Advanced Algebra & Functions
Functions, exponentials, logarithms and complex equations
Explanation
Exponentials & Logarithms
- Exponential growth: y = aᵇˣ where b > 1; decay: 0 < b < 1
- log_b(x) = y means bʸ = x
- ln = natural log (base e)
- Laws: log(ab) = log a + log b; log(aⁿ) = n·log a; log(a/b) = log a − log b
Rational Expressions
- Simplify by factoring numerator and denominator, then cancel common factors.
- Adding/subtracting: find LCD, rewrite with common denominator.
- Restrictions: denominator ≠ 0 — always state excluded values.
Absolute Value & Radicals
- |x| = a → x = a or x = −a (two solutions)
- |x| < a → −a < x < a (interval)
- √(a²) = |a|, not a (important for even-degree roots)
- Rationalise the denominator: multiply by √conjugate
Practice Questions
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What does Advanced Algebra & Functions cover in the ISEE Upper Level exam?
Functions, exponentials, logarithms and complex equations.
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