Must-Know Math Skills for Success on the TEAS Exam

Arithmetic is a critical skill set for the TEAS exam. It tests your ability to perform basic mathematical operations and understand essential number concepts. Nurses must be adept at computations, as they frequently need to calculate medication dosages and interpret data for patient care. Thus, mastering arithmetic is not only necessary for the exam but also for real-world applications in healthcare. Below are the key arithmetic skills that will help you succeed on the TEAS exam.

Place Value

Understanding place value is the foundation of all other arithmetic operations. In basic terms, place value refers to the value of a digit based on its position in a number. For example, in the number 3,456, the digit 3 represents three thousand, while the digit 4 represents four hundred. You need to know how to identify the place value of each digit, whether in large numbers or decimals.

When working with decimals, place value becomes even more important. For instance, in the decimal number 12.345, the digit 1 is in the tens place, 2 is in the ones place, 3 is in the tenths place, 4 is in the hundredths place, and 5 is in the thousandths place. Mastering place value will help you with operations like addition, subtraction, and rounding, all of which are common on the TEAS exam.

Number Order and Comparison

Number order and comparison are crucial skills for understanding how numbers relate to one another. You’ll often need to arrange numbers in ascending or descending order, especially when interpreting data or solving problems involving sequences. Being able to quickly identify which numbers are greater or smaller is important for solving problems efficiently.

This includes comparing whole numbers, fractions, and decimals. For example, when comparing fractions, it’s important to recognize that 3/4 is greater than 2/3 because the numerators are equal, but the denominator of 4 results in a smaller piece. Similarly, comparing decimals requires understanding the place values of the digits. For instance, 0.75 is greater than 0.5 because 75 hundredths is more than 50 hundredths.

Negative Numbers

Negative numbers can appear in subtraction, multiplication, and division problems on the TEAS exam. It’s important to be comfortable working with negative numbers, as they often come up in situations like temperature changes, financial calculations, or distance measurements.

In subtraction, you’ll encounter problems like “5 – 8,” which results in -3. In multiplication, you need to remember that multiplying two negative numbers results in a positive product, while multiplying a negative number by a positive number results in a negative product. Similarly, division follows the same rules: dividing two negative numbers gives a positive result, and dividing a negative by a positive or vice versa gives a negative result.

Fractions

Fractions are another vital concept on the TEAS exam. Being able to understand and perform operations with fractions will help you solve many problems in the math section. There are several key skills you should master when working with fractions.

One of the most important skills is simplifying fractions. For example, you should know how to reduce 6/9 to its simplest form, which is 2/3. You should also be able to find equivalent fractions, such as understanding that 1/2 is equivalent to 2/4 or 3/6.

Another critical concept is ordering fractions by value. To compare fractions, it’s helpful to convert them to have a common denominator. Once the fractions share the same denominator, comparing the numerators will tell you which fraction is greater. You’ll need this skill to solve problems that require you to identify the largest or smallest fraction.

Conversion of Mixed Numbers and Improper Fractions

You’ll also need to be proficient in converting between mixed numbers and improper fractions. A mixed number is a number that combines a whole number and a fraction, such as 2 1/3. To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction and then add the numerator. For example, 2 1/3 becomes (2 * 3) + 1 = 7/3.

Conversely, converting an improper fraction to a mixed number involves dividing the numerator by the denominator. For instance, 7/3 becomes 2 1/3 because 7 ÷ 3 equals 2 with a remainder of 1. This skill is crucial for solving a variety of problems involving fractions on the TEAS exam.

Operations with Like and Unlike Denominators

When adding or subtracting fractions, you need to know how to handle fractions with like and unlike denominators. If the fractions have the same denominator, you can simply add or subtract the numerators. For example, 1/5 + 2/5 = 3/5.

However, if the fractions have different denominators, you must first find a common denominator. For example, to add 1/4 and 1/6, you need to find the least common denominator (LCD), which in this case is 12. Then, you rewrite the fractions as equivalent fractions with a denominator of 12: 1/4 becomes 3/12, and 1/6 becomes 2/12. Now you can add the numerators: 3/12 + 2/12 = 5/12.

Decimals

Decimals are an essential part of arithmetic on the TEAS exam, and you’ll need to understand how to add, subtract, multiply, and divide decimal numbers. One important concept is aligning the decimal points when performing addition or subtraction. For example, when adding 3.45 and 2.1, you should align the decimal points to ensure accuracy.

When multiplying decimals, you multiply the numbers as if they were whole numbers and then place the decimal point in the correct position. For example, to multiply 0.5 by 0.4, you multiply 5 by 4 to get 20, then place the decimal point to get 0.20.

