TEAS Math Practice Questions: 40+ Problems with Step-by-Step Solutions for Every Topic

The TEAS Math section contains 38 questions and covers four major areas: Numbers and Algebra, Measurement and Data, and applied problem-solving. Unlike many standardized tests, the TEAS does not allow a calculator — making it essential to practice mental math, estimation, and structured problem-solving techniques.

This article provides 40+ practice questions with complete step-by-step solutions. Each solution shows the exact method you should use on test day, including shortcuts and common traps to avoid.

Part 1: Numbers and Operations (12 Questions)

Fractions and Decimals

Question 1: What is 3/4 + 2/3? A) 5/7 B) 17/12 C) 5/12 D) 1 5/12 ✅ Answer: B (or equivalently, D: 1 5/12) Step-by-step solution: 1. Find the LCD of 4 and 3: LCD = 12 2. Convert fractions: 3/4 = 9/12 and 2/3 = 8/12 3. Add: 9/12 + 8/12 = 17/12 4. Convert to mixed number: 17/12 = 1 5/12 Key concept: Always find the least common denominator before adding fractions. Never add numerators and denominators separately (that's the most common mistake: 3+2/4+3 = 5/7 is wrong).

Question 2: Convert 0.375 to a fraction in simplest form. A) 375/1000 B) 3/8 C) 75/200 D) 15/40 ✅ Answer: B Step-by-step solution: 1. Write as a fraction: 0.375 = 375/1000 2. Find the GCF of 375 and 1000: GCF = 125 3. Divide both by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8 4. Result: 3/8 Shortcut: Recognize that 0.375 = 0.125 × 3 = 1/8 × 3 = 3/8. Memorize key decimal-fraction equivalents: 0.125 = 1/8, 0.25 = 1/4, 0.5 = 1/2, 0.75 = 3/4.

Question 3: What is 2.5 × 0.04? A) 0.1 B) 1.0 C) 0.01 D) 10 ✅ Answer: A Step-by-step solution: 1. Multiply ignoring decimals: 25 × 4 = 100 2. Count total decimal places: 2.5 has 1, 0.04 has 2 → total = 3 3. Place decimal: 100 → 0.100 = 0.1 Common trap: Students often miscount decimal places. Count from the right in each number.

Percentages

Question 4: A nursing program accepts 45 out of 300 applicants. What percentage of applicants are accepted? A) 12% B) 15% C) 18% D) 20% ✅ Answer: B Step-by-step solution: 1. Set up the equation: percentage = (part/whole) × 100 2. Calculate: (45/300) × 100 3. Simplify: 45/300 = 0.15 4. Multiply: 0.15 × 100 = 15% Shortcut: 45/300 = 45 ÷ 3/300 ÷ 3 = 15/100 = 15%.

Question 5: A patient's weight increased from 150 lbs to 162 lbs. What is the percent increase? A) 7% B) 8% C) 10% D) 12% ✅ Answer: B Step-by-step solution: 1. Find the change: 162 - 150 = 12 lbs 2. Divide by original: 12/150 = 0.08 3. Convert to percentage: 0.08 × 100 = 8% Key formula: Percent change = (New - Original) / Original × 100. Always divide by the original value, not the new value.

Question 6: A medication is marked down 20% from its original price of $85. What is the sale price? A) $17 B) $65 C) $68 D) $72 ✅ Answer: C Step-by-step solution: 1. Calculate discount: 20% of $85 = 0.20 × 85 = $17 2. Subtract from original: $85 - $17 = $68 Shortcut: If it's 20% off, you pay 80%. Calculate 0.80 × 85 = $68 directly.

Ratios and Proportions

Question 7: A solution requires a 3:5 ratio of medication to saline. If you use 12 mL of medication, how much saline is needed? A) 15 mL B) 20 mL C) 25 mL D) 30 mL ✅ Answer: B Step-by-step solution: 1. Set up the proportion: 3/5 = 12/x 2. Cross multiply: 3x = 60 3. Solve: x = 20 mL Key concept: Cross multiplication works for all proportion problems. Always set up the ratio with matching units on each side.

