CORE_MATH • SHS 1Term 1WAEC / WASSCE SyllabusFree Trial Topic
Real Number System, Surds & Standard Form
Rational vs irrational numbers, simplifying surds, rationalizing binomial surds, and scientific notation calculations.
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Real-World Context & Relevance in Ghana
Civil engineers constructing the Pokuase Interchange calculate hypotenuses of ramps using exact surd values to prevent cumulative rounding errors across spans.
Key Syllabus Learning Objectives
- 1Distinguish clearly between rational and irrational numbers
- 2Simplify radicals by extracting perfect square factors
- 3Rationalize monomial and binomial denominators using conjugates
- 4Perform scientific notation computations with significant figures
1
Conjugate Binomial Surds
The conjugate of (a + √b) is (a - √b). Using the algebraic identity (x + y)(x - y) = x² - y², multiplying a surd by its conjugate eliminates all square roots from the denominator.
- Conjugate of (3 + √5) is (3 - √5).
- Conjugate of (2√3 - 5) is (2√3 + 5).
- Always multiply both numerator and denominator by the conjugate.
Core Takeaway:
Multiplying by the conjugate creates the difference of two squares, clearing all radicals from the denominator.
WAEC / WASSCE Examiner Tips
- Express your final answer in the exact form requested (e.g. a + b√c where a and b are rational).
- Show all factorization steps under the radical; do not jump straight to the decimal on your calculator.
- For standard form, ensure 1 ≤ A < 10 (e.g. write 4.5 × 10³, not 45 × 10²).
Common Candidate Pitfalls & Errors to Avoid
- Writing √(a + b) = √a + √b (this is completely false!).
- Leaving a radical in the denominator of a final answer.
- Errors in signs when multiplying binomial surds.
Topic Mastery Checklist
- Can I reduce √72 into 6√2?
- Can I find the conjugate of (4 - 3√2)?
- Can I rationalize (2 + √3) / (2 - √3)?
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