Solving for Variables and Unknowns
Algebraic proficiency on the TEAS is centered on the ability to isolate an unknown variable within a linear equation. The fundamental principle is the Addition Property of Equality, which dictates that any operation performed on one side of an equation must be mirrored on the other to maintain balance. When faced with a multi-step equation, candidates should follow the inverse order of operations to isolate the variable. For instance, in an equation like 3x + 5 = 20, one must first subtract the constant before dividing by the coefficient. The TEAS algebra formulas you need most often involve the slope-intercept form: y = mx + b. Here, 'm' represents the slope (rise over run) and 'b' represents the y-intercept. You may be asked to find the slope between two points using the formula m = (y₂ - y₁) / (x₂ - x₁). Understanding this relationship is critical for interpreting how one variable changes in response to another, a frequent requirement in nursing-related math scenarios involving dosage adjustments or patient monitoring trends.
Ratios, Proportions, and Percentages
Proportions are the backbone of the TEAS math section, particularly because they mirror real-world nursing tasks like calculating medication concentrations. A proportion is an equation stating that two ratios are equal: a/b = c/d. To solve for an unknown in a proportion, use cross-multiplication, which results in the equation ad = bc. This method is highly effective for unit conversions and scaling. Percentages are often tested through the percent change formula: [(New Value - Old Value) / Old Value] × 100. This calculation determines the percentage of increase or decrease, which is a common assessment detail in questions regarding weight loss, fluid intake, or budget changes. Additionally, the basic percent formula (Part = Percent × Whole) is essential. Candidates must be comfortable converting between decimals, fractions, and percentages rapidly, as the exam often presents data in one format and asks for the solution in another to test numerical fluency.
Working with Expressions and Inequalities
Beyond simple equations, the TEAS requires candidates to manipulate expressions and solve inequalities. An expression lacks an equals sign and requires simplification through the distribution of terms or the combining of like terms. When solving inequalities, the most critical rule to remember is the Inequality Reversal Rule: if you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign must be flipped. For example, if -2x < 10, dividing by -2 results in x > -5. This logic is vital for determining ranges, such as safe dosage windows or heart rate boundaries. The exam also tests the ability to translate verbal phrases into algebraic expressions. Phrases like "less than" or "increased by" must be mapped to subtraction and addition respectively. Mastery of this TEAS 7 math formulas subset ensures that you can set up the correct mathematical model before attempting the calculation.
Geometry questions on the TEAS focus heavily on two-dimensional shapes. The perimeter represents the total distance around the edge of a shape, while area measures the space inside. For rectangles, the formulas are P = 2l + 2w and A = lw. However, circles require specific TEAS geometry formulas involving the constant Pi (approximately 3.14). The circumference (the perimeter of a circle) is calculated as C = 2πr or C = πd, where 'r' is the radius and 'd' is the diameter. The area of a circle is A = πr². A common trap on the exam is providing the diameter when the area formula requires the radius; candidates must remember that r = d/2. For triangles, the area is A = ½bh. In these problems, the 'height' must be the perpendicular height, not the slant height of the side. Recognizing these distinctions is essential for accuracy in the measurement sub-section of the exam.
Volume and Surface Area for 3D Shapes
Three-dimensional geometry on the TEAS typically involves rectangular prisms and cylinders. The volume of a rectangular prism is found using V = l × w × h. For a cylinder, the volume formula is V = πr²h, which is essentially the area of the circular base multiplied by the height. These formulas are frequently applied in questions involving fluid volume, such as calculating the capacity of a container or the amount of liquid in a cylindrical tank. Surface area is less common but may appear; for a rectangular prism, it is the sum of the areas of all six faces: SA = 2(lw + lh + wh). Understanding the equations for TEAS math in 3D space requires a firm grasp of units. Volume is always expressed in cubic units (e.g., cm³ or mL), and candidates must be prepared to convert between these units, knowing that 1 cm³ is equivalent to 1 mL, a standard conversion in clinical settings.
Angles and Coordinate Geometry Principles
Angle relationships are a staple of the geometry section. Candidates must identify complementary angles (sum to 90°) and supplementary angles (sum to 180°). The Pythagorean Theorem, a² + b² = c², is indispensable for solving problems involving right triangles, where 'c' is the hypotenuse. This theorem is often used in word problems to find the distance between two points or the length of a diagonal path. In the coordinate plane, you may need to find the distance between two points (x₁, y₁) and (x₂, y₂) using the distance formula, which is a derivation of the Pythagorean Theorem: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. While the TEAS does not require advanced trigonometry, understanding these fundamental spatial relationships allows you to solve complex visualization problems that involve multiple geometric steps.
Statistics on the TEAS focus on measures of central tendency and variability. The Arithmetic Mean is the average found by summing all values in a data set and dividing by the count of those values (Σx / n). The median is the middle value when the data is arranged in ascending order; if there is an even number of observations, the median is the mean of the two middle numbers. The mode is the value that appears most frequently. To measure spread, the range is calculated as the difference between the maximum and minimum values. Candidates must be careful with data sets containing outliers, as these significantly affect the mean but have little impact on the median. In a clinical context, choosing the right measure (such as using the median to describe typical patient recovery times when a few patients stay much longer than others) is a key analytical skill tested on the exam.
