1.3 Calculator, Scratchwork, and Setup Habits
Key Takeaways
- ACT allows calculators only on the Math section, and students must use a permitted calculator under ACT policy.
- ACT states that all Math problems can be solved without a calculator, so setup and judgment matter more than keystroke speed.
- CAS calculators and several device types are prohibited; digital ACT testers have access to Desmos during the Math section.
- Efficient scratchwork should record the target, formula, units, and final check so intermediate results do not become wrong answers.
Know the Calculator Policy Before Test Day
ACT allows calculators on the Mathematics test, but the calculator must be permitted. ACT says testing staff do not provide calculators, sharing calculators is not permitted, and students are responsible for making sure their calculator follows the policy. Four-function, scientific, and graphing calculators are generally allowed unless a specific model or feature is prohibited.
The major policy trap is computer algebra system functionality, often called CAS. ACT prohibits calculators with built-in or downloaded CAS functionality, including TI-89 or TI-92 models, TI-Nspire CAS, HP Prime, HP 48GII, HP 40G, HP 49G, HP 50G, and several Casio ClassPad or Algebra fx models. ACT notes that TI-Nspire without CAS is permitted.
| Policy area | What to do | Why it matters |
|---|---|---|
| Permitted model | Check ACT's current calculator policy before the test. | A prohibited model can lead to dismissal for prohibited behavior. |
| Power | Bring fresh batteries or a charged calculator, plus backup if allowed by your test setting. | A dead calculator should not decide a Math score. |
| Programs/documents | Remove documents and remove programs with CAS functionality. | ACT requires modifications for certain calculators. |
| Digital ACT | Practice with the built-in Desmos graphing calculator if testing online. | Familiar tools are faster than new tools under pressure. |
| Sharing | Do not plan to borrow from another examinee. | ACT does not permit calculator sharing. |
The policy is not the same as strategy. A calculator may be allowed, but ACT's official guidance says all Math problems can be solved without one and many are best done without one. That sentence should change how you practice: choose the tool after reading the math, not before.
Calculator Judgment: Setup First, Keystrokes Second
A calculator cannot fix the wrong equation. On ACT Math, the most expensive calculator mistakes usually begin before the first button press: using diameter where radius is needed, entering -3^2 when the intended value is (-3)^2, staying in radians for a degree trig problem, or calculating the mean when the median is requested.
Use this decision guide:
| If the question asks for... | Usually do this first | Calculator role |
|---|---|---|
| A simple linear equation | Isolate the variable by hand. | Check arithmetic only if numbers are ugly. |
| Percent change | Write (new - original) / original. | Divide and convert to percent. |
| A graph or table trend | Read axes, units, and scale. | Compute slope or regression only after the model is clear. |
| Trig in a right triangle | Label opposite, adjacent, hypotenuse. | Evaluate sine, cosine, or tangent if needed. |
| A quadratic | Try factoring or identify the formula. | Use numeric solving only after deciding what solution means. |
| A probability chain | Define the sample space and whether events are independent. | Multiply or divide once the cases are correct. |
Worked Example: Calculator Helps, But Setup Wins
A price rises from 80 dollars to 92 dollars. The question asks for percent increase. A calculator-first student may type 92 / 80 = 1.15 and accidentally answer 115%. The setup-first student writes percent change = (92 - 80) / 80 = 12 / 80 = 0.15, so the percent increase is 15%. The calculator was useful only after the numerator and denominator were chosen correctly.
Worked Example: Backsolving Has a Time Limit
Backsolving is powerful when choices are numeric and the algebra is messy. Start with a middle-sized choice if the choices are ordered, substitute, and see whether the result is too high or too low. But ACT's official Math tips warn that working backward from all four choices can take too much time. Use backsolving as a targeted tactic, not as the default for every problem.
Scratchwork That Prevents ACT Math Errors
Good scratchwork is not a full notebook solution. It is a control system. Its job is to preserve the target, the structure, and the final check while you move quickly. For each nontrivial problem, write four pieces: question number, target variable, setup, and final unit or reasonableness check.
A compact template looks like this:
- Q# and target: Q18, find radius, not diameter.
- Formula/model: A = pi r^2 or slope = change in y / change in x.
- Substitution: Put numbers into the model before simplifying.
- Check: Unit, sign, size, and whether the question asked for an intermediate or final value.
This habit catches common ACT traps. If a circle question gives diameter 10, writing target: radius makes you use 5 in area. If a similar-figures question gives side scale 3, writing area scale = k^2 prevents using 3 when the area factor is 9. If a radical equation required squaring both sides, writing check original reminds you to test for extraneous solutions.
Setup Habits by Problem Type
- Algebra: Line up equal signs vertically and circle the final requested variable. Inequalities need an extra sign-flip check when multiplying or dividing by a negative.
- Functions: Substitute inside out. For f(g(3)), compute g(3) first, then feed that result into f.
- Geometry: Redraw messy figures if needed, label units, and mark right angles, parallel lines, radius, diameter, and equal sides.
- Statistics: Sort before finding a median. Identify outliers before deciding whether mean or median is more stable.
- Probability: Write total outcomes and favorable outcomes. For at least one, consider complement probability.
Test-Ready Setup Routine
Before a timed practice section, set the calculator to the mode you expect to need, clear distracting old entries, and place scratch paper or the test booklet so your work stays aligned. During the section, write enough to let you return to a skipped item without rereading from zero. After the section, review not just wrong answers but messy right answers. A correct answer with disorganized work may become a miss under pressure.
The goal is not to avoid the calculator. The goal is to make the calculator serve the math you already understand.
Which statement best matches ACT calculator policy and strategy?
A circle problem gives a diameter of 12 and asks for area. Which scratchwork habit best prevents the common trap?
When is backsolving most appropriate on ACT Math?