TEAS 7 Mathematics Study Guide

The TEAS Mathematics section tests your basic math skills that nurses use every day. This section has 38 questions and you get 57 minutes to complete it. You’ll use an on-screen calculator for most problems.

This guide covers everything you need to know for the math section. Each topic includes clear explanations, step-by-step examples, and practice questions. By studying this guide, you’ll feel confident solving any math problem on the TEAS.

The math section focuses on practical skills. You’ll solve problems about medication doses, patient measurements, and healthcare statistics. These are real situations you’ll face as a nurse.

Overview of the Mathematics Section

What You Need to Know

The Mathematics section contains 38 total questions. Only 34 questions count toward your score. The other 4 questions are unscored test questions that don’t affect your grade.

You have 57 minutes to complete this section. That gives you about 1 minute and 30 seconds per question. Some problems will take longer than others, so manage your time wisely.

You’ll have access to an on-screen calculator for the computer-based test. The calculator can handle basic operations, fractions, and decimals. Practice using a similar calculator before your test day.

Types of Math Problems

Most questions are multiple choice with four answer options. Some questions ask you to select all correct answers from a list. A few questions require you to type in a number as your answer.

Problems cover two main areas: Numbers and Algebra, and Measurement and Data. You’ll see word problems, calculations, and questions about charts and graphs.

All problems use situations you might encounter in healthcare. You don’t need advanced math knowledge, just solid basic skills applied to real-world scenarios.

Numbers and Algebra

This section tests your ability to work with numbers and solve basic equations. You’ll see 18 questions about these topics. These skills form the foundation for all nursing math calculations.

Good number sense helps you calculate medication doses accurately and solve everyday math problems quickly. These skills keep patients safe and help you work efficiently.

Converting Fractions, Decimals, and Percentages

Nurses constantly convert between fractions, decimals, and percentages. You might need to change a decimal dose to a fraction or convert a percentage to a decimal for calculations.

To convert a fraction to a decimal, divide the top number by the bottom number. To convert a decimal to a percentage, multiply by 100 and add the percent sign. To convert a percentage to a decimal, divide by 100.

Remember these common conversions:
1/2 = 0.5 = 50%,
1/4 = 0.25 = 25%,
3/4 = 0.75 = 75%.
Memorizing these saves time on the test.

Example: Convert 3/8 to a decimal and percentage.

Step 1: Convert to decimal: 3 ÷ 8 = 0.375
Step 2: Convert to percentage: 0.375 × 100 = 37.5%

Practice Question:

A patient’s medication is 0.6 mg. What is this as a fraction in simplest form?

A) 6/10
B) 3/5
C) 60/100
D) 6/100

Answer: B) 3/5

Explanation: First, write 0.6 as 6/10. Then simplify by dividing both the top and bottom by their greatest common factor, which is 2. So 6/10 = 3/5.

Arithmetic Operations with Rational Numbers

Rational numbers include whole numbers, fractions, and decimals. You need to add, subtract, multiply, and divide these numbers accurately for medication calculations and patient measurements.

When adding or subtracting fractions, find a common denominator first. When multiplying fractions, multiply the tops together and the bottoms together. When dividing fractions, multiply by the reciprocal (flip the second fraction).

For decimals, line up the decimal points when adding or subtracting. When multiplying decimals, count the total decimal places in both numbers and put that many places in your answer.

Example: Calculate 2 1/3 + 1 3/4

Step 1: Convert to improper fractions: 7/3 + 7/4
Step 2: Find common denominator: 28/12 + 21/12
Step 3: Add: 49/12 = 4 1/12

Practice Question:

A patient needs 2.5 mL of medication three times per day. How much medication does the patient need in total each day?

A) 6.5 mL
B) 7.0 mL
C) 7.5 mL
D) 8.0 mL

Answer: C) 7.5 mL

Explanation: Multiply 2.5 mL × 3 times = 7.5 mL total per day.

Comparing and Ordering Numbers

Nurses often need to compare medication doses, vital signs, and lab values. You must know which numbers are larger or smaller to make safe decisions about patient care.

