Algebra Foundations

Review algebra habits that support calculus, including factorising, indices, and rational expressions.

Focus points

Simplify expressions without losing sign accuracy.

Manipulate powers, roots, and fractional indices.

Factorise quadratics and common polynomial structures.

Session plan

Start with the first two questions to warm up before moving into the harder ones.

Use the calculator only after you have set up the working or estimated the answer.

Work through the page like a focused study sheet instead of jumping around.

How to use this page

A cleaner maths workflow

1. Read the prompt carefully

These pages are meant to feel consistent with the rest of the site, but the maths stays front and center.

2. Solve in order

The question list works best as a progression rather than a random set of cards.

3. Use support tools when needed

You can jump back to the calculator or home without losing the overall flow.

Practice set

6 revision prompts

Question 1

Simplify

\frac{6 x^{3}}{2 x}

Question 2

Factorise

x^{2} - 9

Question 3

Solve

2 x^{2} - 7 x + 3 = 0

Question 4

Rewrite

\sqrt[3]{x^{5}}

using fractional indices.

Question 5

Simplify

\frac{x + 3}{x + 1} + \frac{x - 1}{x + 1}

Question 6

Expand

(3 x - 2) (x + 5)