The ACT Math test is a marathon: you will have 60 minutes to answer 60 multiple-choice questions. In order to prepare for the race, you’ll want a thorough knowledge of the content of the test and to train yourself in timing and problem-solving strategies.

### Timing Strategies

#### Mark it and Skip it

As we said, you will have 60 minutes to answer 60 multiple choice questions so you do not want to spend too much time on any one problem. Don’t let a question stump you for too long before you **mark it, skip it, and move on**. You can also mark the questions you answered but were unsure if you answered correctly. Make sure you have a watch or can see the clock because you really need to keep track of the time.

Return to your unanswered or unsure questions when you have just a few minutes left in that hour. **There is not a penalty for incorrect responses**; instead, you receive credit for each question you answer correctly, so do not leave any answers blank.

If you do find you have a bit of extra time, go back to those problems you were unsure of, and check them, but *don’t* do them the way you did them the first time. Instead, try another strategy or plug in your answer and see if it checks out.

#### Solve Quickly (but Accurately)

You need to use your reasoning to try to find the **quickest **way to solve each problem. While you are permitted a calculator for the** entire ACT test**, all problems can be solved without one, and frequently the fastest route does not involve using a calculator. Make sure you are familiar with the calculator you bring to the test (and that it is one which is accepted for use) and know when to use it and when you can surely work more quickly without it. In fact, every problem is written so that it can be solved without a calculator, so you may be better served by reserving your calculator for when you return to check answers.

Generally, the questions for the ACT math section get more difficult as you progress towards the end of the test. This means two things. One, you would like to have more time for the more challenging problems at the end, but two, you really do want to make sure you spend enough time to get those first questions correct. You need to get those easier problems right, so move quickly, but not so fast that you make careless errors.

In addition, unlike the SAT, the ACT does not give a formula sheet. If a question uses an unusual formula that you would not be expected to know, that formula will be present in the question. There are some formulas you are expected to know, and some others that sure would make the test a lot easier if you knew them. Check out our study guide of ACT math formulas here.

ACT Math Study Guide

What Calculator to Use on the ACT

### Some tips for studying for the ACT math section

#### Do a practice timed test

In order to best mimic the process that you will use when you take the actual ACT, print out a practice test and a bubble sheet, set a timer for 60 minutes, and start problem-solving. If you do not finish in 60 minutes, go ahead and finish the remainder of the questions, but mark that you needed additional time for each question that you did not answer in those 60 minutes.

#### Identify Your Weaknesses & Learn From Them

Once you’ve completed your practice test, check your answers. Of the ones you missed, you should really look for a couple of things:

One, are there patterns in your mistakes? Are you missing geometry questions, or abstract questions, or questions with lots of words? Did you need extra time? What can you do to speed up your process? Identify your weaknesses.

Two, when you check your answers, try to figure out what you did wrong. Don’t just say, “Oh, I missed those eight questions.” Figure out how to do them! Wrap your brain around the problem. See if you can figure out how to do it before you even look at the explanation. And then, try another question like it (you can always just change the numbers to write a new problem for yourself).

All of this is called “metacognition” which just means “thinking about your own thinking.” If you do not analyze your mistakes, you can do all the practice tests in the world, but you’re just going to keep making the same mistakes. Practice does NOT make perfect. Perfect practice makes perfect!

#### Do More Problems; Attack with Strategy and Purpose

Because you need to move quickly, consider how you go about each problem. This is not a test like you take in high school where the teacher tells you that you will not get credit if you don’t do it the way he or she wants. Do what works for you, but keep in mind you should be jotting and drawing, and trying out numbers, looking for patterns, writing algebraic equations, and basically spitting out your ideas on paper. What kinds of strategies might you try?

You should be jotting and drawing, and trying out numbers, looking for patterns, writing algebraic equations, and basically spitting out your ideas on paper.

### Strategies for the ACT Math Test

#### Draw a Picture

Some questions are abstract and a quick sketch may help you “see” what the problem is asking.

*Example: A cube has 2 faces painted red and the remaining faces painted blue. The total area of the red faces is 32 cm*^{2}*. What is the volume of the cube in cubic centimeters?*

Draw a quick sketch of the cube and mark what you know so that you can see what the problem is asking:

Oh, each red side must have an area of **16 cm2** so each side must be 4 cm. The Volume must be 4 x 4x 4 or 64 cm3.** **

#### Plug in Numbers

Variables got you down? Sometimes the variables make the problem seem more difficult than it actually is. Try to substitute numbers (and pick “smart” numbers that make the problem easier) and see if you can manipulate the problem that way.

*Example: When the positive integer n is divided by 9, the remainder is 7. What is the remainder when n+3 is divided by 9?*

Try a number. Let’s see, what number could be divided by 9 and leave a remainder of 7? Well, 16 divided by 9 is 1 and the remainder would be 7. So what is the remainder for 16+3 divided by 9?

#### Make a Table or List and Look for a Pattern

It doesn’t have to be beautiful, but it needs to be organized enough that you know what you mean and what you are looking for.