When comparing decimals, look at each place value from left to right. When comparing fractions, convert to the same denominator or change to decimals. When comparing mixed numbers, compare the whole number parts first.

Use the symbols correctly: < means “less than,” > means “greater than,” ≤ means “less than or equal to,” and ≥ means “greater than or equal to.”

Example: Order from smallest to largest: 0.75, 3/4, 0.8, 4/5

Step 1: Convert all to decimals: 0.75, 0.75, 0.8, 0.8
Step 2: Order: 0.75 = 3/4, then 0.8 = 4/5

Practice Question:

Which list shows these temperatures in order from lowest to highest? 98.2°F, 98.6°F, 98.15°F, 98.09°F

A) 98.09°F, 98.15°F, 98.2°F, 98.6°F
B) 98.6°F, 98.2°F, 98.15°F, 98.09°F
C) 98.15°F, 98.09°F, 98.2°F, 98.6°F
D) 98.09°F, 98.2°F, 98.15°F, 98.6°F

Answer: A) 98.09°F, 98.15°F, 98.2°F, 98.6°F

Explanation: Compare decimal places carefully. 98.09 < 98.15 < 98.2 < 98.6. Remember that 98.2 is the same as 98.20, which is greater than 98.15.

Solving Equations with One Variable

Many nursing calculations involve solving for an unknown value. You might need to find the correct medication dose or calculate how long a treatment should last.

To solve equations, isolate the variable by doing the same operation to both sides. If a number is added to the variable, subtract it from both sides. If the variable is multiplied by a number, divide both sides by that number.

Always check your answer by substituting it back into the original equation. This helps catch calculation errors.

Example: Solve for x: 3x + 7 = 22

Step 1: Subtract 7 from both sides: 3x = 15
Step 2: Divide both sides by 3: x = 5
Step 3: Check: 3(5) + 7 = 15 + 7 = 22 ✓

Practice Question:

A patient’s IV drip rate is calculated using the formula: Rate = Volume ÷ Time. If the volume is 250 mL and the rate is 50 mL/hour, how many hours will the IV run?

A) 3 hours
B) 4 hours
C) 5 hours
D) 6 hours

Answer: C) 5 hours

Explanation: Use the formula Rate = Volume ÷ Time, so 50 = 250 ÷ Time. Solve for Time: Time = 250 ÷ 50 = 5 hours.

Real World Problems with Real Numbers

Word problems test your ability to translate real situations into math equations. Read carefully to identify what information you’re given and what you need to find.

Look for key words that tell you which operation to use. “Total,” “sum,” and “altogether” suggest addition. “Difference,” “left,” and “remaining” suggest subtraction. “Times,” “of,” and “each” suggest multiplication.

Set up the problem step by step. Write down what you know, what you need to find, and then create an equation to solve the problem.

Example: A hospital has 150 beds. If 87% are occupied, how many beds are empty?

Step 1: Find occupied beds: 150 × 0.87 = 130.5, round to 131 beds Step 2: Find empty beds: 150 – 131 = 19 beds

Practice Question:

A nurse works 12-hour shifts. In one week, she works 3 shifts. How many total hours does she work that week?

A) 15 hours
B) 24 hours
C) 36 hours
D) 48 hours

Answer: C) 36 hours

Explanation: Multiply 12 hours per shift × 3 shifts = 36 total hours.

Real World Problems with Percentages

Percentages appear frequently in healthcare. You might calculate success rates for treatments, medication concentrations, or changes in patient vital signs.

To find a percentage of a number, convert the percentage to a decimal and multiply. To find what percentage one number is of another, divide the first number by the second and multiply by 100.

For percentage increase or decrease, find the difference between the old and new values, divide by the old value, and multiply by 100.

Example: A patient’s heart rate decreased from 80 beats per minute to 72 beats per minute. What is the percentage decrease?

