Comprehensive Formula Chart for TEAS Mathematics and Science Sections

When preparing for the TEAS Mathematics and Science sections, it’s easy to feel overwhelmed. However, once you understand the core concepts and the fundamental formulas, you’ll notice that math and science are far less intimidating. They follow certain patterns and rules that, once learned, apply consistently every time. One of the key mathematical concepts you’ll need to master for the TEAS exam is fractions and percents. These two topics form the foundation for many mathematical computations in various fields, especially in healthcare and nursing, where precision and accuracy are vital.

Understanding Fractions and Percentages

Fractions and percentages are used in many aspects of life, and in nursing, they are particularly important. Nurses use fractions and percentages regularly for dosage calculations, drug administration, and interpreting medical data. Therefore, having a strong grasp of these concepts is essential for success on the TEAS exam.

At their core, fractions are just numbers expressed as parts of a whole. A fraction is made up of two numbers: the numerator, which is the number of parts you have, and the denominator, which tells you how many equal parts the whole is divided into. For example, in the fraction 1/2, the numerator is 1, and the denominator is 2. This means you have one part out of two equal parts that make up the whole.

Percentages, on the other hand, are a way to express a number as a fraction of 100. The term “percent” comes from the Latin word “per centum,” which means “by the hundred.” A percentage tells you how many parts out of 100 you have. For example, 50% is the same as 50 out of 100, or 1/2.

Key Formulas for Fractions and Percentages

To effectively solve problems involving fractions and percentages, it’s essential to know the key formulas and understand how to use them. Below are some of the fundamental formulas that will help you navigate the world of fractions and percentages, both in your TEAS preparation and in real-world applications:

1. Simplifying Fractions:
   To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify the fraction 6/8, you would divide both the numerator (6) and the denominator (8) by 2, which is their GCD. This gives you the simplified fraction 3/4.
   
   Formula:
   ab=a÷GCD(a,b)b÷GCD(a,b)\frac{a}{b} = \frac{a \div \text{GCD}(a,b)}{b \div \text{GCD}(a,b)}ba​=b÷GCD(a,b)a÷GCD(a,b)​
2. Converting Fractions to Decimals:
   A fraction can be converted into a decimal by dividing the numerator by the denominator. For example, 1/4 is equal to 0.25 because 1 ÷ 4 = 0.25.
   
   Formula:
   Decimal=ab\text{Decimal} = \frac{a}{b}Decimal=ba​
3. Converting Fractions to Percentages:
   To convert a fraction to a percentage, you first convert the fraction to a decimal and then multiply by 100. For example, to convert 1/2 to a percentage, first divide 1 by 2 to get 0.5, and then multiply 0.5 by 100 to get 50%.
   
   Formula:
   Percentage=(ab)×100\text{Percentage} = \left( \frac{a}{b} \right) \times 100Percentage=(ba​)×100
4. Converting Percentages to Decimals:
   To convert a percentage to a decimal, simply divide the percentage by 100. For example, 25% is equal to 0.25 because 25 ÷ 100 = 0.25.
   
   Formula:
   Decimal=Percentage100\text{Decimal} = \frac{\text{Percentage}}{100}Decimal=100Percentage​
5. Converting Percentages to Fractions:
   To convert a percentage to a fraction, first express the percentage as a decimal, then convert the decimal to a fraction. For example, to convert 25% to a fraction, first express it as 0.25 and then convert 0.25 to 1/4.
   
   Formula:
   Fraction=Percentage100→Convert the decimal to a fraction\text{Fraction} = \frac{\text{Percentage}}{100} \rightarrow \text{Convert the decimal to a fraction}Fraction=100Percentage​→Convert the decimal to a fraction

Solving Problems with Fractions and Percentages

One of the most important aspects of working with fractions and percentages is knowing how to solve practical problems. Nurses, for example, often deal with dosage calculations that require the use of fractions and percentages. Whether you are calculating the amount of medication to administer based on a patient’s weight or adjusting formulas to match prescribed dosages, having a solid understanding of these concepts will serve you well.

