239 Mathematics questions written for the TEAS 7, each with a rationale explaining why the correct answer is correct and why the others are not. Free, no account required. 10 examples are shown below.
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The answer: C (10 mL) Think of it this way: the bottle gives you 250 mg in every 5 mL. You need 500 mg — that's exactly double. Double the dose means double the liquid. Why C is right: 500 mg is twice 250 mg, so you need twice 5 mL = 10 mL. (Formula version: desired ÷ available × volume = 500 ÷ 250 × 5 = 10 mL.) Why the others are wrong: - A (2.5 mL): That's half of 5 mL — the wrong direction. You need more than 5 mL, not less. - B (5 mL): That's the amount for only 250 mg, but you need 500 mg. - D (15 mL): That's triple — too much. Remember: How many times bigger is the dose you want? Multiply the liquid by that. 500 is 2× of 250, so 5 mL × 2 = 10 mL. Technical note: Desired dose / available concentration × volume = (500 mg / 250 mg) × 5 mL = 10 mL.
The answer: B — 2,000 mL Think of it this way: There are 1,000 milliliters in 1 liter. To convert liters to milliliters, multiply by 1,000. Why B is right: 2 L × 1,000 = 2,000 mL. Why the others are wrong: - A (200 mL): This would only be 0.2 L — dividing by 10 instead of multiplying by 1,000. - C (20,000 mL): This would be 20 liters — multiplying by 10,000 instead of 1,000. - D (20 mL): This would be only 0.02 L — a tiny fraction of 2 liters. Remember: L to mL = multiply by 1,000. mL to L = divide by 1,000. Common clinical volumes: 1 bag of normal saline = 1,000 mL = 1 L; standard IV bag = 500–1,000 mL.
The answer: A — 11 Think of it this way: Always follow the order of operations — parentheses first, then exponents, then multiplication/division left to right, then addition/subtraction left to right. Why A is right: Using PEMDAS: (5 − 1) = 4, then 4² = 16, then 2 × 16 = 32, then 32 ÷ 4 = 8, finally 3 + 8 = 11. Why the others are wrong: - B (20): Likely added 3 and 2 first, ignoring order. - C (8): Stopped after the division and forgot to add the 3. - D (35): Possibly squared after multiplying or misordered operations. Remember: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is your guide. Work from left to right within multiplication and division, and again within addition and subtraction.
The answer: A — 5n − 3 = 12 Think of it this way: Break down the phrase step by step: "the product of a number and 5" means 5n; "decreased by 3" means subtract 3; "is 12" means equals 12. Why A is right: The phrase translates directly to 5n − 3 = 12. This matches all parts: product (multiplication), decreased (subtraction), is (equals). So A is correct. Why the others are wrong: - B (5(n − 3) = 12): This would mean "the product of 5 and the quantity (number decreased by 3)" — the order is different. The phrase says the product decreased by 3, not the product of 5 and a decreased number. - C (3 − 5n = 12): This reverses subtraction; "decreased by 3" means subtract 3 from the product, not subtract the product from 3. - D (5n + 3 = 12): This represents an increase, not a decrease. The phrase says decreased, so addition is wrong. Remember: When translating, pay careful attention to the order of operations implied by the phrasing. "Decreased by" means subtract after the product.
The answer: A — 1 Think of it this way: Parentheses first, then division and multiplication left to right, then subtraction. Why A is right: Step 1 — parentheses: (3 + 1) = 4. Step 2 — division and multiplication left to right: 12 ÷ 4 = 3, then 3 × 2 = 6. Step 3 — subtraction: 6 − 5 = 1. Why the others are wrong: - B (3): This is the result of 12 ÷ 4, stopping before multiplying by 2 and subtracting 5. - C (4): Could come from evaluating the parentheses but then not applying the correct order for the remaining terms. - D (7): Possibly from doing subtraction before multiplication: 12 ÷ 4 = 3, 3 × (2−5)? Or left-to-right error. Remember: After parentheses, treat × and ÷ as equal priority and process left to right. Don't stop halfway — complete all multiplication and division before moving to subtraction.