Question 8: If 3 nurses can complete patient rounds in 4 hours, how long would it take 6 nurses to complete the same rounds? A) 1 hour B) 2 hours C) 3 hours D) 8 hours ✅ Answer: B Step-by-step solution: 1. This is an inverse proportion (more workers = less time) 2. Calculate total work: 3 nurses × 4 hours = 12 nurse-hours 3. Divide by new workers: 12 ÷ 6 = 2 hours Key concept: When quantities are inversely proportional, their product stays constant. Don't set up a direct proportion here — that's the most common mistake.

Order of Operations and Negative Numbers

Question 9: Evaluate: -3² + 4 × (-2) - 1 A) -18 B) -14 C) 0 D) -4 ✅ Answer: A Step-by-step solution (PEMDAS): 1. Exponent first: -3² = -(3²) = -9 (Note: the negative is NOT squared) 2. Multiplication: 4 × (-2) = -8 3. Combine: -9 + (-8) - 1 = -9 - 8 - 1 = -18 Critical trap: -3² ≠ (-3)². Without parentheses around -3, only the 3 is squared, then the result is negated. This is the #1 order-of-operations mistake on the TEAS.

Question 10: Simplify: 12 ÷ 4 + 3 × 2 - 5 A) 4 B) 9 C) 7 D) 1 ✅ Answer: A Step-by-step solution: 1. Division: 12 ÷ 4 = 3 2. Multiplication: 3 × 2 = 6 3. Left to right: 3 + 6 - 5 = 4 Remember PEMDAS: Multiplication and Division have equal priority (left to right), then Addition and Subtraction have equal priority (left to right).

Question 11: What is the absolute value of -17? A) -17 B) 17 C) 0 D) 1/17 ✅ Answer: B Explanation: Absolute value measures distance from zero on a number line. Distance is always positive. |-17| = 17. On the TEAS, absolute value questions are free points if you understand this concept.

Question 12: Which number is between -2/3 and -1/4 on a number line? A) -3/4 B) -1/2 C) -1/8 D) -5/6 ✅ Answer: B Step-by-step solution: 1. Convert to decimals: -2/3 ≈ -0.667, -1/4 = -0.25 2. We need a number between -0.667 and -0.25 3. Check options: -3/4 = -0.75 (too low), -1/2 = -0.5 ✓, -1/8 = -0.125 (too high), -5/6 ≈ -0.833 (too low) 4. -1/2 = -0.5 falls between -0.667 and -0.25 Strategy: Converting fractions to decimals makes number line problems much easier.

Part 2: Algebra (10 Questions)

Solving Equations

Question 13: Solve for x: 3x + 7 = 22 A) 3 B) 5 C) 7 D) 15 ✅ Answer: B Step-by-step solution: 1. Subtract 7 from both sides: 3x = 15 2. Divide both sides by 3: x = 5 3. Check: 3(5) + 7 = 15 + 7 = 22 ✓

Question 14: Solve for x: 2(x - 3) = 4x + 6 A) -6 B) -3 C) 0 D) 6 ✅ Answer: A Step-by-step solution: 1. Distribute: 2x - 6 = 4x + 6 2. Subtract 2x from both sides: -6 = 2x + 6 3. Subtract 6 from both sides: -12 = 2x 4. Divide by 2: x = -6 5. Check: 2(-6 - 3) = 2(-9) = -18; 4(-6) + 6 = -24 + 6 = -18 ✓

Question 15: A nurse earns $32 per hour plus a $150 shift differential. If her total pay for a shift is $406, how many hours did she work? A) 6 B) 7 C) 8 D) 9 ✅ Answer: C Step-by-step solution: 1. Set up equation: 32h + 150 = 406 2. Subtract 150: 32h = 256 3. Divide by 32: h = 8 hours TEAS tip: Word problems are just equations in disguise. Identify the variable, write the equation, then solve step by step.