Step 1: Find the decrease: 80 – 72 = 8 beats per minute
Step 2: Calculate percentage: (8 ÷ 80) × 100 = 10% decrease

Practice Question:

A medication is 25% more effective when taken with food. If the medication is normally 60% effective, what is its effectiveness when taken with food?

A) 75%
B) 85%
C) 65%
D) 80%

Answer: A) 75%

Explanation: Calculate 25% of 60%: 0.25 × 60 = 15. Add this to the original: 60% + 15% = 75%.

Estimation Strategies and Rounding

Estimation helps you check if your answers are reasonable. It’s especially important for medication calculations where errors can be dangerous.

Round numbers to make calculations easier. For addition and subtraction, round to the same place value. For multiplication and division, round each number to one or two significant digits.

Use estimation to eliminate obviously wrong answer choices on multiple choice questions. Your estimate should be close to one of the options.

Example: Estimate 19.7 × 31.2

Step 1: Round to easier numbers: 20 × 30
Step 2: Calculate: 20 × 30 = 600
Step 3: The actual answer should be close to 600

Practice Question:

A patient needs approximately 2.1 mg of medication per kilogram of body weight. If the patient weighs 68.7 kg, about how much medication is needed?

A) About 120 mg
B) About 140 mg
C) About 160 mg
D) About 180 mg

Answer: B) About 140 mg

Explanation: Round 2.1 to 2 and 68.7 to 70. Then 2 × 70 = 140 mg. This is close enough for estimation purposes.

Real World Problems with Proportions

Proportions help you solve problems when you know that two ratios are equal. This is very useful for medication dosing calculations where you need to find the right amount for a specific patient.

Set up proportions by writing two equal ratios. Cross multiply to solve for the unknown value. Always check that your units match correctly on both sides.

Label your units clearly to avoid errors. Make sure the same types of quantities are in the same positions in both ratios.

Example: If 2 tablets contain 500 mg of medication, how many milligrams are in 3 tablets?

Step 1: Set up proportion: 2 tablets/500 mg = 3 tablets/x mg
Step 2: Cross multiply: 2x = 500 × 3 = 1500
Step 3: Solve: x = 1500 ÷ 2 = 750 mg

Practice Question:

A medication label says 5 mL contains 250 mg. How many mL contain 100 mg?

A) 1 mL
B) 2 mL
C) 3 mL
D) 4 mL

Answer: B) 2 mL

Explanation: Set up the proportion: 5 mL/250 mg = x mL/100 mg. Cross multiply: 250x = 500, so x = 2 mL.

Real World Problems with Ratios and Rates of Change

Ratios compare two quantities. Rates are special ratios that compare different types of units, like miles per hour or milligrams per kilogram.

Unit rates have a denominator of 1. They’re useful for comparing options and making calculations. To find a unit rate, divide the first quantity by the second quantity.

In healthcare, you’ll use rates for IV drip calculations, medication dosing per body weight, and vital sign monitoring over time.

Example: A patient’s heart rate changed from 72 beats per minute to 84 beats per minute over 2 hours. What is the rate of change per hour?

Step 1: Find total change: 84 – 72 = 12 beats per minute
Step 2: Find rate per hour: 12 ÷ 2 = 6 beats per minute per hour

Practice Question:

An IV bag contains 1000 mL and drips at 125 mL per hour. How long will it take to empty?

A) 6 hours
B) 7 hours
C) 8 hours
D) 9 hours

Answer: C) 8 hours

Explanation: Divide total volume by rate: 1000 mL ÷ 125 mL/hour = 8 hours.

Measurement and Data

This section tests your ability to work with measurements, convert between units, and understand data presentations. You’ll see 16 questions about these topics. These skills help you read charts, convert measurements, and analyze patient data.

Nurses use measurements constantly. You need to convert between different units, read medical charts, and understand statistical information about treatments and outcomes.

Standard and Metric System Conversions

Healthcare uses both US customary units and metric units. You must convert between systems and within each system accurately. Mistakes in conversions can lead to serious medication errors.