Working with Fractions in TEAS

A typical problem you might encounter on the TEAS exam could involve adding or subtracting fractions. To solve such problems, you need to ensure that the fractions have a common denominator. For example, if you are asked to add 1/4 and 1/2, you must first find a common denominator, which in this case is 4. You would then rewrite 1/2 as 2/4, so the problem becomes 1/4 + 2/4, which equals 3/4.

For multiplication and division of fractions, the process is straightforward. To multiply fractions, simply multiply the numerators and denominators together. For example, 1/4 × 2/3 equals 2/12, which can be simplified to 1/6.

When dividing fractions, you multiply by the reciprocal of the divisor. For example, to divide 1/2 by 1/4, you multiply 1/2 by 4/1, which equals 4/2, or 2.

The Importance of Fractions and Percentages in Nursing

In nursing, a significant portion of daily calculations revolves around fractions and percentages. Whether you are determining the right dosage of a drug or calculating a patient’s body mass index (BMI), these concepts are crucial. For example, drug dosages are often prescribed based on a patient’s weight and may require you to multiply a fraction (e.g., 1/2) by a certain number (e.g., 150 pounds) to determine how much medication to administer.

Additionally, percentages are used in a variety of medical and clinical applications. Nurses frequently use percentages when calculating blood volume, interpreting lab test results, or adjusting intravenous fluids. Understanding the relationship between fractions, decimals, and percentages ensures that calculations are accurate and consistent, which is critical for patient safety.

Fractions and percentages are not just abstract concepts but practical tools that you will use throughout your nursing career. They serve as a foundation for more complex calculations in healthcare, from dosing medication to analyzing medical data. On the TEAS exam, mastering these formulas and concepts will give you the confidence to approach math questions with ease. In the next sections, we will explore additional key topics in algebra, geometry, and statistics, which build upon the principles of fractions and percentages to help you prepare for success on the TEAS test.

Algebra in TEAS Mathematics

Algebra is one of the fundamental branches of mathematics that you will encounter in the TEAS Mathematics section. Although it might not immediately seem relevant to nursing, algebra is crucial for solving equations, interpreting data, and making accurate calculations. Many of the concepts in algebra directly apply to healthcare-related scenarios, from understanding patient data to calculating dosages and making medical predictions.

Understanding Algebraic Equations

Algebra involves the use of symbols and letters (often called variables) to represent numbers in equations and formulas. The goal of algebra is to solve for unknown values by manipulating the equation using various mathematical operations such as addition, subtraction, multiplication, and division.

An algebraic equation is a statement that shows the equality of two expressions. For example, the equation “x + 3 = 7” means that the value of “x” plus 3 is equal to 7. The objective is to solve for “x” by isolating the variable on one side of the equation. In this case, you subtract 3 from both sides of the equation to find that “x = 4.”

In healthcare, algebraic equations can be used to solve a variety of practical problems, such as determining the correct medication dosage based on a patient’s weight or understanding the relationship between different physiological measurements.

Key Algebraic Formulas for TEAS

To successfully solve algebraic problems on the TEAS exam, you need to be familiar with a few key formulas and concepts. Below are some of the most important algebraic formulas and techniques you will need:

Solving Basic Equations

The fundamental skill in algebra is solving simple equations. For example, to solve the equation “3x = 12,” you divide both sides of the equation by 3 to isolate the variable “x.” This gives you “x = 4.”

Formula:

ax=b⇒x=baax = b \quad \Rightarrow \quad x = \frac{b}{a}ax=b⇒x=ab​

Where “a” and “b” are constants, and “x” is the variable.

Linear Equations and Slope-Intercept Form

Linear equations are equations that form straight lines when graphed. The general form of a linear equation is “y = mx + b,” where “m” is the slope of the line and “b” is the y-intercept (the point where the line crosses the y-axis).

This formula is essential for interpreting data and understanding relationships between different variables. For example, if you are given the equation “y = 2x + 5,” you know that for every increase of 1 unit in “x,” the value of “y” increases by 2 units.

Formula:

y=mx+by = mx + by=mx+b

Where “m” is the slope, “b” is the y-intercept, and “x” and “y” are the variables.