Inequalities and Expressions

Question 16: Solve: -2x + 5 > 11 A) x > 3 B) x < 3 C) x > -3 D) x < -3 ✅ Answer: D Step-by-step solution: 1. Subtract 5: -2x > 6 2. Divide by -2 (FLIP the inequality sign!): x < -3 Critical rule: When you multiply or divide an inequality by a negative number, you must reverse the inequality sign. This is the most commonly tested inequality concept on the TEAS.

Question 17: Simplify: 4x² - 3x + 2x² + 7x A) 6x² + 4x B) 6x² - 4x C) 6x⁴ + 4x D) 10x³ ✅ Answer: A Step-by-step solution: 1. Combine like terms for x²: 4x² + 2x² = 6x² 2. Combine like terms for x: -3x + 7x = 4x 3. Result: 6x² + 4x Key concept: Only terms with the same variable AND the same exponent can be combined. x² and x are not like terms.

Coordinate Geometry

Question 18: What is the slope of a line passing through points (2, 5) and (6, 13)? A) 1/2 B) 2 C) 4 D) 8 ✅ Answer: B Step-by-step solution: 1. Slope formula: m = (y₂ - y₁) / (x₂ - x₁) 2. Substitute: m = (13 - 5) / (6 - 2) 3. Calculate: m = 8/4 = 2 Remember: Slope = rise/run = change in y / change in x. A positive slope goes up from left to right.

Question 19: Which equation represents a line with slope 3 and y-intercept -2? A) y = -2x + 3 B) y = 3x - 2 C) y = 3x + 2 D) y = -2x - 3 ✅ Answer: B Explanation: Slope-intercept form is y = mx + b, where m = slope and b = y-intercept. With m = 3 and b = -2: y = 3x + (-2) = 3x - 2.

Question 20: Which of the following points lies on the line y = 2x - 1? A) (0, 1) B) (1, 1) C) (2, 5) D) (3, 4) ✅ Answer: B Step-by-step solution: Plug each point into y = 2x - 1: - (0, 1): 1 = 2(0) - 1 = -1 ✗ - (1, 1): 1 = 2(1) - 1 = 1 ✓ - (2, 5): 5 = 2(2) - 1 = 3 ✗ - (3, 4): 4 = 2(3) - 1 = 5 ✗

Question 21: What is the y-intercept of the equation 3x + 6y = 18? A) 2 B) 3 C) 6 D) 18 ✅ Answer: B Step-by-step solution: 1. Set x = 0 (y-intercept is where the line crosses the y-axis): 3(0) + 6y = 18 2. Solve: 6y = 18, so y = 3 3. The y-intercept is (0, 3), or simply 3. Alternative: Convert to slope-intercept form: 6y = -3x + 18 → y = -1/2x + 3. The y-intercept is 3.

Question 22: The cost of medical supplies follows the equation C = 15n + 50, where n is the number of supply kits. What does the 50 represent? A) The cost per kit B) The total cost C) A fixed base cost D) The number of kits ✅ Answer: C Explanation: In the equation C = 15n + 50, the 50 is the y-intercept — it's the cost when n = 0 (no kits purchased). This represents a fixed fee, base cost, or flat charge. The 15 is the slope, representing the cost per kit.

Part 3: Measurement and Data (10 Questions)

Unit Conversions

Question 23: Convert 5.5 kilograms to pounds. (1 kg ≈ 2.2 lbs) A) 10.1 lbs B) 11.0 lbs C) 12.1 lbs D) 2.5 lbs ✅ Answer: C Step-by-step solution: 1. Multiply: 5.5 × 2.2 = 12.1 lbs TEAS tip: The TEAS provides conversion factors, but you must know how to use them. Multiplying kg by 2.2 converts to lbs. Dividing lbs by 2.2 converts to kg.

