ACT Math Prep For Dummies
Overview
Improve your score on the math section of the ACT
A good math score on the ACT exam can set you on the path to a number of rewarding college programs and future careers, especially in the STEM fields. ACT Math Prep For Dummies walks you through this challenging exam section, with simple explanations of math concepts and proven test-taking strategies. Now including access to an all-new online test bank—so you can hammer out even more practice sessions—this book will help you hone your skills in pre-algebra, algebra, geometry, trigonometry and beyond. Handy problem-solving
tips mean you’ll be prepared for the ever-more-advanced questions that the ACT throws at students each year.
- Learn exactly what you’ll need to know to score well on the ACT math section
- Get tips for solving problems quicker and making good guesses when you need to
- Drill down into more complex concepts like matrices and functions
- Practice, practice, practice, with three online tests
If you’re a high school student preparing to take the ACT and you need extra math practice, ACT Math Prep For Dummies has your back.
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About The Author
Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.
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act math prep for dummies
CHEAT SHEET
Making sure you have a handle on algebra, geometry, and trigonometry is a solid start for success on the math section of the ACT. However, to boost your confidence — and your score — even higher, you should master some helpful test-taking strategies, as well as make sure you know how to translate word problems into equations and use sketches to figure out what a tricky-sounding question is really asking.
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Making sure you have a handle on algebra, geometry, and trigonometry is a solid start for success on the math section of the ACT. However, to boost your confidence — and your score — even higher, you should master some helpful test-taking strategies, as well as make sure you know how to translate word problems into equations and use sketches to figure out what a tricky-sounding question is really asking.
ACT
For the ACT Math test, you definitely want to know how to work with matrices. Fortunately, adding and subtracting matrices are both simple and similar operations.
A matrix is a grid of numbers or variables arranged in horizontal rows and vertical columns.
The figure shows a variety of matrices.
Examples of three matrices.
ACT
Some math questions on the ACT will involve ratios and proportions. Both ratio and proportion problems involve comparing quantities, and they require that you know how to work with fractions and how to solve by using algebra.
A ratio is a comparison of two quantities based on the operation of division. For example, if a school has one teacher for every eight students, you can express the teacher-to-student ratio in any of the following ways:
Notice that this ratio expresses the ratio of teachers to students.
ACT
On the ACT Math test, you’ll probably have to multiply pairs of matrices that have either one row or one column. An easy way to multiply a horizontal matrix by a vertical matrix is to set up a small grid. This method allows you to fill in the numbers to get the right answer.
Matrix multiplication is not commutative, because the order in which you multiply two matrices can change the result.
ACT
You may encounter ACT Math questions that ask you to multiply an entire matrix by a real number. Fortunately, this is a straightforward operation: Simply multiply the integer by every element in the matrix. Doing so is similar to using the distributive property to multiply a number by each term inside a set of parentheses.
ACT
On the ACT Math test, you’ll probably have to multiply pairs of matrices that have either one row or one column. An easy way to multiply a vertical matrix by a horizontal matrix is to set up a small grid that resembles a multiplication table. This method allows you to fill in the numbers to get the right answer.
ACT
A determinant is a common operation performed on a square matrix. On the ACT Math test, the only determinant formula you need to be familiar with is for a 2 x 2 matrix. Here’s the formula for the determinant of
Note that the determinant of a matrix is simply a number, not a matrix. To solve a problem with a determinant, you simply plug the numbers from the matrix into the formula and solve.
ACT
To save time when graphing a quadratic function on the ACT Math test, you can quickly find the location of the y-intersept of the parabola based on the sign of the variable c.
The variable c is the constant term of the quadratic equation, y = ax2 + bx + c.
Keep the following rules in mind:
When c is positive, the y-intercept is positive.
ACT
To save time when graphing a quadratic function on the ACT Math test, you can quickly determine the direction of the parabola using a simple trick based on the coefficient a.
