Mastering the ACT Math Section: 21 Essential Formulas You Need to Know

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Do you are preparing for ACT math section? If you are searching for a formula for mastering the ACT math section, this post is for you.

The math section of the ACT is a critical component that can make or break your overall score.

So, math formulas are the keys to clear the ACT math section. Math formulas help you to solve math problems quickly.

If you want to learn 21 essential formulas for the ACT math section, this post is for you.

I will share 21 essential math formulas for the ACT math section in this article.

What is the ACT Math Section?

The ACT is a standardized college admissions exam in the United States, including a math section. The ACT Math Section evaluates your mathematical knowledge up to the start of the 12th grade.

It includes information on quantity and number, algebra, functions, geometry, statistics and probability, and modeling. This phase allows using a calculator, and you have 60 minutes to complete the 60 questions.

Importance of Math Formulas for the ACT

Before we dive into the essential formulas, let’s discuss why math formulas are crucial in the ACT math section.

As the ACT is, MCQs types test. In its math section, there are a total of 60 MCQs. You need to solve it in 60 minutes.

That means you only have one minute for one question. But it’s difficult to answer math MCQs in one minute when you don’t know the formula.

Therefore, you must be familiar with the method to determine the response to the particular questions to expedite the procedure and readily analyze things in time. Your job is more accurate and efficient as a result.

In high school, you read about fundamental mathematical ideas. How well you understand these mathematical ideas is tested on the ACT maths part. The questions in this area, however, are not simple. To correctly solve problems, you need critical thought and problem-solving capacity. You can confidently solve the questions if you know the necessary formulas.

21 Essential Math Formulas You Need to Know for the ACT

Let’s explore the 21 essential math formulas you need to know for the ACT.

We categorized these 21 formulas into four sections. These four sections are:

1. Formulas for algebraic expressions and equations
2. Formulas for geometry and trigonometry,
3. Formulas for functions and graphs, and
4. Formulas for statistics and probability.

Let’s discuss all the formulas individually and explore how they help us to solve different MCQs in their categories.

Formulas for Algebraic Expressions and Equations

Algebraic expressions and equations are the main parts of any mathematical type test. There are many concepts in this field, but here for the ACT math section, we choose the Top 3 formulas used in every math test.

Let’s dive further and learn the formulas and how we use them to solve problems quickly.

A quadratic equation is one of the most fundamental math concepts used in mathematics. One or more questions from the quadratic equation are part of every mathematics test.

There is a different method to solve a quadratic equation. The quadratic formula is one of the most popular methods implemented in every quadratic equation.

The quadratic formula helps find the roots of a quadratic equation, $$ax^2 + bx + c = 0$$.

The quadratic formula to find the roots of the equation is

$$x =\frac{-b ± \sqrt{b^2 – 4ac}}{2a}.$$

Example

Solve the quadratic equation $$4x^2 + 5x + 6 = 0.$$

$$a = 1, b = 5, c = 6$$

$$x =\frac{-5 ± \sqrt{5^2 – 4(1)(6))}}{2 * 1}$$

$$x =\frac {-5 ± \sqrt{(25 – 24)}} {2}\\$$

$$x = \frac{-5 ± \sqrt{(1)}}{2}\\$$

$$x = {-5 ± 1}{2}\\$$

$$x_1 = -3$$

$$x_2 = -2$$

Distance Formula

The distance formula is another fundamental concept in algebra. If two points are given, we can find the distance between them with the help of the distance formula. Let’s find the distance between two points, $$(x_1, y_1)$$ and $$(x_2, y_2)$$.

The formula is

$$d = \sqrt{(x_2 – x_1)^2+(y_2 – y_1)^2}$$

Example

Find the distance between the points (-3, 4) and (4, 6).

$$d =\sqrt{(4 – (-3))^2 + (6 – 4)^2}$$

$$d = \sqrt{7^2 + 2^2}$$

$$d = \sqrt{53}$$

$$d ≈ 7.28$$

Slope Formula

Do you know what is the slope and how we find it? The slope is the ratio of the rise and run. You can find the slope of a line passing through two points, $$(x_1, y_1)$$ and $$(x_2, y_2)$$.

The formula is

$$m = \frac{y_2 – y_1}{x_2 – x_1}.$$

Example

Find the slope of the line that passes through the points $$(2, 5)$$ and $$(6, 11)$$.

Solution: Plug in the coordinates into the formula:

$$m = \frac{11 – 5}{6 – 2}\\ = \frac{6}{4}\\= \frac{3}{2}$$

The slope of the line is $$\frac{3}{2}$$.

Formulas for Geometry and Trigonometry

Geometry and trigonometry are the two major fields in mathematics. There are many formulas in geometry and trigonometry; We have selected the top three formulas that are parts of the ACT Math section every year.

