# The ACT Math Test

### Written by tutor Nicole T.

Many of you have taken the ACT and possibly have taken it multiple times. For those of you who are preparing for the first time or who have taken it before and want to improve your score, we want to equip you to do your best. **The ACT math** problems are very reflective of the classic high school math track of Prealgebra, Algebra I & II, Geometry, and Trigonometry. There is no Precalculus or Calculus on the test – fantastic, right?

Let’s look at some specifics of the test. The math test is 60 minutes with 60 multiple-choice questions. The material for the questions are taken from six areas:

- Prealgebra
- Elementary Algebra
- Intermediate Algebra
- Coordinate Geometry
- Planar Geometry
- Trigonometry

There are 14 Prealgebra questions, 10 Elementary Algebra questions, 9 Intermediate Algebra questions, 9 Coordinate Geometry questions, 14 Plane Geometry questions, and 4 Trigonometry questions. So 33 of the 60 questions are from the algebra categories.

## Content Descriptions

### Prealgebra

The Prealgebra concepts test your skills of the math you learned throughout elementary and middle school. The math topics include decimals, fractions, ratios and proportions, absolute values, place values, basic exponents, data interpretation, integers, order of operations, monomials (linear equation or polynomial with 1 variable), number sequences, negative numbers, basic probability and statistics, and square roots.

### Intermediate Algebra

The Intermediate Algebra concepts test your skills and reasoning of Algebra II topics. The math topics include absolute value equations with inequalities, complex numbers, rational expressions, radical expressions, systems of linear equations, matrix algebra, sequences and series, polynomials, and roots of polynomials.

### Coordinate Geometry

The Coordinate Geometry concepts test your skill and reasoning of Geometry, which is typically taught along with Plane Geometry concepts in the sophomore or junior year. The math topics include graphing, ordered pair (or points), lines (parallel, perpendicular, slope, midpoints), circles, curves (conics), and more polynomials.

### Plane Geometry

The math topics include properties of polygons, triangles, quadrilaterals, circles; area, volume, formulas; area, volume, circumference, perimeter; parallel lines, perpendicular lines, angles, and proofs.

### Trigonometry

The math topics include trigonometric identities, relationships, properties, functions, values, and equations of right triangles.

## Preparation and Test Strategy

I know what you are thinking: This is a lot of material. Nine times out of ten, students probably like math the least. It is possible for you to perform well on the ACT despite that, if you want to. Preparation is the key. It is unrealistic for most students to walk in and perform well on the test. If you give yourself time to review and practice, you have just as much chance to get the score you want as if you liked math. Plus we will cover some strategies with you but there are no smoke and mirror tricks to achieve a 36. Anyone can do well on the math test with good studying and practice of the concepts. It typically takes 3-4 years to take all of the courses included in the ACT math content, so it only makes sense that it will also take time to prepare. Take advantage of free ACT prep courses through your school (if offered). It is becoming commonplace for high schools to provide preparation classes. The caveat however is: Engage yourself, do some problems at home, take it seriously and come to class with questions. Get the help you need “while the getting is good.” The preparation is for you, but you get out of it what you put into it.

Additionally taking the test more than once to achieve your best score is a good idea. Test-taking is a skill in and of itself. I suggest taking the test for the first time at midterm or after of the junior year just for practice. The average student has taken math classes covering most of the test content at that grade level. The objectives for repetitive ACT tests should be overcoming test anxiety, noting your weak areas, focusing your review efforts on your low scoring areas after each test, and improving your score with each test. When you register for the ACT select the option to receive the answers with your score report. Part of learning is finding out which problems you missed, reviewing the concepts, and working or re-working the problems correctly.

## Tips for the ACT Math Section

**Create a study schedule.** You probably have other obligations in your life. You might be an athlete, and have practice and games to balance. Starting at least 6-8 weeks prior to the test is ideal if you can. This will allow you to break up each math category and spend an hour or two, 2-3 evenings per week reading, studying, and working practice problems. If you are preparing by yourself, the more time you schedule out from the test and spend working/practicing, the better.

**Start with Prealgebra and progress through Elementary Algebra, Intermediate Algebra, Plane Geometry, Coordinate Geometry, and Trigonometry in your review and study plan.** Use your judgment and spend more or less time where you need it most. If you need more time on Intermediate Algebra and Geometry concepts , then take it. It will pay off. This is a great order to study because it builds in difficulty. Plus, let’s say you review the first 3-4 categories prior to a test and don’t get to the last 2. You have reviewed the categories that offer the most points. The first four categories provide the following number of points respectively: 14 + 10 + 9 + 14 = 47 total.

**Wear a watch and time yourself during the test.** With 60 minutes to answer 60 questions that averages 1 min/question. That is pretty tight even for the best of math students.