Question 24: A patient needs 2,000 mL of IV fluid. How many liters is this? A) 0.2 L B) 2 L C) 20 L D) 200 L ✅ Answer: B Step-by-step solution: 1. Recall: 1 L = 1,000 mL 2. Divide: 2,000 ÷ 1,000 = 2 L Metric conversions to memorize: kilo- = 1,000, centi- = 1/100, milli- = 1/1,000. These prefixes apply to meters, liters, and grams.

Question 25: Convert 98.6°F to Celsius. Use the formula: C = (F - 32) × 5/9 A) 35°C B) 37°C C) 39°C D) 40°C ✅ Answer: B Step-by-step solution: 1. Subtract 32: 98.6 - 32 = 66.6 2. Multiply by 5/9: 66.6 × 5/9 = 333/9 = 37°C Medical context: 98.6°F (37°C) is the standard normal body temperature. This is a commonly tested conversion.

Data Interpretation

Question 26: A bar graph shows patient satisfaction scores: January = 82, February = 78, March = 85, April = 90. What is the mean (average) satisfaction score? A) 82 B) 83.25 C) 83.75 D) 85 ✅ Answer: C Step-by-step solution: 1. Add all values: 82 + 78 + 85 + 90 = 335 2. Divide by count: 335 ÷ 4 = 83.75 Key concept: Mean = sum of all values ÷ number of values.

Question 27: Find the median of this data set: 12, 15, 8, 22, 18, 15, 10 A) 14 B) 15 C) 14.3 D) 12 ✅ Answer: B Step-by-step solution: 1. Arrange in order: 8, 10, 12, 15, 15, 18, 22 2. Find the middle value: There are 7 numbers, so the middle is the 4th value 3. Median = 15 For even-numbered sets, the median is the average of the two middle values.

Question 28: What is the range of this data set: 72, 85, 91, 68, 79? A) 13 B) 17 C) 23 D) 79 ✅ Answer: C Step-by-step solution: 1. Find highest value: 91 2. Find lowest value: 68 3. Range = highest - lowest = 91 - 68 = 23

Geometry and Measurement

Question 29: What is the area of a rectangle with length 12 cm and width 8 cm? A) 20 cm² B) 40 cm² C) 80 cm² D) 96 cm² ✅ Answer: D Step-by-step solution: 1. Area formula for rectangle: A = length × width 2. Calculate: A = 12 × 8 = 96 cm² Note: Perimeter would be 2(12 + 8) = 40 cm. Don't confuse area and perimeter — the TEAS tests both.

Question 30: A circular wound has a diameter of 6 cm. What is its approximate area? (Use π ≈ 3.14) A) 9.42 cm² B) 18.84 cm² C) 28.26 cm² D) 113.04 cm² ✅ Answer: C Step-by-step solution: 1. Find the radius: r = diameter/2 = 6/2 = 3 cm 2. Area formula: A = πr² 3. Calculate: A = 3.14 × 3² = 3.14 × 9 = 28.26 cm² Common mistake: Using diameter instead of radius in the formula. Always halve the diameter first.

Question 31: A triangular bandage has a base of 10 inches and a height of 6 inches. What is its area? A) 16 in² B) 30 in² C) 60 in² D) 120 in² ✅ Answer: B Step-by-step solution: 1. Triangle area formula: A = 1/2 × base × height 2. Calculate: A = 1/2 × 10 × 6 = 30 in² Remember: Triangle area is always half of the rectangle formed by the same base and height.

Question 32: Convert 3 feet 8 inches to inches. A) 38 inches B) 44 inches C) 36 inches D) 48 inches ✅ Answer: B Step-by-step solution: 1. Convert feet to inches: 3 × 12 = 36 inches 2. Add remaining inches: 36 + 8 = 44 inches Key conversion: 1 foot = 12 inches. This appears frequently on the TEAS.