Pythagorean Theorem:

Pythagoras’ theorem is the most fundamental concept used in trigonometry. Now if two sides of a right triangle are given, you can use Pythagoras theorem to find the other side.

The formula is a² + b² = c², where c is the hypotenuse.

Example

Find the length of the hypotenuse of a right triangle with legs of lengths 3 and 4.

$$c^2 = 3^2 + 4^2$$

$$c^2= 9 + 16$$

$$c^2 = 25$$

$$c = \sqrt{25}$$

$$c = 5$$

Therefore, the length of the hypotenuse is 5.

Area of a Circle

If you know the radius of the circle then you can use this formula to find the area of a circle with a radius r.

The formula is $$A = \pi r^2.$$

Example

Find the area of a circle with a radius 5.

$$A = π(5)^2$$

$$A = 25π$$

Therefore, the area of the circle is 25π.

Volume of Sphere

The volume of a Sphere formula helps find the volume of a sphere with radius r. The formula is V = (4/3)πr³.

Example

Find the volume of a sphere with a radius 6.

$$V = (4/3)π(6)^3$$

$$V = (4/3)π(216)$$

$$V = 904.78$$

Therefore, the volume of the sphere is approximately 904.78 cubic units.

Formulas for Functions and Graphs

Now after viewing algebra, geometry, and basic trigonometry formulas, move on to calculus.

The most popular topic from Calculus in the ACT math section is the Domain, range, and slope interscpet forms.

Domain

Do you know what is the domain of a function? The domain is the set of all possible input values that produce a good output.

So, to find the domain find the set of all possible input values that gives you unique and well-defined output.

Example

We have a function $$f(x) = √(x + 3)$$.

To find the domain of this function, we apply the rule $$x + 2 ≥ 0.$$

Solving this inequality, we get $$x ≥ -2.$$

Thus, the domain of f(x) is (-2, ∞)

Range

This formula helps find the range of a function. The range is the set of all possible output values.

Slope Intercept form

This formula helps find the equation of a line in slope-intercept form, $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept.

Example

Write an equation in slope-intercept form for the line with a slope of $$-2$$ and passing through the point $$(3, 7)$$.

Solution: Plug in the slope and the point into the equation:

$$y = -2x + b$$

$$7 = -2(3) + b$$

Solve for $b$:

$$b = 7 + 6 = 13$$

The equation in slope-intercept form is:

$$y = -2x + 13$$

Formulas for Statistics and Probability

Statistics and Probability are other fundamental concepts for any type of admission or merit test. The basic concept you need to know in statistics is mean, median, mode, and probability.

Mean

Sometimes, you need to find the average value to interpret the data. For example, if someone asks what the average age limit is in Pakistan. The average gives an overview of the given data.

You can calculate the mean by adding all the numbers and dividing by the total values.

Example

Suppose $$x_1, x_2, x_3,……, x_n$$ be n observations of a data set, then the mean of these values is:

$$x ― = \frac{∑ x_i}{ n}$$

Here, $$xi = ith$$ observation, $$1 ≤ i ≤ n$$ $$∑xi = \text{Sum of observations}$$

$$n = \text{Number of observations}$$

For example, if the marks of 6 students are 10, 20, 30, 32, 37, or 40, the mean is calculated as follows:

$$\frac{10 + 20 + 30 + 32 + 37 + 40}{6}$$

$$= 28.17 (approx).$$

Median

The median is also popular formula from statistics for interpreting the set of values in the data. So if you need the middle value of given data set, you can use the median to find it. If there are an even number of values, the median is the average of the two middle values.

Example

Consider the data: 4, 4, 6, 3, and 2.

• Let’s arrange this data in ascending order: 2, 3, 4, 4, 6.
• Count the number of values.
• There are 5 values.
• Look for the middle value. The middle value is the median. Thus, median = 4

Mode

Mode helps you find the value in the data that is repeated more times. This formula helps find the value that appears most frequently in a set of numbers.

Consider the following numbers: 2, 4, 5, 5, 6, 7. The mode of the data set is five since it has appeared in the set twice

Probability

This formula helps find the likelihood of an event occurring. The formula is

$$P(A) = \frac{\text{Number of favorable outcomes for event A}}{\text{Total number of possible outcomes}}.$$

Example

How to find the probability of an event. Let’s say you have a bag with five marbles in it: 4 are blue, and one is red. What is the probability that a blue marble gets picked?

The probability of picking a blue marble is the number of ways you can pick a blue marble divided by the total number of marbles in the bag. In this case, there are four blue marbles and one red marble, so there are five total marbles.