Point-Slope Form

Another important form of linear equations is the point-slope form, which is especially useful when you are given a specific point on a line. The point-slope form is written as “y-y₁ = m(x-x₁),” where “m” is the slope, and (x₁, y₁) is a known point on the line.

This formula is useful for solving problems where you need to write the equation of a line given a point and the slope. For example, if the slope is 3 and the line passes through the point (2, 4), the equation of the line is “y – 4 = 3(x – 2).”

Formula:

y−y1=m(x−x1)y – y₁ = m(x – x₁)y−y1​=m(x−x1​)

Where “m” is the slope and “(x₁, y₁)” is a point on the line.

Practical Applications of Algebra in Nursing

Algebra is not just a theoretical concept but a practical skill that is used daily in healthcare settings. Nurses and healthcare professionals use algebra to calculate drug dosages, understand patient data, and interpret lab results. Here are some examples of how algebra is applied in nursing:

Medication Dosage Calculations

One common use of algebra in nursing is calculating the correct medication dosage based on a patient’s weight. For example, if a doctor prescribes a medication at a dose of 5 mg per kilogram of body weight, and the patient weighs 70 kilograms, you can use algebra to calculate the total dosage:

Total Dose=Dose per kg×Patient’s weight\text{Total Dose} = \text{Dose per kg} \times \text{Patient’s weight}Total Dose=Dose per kg×Patient’s weight Total Dose=5 mg/kg×70 kg=350 mg\text{Total Dose} = 5 \, \text{mg/kg} \times 70 \, \text{kg} = 350 \, \text{mg}Total Dose=5mg/kg×70kg=350mg

IV Drip Rate Calculations

Nurses often use algebra to calculate the appropriate IV drip rate, which is essential for administering fluids and medications at the correct speed. For example, if a doctor orders 1 liter of fluid to be administered over 8 hours, you can calculate the drip rate as follows:

Drip Rate=VolumeTime=1000 mL8 hours=125 mL/hour\text{Drip Rate} = \frac{\text{Volume}}{\text{Time}} = \frac{1000 \, \text{mL}}{8 \, \text{hours}} = 125 \, \text{mL/hour}Drip Rate=TimeVolume​=8hours1000mL​=125mL/hour

Determining Patient Outcomes

Algebra can also be used to predict patient outcomes based on existing data. For example, if you know that a patient’s blood pressure is affected by certain factors (such as age, weight, and medication), you can use algebraic equations to understand how changes in these factors will influence the patient’s condition.

Solving Systems of Equations

In some cases, you may need to solve systems of equations, which involve two or more equations that must be solved simultaneously. For example, you might have the following system of equations:

x+y=10x + y = 10x+y=10 2x−y=32x – y = 32x−y=3

To solve this system, you can use substitution or elimination methods. In substitution, you solve one equation for one variable and substitute that value into the other equation. In elimination, you add or subtract the equations to eliminate one variable and solve for the other.

Formula for substitution:

x=10−y(from the first equation)x = 10 – y \quad \text{(from the first equation)}x=10−y(from the first equation)

Substitute this into the second equation:

2(10−y)−y=32(10 – y) – y = 32(10−y)−y=3

Simplifying, you can solve for “y” and then substitute that value back to solve for “x.”

Algebra is an essential skill for the TEAS exam, as it is used in many areas of the test, including problem-solving, data interpretation, and practical healthcare scenarios. By mastering basic algebraic equations, linear equations, and systems of equations, you will not only perform well on the TEAS but also be better prepared for real-life nursing challenges. Understanding how to manipulate variables and solve equations will help you calculate dosages, interpret data, and make informed decisions in patient care. In the next section, we will explore geometry, which also plays a critical role in your TEAS Mathematics preparation.

Geometry in TEAS Mathematics

Geometry is an essential area of mathematics that you will encounter on the TEAS exam. Although geometry might seem abstract at first, it has many practical applications in nursing and healthcare. Understanding geometric shapes, measurements, and formulas can help you with various tasks such as determining the right medication dosage, calculating body mass index (BMI), interpreting graphs and charts, and more.

