Number and symbolic readiness diagnostic

This precalculus readiness diagnostic helps you decide which number and symbolic skills deserve review before beginning the main course. It samples signed numbers, fraction arithmetic, percentages, measurement units, substitution, equivalent expressions, exponent notation and principal roots. The aim is to separate a calculation slip from a misunderstanding of notation or a rule.

Attempt the questions without a calculator and write down your reasoning before inspecting the choices. Some questions have one correct answer; others ask you to select every correct statement. If a topic is unfamiliar, make a note of that rather than treating an uncertain guess as evidence of readiness. Review explanations after the attempt to keep the first result useful.

Use patterns in your mistakes to choose practice: real numbers and distance, signed arithmetic, ratios and units, variables and expressions, integer exponents, or principal roots. Each area has several questions, but this short diagnostic does not establish mastery or impose an admission threshold. Revisit the relevant foundation sets, then check your reasoning on new examples rather than memorizing these answers.