Interpreting Charts, Graphs, and Tables
Data interpretation questions require you to extract information from visual representations like bar graphs, line graphs, and pie charts. A common task is calculating the value of a sector in a pie chart given the total. For example, if a pie chart represents a total of 500 patients and one sector is 20%, the number of patients in that category is 0.20 × 500 = 100. Line graphs often require you to calculate the Rate of Change between two points, which is essentially finding the slope of the line segment. You must pay close attention to the axes labels and scales, as some graphs may use increments other than one. The ability to move between a visual data point and a mathematical formula is a core competency, as the TEAS assesses your ability to synthesize information from multiple sources to reach a conclusion.
Understanding Probability and Rates
Probability measures the likelihood of an event occurring and is expressed as the ratio of favorable outcomes to the total number of possible outcomes (P = desired / total). Probability values always range from 0 to 1, or 0% to 100%. If an event is certain, its probability is 1; if impossible, it is 0. For independent events, the probability of both occurring (Event A AND Event B) is found by multiplying their individual probabilities. Rates, such as speed or flow rates, are also prevalent. The Distance Formula (Distance = Rate × Time) is a versatile tool for these questions. In a medical context, this might be adapted to find the total volume of an IV drip over a set period (Volume = Flow Rate × Time). Mastering these rates allows you to solve problems where multiple factors are changing simultaneously.
Applied Math: Word Problems and Real-World Context
Converting Units in the Metric System
Unit conversion is perhaps the most frequent application of math on the TEAS. The exam relies heavily on the metric system, requiring knowledge of prefixes: kilo- (1000), hecto- (100), deka- (10), deci- (0.1), centi- (0.01), and milli- (0.001). A common mnemonic is "King Henry Died By Drinking Chocolate Milk" (Kilo, Hecto, Deka, Base, Deci, Centi, Milli). To convert from a larger unit to a smaller unit, you multiply by powers of ten (move the decimal to the right); to convert from smaller to larger, you divide (move the decimal to the left). For example, 2.5 grams is equal to 2,500 milligrams. Understanding the TEAS math formulas list for conversions is not just about the metric system; you must also know US Customary conversions, such as 12 inches in a foot, 3 feet in a yard, and 16 ounces in a pound. In the medical field, the conversion between kilograms and pounds (1 kg ≈ 2.2 lbs) is critical for weight-based medication dosing.
Solving Multi-Step Measurement Problems
Many TEAS questions are not solved with a single formula but require a sequence of operations. These multi-step problems often involve a conversion followed by a calculation of area, volume, or rate. For instance, you might be asked to find the area of a room in square meters when the dimensions are given in centimeters. The first step is to convert the length and width to meters, and the second is to apply the area formula. A common error is calculating the area in centimeters first and then trying to convert to meters; this is difficult because one square meter equals 10,000 square centimeters (100 × 100). Following the Order of Operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is mandatory to ensure the correct sequence of steps. Developing a systematic approach—identifying the goal, listing knowns, converting units, and then calculating—is the best way to avoid simple mistakes on these complex items.
Estimating and Rounding for Practical Solutions
Estimation is a powerful tool for verifying the reasonableness of an answer and is sometimes a required skill on the TEAS. Rounding rules are strictly enforced: if the digit to the right of the target place value is 5 or greater, round up; if it is 4 or less, keep the digit the same. The exam may ask you to round to the nearest tenth, hundredth, or whole number. For example, 15.678 rounded to the nearest hundredth is 15.68. In word problems, you might use Front-End Estimation to quickly narrow down multiple-choice options. If a problem asks for the product of 19.95 and 5.02, estimating it as 20 × 5 = 100 allows you to immediately discard choices that are significantly higher or lower. This skill is particularly useful for the time-pressured environment of the TEAS, where quick mental checks can prevent significant errors in calculation.
Since no reference material is allowed during the test, creating your own TEAS math formulas cheat sheet during your study sessions is a proven method for retention. Start by grouping formulas by category—algebra, geometry, and statistics—rather than trying to learn them in a random list. Use active recall by writing the formulas from memory on a blank sheet of paper every day. This builds muscle memory and reinforces the neural pathways needed for retrieval. Focus on the relationships between formulas; for example, notice how the volume of a cylinder (V = πr²h) is just the area of a circle (A = πr²) with a height component added. By understanding these connections, you reduce the total amount of "unique" information you need to memorize, making the recall process much more efficient during the actual exam.
Visual learners benefit from associating formulas with specific shapes or scenarios. When memorizing the Pythagorean Theorem, always sketch a right triangle and label the legs 'a' and 'b' and the long diagonal 'c'. For the TEAS geometry formulas, draw a circle and label the radius (center to edge) and the diameter (edge to edge through center). Visualizing the "why" behind a formula—such as seeing that the area of a triangle is exactly half of a rectangle with the same base and height—makes the formula A = ½bh much harder to forget. This technique also helps in word problems, where your first step should often be to draw a quick diagram of the scenario described. This bridges the gap between the text of the question and the abstract formula needed to solve it.
Speed is a major factor in the TEAS math section. You have approximately one minute per question, which leaves little time for pondering which formula to use. Practice drills should focus on Formula Identification rather than just calculation. Take a set of 20 practice problems and, without solving them, simply write down the formula required for each. This forces your brain to recognize the "trigger words" in a problem—such as "encloses" for area, "around" for perimeter, or "ratio" for proportions. Once you can identify the correct tool for the job instantly, the actual arithmetic becomes a secondary, more manageable task. Consistent practice with timed sets of questions will build the stamina and confidence necessary to execute these formulas accurately even when the exam timer is ticking down.