The Role of Geometry in Nursing

In nursing, geometry is used in many practical applications, such as determining the correct dosage of medication, calculating the area of a wound, or interpreting medical data. Geometry also helps healthcare professionals understand the structure of the human body, analyze medical imaging, and interpret graphs related to patient health.

For example, when calculating a patient’s body surface area (BSA), nurses often use geometric formulas to estimate the total area of the body. Similarly, geometric concepts are used when measuring the volume of fluids or calculating the dosage of intravenous (IV) fluids.

On the TEAS exam, geometry will test your knowledge of various shapes, their properties, and the formulas used to calculate perimeter, area, and volume. Understanding how to apply these formulas will help you solve a variety of problems on the test.

Key Geometric Formulas for TEAS

To succeed in the geometry portion of the TEAS exam, you need to be familiar with the key formulas that will help you calculate the perimeter, area, and volume of different shapes. Below are some of the most important geometric formulas that you’ll need to know:

Perimeter Formulas

The perimeter is the distance around the edge of a shape. For example, if you are given a rectangular or square shape, you can use the following formulas to calculate the perimeter.

Perimeter of a Square:
A square is a four-sided shape where all sides are equal in length. To find the perimeter of a square, multiply the length of one side by 4.

Formula:
P=4×sP = 4 \times sP=4×s
Where “s” is the side length.

Perimeter of a Rectangle:
A rectangle has two pairs of equal sides. To find the perimeter of a rectangle, you add the lengths of all four sides. This can be simplified to 2 times the sum of the length and width.

Formula:
P=2×(l+w)P = 2 \times (l + w)P=2×(l+w)
Where “l” is the length and “w” is the width.

Perimeter of a Triangle:
A triangle has three sides. To find the perimeter of a triangle, you add the lengths of all three sides together.

Formula:
P=s1+s2+s3P = s_1 + s_2 + s_3P=s1​+s2​+s3​
Where “s1,” “s2,” and “s3” are the lengths of the three sides.

Perimeter of a Circle (Circumference):
The perimeter of a circle is referred to as the circumference. To calculate the circumference, multiply the diameter of the circle by π (approximately 3.14159).

Formula:
C=π×dC = \pi \times dC=π×d
Where “d” is the diameter of the circle.

Area Formulas

The area of a shape is the amount of space inside the boundary of that shape. Understanding how to calculate the area of different geometric shapes is essential for the TEAS exam, as it is used in various real-world applications like determining the area of a wound or calculating the surface area of objects.

Area of a Square:
The area of a square is the length of one side squared.

Formula:
A=s2A = s^2A=s2
Where “s” is the side length.

Area of a Rectangle:
The area of a rectangle is found by multiplying the length by the width.

Formula:
A=l×wA = l \times wA=l×w
Where “l” is the length and “w” is the width.

Area of a Parallelogram:
The area of a parallelogram is found by multiplying the base by the height.

Formula:
A=b×hA = b \times hA=b×h
Where “b” is the base and “h” is the height.

Area of a Triangle:
The area of a triangle is found by multiplying the base by the height and dividing by 2.

Formula:
A=12×b×hA = \frac{1}{2} \times b \times hA=21​×b×h
Where “b” is the base and “h” is the height.

Area of a Trapezoid:
The area of a trapezoid is found by averaging the lengths of the two parallel sides and multiplying by the height.

Formula:
A=12×(b1+b2)×hA = \frac{1}{2} \times (b_1 + b_2) \times hA=21​×(b1​+b2​)×h
Where “b1” and “b2” are the lengths of the parallel sides, and “h” is the height.

Area of a Circle:
The area of a circle is calculated by multiplying π by the square of the radius.

Formula:
A=π×r2A = \pi \times r^2A=π×r2
Where “r” is the radius.

Volume Formulas

Volume is the amount of space inside a three-dimensional object. Nurses use volume calculations frequently when measuring the volume of fluids, such as in the administration of IV fluids or calculating the volume of a medication. Below are formulas for the volume of various shapes.