The answer: A — 3x + 7 Think of it this way: 'Three times a number' means 3 × x, and 'the sum of ... and 7' means add 7. So it is 3x + 7. Why A is right: The phrase breaks down as: 'three times a number' = 3x, 'the sum of ... and 7' = + 7. Combined, 3x + 7. Why the others are wrong: - B (3(x + 7)): This represents 'three times the sum of a number and 7', which is a different phrase. The parentheses change the meaning. - C (3x + 7x): This simplifies to 10x, which means 'ten times a number', not 'three times a number plus 7'. It incorrectly adds another 7x. - D (x + 10): This could represent 'a number plus 10' or 'the sum of a number and 10', not the given phrase. There is no multiplication by 3. Remember: In translating word problems, pay attention to the order of operations implied by the words. 'Sum of A and B' means A + B, and 'three times a number' is 3x.
The answer: A — 3 5/6 Think of it this way: Convert mixed numbers to improper fractions, find a common denominator, add, and convert back to a mixed number. Why A is right: 1 1/3 = 4/3; 2 1/2 = 5/2. LCM of 3 and 2 is 6. 4/3 = 8/6, 5/2 = 15/6. Sum = 23/6 = 3 5/6 (since 23 ÷ 6 = 3 remainder 5). Why the others are wrong: - B (3 5/12): Used common denominator 12 but added numerators incorrectly (8/12 + 15/12 = 23/12 → 1 11/12, not 3 5/12). - C (3 2/5): Added whole numbers (1+2=3) but added fractions as 1/3+1/2 = 2/5 (wrong). - D (3 1/3): Added whole numbers and took one of the fraction parts. Remember: Never add denominators directly. Always use a common denominator. Convert mixed numbers to improper fractions for easier calculation.
The answer: B — 2500 mm Think of it this way: Milli means thousandth, so there are 1000 millimeters in a meter. Why B is right: 1 meter = 1000 mm, so 2.5 m = 2.5 × 1000 = 2500 mm. Why the others are wrong: - A (250 mm): This would be 0.25 m, moving the decimal one place instead of three. - C (25000 mm): That would be 25 m, multiplying by 10000. - D (25 mm): That would be 0.025 m, dividing by 100. Remember: Metric conversions use powers of 10: 1 m = 10^3 mm, so to convert meters to millimeters, multiply by 1000.
The answer: B — 3500 Think of it this way: 'kilo' means thousand, so 1 km = 1000 m. Why B is right: To convert kilometers to meters, multiply the number of kilometers by 1000. 3.5 × 1000 = 3500 meters. Why the others are wrong: - A (350): This would be correct only if 1 km = 100 m, which is false. - C (35,000): This results from multiplying by 10,000 instead of 1,000. - D (0.35): This would be correct for converting meters to kilometers (divide), not the opposite. Remember: The metric prefix 'kilo-' means 1000. To convert from a larger unit (km) to a smaller unit (m), multiply. For a quick check: there are 3.5 × 1000 = 3500 m. Always keep track of the direction of conversion.
The answer: a — 452.16 Think of it this way: Volume of a cylinder is the area of the circular base times height. The base area is πr², so V = πr²h. Why a is right: r = 4 ft, so r² = 16. V = 3.14 × 16 × 9 = 3.14 × 144 = 452.16 cubic feet. Why the others are wrong: - b (400.48): Possibly from using r = 4 but height = 8 (instead of 9) or miscalculating 3.14 × 16 = 50.24, then × 8 = 401.92 (close to 400.48 but not exact). - c (502.40): This might come from using the formula for surface area or using diameter (8) squared instead of radius (4) squared. - d (565.20): Could result from using π = 3.14 × (4²) = 50.24 and multiplying by 11.25 instead of 9, or using radius = 5. Remember: For cylinder volume, use V = πr²h. Always square the radius (not the diameter) and multiply by height. Check your multiplication carefully.