Common metric conversions:
1000 mg = 1 g,
1000 mL = 1 L,
100 cm = 1 m,
1000 m = 1 km.
Common US customary conversions: 16 oz = 1 lb, 12 in = 1 ft, 3 ft = 1 yd.

To convert between systems, use conversion factors. For example, 1 inch = 2.54 cm, 1 kg = 2.2 lbs, 1 L = 1.06 qt.

Example: Convert 15 mL to teaspoons (1 tsp = 5 mL)

Step 1: Set up conversion: 15 mL × (1 tsp/5 mL)
Step 2: Calculate: 15 ÷ 5 = 3 teaspoons

Practice Question:

A patient weighs 154 pounds. What is this weight in kilograms? (1 kg = 2.2 lbs)

A) 68 kg
B) 70 kg
C) 72 kg
D) 74 kg

Answer: B) 70 kg

Explanation: Divide pounds by 2.2: 154 ÷ 2.2 = 70 kg.

Tables, Charts, and Graphs

Healthcare professionals read many types of data displays. Bar graphs compare quantities, line graphs show changes over time, and pie charts show parts of a whole.

When reading graphs, always check the title, axis labels, and scale. Pay attention to what each axis represents and what units are used.

Look for trends and patterns in the data. Can you see increases, decreases, or cycles? This information helps you understand patient conditions and treatment effectiveness.

Example: Look at this table showing patient vital signs:

Practice Question:

Based on the table above, what trend do you see in the patient’s heart rate?

A) Steadily increasing
B) Steadily decreasing
C) Increasing then decreasing
D) No clear pattern

Answer: C) Increasing then decreasing

Explanation: The heart rate goes from 72 to 78 (increase), then to 75 and 70 (decrease), showing an increase followed by a decrease.

Statistics and Data Analysis

Statistics help healthcare workers understand large amounts of data. Mean, median, and mode are three ways to describe the center of a data set.

Mean is the average – add all values and divide by how many values you have. Median is the middle value when data is arranged in order. Mode is the value that appears most often.

Range shows how spread out data is – subtract the smallest value from the largest value. These statistics help you understand patient populations and treatment outcomes.

Example: Find the mean, median, and range for these blood glucose readings: 95, 110, 105, 95, 115, 100, 95

Step 1: Mean = (95+110+105+95+115+100+95) ÷ 7 = 715 ÷ 7 = 102.1
Step 2: Median = arrange in order (95,95,95,100,105,110,115), middle value = 100
Step 3: Range = 115 – 95 = 20

Practice Question:

Five patients have the following ages: 45, 52, 38, 45, 60. What is the mode?

A) 45
B) 48
C) 52
D) There is no mode

Answer: A) 45

Explanation: The mode is the value that appears most frequently. The age 45 appears twice, while all other ages appear only once.

Calculating Geometric Quantities

Geometry helps you calculate areas, volumes, and distances in healthcare settings. You might need to find the area of a wound, the volume of medication in a syringe, or the surface area for dosing calculations.

Use the correct formula for each shape. For rectangles, area = length × width. For circles, area = π × radius². For rectangular boxes, volume = length × width × height.

Always include the correct units in your answer. Area uses square units (cm², in²) and volume uses cubic units (cm³, mL).

Example: A circular wound has a radius of 2 cm. What is its area?

Step 1: Use formula A = πr² Step 2: Calculate: A = π × 2² = π × 4 = 4π ≈ 12.57 cm²

Practice Question:

A rectangular bandage measures 4 inches by 6 inches. What is its area?

A) 10 square inches
B) 20 square inches
C) 24 square inches
D) 28 square inches

Answer: C) 24 square inches

Explanation: Area = length × width = 4 inches × 6 inches = 24 square inches.

Relationships Between Two Variables

In healthcare, many variables are related to each other. For example, medication dose often depends on patient weight. Understanding these relationships helps you make predictions and adjustments.

On a graph, the x-axis shows the independent variable (the input) and the y-axis shows the dependent variable (the output). Look for patterns like positive correlation (both increase together) or negative correlation (one increases as the other decreases).