Volume of a Rectangular Prism:
A rectangular prism is a 3D object with six rectangular faces. To calculate its volume, multiply the length, width, and height.

Formula:
V=l×w×hV = l \times w \times hV=l×w×h
Where “l” is the length, “w” is the width, and “h” is the height.

Volume of a Right Prism:
A right prism is similar to a rectangular prism, but it can have different base shapes. The volume is found by multiplying the area of the base by the height.

Formula:
V=B×hV = B \times hV=B×h
Where “B” is the area of the base and “h” is the height.

Volume of a Cylinder:
A cylinder is a 3D shape with two parallel circular bases. To calculate its volume, multiply the area of the base (πr²) by the height.

Formula:
V=π×r2×hV = \pi \times r^2 \times hV=π×r2×h
Where “r” is the radius and “h” is the height.

Volume of a Pyramid:
A pyramid has a polygonal base and triangular sides that meet at a point. To calculate its volume, multiply the area of the base by the height and divide by 3.

Formula:
V=13×B×hV = \frac{1}{3} \times B \times hV=31​×B×h
Where “B” is the area of the base and “h” is the height.

Volume of a Cone:
A cone is similar to a pyramid but with a circular base. The volume is calculated by multiplying the area of the base by the height and dividing by 3.

Formula:
V=13×π×r2×hV = \frac{1}{3} \times \pi \times r^2 \times hV=31​×π×r2×h
Where “r” is the radius and “h” is the height.

Volume of a Sphere:
A sphere is a perfectly round 3D shape. The volume is calculated using the radius and the constant π.

Formula:
V=43×π×r3V = \frac{4}{3} \times \pi \times r^3V=34​×π×r3
Where “r” is the radius.

Statistics in TEAS Mathematics

Statistics is an essential field of mathematics that deals with the collection, analysis, interpretation, and presentation of data. Understanding basic statistical concepts is vital not only for performing well on the TEAS exam but also for practical applications in nursing and healthcare. Nurses use statistics to interpret medical data, evaluate treatment effectiveness, understand trends, and make evidence-based decisions. On the TEAS exam, you’ll encounter statistical concepts that are necessary for analyzing and interpreting data in both the mathematics and science sections.

The Role of Statistics in Nursing

In the nursing field, statistics is used to evaluate and interpret data from clinical studies, patient records, lab results, and various other sources. For example, when analyzing a patient’s vital signs over time, nurses rely on statistical measures like mean, median, and standard deviation to identify trends and assess changes in a patient’s condition. Furthermore, nurses may use statistical methods to interpret laboratory test results, predict patient outcomes, and determine the effectiveness of medical treatments.

Statistics help healthcare professionals make informed decisions based on real-world data. Nurses use these concepts to monitor the health of individual patients, contribute to healthcare research, and assess the performance of healthcare systems.

On the TEAS exam, understanding the basic principles of statistics will help you solve problems related to data interpretation, central tendency, variability, and more. Below are some of the key statistical formulas and concepts you will need to know.

Key Statistical Formulas for TEAS

To effectively solve statistical problems on the TEAS exam, it’s important to understand and apply various statistical formulas. The following formulas are some of the most commonly used in statistics and will help you with questions on the test.

Mean (Average)

The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in a data set and dividing the sum by the total number of values.

Formula:

Mean=∑xin\text{Mean} = \frac{\sum x_i}{n}Mean=n∑xi​​

Where:

• ∑xi\sum x_i∑​ is the sum of all data points 
• nnn is the number of data points 

For example, if you have a data set of test scores: 70, 80, 90, and 100, the mean is:

Mean=70+80+90+1004=3404=85\text{Mean} = \frac{70 + 80 + 90 + 100}{4} = \frac{340}{4} = 85Mean=470+80+90+100​=4340​=85

Median

The median is the middle value of a data set when the numbers are arranged in ascending or descending order. If there is an odd number of data points, the median is the middle number. If there is an even number of data points, the median is the average of the two middle numbers.

