Exponents and Surds notes

This section is the Grade 10/11 picture of the real number system that Grade 12 Paper 1 still assumes. You classify numbers and convert a recurring decimal. You do not work exponent laws, operations…

This section is Grade 10/11 operations with surds that Grade 12 Paper 1 still uses when you simplify. Irrationals are the reals that are not rational: $\mathbb{R}\setminus\mathbb{Q}$. You simplify, add like…

This section is Grade 10/11 exponent laws that Grade 12 Paper 1 still uses when you simplify. You multiply, divide and raise powers, including rational exponents as notation for a root. You do not…

This section solves exponential equations by rewriting both sides as powers of the same base, then equating the exponents. The exponent laws from Exponents are tools here (negative, product, power…

This section solves equations with rational exponents and surds that reduce to a quadratic. Isolate the root or $x^{m/n}$, raise both sides to the reciprocal power, then check domain and extraneous…

This section is mixed Paper 1 exam-type examples for Exponents and Surds. It integrates the four skills you already have: classify and simplify a surd (rationalise if asked); rewrite with exponent…