*Example: Each term in a certain arithmetic sequence is always greater than the one preceding it, and the difference between two consecutive numbers is always the same. If the 3rd and 5th terms are 19 and 79, what is the 7th term?*

#### “Act” It Out

Obviously you can’t just stand up in the testing room and start moving things around, but you can essentially “act” out a problem by jotting things down on paper.

*Example: A classroom has 8 tables that will seat up to 4 people. If 26 students are seated at the tables and none of the tables are empty, what is the greatest possible number of tables at which 4 people are seated?*

#### Use Logic

Don’t make random guesses, at least make them logical.

*Example: In the xy-coordinate plane, lines s and t are perpendicular. Line s goes through the origin and contains point (-2,-1). Line t also contains the point (-2,-1) and point (0,n). What is the value of n?*

If the answer choices are A) -5 B) -3 C) -2 D) 2 E) 3 then a very quick sketch shows that the answer cannot be positive. At least use your logic here and eliminate poor answer choices.

#### Don’t Make the Problem Harder Than It Is

Make sure you answer the problem that is asked. Don’t do steps that are unnecessary.

*Example: If (2x-8)(2x+8)=36, what is the value of 4×2?*

(2x-8)(2x+8)=36

4×2-64=36

4×2=100

Stop here! You don’t need to solve for x. Notice what the question was asking.

### Concepts You Can Expect to be Covered on the Test

For the ACT math section, your report will show nine scores: your overall “scale score” which ranges from 1 to 36, plus eight subscores which show the percentage you answered correctly in each category.

What kinds of questions can you expect? The content can be grouped as follows: **number & quantity, algebra, functions, geometry, and statistics & probability**.

For the **Number & Quantity **questions you may need to:

- Manipulate, order, and solve problems involving whole numbers, fractions, decimals, percents, and percentage change
- Compute values using proportional relationships and ratios
- Understand factoring, greatest common factor, and least common multiple
- Find distance on a number line, between points on a coordinate plane, or in terms of absolute value
- Manipulate exponents in powers of 10 and apply properties of rational exponents
- Demonstrate knowledge of the real number system – rational, irrational, and complex numbers
- Demonstrate knowledge of operations on matrices and vectors

**Algebra **concepts may test your ability to:

- Use word to symbol translation to solve real-world problems
- Manipulate and evaluate variable expressions and equations (including absolute value)
- Solve linear and quadratic inequalities and match with appropriate graphs
- Find and interpret slope and intercepts from equations, word problems and graphs (also using properties of parallel and perpendicular lines
- Match, interpret, and analyze information from graphs in the coordinate plane
- Add, subtract, multiply, and divide polynomials
- Solve quadratic equations
- Manipulate exponents such as squares, cubes, roots, and scientific notation
- Solve and interpret systems of linear equations
- Solve multi-step problems using proportions, rate, percentages, and/or conversion of units of measure

**Functions **questions may ask you to:

- Understand the concept of what makes a function (one input cannot have more than one output value)
- Interpret and evaluate functions and composite functions
- Find the domain and range of functions (and vertical asymptote of rational functions)
- Write functions that are directly or inversely proportional or exponential
- Extend patterns (constant increase or decrease or factor)
- Demonstrate knowledge of arithmetic and geometric sequences
- Understand the trigonometry of the unit circle, basic trigonometric graphs, and basic trig identities to solve problems
- Demonstrate knowledge of logarithms
- Identify a function when the graph of a given function is translated horizontally or vertically

**Geometry **questions will test your ability to:

- Calculate lengths and midpoints of line segments (overlapping segments and those in the coordinate plane)
- Compute perimeter and area of polygons and circumference and area of circles
- Use properties of parallel lines and other angle properties to find missing angle measures
- Use properties of isosceles and right triangles to compute unknown side lengths and angle measures (symmetry, Pythagorean theorem, etc…)
- Translate points horizontally, vertically, reflectively, or rotationally in a coordinate plane
- Demonstrate knowledge of right triangles (30
^{o}, 60^{o}, 90^{o}; 45^{o}, 45^{o}, 90^{o}) and apply trigonometric ratios (sine, cosine, tangent) to solve for missing values - Manipulate between area, volume, and surface area
- Understand special characteristics of conics (circle, ellipse, parabola, hyperbola) such as the center, radius, or vertex
- Compute angles (degrees and radians), arcs, and distances in a circle

For **Statistics and Probability **concepts you will need to:

- Interpret data, charts, frequency tables, and graphs to get information for computations or for transformation into a different type of data display
- Demonstrate knowledge of measures of central tendency and distribution (mean, median, mode, range), how to compute each, and how to compute for missing data point given a measure of central tendency
- Compute probabilities of an event, its complement, and combinations (conditional and joint probability)
- Demonstrate knowledge of the fundamental counting principle and Venn Diagrams
- Understand the fundamentals of statistics (random sampling, distribution, deviation, confidence interval, and interpretation of results)

Now that you’re armed with timing and problem-solving strategies, and knowledge of the content of the test, you’re ready to train for the math marathon that is the ACT math section! You can find hundreds of practice problems with explanations that teach you the concepts you need to know in The Olive Book ACT course. Or, you can study directly on the ACT website with their free resources.

Further Reading:

See Math Like a Mathematician

ACT Math Study Guide

What Calculator to Use on the ACT

3 Steps to Boost Your ACT Score

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