Practice Choosing a Route

1: B. Hand. This is simple, visible algebra; a calculator adds keystrokes to something already fast.

2: F. Desmos. The lines are already graphed there, and reading the intersection is exactly what Desmos does.

3: B. Handheld. Standard deviation on 15 known values is repeated arithmetic a statistics-mode calculator handles quickly.

4: G. Hybrid. The phrase must be translated into equations first; only then does a tool help with solving them.

5: A. Hand. Recognizing a non-terminating, non-repeating pattern as irrational is a conceptual judgment, not a calculation.

6: H. Handheld. A non-standard angle like 37° needs a calculator's trig function instead of a memorized value.

7: D. Desmos. Graphing the two lines directly shows whether they meet.

8: H. Handheld. A calculator's built-in matrix functions multiply two 3×3 matrices directly, faster and less error-prone than by hand. The ACT's embedded Desmos tool has no dedicated matrix mode to rely on here.

9: C. Hand. Deciding which similarity theorem applies is a conceptual judgment; no tool makes that call.

10: J. Desmos. Reading real roots off a graph is exactly the task Desmos is built for.

11: D. Hybrid. Scaling the recipe is one setup step, and the unit conversion is a separate calculation after it.

12: H. Handheld. A single exact multiplication and division on known values.

13: A. Hand. Simplifying 18/24 is faster by recognizing the common factor than by reaching for a tool.

14: F. Handheld. Compound interest over 10 years is repeated arithmetic on known values.

15: B. Hybrid. The rate must be translated into an equation before any calculation can begin.

16: J. Hand. Recognizing that a probability cannot exceed 1 is a conceptual check, not a calculation.

17: A. Desmos. Reading a vertex directly off a graph is exactly the task Desmos is built for.

18: G. Handheld. A straightforward multiplication of two four-digit numbers.

19: B. Hand. Domain restrictions are found symbolically, a conceptual step no tool performs for you.

20: G. Handheld. A single percent calculation on a known bill total.

21: D. Desmos. Table mode evaluates several inputs at once instead of one at a time.

22: J. Desmos. Graphing sidesteps the fraction arithmetic that makes solving this by hand error-prone.

23: C. Hand. Whether a study design supports a causal claim is a conceptual judgment.

24: H. Handheld. A combination calculation a calculator's nCr function handles directly.

25: C. Hand. The five-number summary is already printed on the box plot; no tool is needed to read it.

26: F. Hand. Translating a phrase into an expression is a conceptual step, not a calculation.

27: B. Desmos. An unfamiliar circle equation is faster to graph directly than to manipulate algebraically.

28: J. Hand. Checking whether a sign makes sense given the problem's context is a conceptual judgment.

29: A. Handheld. Repeated arithmetic across several complex numbers with different signs.

30: H. Hybrid. The rate and percent must be set up correctly before any calculation begins.

31: A. Hybrid. Reasoning through the inverse relationship by hand, then confirming with a few numerical checks.

32: H. Handheld. A single evaluation at a decimal input.

33: C. Desmos. Reading x-intercepts directly off a graphed cubic.

34: F. Hybrid. The scale drawing requires a setup step before the unit conversion that follows.

35: D. Hybrid. Setting up the time for each leg is a hand step; the arithmetic that follows can use any tool.

36: G. Hand. A single substitution to check is faster without reaching for a tool.

37: C. Desmos. Comparing two graphed functions directly confirms the described transformation.

38: F. Handheld. A single volume calculation on known values.

39: D. Hybrid. The percent change and the unit conversion both require setup before any calculation.

40: J. Hand. Classifying a conic from its equation is a conceptual judgment, not a calculation.