Mathematics from zero
Algebra: free-recall review
Recall beats re-reading. For each prompt, say or write a full answer from memory — work the small example by hand — before you open the model answer. The effort of pulling it back is what makes it stick.
Reconstruct the unit’s spine without looking back: what a variable is, how an expression differs from an equation, what combining like terms means, why the balance rule keeps an equation true, and why an inequality’s answer is a range.
- 01What is a variable, and what two jobs can it do?
- 02How does an expression differ from an equation, and how do you find an expression's value?
- 03What are like terms, and why can only like terms be combined?
- 04State the balance rule and explain why solving an equation depends on it.
- 05Why is an inequality's answer a range rather than a single number?
- 06How is solving an inequality the same as solving an equation, and what is the one extra care point at this level?
If you could reconstruct each answer from memory, you hold the unit’s spine: a variable names a number (unknown or changing); an expression is a recipe you evaluate by substituting and simplify by combining like terms; an equation adds an equals sign and is solved by the balance rule — same move to both sides — undoing operations with inverses; and an inequality uses the same rule but, because it asks which side of a boundary, answers with a whole range. The chain runs from naming a number to pinning it to bounding it.