For division, you may need to convert the divisor into a whole number by moving the decimal point. For example, to divide 3.6 by 0.2, you multiply both the numerator and denominator by 10, resulting in 36 ÷ 2, which equals 18.

Percents

Understanding percentages is crucial for solving problems involving discounts, interest rates, and other real-world scenarios. To convert a fraction to a percentage, multiply the fraction by 100. For example, 3/4 is equal to 75% because 3 ÷ 4 = 0.75, and 0.75 × 100 = 75.

You’ll also need to know how to find a percentage of a number. For example, to find 25% of 80, multiply 80 by 0.25 (since 25% = 0.25), which equals 20. Similarly, to increase a number by a certain percentage, you can calculate the percentage increase and then add it to the original number.

Order of Operations

The order of operations is a fundamental concept that ensures that mathematical expressions are solved correctly. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). For example, in the expression 3 + 2 × 5, you would first multiply 2 by 5 to get 10, then add 3 to get 13.

Mastering the order of operations will help you solve complex multi-step problems and is essential for success on the TEAS exam.

Estimation and Rounding

Estimation and rounding are useful skills for quickly solving problems without needing exact answers. Estimation involves finding a value that is close to the correct answer but easier to work with. For example, estimating 48 + 39 as 50 + 40 gives a rough answer of 90, which can be sufficient in some cases.

Rounding is another technique that simplifies calculations. You might need to round a number to the nearest ten, hundred, or decimal place, depending on the context. For instance, rounding 3.678 to the nearest hundredth gives 3.68. Understanding when and how to use estimation and rounding will help you solve problems more efficiently on the TEAS exam.

Algebra Skills for the TEAS Exam

Algebra is another crucial area of mathematics covered in the TEAS exam. It tests your ability to manipulate variables and equations, an essential skill for solving many real-world problems, especially in the healthcare field. Nurses often encounter algebraic situations, such as calculating medication dosages or interpreting laboratory results, where they need to solve for unknowns. Below are the key algebraic concepts that will help you succeed on the TEAS exam.

Constants versus Variables

The first step in understanding algebra is distinguishing between constants and variables. A constant is a fixed value, like 5 or 10, while a variable represents an unknown quantity, usually represented by a letter such as x, y, or z. For example, in the expression 2x + 5 = 15, 5 and 15 are constants, while x is the variable.

Being able to identify constants and variables will help you understand how algebraic expressions work. You’ll also need to be comfortable working with both types of values when solving equations or simplifying expressions.

Simplifying Expressions Containing Variables

Simplifying algebraic expressions is a key skill in algebra. This involves combining like terms and reducing the expression to its simplest form. Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x + 2x, both terms have the variable x, so you can combine them to get 5x.

In more complex expressions, you may also need to apply the distributive property. The distributive property states that a(b + c) = ab + ac. For example, if you have the expression 2(x + 3), you would distribute the 2 to both x and 3, resulting in 2x + 6.

Simplifying algebraic expressions is an important skill for solving more complex problems on the TEAS exam.

Solving Equations by Isolating Variables

One of the most fundamental tasks in algebra is solving equations, particularly by isolating the variable. To solve an equation, you need to manipulate it to get the variable by itself on one side of the equation. For example, in the equation 2x + 5 = 15, you want to isolate x.

The first step is to subtract 5 from both sides of the equation to get 2x = 10. Then, divide both sides by 2 to get x = 5. The goal is to perform the same operation on both sides of the equation to keep the equation balanced while isolating the variable.

It’s important to practice this skill because many problems on the TEAS exam require solving equations to find an unknown value, such as in dosage calculations or interpreting medical data.

Problem-Solving: Creating Expressions and Equations

Problem-solving is a critical skill for algebra, as you often need to translate word problems into algebraic expressions or equations. This process involves reading the problem carefully, identifying the unknowns, and using variables to represent them.

For example, suppose a problem asks: “A nurse administers 4 milligrams of medication every 3 hours. How many milligrams will be administered in 12 hours?” To solve this, you would create an equation. Let x represent the number of milligrams administered in 12 hours. You know that the nurse administers 4 milligrams every 3 hours, so the equation is:

x = (4 milligrams / 3 hours) × 12 hours

By simplifying, you find that x = 16 milligrams. Being able to translate real-world problems into equations is a valuable skill, especially in nursing scenarios where you need to calculate dosages.

Multi-Step Problems

Many algebraic problems on the TEAS exam involve multiple steps. Multi-step problems require you to solve several parts of the equation or expression before reaching the final answer. For example, a problem might involve both simplifying an expression and solving for the variable.