Part 4: Applied Math and Mixed Review (10 Questions)

Question 33: A medication dosage is 5 mg per kg of body weight. If a patient weighs 70 kg, what is the correct dosage? A) 14 mg B) 75 mg C) 350 mg D) 500 mg ✅ Answer: C Step-by-step solution: 1. Multiply: 5 mg/kg × 70 kg = 350 mg Dosage calculations are heavily tested on the TEAS. The formula is always: Dose = Rate × Weight.

Question 34: A hospital has 240 beds. If 85% are occupied, how many beds are empty? A) 24 B) 36 C) 40 D) 204 ✅ Answer: B Step-by-step solution: 1. Calculate empty percentage: 100% - 85% = 15% 2. Calculate empty beds: 15% × 240 = 0.15 × 240 = 36 Shortcut: Calculate the complement directly rather than finding occupied beds first.

Question 35: If a recipe calls for 2/3 cup of flour and you want to make 1.5 times the recipe, how much flour do you need? A) 3/4 cup B) 1 cup C) 5/6 cup D) 2/3 cup ✅ Answer: B Step-by-step solution: 1. Multiply: 2/3 × 1.5 = 2/3 × 3/2 = 6/6 = 1 cup Tip: Converting 1.5 to the fraction 3/2 makes the multiplication cleaner.

Question 36: A patient receives IV fluid at 125 mL/hour. How many mL will the patient receive in 8 hours? A) 500 mL B) 750 mL C) 1,000 mL D) 1,500 mL ✅ Answer: C Step-by-step solution: 1. Rate × time = total: 125 mL/hr × 8 hr = 1,000 mL

Question 37: What is 15% of 80? A) 8 B) 10 C) 12 D) 15 ✅ Answer: C Step-by-step solution: 1. Convert to decimal: 15% = 0.15 2. Multiply: 0.15 × 80 = 12 Mental math shortcut: 10% of 80 = 8, plus 5% of 80 = 4, total = 12.

Question 38: Round 4.7851 to the nearest hundredth. A) 4.78 B) 4.79 C) 4.80 D) 4.785 ✅ Answer: B Step-by-step solution: 1. Identify the hundredths place: 4.78|51 2. Look at the digit after: 5 3. Since it's 5 or greater, round up: 4.79 Rounding rule: If the digit after your target place is 5 or more, round up. If it's 4 or less, round down.

Question 39: Solve: What percent of 60 is 9? A) 12% B) 15% C) 18% D) 20% ✅ Answer: B Step-by-step solution: 1. Set up: x/100 × 60 = 9 2. Simplify: 60x/100 = 9 3. Solve: x = 9 × 100/60 = 900/60 = 15% Alternative: 9/60 = 0.15 = 15%.

Question 40: A student scored 78, 85, 92, and 88 on four tests. What score does she need on the fifth test to have an average of 86? A) 87 B) 86 C) 89 D) 85 ✅ Answer: A Step-by-step solution: 1. Target total: 86 × 5 = 430 2. Current total: 78 + 85 + 92 + 88 = 343 3. Needed score: 430 - 343 = 87 This is a classic "working backwards from the mean" problem that appears frequently on the TEAS.

Key Takeaways and Next Steps

The TEAS math section is very learnable. Most questions test the same core concepts repeatedly: fractions, percentages, proportions, basic algebra, unit conversions, and data interpretation. If you can solve these 40 questions confidently, you have the skills to score well on test day.

• Focus on your weak areas — If you struggled with fractions, spend extra time on finding common denominators and converting between fractions and decimals.
• Practice without a calculator — Every problem above should be solvable by hand in under 90 seconds. Time yourself.
• Memorize key formulas — Area, perimeter, slope, percentage change, and unit conversions are tested every time.
• Double-check by plugging in — For algebra problems, always verify your answer by substituting it back into the original equation.
• Use estimation to eliminate answers — If a problem asks for 15% of 80, you know 10% = 8 and 20% = 16, so the answer must be between 8 and 16.