78 Mathematics questions written for the HESI A2, 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.
Practice all 78 questions →Answers are shown so you can read these as worked examples. To answer them yourself and track what you get wrong, start a practice set.
The answer: a — 3:7 Think of it this way: Simplifying a ratio is like reducing a fraction — find the biggest number that divides both parts evenly. Why a is right: The greatest common factor of 15 and 35 is 5. Divide both numbers by 5: 15 ÷ 5 = 3 and 35 ÷ 5 = 7, giving the simplified ratio 3:7. Why the others are wrong: - b (5:12): This would come from dividing 15 by 3 and 35 by 3, but 3 is not a common factor of both. - c (3:5): This would come from dividing 15 by 5 and 35 by 7, which uses different divisors. - d (5:7): This would come from dividing 15 by 3 and 35 by 5, which also uses different divisors. Remember: To simplify a ratio, divide both parts by their greatest common factor (GCF). For 15 and 35, the GCF is 5.
The answer: a — 6 mg/mL Think of it this way: When finding mg/mL, make sure both numbers are in the right units — grams need to become milligrams first. Why a is right: Convert 3 grams to milligrams: 3 × 1,000 = 3,000 mg. Then divide by the volume: 3,000 mg ÷ 500 mL = 6 mg/mL. Why the others are wrong: - b (0.6 mg/mL): This comes from dividing 3 by 500 without converting grams to milligrams. - c (60 mg/mL): This would happen if you mistakenly used 50 mL instead of 500 mL. - d (0.06 mg/mL): This would come from dividing 3 by 500 and then dividing by 100 incorrectly. Remember: For concentration in mg/mL, convert grams to milligrams first (multiply by 1,000), then divide by the volume in mL.
The answer: b — 2 tablets Think of it this way: Always convert to the same unit first — here, grams to milligrams — before figuring out how many tablets. Why b is right: Convert 0.25 g to mg: 0.25 × 1,000 = 250 mg per tablet. The order is for 500 mg. So 500 ÷ 250 = 2 tablets. Why the others are wrong: - a (0.5 tablet): This would come from dividing 250 by 500 instead of the other way. - c (4 tablets): This would come from dividing 500 by 125 instead of 250. - d (1 tablet): This would be correct if each tablet were 500 mg, but it's 250 mg. Remember: Convert all units to the same scale (here, mg), then divide the ordered dose by the available strength per tablet.
The answer: A — 3/8 Think of it this way: Dividing by 2 is the same as multiplying by 1/2. Just flip the second number and multiply. Why A is right: (3/4) divided by 2 equals (3/4) times (1/2) = 3/8. Each patient gets 3/8 of the ampule. Why the others are wrong: - B (1/2): This would be the answer if you divided 3/4 by 1.5 instead of 2. - C (6/4): This comes from multiplying 3/4 by 2 instead of dividing. - D (3/2): This comes from multiplying 3/4 by 2 instead of dividing. Remember: To divide fractions, multiply by the reciprocal. Dividing by 2 is the same as multiplying by 1/2.
To find the total dose, multiply the number of tablets by the amount in each tablet: 5 x 3/8 mg. Multiply the whole number by the numerator and keep the denominator: (5 x 3)/8 = 15/8 mg. Convert this improper fraction to a mixed number by dividing 15 by 8: 8 goes into 15 once with 7 left over, giving 1 7/8 mg. The choice '5 3/8 mg' comes from adding 5 and 3/8 instead of multiplying; '2 mg' comes from rounding; and '15/3 mg' comes from dividing by the wrong number.
The answer: A — 29 1/3 mg Think of it this way: Multiply the weight by the dose per pound. Then convert the improper fraction to a mixed number. Why A is right: 44 x (2/3) = (44 x 2) / 3 = 88/3 = 29 1/3 mg. Why the others are wrong: - B (88/3 mg): This is the same as 29 1/3, but it's not simplified to a mixed number. The question expects the mixed number. - C (30 mg): This might come from rounding or a calculation error. - D (88 mg): This might come from multiplying 44 by 2 instead of 2/3. Remember: Multiply the whole number by the numerator of the fraction, then divide by the denominator. Simplify to a mixed number.
The answer: B — 66.7% Think of it this way: 2/3 is like having two out of three slices of pizza — that's about 67% of the whole pizza. Why B is right: To convert 2/3 to a percentage, multiply by 100: (2/3) × 100 = 200/3 = 66.67%, which rounds to 66.7%. Why the others are wrong: - A (33.3%): This is 1/3, not 2/3. - C (60%): This is 3/5, not 2/3. - D (75%): This is 3/4, not 2/3. Remember: To convert a fraction to a percentage, divide top by bottom and multiply by 100. 2/3 ≈ 66.7% — think "two-thirds is about 67%."
The answer: B — 144 Think of it this way: 3/5 of 240 means you divide 240 into 5 equal parts and take 3 of them. Why B is right: 3/5 of 240 = (3 × 240) ÷ 5 = 720 ÷ 5 = 144 beds are occupied. Why the others are wrong: - A (120): This is 1/2 of 240, not 3/5. - C (160): This is 2/3 of 240, not 3/5. - D (180): This is 3/4 of 240, not 3/5. Remember: To find a fraction of a number, multiply the number by the numerator and divide by the denominator. 3/5 of 240 = (240 × 3) ÷ 5 = 144.
The answer: a — 0.075 mL Think of it this way: The vial has 5 mg in every 1 mL, so to get just 0.375 mg, you need a tiny fraction of that 1 mL. Why a is right: The order is for 0.375 mg. Since the concentration is 5 mg/mL, divide the dose by the concentration: 0.375 mg / 5 mg/mL = 0.075 mL. This is also equal to 3/8 of 1 mL. Why the others are wrong: - b (0.075 of the vial): This is a fraction of the vial, not the volume in mL. The question asks for mL. - c (3/8 mL): 3/8 of 1 mL is 0.375 mL, but that's the volume that would contain 1.875 mg, not the ordered 0.375 mg. - d (0.375 mL): This is the dose in mg, not the volume in mL. You need to divide by the concentration. Remember: Dose ordered divided by concentration on hand equals volume to give. Always check your units — mg divided by mg/mL gives mL.
The answer: B — 5% Think of it this way: Percentage concentration (w/v) is (grams of solute / mL of solution) × 100%. Why B is right: (25 g / 500 mL) × 100% = 0.05 × 100% = 5%. Why the others are wrong: - A (2.5%): This would result from (25/1000)×100 or from dividing incorrectly. - C (20%): This might come from (100/500)×100 or from confusing grams and mEq. - D (25%): This is the raw fraction of grams without dividing by volume, or from (25/100)×100. Remember: For weight/volume percent, divide grams of solute by total mL and multiply by 100. This is a common way to express IV solution concentrations like D5W (5% dextrose).