The probability of picking a blue marble is:

$$P(blue) = \frac{\text{number of ways to pick a blue marble}}{\text{ total number of marbles P(blue)}}$$

$$= \frac{4}{5}$$

So the probability of picking a blue marble is 4/5 or 0.8.

Tips for Memorizing Math Formulas

Now that we have gone through the essential formulas, the question is, how do you memorize them? Here are some tips to help you:

• Relate the formula with something that you can easily remember. Associate the numbers, operands, and variables to certain elements that are non-mathematical and easy to remember. For example, a plus sign can be remembered as first aid.
• Once you name each unit in the formula, visualize a short story as the formula progresses.
•  Repetition is key. One of the best ways to commit something to memory is to repeat it repeatedly. Write out the formulas you need to know and say them out loud as you write them.
• A traditional way to memorize them is to read the formula repeatedly until it gets fixed in your mind. Another method is to write down the formula many times.
• Understand the formation of the formula’s units, equations, or signs.
• Use innovative methods to learn the formulas: Try to memorize the formulas in your mind by closing your eyes and visualize writing the formula in a blank space.[1]

Practice Problems Using the Essential Formulas

To help you apply the essential formulas, here are some practice problems:

• Find the roots of the quadratic equation, 3x² + 4x – 2 = 0.
• Find the distance between the points (2, 5) and (5, 8).
• Find the slope of the line passing through the points (3, 4) and (7, 10).
• Find the area of a circle with a radius 5.
• Find the volume of a sphere with radius 2.
• Find the domain and range of the function, f(x) = x² – 3x + 2.
• Find the equation of the line passing through the point (4, 3) with a slope of 2/3.
• Find the mean, median, and mode of the following set of numbers: 2, 4, 8, 8, 10, 12.
• Find the probability of rolling a 4 on a standard six-sided die.
• Find the probability of drawing a red card from a standard deck of 52 cards.

Where to Find a Math Formulas Sheet for the ACT

It’s important to note that the ACT provides a math formulas sheet you can use during the exam. You can find a copy of the sheet on the ACT website, and we highly recommend that you familiarize yourself with it before the exam. This will save you time and help you focus on solving the problems instead of trying to remember the formulas.

Here are some resources where you can find Math Formulas Sheet for the ACT:

Other Common Math Formulas to Know for the ACT

In addition to the essential formulas we have discussed, here are some other common math formulas that you should know for the ACT:

• Perimeter and Area Formulas for Shapes (rectangle, triangle, parallelogram, trapezoid)
• Volume and Surface Area Formulas for Geometric Solids (cube, rectangular prism, cylinder, cone, pyramid)

Famous Math Formulas and Their Applications

Mathematics has many famous formulas that have made significant contributions to the field. While you don’t necessarily need to know them for the ACT, knowing their applications is interesting. Here are some famous math formulas and their applications:

• E = mc² (Einstein’s Theory of Relativity)
• F = ma (Newton’s Second Law of Motion)
• a² + b² = c² (Pythagorean Theorem)
• sin²θ + cos²θ = 1 (Trigonometric Identity)

Resources for Mastering the ACT Math Section

To help you prepare for the ACT Math section, here are some resources that you can use:

• ACT website: The official website has a wealth of information on the exam, including practice tests and sample questions.
• Khan Academy: Khan Academy offers free online courses in math that cover the topics tested in the ACT.

Conclusion and Summary

Mastering the ACT Math section requires familiarity with the essential math formulas. By learning and practicing these formulas, you can confidently approach and solve the questions efficiently. Use the ACT math formulas sheet provided during the exam to save time. Finally, use the resources available to prepare adequately for the exam.

FAQs

What is the difference between ACT and SAT?

The ACT and SAT are standardized exams used in the US for college admissions.

•  The ACT features a science portion and an optional essay.
• Whereas the SAT features a math portion that is calculator-free.
• The ACT has more arithmetic topics, while the SAT emphasizes logical reasoning.
•  SAT grades each section on a scale of 200–400, while the ACT assigns a score to each question on a scale of 1-36.
•  ACT has more questions but less time allotted for each, the SAT has fewer questions but more time allotted for each.

What is the ACT Math Section?

The ACT Math Section is a component of the ACT (American College Testing) exam which measures a student’s math skills in various fields.

What is the purpose of this post?

The purpose of the post is to provide guidance to students who are preparing for the ACT math section by introducing them to commonly used math formulas essential for mastering the math section. The post also provides resources for practicing the math section.

What is the ACT?

The ACT stands for American College Testing and is a standardized college admissions exam in the US that includes a math section.

What is the time limit for the ACT math section?

The time limit for the ACT math section is 60 minutes.

What are the main parts of any mathematical type test?

The main parts of any mathematical type test are algebraic expressions and equations.

What are the main parts of any mathematical type test?

What are the important statistical concepts to understand?

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