For instance, consider the problem: “Solve for x in the equation 3x – 4 = 2x + 6.” To solve this, follow these steps:

1. Subtract 2x from both sides: 3x – 2x – 4 = 6

2. Simplify: x – 4 = 6

3. Add 4 to both sides: x = 10

Multi-step problems often involve more than one operation, so being comfortable with addition, subtraction, multiplication, and division is key to solving these problems efficiently.

Necessary versus Unnecessary Information

In some algebraic word problems, not all the information given is necessary to find the solution. Identifying which information is relevant and which is extraneous can help simplify the problem and save time.

For example, consider the problem: “A nurse is preparing a dosage of medication for a patient. The medication needs to be given at a rate of 5 milligrams per kilogram of body weight. The patient weighs 60 kilograms, and the dosage is to be administered every 4 hours. How many milligrams will the patient receive in one day?”

While the information about the dosage being administered every 4 hours might be helpful for some aspects of the problem, you only need to focus on the weight and the dosage per kilogram to calculate the total amount needed for one day. Thus, identifying necessary versus unnecessary information is an important skill for simplifying the problem and focusing on the key details.

Ratio and Proportions

Ratios and proportions are commonly tested on the TEAS exam and are essential in many healthcare calculations. A ratio is a relationship between two quantities, often expressed as a fraction. For example, a ratio of 2:3 means that for every 2 units of one quantity, there are 3 units of another quantity.

Proportions are equations that express the equality of two ratios. For example, if you know that the ratio of medicine to body weight is 2:3, and you need to find the amount of medicine for a patient who weighs 90 kilograms, you can set up the proportion as follows:

2/3 = x/90

Cross-multiply and solve for x to find that the patient needs 60 milligrams of medicine. Proportions are often used to calculate dosages and understand the relationships between different quantities.

Rate of Change

The rate of change measures how one quantity changes about another, and it’s often used in problems involving speed, time, or cost. For example, the rate of change could be the speed of a moving vehicle, the rate at which a patient’s condition is improving, or the rate at which a nurse administers medication.

On the TEAS exam, you may encounter problems where you need to calculate the rate of change. A common formula used for this is:

Rate of Change = (Change in Quantity) / (Change in Time)

For example, if a nurse administers 10 milliliters of medication over 5 minutes, the rate of change is:

Rate of Change = 10 milliliters / 5 minutes = 2 milliliters per minute

Understanding how to calculate the rate of change will help you solve many real-world problems, especially in healthcare contexts.

Statistics and Advanced Data Interpretation for the TEAS Exam

The final part of the math section on the TEAS exam focuses on statistics and data interpretation. This section assesses your ability to interpret and analyze statistical data, understand trends, and make informed decisions based on numerical information. As a future nurse, you will frequently encounter statistical data, such as lab results, patient charts, or health trends, making these skills essential for both the exam and your practice. Below are the key statistical concepts and data interpretation skills you need to master for the TEAS exam.

Normal Distribution and Skews

One of the most important statistical concepts to understand is normal distribution, which describes how data is spread out around a central value. In a normal distribution, most of the data points cluster around the mean, or average, and the distribution forms a bell-shaped curve.

The mean is the sum of all data values divided by the number of values, and it represents the central value of the data set. The median is the middle value when the data is ordered, and the mode is the most frequently occurring value.

In a normal distribution, the data is symmetrical, meaning that the left and right sides of the curve are mirror images of each other. Understanding normal distribution is essential for interpreting trends, particularly when assessing patient data, such as body temperature or blood pressure, where values typically fall within a certain range.

A skewed distribution occurs when the data is not symmetrical. In a positively skewed distribution, most of the data points are concentrated on the left side of the distribution, and the tail of the curve extends to the right. In a negatively skewed distribution, the opposite is true, with most data points concentrated on the right side and the tail extending to the left. Recognizing skewed distributions is important when analyzing data for outliers or unusual patterns.

Bimodal and Uniform Distributions

In addition to normal and skewed distributions, there are other types of distributions that you may encounter in the TEAS exam:

• Bimodal distribution: This type of distribution has two distinct peaks or modes. It indicates that there are two different groups or categories within the data. For example, if you were analyzing test scores, a bimodal distribution might indicate that there are two groups of students—one with high scores and one with low scores—rather than a single group with a range of scores.

• Uniform distribution: In a uniform distribution, all data points are equally likely to occur, and the distribution is flat. This means there is no clustering around a central value, and the data is spread out evenly. Understanding uniform distributions is important for interpreting situations where there is no preference or bias in the data, such as in random sampling.

