The ACT requires basic skills in arithmetic, geometry, algebra, and a little bit of trigonometry. If you have had two semesters of algebra, two semesters of geometry, and a general math background, you can answer probably 90 percent of the questions.
The ACT Mathematics Test asks you to answer 60 multiple-choice questions in 60 minutes. The questions are designed to measure your achievement of the mathematical knowledge, skills, and reasoning techniques; they cover a full range of math topics, from pre-algebra and elementary algebra through intermediate algebra, coordinate geometry, plane geometry, and even trigonometry. You are allowed to use a calculator on the Mathematics Test. However, the questions on the test are designed to emphasize your ability to reason mathematically, not to test your computation ability or your ability to recall definitions, theorems, or formulas.
Pre-algebra questions involve solving problems using the mathematics like operations using whole numbers, fractions, decimals, and integers; numbers raised to positive integer powers and square roots of numbers; ratio, proportion, and percent; multiples and factors of integers; absolute value; ordering numbers from least to greatest or greatest to least; linear equations with one variable; simple probability and counting the number of ways something can happen; representation and interpretation of data in charts, tables, and graphs; and simple descriptive statistics like mean, median, etc.
Elementary algebra questions test your ability to solve problems using variables to express functional relationships, substitution, operations on polynomials, factoring and solving simple quadratic equations, linear inequalities with one variable, and properties of integer exponents and square roots.
Intermediate algebra questions ask you to apply your knowledge, skills, and reasoning ability to solve problems like the quadratic formula, radical and rational expressions, inequalities and absolute value equations, sequences, systems of equations, quadratic inequalities, functions, matrices, roots of polynomials, and complex numbers.
Coordinate geometry questions deal with the real number line and the (x,y) coordinate plane. They cover number line graphs as well as graphs of points, lines, polynomials, and other curves in the (x,y) coordinate plane. They also cover relationships between equations and graphs, slope, parallel and perpendicular lines, distance, midpoints, and conics.
Plane geometry questions test your grasp of topics that are usually part of high school geometry. Included are the properties and relations of plane figures; angles, parallel lines, and perpendicular lines; translations, rotations, and reflections; proof techniques; simple three-dimensional geometry; and measurement concepts like perimeter, area, and volume.
Trigonometry questions cover the trigonometric ratios defined for right triangles; the values, properties, and graphs of the trigonometric functions; trigonometric identities; and trigonometric equations.
Here is what the Math directions may look like:
Directions: Solve each of the following problems, select the correct answer, and then fill in the corresponding space on your answer sheet.|
Don't linger over problems that are too time-consuming. Do as many as you can, then come back to the others in the time you have remaining.
Note: Unless otherwise noted, all of the following should be assumed.
- Illustrative figures are not necessarily drawn to scale.
- All geometric figures lie in a plane.
- The term line indicates a straight line.
- The term average indicates arithmetic mean.
Again, don't read the directions on the test day. Know the directions beforehand.
About a third of the Math questions either give you a diagram or describe a situation that should be diagrammed. For these question, the diagrams are crucial and you should pay close attention to them.
In ACT math questions, the answer choice "cannot be determined" is rare. When you see it, it's very likely wrong. It's almost always wrong in a question that comes with a diagram or for which you can draw one.
Testing strategies for Math Questions are discussed in the later section "ACT Strategies".
If you want to start practicing now, click here to login "ACT Practice" section.