For example, for the data set 70, 80, 90, 100, the median would be the average of 80 and 90, which is:

Median=80+902=85\text{Median} = \frac{80 + 90}{2} = 85Median=280+90​=85

If the data set were 70, 80, 90, 100, and 110, the median would be 90, as it is the middle value in the ordered set.

Mode

The mode is the value that appears most frequently in a data set. A data set can have no mode, one mode, or multiple modes if there are multiple values that occur with the same highest frequency.

For example, in the data set 70, 80, 80, 90, 100, the mode is 80 because it appears twice, while all other values appear only once.

Range

The range is the difference between the highest and lowest values in a data set. It is a measure of the spread of the data.

Formula:

Range=Maximum value−Minimum value\text{Range} = \text{Maximum value} – \text{Minimum value}Range=Maximum value−Minimum value

For example, for the data set 70, 80, 90, 100, the range is:

Range=100−70=30\text{Range} = 100 – 70 = 30Range=100−70=30

Standard Deviation

Standard deviation is a measure of how spread out the values in a data set are. A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are more spread out.

Formula:

s=∑(xi−xˉ)2n−1s = \sqrt{\frac{\sum (x_i – \bar{x})^2}{n-1}}s=n−1∑(xi​−xˉ)2​​

Where:

• xix_ixi​ represents each data point 
• xˉ\bar{x}xˉ is the mean of the data set 
• nnn is the number of data points 

To calculate standard deviation, you subtract the mean from each data point, square the result, sum those squared differences, and then divide by the number of data points minus one. Finally, you take the square root of that result.

Variance

Variance is closely related to standard deviation, as it measures the spread of data points in a data set. The variance is simply the square of the standard deviation.

Formula:

Variance=s2\text{Variance} = s^2Variance=s2

Variance is used in many statistical analyses, particularly when assessing the variability of a data set or comparing different groups of data.

Coefficient of Variation (CV)

The coefficient of variation is a standardized measure of the dispersion of a data set. It is useful for comparing the variability of two or more data sets that have different means.

Formula:

CV=sxˉ×100CV = \frac{s}{\bar{x}} \times 100CV=xˉs​×100

Where:

• Sss is the standard deviation 
• xˉ\bar{x}xˉ is the mean of the data set 

The coefficient of variation is often used in medical studies to compare the variability of test results or measurements across different groups of patients.

Practical Applications of Statistics in Nursing

Nurses regularly use statistics in their practice to monitor and interpret patient health data. Some examples include:

Interpreting Vital Signs

Nurses collect data on a patient’s vital signs (heart rate, blood pressure, respiratory rate, temperature) and use statistics to track trends over time. For instance, by calculating the mean blood pressure readings, nurses can identify changes or abnormalities that require attention. Standard deviation can help nurses understand the variability in a patient’s blood pressure readings, while the range can highlight extreme values that may need further investigation.

Analyzing Lab Results

Medical laboratories provide a wealth of data from tests that nurses need to interpret. Nurses use statistical measures like mean, median, and range to understand lab results and make informed decisions. For example, if a patient’s blood sugar levels are consistently above the mean for their age group, the nurse may need to take action.

Research and Evidence-Based Practice

Statistics play a significant role in healthcare research and evidence-based practice. Nurses rely on statistical analyses to evaluate the effectiveness of treatments, interventions, and therapies. For example, clinical trials often report statistical measures such as p-values, confidence intervals, and effect sizes to determine whether a treatment is effective.

Quality Control in Healthcare

Hospitals and healthcare organizations use statistics to monitor the quality of care. For example, patient satisfaction surveys often use statistical analysis to assess the overall experience of patients. The data collected can be analyzed to identify areas for improvement in patient care and operational efficiency.

Conclusion

A strong understanding of statistics is essential for both the TEAS exam and your career in nursing. On the TEAS exam, statistical concepts like mean, median, mode, standard deviation, and variance will help you solve a variety of problems. In nursing, statistics play a crucial role in interpreting data, evaluating patient outcomes, and making informed care decisions. By mastering these statistical concepts, you’ll be well-equipped to succeed on the TEAS exam and excel in your nursing practice.