ACT Math Guide: What’s Tested and How to Score Higher

• 45 questions in 50 minutes, or about 67 seconds each. 41 are scored. The other 4 are unmarked field-test questions, so treat every one as real.
• Four answer choices per question, down from five on the legacy ACT.
• Calculator allowed for the whole section. The online test has a Desmos graphing calculator built in. On paper, bring your own permitted calculator. CAS models such as the TI-89 and TI-Nspire CAS are banned. ACT says every problem can be solved without a calculator, and that's worth remembering when you're tempted to punch in something you could do in your head.
• No penalty for wrong answers. Guess on everything you don't finish.

ACT reports math in two big buckets plus a cross-cutting Modeling category. These are ACT's published ranges for the enhanced test:

What that means for you: with 80% of the test in higher math, algebra and functions fluency is where the points are. Arithmetic shortcuts won't carry you. If you're short on time, prioritize linear equations and systems, function notation and graphs, and triangle/circle geometry. Together they cover a big share of the test.

1. Algebra (Modeling): the break-even trap

Gym A charges a $40 sign-up fee plus $25 per month. Gym B has no sign-up fee and charges $33 per month. After how many whole months is Gym A cheaper than Gym B? Choices: 4, 5, 6, 8.

Set up the inequality: 40 + 25m < 33m, so 40 < 8m and m > 5. At exactly 5 months the costs are equal ($165 each), so Gym A is first cheaper at 6 months. The trap is 5: that's break-even, not cheaper. Read the inequality word ("cheaper," "at least," "more than") twice.

2. Functions: composition order

If f(x) = 2x − 3 and g(x) = x², what is g(f(4))? Choices: 13, 25, 29, 64.

Work inside out: f(4) = 2(4) − 3 = 5, then g(5) = 25. The answer is 25. The trap is 29, which is f(g(4)) = 2(16) − 3. The function written closest to the x goes first.

3. Statistics: what an outlier does

A data set is 12, 15, 15, 18, 20. If the 20 is replaced with 60, what happens? Choices: the mean increases and the median stays the same; the median increases and the mean stays the same; both increase; neither changes.

The median is still the middle value, 15. The mean jumps from 80 ÷ 5 = 16 to 120 ÷ 5 = 24. Mean increases, median stays the same. Outliers drag the mean and barely touch the median. That's a favorite ACT concept.

1. Two passes. On the first pass, answer everything you can do in about a minute and flag the rest. On the second pass, go back to the flagged ones. Never let one problem eat three minutes while easier points wait later in the section.
2. Backsolve with four choices. When the question asks for a number and the choices are numbers, plug them in. Start with a middle value. If it's too big, you know which way to go.
3. Pick your own numbers for "which expression" questions with variables or percents. Let x = 2 or the price be $100, then test each choice.
4. Use Desmos for what it's good at (online test): graph both sides of an equation to find intersections, check a system, or find a vertex. Don't use it to double-check 7 × 8.
5. Write the setup. Label what x means before you solve. It takes five seconds and prevents the classic miss where you solve correctly for the wrong thing.
6. Circle the question's last words. "Student tickets," "in square miles," "to the nearest tenth": the answer to the wrong question is often among the choices.
7. Sanity-check with estimation. If a 20% discount leaves the price higher than the original, stop.

• Solving for the wrong variable. You find adult tickets, but the question asked for student tickets.
• Percent of a new base. A 20% drop followed by a 20% rise leaves you at 96%, not 100%.
• Area scale factors. If lengths scale by k, areas scale by k², and volumes by k³.
• Reversed conditional probability. "Of students who prefer online, what fraction are juniors?" divides by a different total than "Of juniors, what fraction prefer online?"
• "Without replacement." The second draw has one fewer item in both the numerator and the denominator.
• Minutes are not decimals. 1 hour 20 minutes is 4/3 hours, not 1.2 or 1.3.
• Negative signs and exponents. −3² = −9, but (−3)² = 9. Put parentheses around negative inputs.
• Radicals don't add inside. √9 + √16 = 7, not √25.

• Slope (y₂ − y₁)/(x₂ − x₁); slope-intercept y = mx + b; midpoint and distance formulas
• Quadratic formula; vertex x = −b/(2a); factoring patterns such as a² − b² = (a + b)(a − b)
• Exponent rules, including a^m/n = (ⁿ√a)^m
• Pythagorean theorem; 30-60-90 (1 : √3 : 2) and 45-45-90 (1 : 1 : √2) triangles; SOHCAHTOA
• Circle: area πr², circumference 2πr, equation (x − h)² + (y − k)² = r²
• Volume: prism lwh, cylinder πr²h; area of a triangle ½bh
• Probability = favorable ÷ total; P(A and B) = P(A) · P(B given A)

Keep an error log with three columns: the question, why you missed it (concept, setup, careless, or time), and the fix. Patterns show up within a week, and fixing them is faster than doing more random problems. For the full test picture, see our ACT guide.