This trick relates to the sign of the variable a (in the term ax2):
When a is positive, the graph is concave up. In other words, you can imagine pouring water in it like a cup.
ACT
To save time when graphing a quadratic function on the ACT Math test, you can quickly find the location of the vertex of the parabola in relation to the y-axis. Just use the following simple trick based on the variables a and b (in the terms ax2 and bx):
When the signs of a and b are the same (either both positive or both negative), the graph shifts to the left.
ACT
Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you should remember:
Midpoint formula. The formula for coordinates of the midpoint of a line segment between any two points (x1, y1) and (x2, y2) is:
Distance formula.
ACT
Many students find math questions that involve percent increase and percent decrease somewhat confusing. The first step to answering these questions correctly on the ACT is identifying them when they’re presented.
Some common scenarios for percent increase questions are
Sales tax added to the price of an item
Tipping a server at a restaurant
Interest earned on an investment
Some typical situations for percent decrease questions are
Money lost on an investment
Discount on an item being sold
Deduction from a paycheck due to taxes
After you know whether you’re dealing with percent increase or percent decrease, here’s how you handle the calculations:
Increase.
Using your calculator to find a result on the ACT is straightforward when you know the number you’re calculating with and the percentage you’re taking. However, some math questions on the ACT will involve complex percent problems that will be challenging to solve, even with a calculator.
When answering a question that involves percentages, the trick is to translate it into an equation.
ACT
As when solving an ACT Math problem that includes an expression with absolute value, you also need to split an inequality with absolute value into two separate inequalities. However, keep in mind one twist: One of the two resulting inequalities is simply the original inequality with the bars removed. The other inequality is the original inequality with
The bars removed
The opposite side negated (as with absolute value equations)
The inequality reversed (as with inequalities when you multiply or divide by a negative number)
These rules aren’t difficult, but they’re a little complicated, so be careful to do all three parts correctly.
A word problem (also called a story problem or a problem in a setting) gives you information in words rather than in just equations and numbers. To answer an ACT word problem, you have to translate the provided information into one or more equations and then solve.
You can solve some word problems fairly easily.
Some ACT Math questions give you information about what happens when you perform various operations on an unknown number. To answer these questions, you can let x (or any variable you choose) equal the number you’re looking for. Then build an equation and solve it using any of the methods you already know.
Example
When you divide a certain number by 2 and then add 2, the number you end up with is the same as when you add 24 and then divide this result by 3.
ACT
Some of the questions on the ACT Math test deal with plane geometry. Plane geometry is chock-full of useful formulas. If you can’t commit all these formulas to memory and need to prioritize them, memorize everything up to the circumference of a circle. These are the must-know formulas for geometry. Then, if you have time, work your way forward from there.
ACT
If you want a chance to flex your ACT math muscles, you can try this practice test. The test covers algebra, geometry, and trigonometry, and the questions are modeled from past ACT tests. Complete this test, take it seriously, and you’re sure to be much more at ease on exam day.In order to best simulate real exam conditions, you should do the following:
Sit where you won’t be interrupted or tempted to pick up the TV remote or your phone.
ACT
If you want a chance to flex your ACT math muscles, you can try this practice test. The test covers algebra, geometry, and trigonometry, and the questions are modeled from past ACT tests. Complete this test, take it seriously, and you’re sure to be much more at ease on exam day.In order to best simulate real exam conditions, you should do the following:
Sit where you won’t be interrupted or tempted to pick up the TV remote or your phone.
ACT
If you want a chance to flex your ACT math muscles, you can try this practice test. The test covers algebra, geometry, and trigonometry, and the questions are modeled from past ACT tests. Complete this test, take it seriously, and you’re sure to be much more at ease on exam day.In order to best simulate real exam conditions, you should do the following:
Sit where you won’t be interrupted or tempted to pick up the TV remote or your phone.
ACT
Some of the questions on the ACT Math test deal with pre-algebra and algebra problems. There are only a few formulas to remember, but they are vital.
