Hard Mixed Practice
The first eight questions in this set are not organized by chapter. Most combine familiar skills from different parts of the course, while a few present one familiar skill in a less familiar representation. Both forms are useful preparation for mixed ACT Math work, because the real section does not announce which chapter or method applies before a question begins. Each explanation names the content area or areas the question draws from, but the question itself gives you no such hint, matching real test conditions.
These eight questions are a small, deliberate sample of what synthesis looks like on the section. They lead into the larger bank that follows.
Mixed Challenge Practice
This bank extends the mixed practice at much greater volume. Each of the 52 items either combines familiar mathematics from more than one part of the course or presents a familiar skill in a less familiar representation. Content areas are named only in the explanations, never in the questions, so the method has to be recognized from the problem instead of from a chapter heading.
How to work a mixed set
- Classify first. Before writing anything, name what the question is: an equation, a function, a ratio, a geometry figure, a data question, or a parameter question.
- Choose the route. Hand, handheld, Desmos, or hybrid, using the signals from the route lesson. Consider backsolving, plugging in, or estimating when the choices are numbers or expressions.
- Answer the requested object. Many items here end one step after the equation is solved: the perimeter rather than the width, the sum of the roots rather than a root, square yards rather than square feet.
- Check units and the reference base. Percent changes use the original value; area conversions square the factor.
- Use the Error Ledger. When your answer matches a tempting wrong choice, ask which ledger mistake that choice was built to catch.
If you miss an item, do not simply redo it. Name the failure mechanism, then re-solve it a different way, such as with a quick backsolve or by testing a convenient value.