ACT Pre-Algebra & Elementary Algebra: Fast, Careful Fundamentals

This is the largest of the three ACT math topics, and the questions in it are individually easier than the Intermediate Algebra and Geometry topics. The catch is pace: at roughly a minute a question, this topic is won or lost on avoiding small, avoidable slips, not on knowing advanced material.

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Did you know

Because this topic covers foundational material, it's the one section of ACT Math where accuracy should be close to perfect. Missing points here usually costs more than missing an equally-weighted question in a harder topic, since these are the questions you're expected to get right quickly.

What's tested

Five question types show up constantly. Each one below has the quick version, plus a "Learn more" if you want the deeper strategy.

Ratios and proportions

Setting up a proportion correctly and solving for the missing value, often dressed up as a word problem.

Learn more: setting up the proportion so it can't flip

Keep the same units in the same position in both fractions. If the first ratio is miles over hours, the second one has to be miles over hours too, not hours over miles.
Cross-multiply once you've set it up correctly, that's usually the fastest way to solve, faster than simplifying the fraction first.
Word problems often bury the ratio in a sentence. "For every 3 apples, there are 2 oranges" is the ratio 3:2, write it down as a fraction immediately instead of trying to hold it in your head.

Percentages

Percent of a number, percent change, and multi-step percentage problems like discounts followed by tax.

Learn more: the multiplier shortcut and the sequential-percentage trap

Convert percent to a decimal multiplier and multiply directly: "30% of 80" is 0.30 × 80, faster than setting up a proportion for straightforward percent-of questions.
Percent increase or decrease: new value = original × (1 ± the decimal rate). A 15% increase is × 1.15, a 15% decrease is × 0.85.
Sequential percentages don't add. A 20% discount followed by a 10% discount is not a 30% discount, it's 0.80 × 0.90 = 0.72, a 28% total discount. Apply each step separately, in order.

Exponents and radicals

The rules for multiplying, dividing, and raising powers, plus simplifying square roots.

Learn more: the exponent rules that actually get tested

Multiplying same base: add exponents. x³ · x⁴ = x⁷. Dividing same base: subtract exponents. x⁷ ÷ x³ = x⁴.
Power to a power: multiply exponents. (x³)⁴ = x¹². This one gets mixed up with the multiplication rule constantly, double-check which situation you're in.
A negative exponent means reciprocal, not negative. x⁻² = 1/x², not −x². This is one of the most common careless errors on the whole test.
Anything to the zero power is 1 (except 0 itself), regardless of how complicated the base looks.

Linear equations in one variable

Solve for x, the same core skill tested throughout algebra, but usually the most straightforward version of it here.

Learn more: solving cleanly under time pressure

Combine like terms on each side first, before moving anything across the equals sign, it cuts down on sign errors.
Backsolve when the equation looks messy. Plug in answer choice B or C, and let whether the result is too big or too small tell you which direction to try next.
Always double-check your answer in the original equation, not your simplified version, that's the step that catches an arithmetic slip.

Basic probability and simple statistics

Probability of a single event, and reading averages, medians, and simple data sets.

Learn more: probability as a fraction, and the mean shortcut

Probability = favorable outcomes over total outcomes. Count both carefully before dividing, most errors here come from miscounting the total, not the math itself.
Mean = sum of all values divided by how many values there are. If a question gives you the mean and asks for a missing value, work backward: total = mean × count, then subtract the known values.
Median is the middle value once the data is sorted. Always sort first, an unsorted list makes the middle value meaningless.

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Gotcha

Here's the classic trap, almost word for word how it shows up: "A shirt originally priced at $40 is discounted 25%, then the sale price is increased by 25%. What is the final price?" Students often assume the two 25% changes cancel out and answer $40. They don't: 25% off $40 is $30, then 25% of $30 added back is $37.50, not $40. Percent changes applied to different base values never simply cancel. Whenever you see a percent decrease followed by a percent increase (or vice versa), recalculate each step from its own new base value.

A quick sanity check before you lock in an answer

Plug your answer back into the original word problem, not just the equation you built from it, and ask whether the number makes sense in context. A "percentage" answer over 100 or a "number of people" answer that isn't a whole number usually means an earlier step went wrong.

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Quick tip

If a word problem is taking too long to translate into an equation, try backsolving from the answer choices instead. On a topic this pace-sensitive, a fast, reliable method beats a "purer" one that takes twice as long.

Reading about the traps is step one.

Ember has original Pre-Algebra and Elementary Algebra questions, each with the reasoning explained the same way, including exactly which trap answer it's testing.

Practice this topic now