Linear relationships form straight lines on graphs. You can use these patterns to predict values that aren’t directly shown on the graph.

Example: A graph shows that as medication dose increases from 5mg to 15mg, pain relief increases from 20% to 60%. This shows a positive correlation.

Practice Question:

A graph shows patient temperature on the y-axis and hours after taking fever medication on the x-axis. If the line slopes downward from left to right, what does this indicate?

A) Temperature increases as time passes
B) Temperature decreases as time passes
C) Temperature stays the same over time
D) There is no relationship between time and temperature

Answer: B) Temperature decreases as time passes

Explanation: A downward sloping line (negative correlation) means that as the x-value (time) increases, the y-value (temperature) decreases, showing the fever medication is working.

Essential Formulas for TEAS

Key Geometry Formulas

You need to memorize these basic formulas for the test. Practice using them with different numbers so you can apply them quickly during the exam.

Distance formula:
d = rt (distance = rate × time)
Rectangle area: A = lw (area = length × width)
Rectangle perimeter: P = 2l + 2w (perimeter = 2 × length + 2 × width)
Triangle area: A = ½bh (area = ½ × base × height)
Circle area: A = πr² (area = π × radius²)
Circle circumference: C = 2πr (circumference = 2 × π × radius)

Practice Question:

A round medication tablet has a radius of 0.5 cm. What is its circumference?

A) π cm
B) 2π cm
C) 0.5π cm
D) 4π cm

Answer: A) π cm

Explanation: Use C = 2πr = 2π(0.5) = π cm.

Important Algebra Formulas

These formulas help you solve equations and work with relationships between variables.

Slope-intercept form: y = mx + b (where m is slope and b is y-intercept)
Simple interest: I = Prt (interest = principal × rate × time)
Percentage: Part = Whole × Percentage
Pythagorean theorem: a² + b² = c² (for right triangles)

Statistical Formulas

Mean: Add all values and divide by the number of values
Range: Subtract the smallest value from the largest value
Percentage change: (New value – Old value) ÷ Old value × 100%

Problem-Solving Strategies

Understanding Word Problems

Word problems can seem difficult, but they follow predictable patterns. Read the problem twice – once to understand the situation, and once to identify the specific question being asked.

Circle or underline the important numbers and key words. Cross out information you don’t need. This helps you focus on what’s actually required to solve the problem.

Ask yourself: What am I trying to find? What information do I have? What operation or formula should I use?

Example Strategy: “A patient takes 2 tablets every 6 hours. How many tablets are needed for 3 days?”

Step 1: Identify what to find – total tablets needed
Step 2: Identify given information – 2 tablets every 6 hours, for 3 days
Step 3: Calculate doses per day – 24 hours ÷ 6 hours = 4 doses per day
Step 4: Calculate total – 4 doses × 2 tablets × 3 days = 24 tablets

Step-by-Step Problem Solving

Follow the same process for every word problem:

1. Read the problem carefully
2. Identify what you’re looking for
3. List the information you’re given
4. Choose the right operation or formula
5. Set up the calculation
6. Solve step by step
7. Check if your answer makes sense

This systematic approach prevents errors and builds confidence. Practice this method until it becomes automatic.

Using the Calculator Effectively

The on-screen calculator can help with complex calculations, but don’t rely on it for everything. You should be able to do basic operations mentally.

Use the calculator for multiplication and division with decimals, complex fractions, and problems with many steps. But do simple addition, subtraction, and common conversions in your head to save time.

Practice with an online calculator that looks similar to the TEAS calculator. Learn where all the buttons are so you don’t waste time during the test.

Healthcare Applications

Medication Calculations

Medication calculations are some of the most important math skills for nurses. These problems often use proportions or unit conversions.

Common calculation types include: dose per body weight, concentration calculations, and time-based dosing. Always check your work carefully because medication errors can harm patients.

Set up proportions with the same units in the same positions. Label everything clearly to avoid confusion.

Example: A pediatric patient weighs 25 kg and needs 10 mg of medication per kg of body weight. How much medication should be given?

