Algebra notes

This section is expanding products of algebraic expressions and the reverse skill, factorisation. You multiply a monomial, binomial, or polynomial through brackets, then collect like terms. You also…

An algebraic fraction is a fraction whose numerator, denominator, or both contain variables. This section is how to simplify, multiply, divide, add, and subtract those fractions: after you can…

This section is solving quadratic equations: equations of degree 2, where the highest power of the variable is $2$. In Grade 10 you rearrange to standard form, factorise, then use the zero-product…

This section is two skills that sit on top of ordinary equation-solving. Word problems ask you to turn a story in words into an equation, solve it, and answer in context. Literal equations (formulae…

A linear equation is an equation of the first degree: the highest power of the variable is $1$. A linear inequality looks similar, but uses $<$, $>$, $\leq$, or $\geq$ instead of $=$. This section is how to solve…

This section is solving two linear equations in two unknowns at the same time. You find one pair of values $(x,y)$ (or $a,b$) that satisfies both equations. Grade 10 uses two algebraic methods…

This section is the real-number system: how natural, whole, integer, rational and irrational numbers nest inside $\mathbb{R}$, what a surd is, and how to round off real numbers. Stay with classification…

This section is Grade 10 exponents: what a base and exponent are, the laws of exponents, how to simplify expressions, and how to solve exponential equations by matching bases. Surd arithmetic (like…