ACT Math Strategies
ACT Math Strategies and Tactics: ACT Test Prep Tips
- Solve the problem first, then locate your answer, rather than plugging each option into the problem.
- Use all of the time provided. You don’t get extra points for finishing early.
- Go back and check your work. If nothing else, check any problems you weren’t particularly sure of.
- Use scratch paper to figure stuff out. Draw pictures, and simplify algebraic expressions. You don’t receive extra credit for doing math in your head.
- DON’T spend more than one minute on any problem on your first tour through the exam. The test is designed to give you plenty of time, but don’t waste any minutes early on. You are better off missing one hard problem than not getting to four easy problems at the end of the test.
- DON’T do any complicated computations that need a calculator. A calculator isn't required, so if your solution absolutely depends on one, you are probably headed down a time-consuming and incorrect path.
- DON’T leave any questions unanswered. Even if you have no idea what the question means, you should give it your best shot, and then just bubble something in. You have a small chance of guessing correctly, and incorrect guesses aren’t penalized.
There you have it. Next up is a detailed breakdown of each math subject area, or river monster, that you will encounter on the test and instructions on how to hook it successfully. Once you land these fish, you can take a nice photo with the giant before releasing it back into the wild and returning home with a big grin and a great story.
The Monsters, Unabridged: Getting to the Meat of These Predators
Pre-Algebra: The Piranha
When you take on this little tough guy, expect to be tested on the basics. Pre-algebra questions are generally about being able to perform simple operations on whole numbers, integers, fractions, and decimals. This includes exponents, roots, taking the absolute value, and ordering lists of numbers from least to greatest.
You must be able to:
- Compute greatest common multiples
- Find simple probability
- Find factors
- Find ratios, proportions, and percents
- Recognize small primes
- Recognize patterns that describe a sequence
- Solve simple linear equations
- Reading and representing data in charts, tables, and graphs
Elementary Algebra: The Alligator Gar
These fish are super flighty and will vanish if you so much as drop a pebble in the river where they are lurking. In other words, catching this fish depends on a lot of different variables.
Elementary algebra introduces variables, and you’ll mostly be tested on how to use them in a variety of equations and expressions.
You should be:
- Comfortable using equations to relate two variables
- Able to solve linear and quadratic equations and linear inequalities
- Able to add and factor polynomials, as well as solve for their roots
- Able to substitute
- Familiar with order of operations to simplify expressions involving variables
Intermediate Algebra: The Goliath Tigerfish
Like landing an elusive tigerfish in the turbulent cataracts of the Congo Basin, intermediate algebra involves solving more complicated problems.
You must be familiar with:
- The quadratic formula
- Radical and rational expressions
- Complex numbers
You also must be able to:
- Find the roots of polynomials as zeros of an associated function
- Solve systems of equations
- Recognize patterns in sequences
- Solve equations involving absolute value and inequalities (both linear and quadratic)
Plane Geometry: The Giant Freshwater Stingray
Plane geometry involves recognizing shapes that lie on a plane, like a massive, flat stingray.
You will be tested on:
You should understand:
- What angles are and what their measurements can be
- General proof technique should also be familiar to you
- How to compute the surface areas and volumes of simple 3D shapes
- Basic postulates and definitions about parallel and perpendicular lines
- Names of simple 3D shapes should be known
- The basic ways to translate, rotate, and reflect a shape to obtain a congruent shape
- General facts about congruent triangles used in proof
- How to compute perimeters and areas of 2D shapes
Coordinate Geometry: The Goonch Catfish
When you take on this man-eater from the Himalayas, you need to have your graphing skills in line. Coordinate geometry involves familiarity with and the use of the standard (x, y)-coordinate plane (a.k.a. the Cartesian plane). You must be familiar with labeling points in the plane. Familiarity with the real number line, inequalities, and number line graphs are also prerequisites.
You must be able to:
- Graph functions
- Determine slopes of lines
- Recognize and graph the equations for points, lines, polynomials, and circles
- Compute distances between points
- Recognize the equations of parallel and perpendicular lines
- Understand the transformations: translation, rotation, and reflection
- Calculate midpoints of line segments
- Understand the relationship between graphs and functions
And you should be familiar with:
- The graphs and equations of the three major types of conic sections: ellipses, hyperbolas, and parabolas
- Performing transformations of these equations
Trigonometry: The Bull Shark
When you cast your line out for this biggest-of-all river monster, you’ll need to be a little wary.
You must know:
- How to solve trig equations
- How to model simple situations with trig functions
- How to recognize trig graphs
- The values and properties of the trig functions
- The trig identities
- How to use the trig functions to solve for lengths of sides and angles within right triangles
Free excerpts from Shmoop's online ACT subject material:
ACT Science Reasoning