**Shave time on test questions 1-30.** They are typically more basic and can be answered quickly. When you get to number #15 glance at your watch to see where you are and then again around #20 or #25. Your objective is to complete questions 1-30 in less than 30 minutes. Do not look at your watch after every problem, this will create anxiety instead of the edge and confidence we want you to have. For example, if you reduce 20-30 seconds on each question the first half of the test, will give you 10-15 minutes to use on questions 31-60. The latter half of the test is more difficult and may require additional time. It is well worth the effort: getting as many of these questions right is the key to a higher math score. The math score is scaled per the version of test but for example, 31-32 correct answers typically yields a 20 composite score. That is an excellent curve. Getting half of the questions right yields a 20. The national average reports 51% of high school students score a 20 or less on the math portion. Earning just 10 additional points will yield a 25 composite score.

**Do not leave any questions unanswered.** You are not penalized for incorrect or unanswered questions. You have the opportunity to gain points by rationalizing or guessing the answer. I am sure at some time or another you have probably heard the advice to come back to problems you are not sure how to do, when taking a multiple-choice test. I am advising that too. Just do this: select an answer before moving forward in these cases. Jot down the number on your scratch sheet for those problems that you guessed. If you find that you have time to come back to them later, great! But in the event that you don’t have time, at least you didn’t leave it blank. You could forget to come back or run out of time.

**Program your calculator in advance.** You can use an approved calculator on the test. Use this to your advantage. This will also save you a great deal of time plus will help you get those additional points on questions 31-60. This is so super awesome and important!

**Do a stress relieving exercise before the test.** Write down your thoughts and feelings prior to taking the test if you are feeling a high degree of pressure and anxiety. This exercise is powerful. Students respond to stress differently of course but some experience almost crippling stress. This stress creates panic that affects the memory and results in poor performance and ultimately a lower score. Write down your feelings and fears associated with the test. Do this the night before or the morning of. The result of the research showed that when a student wrote all of their fears and feelings about the test down it allowed the students to relax, regain their composure, and perform well on the test. Those feelings were no longer bottled up.

Write short empowering, positive, and encouraging phrases.

- I can do this!
- No problem
- Nothing is too hard for me!
- Envision yourself succeeding and imagine getting a high composite score.

Most students who panic in this manner imagine themselves failing, the repercussions of failing, not getting in to the school they want, etc. Instead of looking at the negative, picture the positive: winning and accomplishing your goals!

## ACT Math Scoring

On the Math section there are 3 subscores that make up the total raw score. The math composite score is scaled and may vary from version to version. The subscore categories come from the following:

Prealgebra/Elementary Algebra | 24 questions | 24 points |

Intermediate Algebra/Coordinate Geometry | 18 questions | 18 points |

Plane Geometry/Trigonometry | 18 questions | 18 points |

Raw Score Total |
60 points |

## Raw Score Conversion Chart

Scale Score |
Raw Score |
Scale Score |
Raw Score |

36 | 60 | 18 | 25 |

35 | 58-59 | 17 | 22-24 |

34 | 56-57 | 16 | 18-21 |

33 | 55 | 15 | 15-17 |

32 | 54 | 14 | 12-14 |

31 | 52-53 | 13 | 9-11 |

30 | 50-51 | 12 | 8 |

29 | 48-49 | 11 | 6-7 |

28 | 46-47 | 10 | 5 |

27 | 43-45 | 9 | 4 |

26 | 41-42 | 8 | — |

25 | 39-40 | 7 | 3 |

24 | 37-38 | 6 | 2 |

23 | 35-36 | 5 | — |

22 | 33-34 | 4 | — |

21 | 31-32 | 3 | 1 |

20 | 30 | 2 | — |

19 | 27-29 | 1 | 0 |

### Example ACT Score 1

Let’s look at the scale ratio. 60 points = 36 composite. Let’s say your raw score is 50. Divide 50 by 60 to determine the % raw score. Then multiply that by the scale score of 36.

**Step 1:** 50/60 = 0.833 x 100% => 83.33%

**Step 2:** .8333 x 36 scale score = 29.9 which rounds up to 30.

That process does not necessarily work as accurately with the middle raw scores. There is a curve, which is great! There is usually a curve for the middle scores but again it varies based on the version and is subject to change by the ACT test makers. You can review at a sample score report provided by the ACT.

### Example ACT Score 2

Let’s say your raw score is 30. We will determine % raw score by dividing 30 by 60.

**Step 1:** 30/60 = 0.500 x 100% => 50.0%

Multiply that by 36…

**Step 2:** 0.500 x 36 = 18

If you multiply the % raw score by 36 it equals 18. However, according to our conversion chart above, a 30 raw score yields a 20 composite score, not an 18. What’s up with that? There is a curve! Let’s see what the curve is. So let’s define our multiplier as x.

**Step 1:** 18x = 20

**Step 2:** Let’s divide both sides by 18 to solve for x.

18/18 x = 20/18 => x = 20/18

x = 1.11

1.11 x 100% = 111%

The curve in this example 111%, which means you gain an additional 11% on the composite score scale. That’s awesome! I’ll take it! Let’s work on what you need to know to get a good score now!