How ACT Math Works

Learn the format, scoring, and tools of ACT Math, plus how this course turns 45 questions in 50 minutes into a 36.

25 min

Ready when you are

7 steps · about 25 minutes

Start with the warm-up.

Start

Step 1 of 7Warm-upDone

Warm-up

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Key terms

Raw score: The number of scored questions you answer correctly, out of 41.
Scale score: The 1–36 score you receive, converted from your raw score.
Field-test questions: The 4 unscored questions hidden among the 45. You can't tell which ones they are, so treat every question as real.
Preparing for Higher Math: About 80% of the scored questions, from Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability.
Integrating Essential Skills: About 20% of the scored questions, built on ratios, percents, rates, units, area, and word problems.
Modeling: A tag on at least 20% of questions that use math to describe a real situation. Those questions also count in their regular category.

Two quick ones to switch your brain into test mode. Watch the negative signs.

Step 2 of 7Try it firstDone

Try it first

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Take a shot before we explain how scoring works. There’s no penalty, and a guess now makes the idea stick later.

Step 3 of 7LearnDone

The big idea

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45 questions, 50 minutes

Think of the test as a 45-lap race on a 50-minute clock. That’s about 67 seconds a lap, but the laps get steeper: questions run from easy to hard. Bank time early so you can spend it on the last ten.

Every question has 4 choices. Some questions share a graph, table, or other information, so check which information belongs to your question.
There’s no formula sheet. Learn the formulas this course uses, including trigonometry; use any additional formulas supplied in a question.
Only 41 questions are scored. The other 4 are hidden field-test questions, and you can’t tell which. Treat every question as real.

Average pace

\frac{50 \times 60 \text{ seconds}}{45 \text{ questions}} \approx 67 \text{ seconds per question}

That’s an average, not a speed limit. Go faster early so you can go slower late.

One plan that fits: 15 × 40 + 15 × 65 + 15 × 95 = 3,000 seconds = 50 minutes.

How the score works

Your raw score is the number of scored questions you get right, out of 41. It converts to a scale score from 1 to 36, and the top of that scale is steep. Here’s how it has worked on recent official forms:

Scored questions missed	Raw score	Scale score
0 or 1	40 or 41	36
2	39	35
5	36	about 30 to 32

Key idea

Accuracy decides a 36

Every question is worth one point, easy or hard. A 36 leaves room for about one scored miss, so the hardest questions at the end decide it. And a careless slip on question 6 costs exactly as much.

What’s on the test

The 41 scored questions fall into reporting categories:

Preparing for Higher Math, about 80% (roughly 33 questions): Number and Quantity (N), Algebra (A), Functions (F), Geometry (G), and Statistics and Probability (S).
Integrating Essential Skills, about 20% (roughly 8 questions): ratios, percents, rates, units, area, and multistep word problems (E).
Modeling, at least 20%: a tag, not a separate pile. A modeling question describes a real situation and still counts in its N, A, F, G, S, or E category.

This course is organized by those same six letters, so you always know which part of the test you’re building.

Trap

The wrong-question trap

Most early misses aren’t hard math. They come from finding $x$ when the question asked for $x^2$ , or stopping at a number from the middle of the work. The ACT puts those exact numbers in the choices. Before you click, reread the ask. That’s what the highlighter is for.

Your tools, and how this course works

The online test gives you an answer eliminator (cross out choices), answer masking (hide choices while you work), a highlighter, a line reader, a magnifier, mark for review, a timer you can hide, and built-in Desmos, which starts in degree mode. There’s no penalty for guessing, so never leave a question blank.

Every lesson follows seven steps: warm-up, try it first, the big idea, worked examples, practice, spot the mistake, and an exit ticket. Choose an answer, select Sure, Think so, or Guessing, then press Check answer. Every confidence choice earns the same Funding; honest calls help target your review. Hints fade as you get stronger, and solid practice earns Funding and fuel for your next launch.

Explore in Desmos

Check the mode

The ACT's Desmos starts in degrees. Read the value next to sin(30): 0.5 means degree mode. In radian mode you'd see about -0.988.

The calculator is live: change anything and see what happens.

Check the mode

Degree mode

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Step 4 of 7Worked examplesDone

Worked examples

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Find your pace

Problem

You have 20 minutes left and 16 questions to go. If you split the time evenly, how many seconds can you spend on each question?

Pace is time left divided by questions left. The answer should be in seconds, so what comes first?

Predict the next move

Convert:

20 \times 60 = 1200

seconds left.

Divide by the questions left: $1200 \div 16 = 75$ seconds per question.

Why does this step work?

Check:

16 \times 75 = 1200

seconds, exactly 20 minutes. That’s above the 67-second average, so you’re in good shape.

Worked example

Example 2: Answer the question they asked

Problem

3(x - 4) = 5x + 2

, what is the value of

x^2

Distribute the 3:

3x - 12 = 5x + 2

Subtract $3x$ from both sides: $-12 = 2x + 2$ .

Predict the next move

Subtract 2:

-14 = 2x

, so

x = -7

. Keep that negative sign.

Now answer the ask. The question wants $x^2$ , not $x$ : $(-7)^2 = 49$ . On the real test, $-7$ and $-49$ would both be waiting in the choices.

Why does this step work?

Faded example · you finish it

Example 3: You finish it

Problem

On one form, raw scores of 40 or 41 convert to a 36, and 39 converts to a 35. Marco answers all 45 questions and misses 3. One of his misses turns out to be an unscored field-test question. What are his raw score and his scale score?

Unscored questions never count, so only

3 - 1 = 2

of Marco’s misses cost him a point.

His raw score is

So his scale score is

Desmos way

The Desmos way for Example 2 (15 seconds)

Type the equation exactly as written: 3(x-4)=5x+2. Desmos draws a vertical line.

Click the line: it sits at

x = -7

The ask is

x^2

, so type (-7)^2 on line 2. Desmos prints

49

The Desmos way for Example 2 (15 seconds)

Degree mode

Loading Desmos…

Step 5 of 7PracticeDone

Practice

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These look like questions from the first third of the test. Read each ask twice before you click.

Speed drills

Quick mixed drills. Aim for under 45 seconds each, and report your confidence honestly before checking.

Step 6 of 7Spot the mistakeDone

Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

Step 7 of 7Exit ticketDone

Exit ticket

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