Step 1: Multiply dose per kg by patient weight
Step 2: 10 mg/kg × 25 kg = 250 mg total dose

Practice Question:

A liquid medication contains 50 mg in every 2 mL. How many mL are needed to give a 75 mg dose?

A) 1.5 mL
B) 2 mL
C) 3 mL
D) 4 mL

Answer: C) 3 mL

Explanation: Set up proportion: 50 mg/2 mL = 75 mg/x mL. Cross multiply: 50x = 150, so x = 3 mL.

Vital Signs and Measurements

Nurses constantly take and record measurements. You need to convert between different units and calculate changes over time.

Temperature conversions between Fahrenheit and Celsius are common. The formulas are: °F = (°C × 9/5) + 32 and °C = (°F – 32) × 5/9.

Blood pressure, heart rate, and respiratory rate measurements help track patient condition. You might need to calculate averages or identify concerning changes.

Practice Question:

A patient’s temperature is 38.5°C. What is this in Fahrenheit?

A) 101.3°F
B) 102.1°F
C) 100.8°F
D) 103.2°F

Answer: A) 101.3°F

Explanation: Use °F = (°C × 9/5) + 32 = (38.5 × 9/5) + 32 = 69.3 + 32 = 101.3°F.

Healthcare Statistics

Understanding statistics helps you interpret research studies and patient outcome data. You might see information about treatment success rates, side effect frequencies, or population health trends.

Pay attention to sample sizes and confidence levels when interpreting studies. Larger samples generally give more reliable results.

Understand the difference between correlation and causation. Just because two things happen together doesn’t mean one causes the other.

Common Mistakes to Avoid

Calculation Errors

Double-check your arithmetic, especially with decimals and fractions. Line up decimal points carefully when adding or subtracting. Count decimal places correctly when multiplying.

Don’t round too early in multi-step problems. Keep extra decimal places during intermediate steps and round only your final answer.

Verify that your answer makes sense in the context of the problem. If you calculate that a patient needs 50 tablets per dose, something is probably wrong.

Unit Confusion

Always include units in your calculations and final answers. Make sure units cancel out correctly in conversion problems.

Don’t mix up similar units like mg and mL, or cm and mm. Read carefully to identify what units the problem is asking for.

Convert to the requested units before choosing your answer. If the problem asks for grams but you calculated milligrams, remember to convert.

Word Problem Misinterpretation

Read the question at the end of the problem first. This tells you exactly what you need to find.

Don’t assume you need to use every number given in the problem. Some information might be extra or used to distract you.

Watch for words that change the meaning: “all,” “each,” “total,” “remaining,” “difference,” and “increase” or “decrease.”

Test-Taking Strategies

Time Management

Spend about 1.5 minutes per question, but be flexible. Quick problems might take 30 seconds, while complex word problems might need 3 minutes.

If you’re stuck on a problem, make your best guess and move on. You can return to it later if time allows.

Don’t spend too much time checking easy problems. Save time for reviewing the harder questions where errors are more likely.

Answer Elimination

On multiple-choice questions, eliminate answers that are clearly unreasonable. If you’re calculating medication doses, answers that are extremely large or small are probably wrong.

Use estimation to narrow down options. If your estimate is around 25, you can eliminate answers like 2.5 or 250.

Look for answers with wrong units. If the problem asks for mL but an answer choice shows mg, it’s probably incorrect.

Building Confidence

Practice with realistic problems similar to TEAS questions. Focus on healthcare scenarios since these are most common on the test.

Learn to recognize problem types quickly. Proportion problems, percentage problems, and conversion problems each have standard approaches.

Trust your preparation. If you’ve studied thoroughly and practiced extensively, rely on your knowledge rather than second-guessing yourself.

This comprehensive guide covers all essential mathematics skills for the TEAS exam. Practice these concepts regularly, work through the example problems, and apply these strategies to build confidence for test day.

Remember that accuracy is more important than speed, so take time to check your work when possible.