Here are two important pre-algebra formulas you need to know:
Here are three useful algebra formulas:
Direct proportionality. Two variables, x and y, are directly proportional when the following equation is true for some constant k:
Inverse proportionality.
ACT
Algebra is chock-full of words that are useful but often misunderstood. To do well on the ACT Math test, you should be able to define these important terms: variable, constant, equation, expression, term, and coefficient.
Variable. A variable is any letter that stands for a number. The most commonly used letters are x and y, but you can use any letter.
ACT
Solving word problems is one of the most common reasons to use a system of equations. For example, some word problems in the ACT Math test that would be difficult to approach using a single variable are relatively easy when you use more than one variable.
A system of equations is a set of two or more equations that include two or more variables.
ACT
The ACT will probably include some math problems that involve direct proportionality. Direct proportionality refers to a connection between two variables based on either multiplication or division, where the variables tend to rise and fall together. That is, as one increases or decreases, the other does the same.
ACT
The ACT will probably include some math problems that involve inverse proportionality. Inverse proportionality refers to a connection between two variables based on either multiplication or division, where the variables tend to rise and fall separately. That is, as one increases, the other decreases, and vice versa.
A word problem (also called a story problem or a problem in a setting) gives you information in words rather than in just equations and numbers. To answer a math word problem on the ACT, you have to translate the provided information into one or more equations and then solve.
You can solve some word problems fairly easily.
ACT
If you have trouble solving an ACT math question, you can apply different strategies with the given answer choices to help you determine which choice is correct. The math section of the ACT is comprised of 60 multiple-choice questions. Each question provides five possible answers. Every multiple-choice question gives you a little extra information, because you know the correct answer must be one of the five choices given.
ACT
Some equations on the ACT Math test may include one or more extra variables. Generally speaking, when an equation has more than one variable, you can’t solve it. As a result, in most cases, you must solve the equation in terms of the other variables — that is, isolate one variable on one side of the equation.
Example 1
In the equation 2pq + 5qr = 3pr, what is the value of p in terms of q and r?
ACT
A system of equations is a set of two or more equations that include two or more variables. To solve a system of equations on the ACT Math test, you need one equation for every variable in the system. This usually means two equations and two variables.
You can solve a system of linear equations in two ways:
With substitution.
ACT
You can’t be too organized, especially for the ACT Math test. To make sure you get off on the right foot, here are ten items to check off as you approach the test.
Put Your ACT Admission Ticket in a Safe Place
As with the movies, but with far less entertainment value, the ACT requires a ticket to get in. You should receive your ticket well in advance of the test after you’ve registered and paid.
ACT
The math portion of the ACT contains 60 questions, and you have 60 minutes to complete that part of the test. So you have roughly 1 minute per question. Every question you answer correctly is worth 1 point toward your raw score on the test. Employing some test-taking strategies can help ensure that you answer all the questions as best you can.
ACT
Some math problems are difficult to visualize, so sketching out a chart or picture of the given information can help you arrive at the correct answer when taking the math portion of the ACT. Here are some tips to keep in mind:
If you’re a visual person — an artist or a photographer, for example — start sketching sooner rather than later.
ACT
If you have just purchased a calculator for the ACT, you should use it for at least one practice test so you can get the feel of where the important function keys are. For example, if you have a fancy graphing calculator, you should know how to create input-output tables, solve equations, and view graphs.
At a minimum, make sure you know how to enter the following:
Negative numbers.
ACT
When choosing a calculator for the ACT, remember that while some are allowed others are not. Your safest choices include basic, scientific, and graphing calculators; conversely, you need to avoid laptops or PDAs that happen to have a calculator, calculators that make too much noise, and those that need an electrical plug-in to work.
A calculator is a great tool for solving ACT math problems more quickly than you can either in your head or using a pencil and scratch paper. At the same time, however, you want to avoid overusing it for calculations that you can easily and accurately do in your head.
When you take a practice test, notice how you use your calculator.
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