Interpreting Trends in Data

Being able to interpret trends in data is an essential skill for understanding the results of experiments or medical data. Trends represent the general direction in which the data is moving over time or across different conditions. For example, in a health-related study, you might analyze a trend showing how a patient’s blood pressure changes over several weeks of treatment.

Key trends to look for include:

• Increasing or decreasing trends: This indicates that the values are rising or falling over time. For example, if a patient’s weight continues to increase, it could indicate a health issue that requires attention.

• Cyclic trends: These are trends that repeat over a regular interval. For example, a patient’s temperature might show cyclical fluctuations, depending on the time of day or a recurring illness.

• Constant trends: These trends show little or no change over time. For instance, if a patient’s vital signs remain stable over a period, it may indicate that the treatment is effective.

Understanding trends will help you interpret medical data, such as lab results, and make informed decisions about patient care.

Mean, Median, Mode

The mean, median, and mode are measures of central tendency, which help summarize a data set by identifying a central value. You should be familiar with when and how to use each measure:

• Mean: The mean is the most common measure of central tendency. It is calculated by adding all the data points and dividing by the number of data points. For example, if the ages of five patients are 20, 25, 30, 35, and 40, the mean age is (20 + 25 + 30 + 35 + 40) ÷ 5 = 30.
  
  The mean is useful when you have a data set that is evenly distributed without outliers. However, the mean can be influenced by extreme values (outliers), so it may not always represent the best central value.

• Median: The median is the middle value when the data is ordered. If there is an odd number of data points, the median is the exact middle number. If there is an even number of data points, the median is the average of the two middle numbers. The median is less affected by outliers, making it a better measure of central tendency when the data contains extreme values.
  
  For example, with the data set 10, 20, 30, 40, and 50, the median is 30. If the data set is 10, 20, 30, 100, and 1,000, the median would be 30, as it is less affected by the outlier of 1,000.

• Mode: The mode is the most frequently occurring value in a data set. A data set can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all. The mode is useful for identifying the most common value in a data set.
  
  For example, in the data set 2, 4, 4, 6, 6, 6, the mode is 6 because it occurs more frequently than any other value.

Range, Spread, Variance, and Standard Deviation

The range of a data set is the difference between the largest and smallest values. The range gives a sense of the spread of the data, but it can be influenced by outliers.

For example, in the data sets 5, 10, 15, and 100, the range is 100 – 5 = 95. This large range is largely influenced by the outlier of 100.

Spread refers to how much the data points vary from the central value. The range is a simple measure of spread, but it does not take into account how the individual values are distributed.

Variance and standard deviation are measures of how much the data points deviate from the mean. Variance is the average of the squared differences between each data point and the mean, while the standard deviation is the square root of the variance.

• Variance: Measures the average squared deviation from the mean.

• Standard deviation: Measures how spread out the data is about the mean. A larger standard deviation indicates greater variability in the data, while a smaller standard deviation indicates that the data points are closer to the mean.

Both variance and standard deviation are commonly used in healthcare to assess the consistency of measurements, such as blood pressure readings or test results.

Covariance and Causality

Covariance is a measure of how two variables change together. If two variables tend to increase or decrease together, their covariance is positive. If one variable increases while the other decreases, their covariance is negative. Covariance helps identify relationships between variables, though it does not indicate the strength or causality of the relationship.

Causality refers to a cause-and-effect relationship between two variables. Unlike covariance, which simply indicates a relationship, causality implies that one variable directly affects the other. For example, if a study shows that increased physical activity leads to weight loss, this suggests a causal relationship between exercise and weight reduction.

Understanding the difference between covariance and causality is crucial for interpreting health data, as not all correlations imply a cause-and-effect relationship.

Response versus Explanatory Variables

In data analysis, it’s important to distinguish between response variables and explanatory variables.

• A response variable is the outcome or the variable that is being measured or predicted. For example, in a study analyzing the effect of medication on blood pressure, blood pressure would be the response variable.

• An explanatory variable is the variable that is used to explain or predict the response variable. In the same study, the medication dosage or the type of medication would be the explanatory variable.

Understanding these variables will help you interpret studies and data correctly, particularly when working with patient data or interpreting research findings.

Conclusion

Statistics and data interpretation are vital skills for the TEAS exam and your nursing career. Understanding how to interpret normal distributions, calculate central tendency measures, and analyze trends in data will help you make informed decisions based on statistical information. These skills are particularly important in healthcare settings, where accurate data analysis can lead to better patient outcomes. By mastering concepts such as mean, median, mode, variance, and understanding relationships between variables, you will be well-prepared to tackle the statistics and data interpretation section of the TEAS exam and succeed in your nursing career.