6
  6. Which of the following is a surd?
    A) √4 B) √9 C) √16 D) √2
  7. Evaluate: 5⁻²
    A) 25 B) 1/25 C) -25 D) -1/25
  8. What is the characteristic of log₁₀ 4567?
    A) 1 B) 2 C) 3 D) 4
  9. Convert 25₁₀ to binary.
    A) 11001β‚‚ B) 11010β‚‚ C) 11100β‚‚ D) 10101β‚‚
  10. Simplify: √8 + √18
    A) 5√2 B) 4√2 C) 3√2 D) 2√2

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

Section B: Short Answer Questions

  1. Convert 101011β‚‚ to base 10.
  2. Evaluate: 4 βˆ’ 9 (mod 5).
  3. Simplify: (2Β³ Γ— 2⁡) Γ· 2⁴.
  4. Evaluate: 27Β²/Β³.
  5. Simplify: logβ‚‚ 16 + logβ‚‚ 4.
  6. Simplify: √27 + √12.
  7. Rationalise: 1/√3.
  8. Solve: 2Λ£ = 64.
  9. Find the characteristic of log₁₀ 0.0456.
  10. Expand: (√2 + √3)².

Section C: Calculation Questions

  1. Add: 101β‚‚ + 111β‚‚.
  2. Subtract: 1101β‚‚ βˆ’ 101β‚‚.
  3. Solve: logβ‚‚ x = 5.
  4. Calculate: 3⁻² Γ— 3⁴.
  5. Simplify: √12 Γ— √3.
  6. Rationalise: 1/(2 βˆ’ √3).
  7. Evaluate: logβ‚‚ 32 βˆ’ logβ‚‚ 4.
  8. Solve: √(2x + 1) = 5.
  9. Simplify: 8√15 ÷ 2√3.
  10. Solve: log₃ (2x + 1) = 2.

Answers to Section B

1. 101011β‚‚ = 1Γ—32 + 0Γ—16 + 1Γ—8 + 0Γ—4 + 1Γ—2 + 1Γ—1 = 43₁₀

2. 4 βˆ’ 9 = βˆ’5; βˆ’5 + 5 = 0

3. (2Β³ Γ— 2⁡) Γ· 2⁴ = 2⁸ Γ· 2⁴ = 2⁴

4. 27²/³ = (³√27)² = 3² = 9

5. logβ‚‚ 16 + logβ‚‚ 4 = 4 + 2 = 6

6. √27 = 3√3, √12 = 2√3, sum = 5√3

7. 1/√3 Γ— √3/√3 = √3/3

8. 64 = 2⁢, so x = 6

9. 0.0456 has 2 zeros β†’ characteristic = βˆ’2

10. (√2)² + 2(√2)(√3) + (√3)² = 2 + 2√6 + 3 = 5 + 2√6

Answers to Section C

1. 101β‚‚ + 111β‚‚ = 1100β‚‚

2. 1101β‚‚ βˆ’ 101β‚‚ = 1000β‚‚

3. 2⁡ = x β†’ x = 32

4. 3⁻² Γ— 3⁴ = 3Β² = 9

5. √12 Γ— √3 = √36 = 6

6. (2 + √3)/(4 βˆ’ 3) = 2 + √3

7. logβ‚‚ 32 βˆ’ logβ‚‚ 4 = 5 βˆ’ 2 = 3

8. 2x + 1 = 25 β†’ 2x = 24 β†’ x = 12

9. 8√15 ÷ 2√3 = 4√5

10. 3Β² = 2x + 1 β†’ 9 = 2x + 1 β†’ x = 4

Examination Preparation Tips

πŸ“Œ 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.
  • Time management – allocate time for each section during the exam.
  • Read questions carefully – identify what is being asked before answering.
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