Isolating, multiplying and writing as intervals every kind of inequality, from the simplest to the rational ones.

We start with 2×2 determinants and work through Sarrus and cofactors (minors) up to 4×4 matrices.

Ordering and laying out the terms, running the algorithm and turning the result back into a polynomial.

We work out how long division (with the box) works, and what the remainder means.

We start with the power rule, rewrite roots and fractions as powers, use the derivative for the tangent line, and end up differentiating (5 − 3x)⁷ with the chain rule.

We learn the table — sine, cosine, exponential, logarithm — and then differentiate functions nested inside others, up to two layers.

Limits in your head: polynomials at a point and at infinity, the three cases of rational functions, who grows faster among ln x, √x, x⁵ and eˣ, and the 0/0 and 1^∞ forms you can do once you know that near 0, sin x looks like x.

What a power is (negative exponents too: 5⁻² = 1/25), the rules for combining them, fractional exponents and roots, and how to simplify 36⁶/6¹¹ by changing the base. All with small numbers.

A logarithm is an exponent: work them out in your head (log₂(1/8) = −3 too), take the exponents of the base and the argument outside, combine log₃ 4.5 + log₃ 2 into a single logarithm, and solve equations like 3ˣ⁺¹ = 1/9.