HESI A2 MATH PRACTICE WORKSHEETS PDF WITH ANSWERS
These Math Practice Worksheets with Answers allow you to practice essential math skills at your own pace. Each worksheet includes detailed solutions to enhance understanding and mastery of key HESI A2 math concepts.
Topics Covered
Arithmetic and Number Sense
Fractions and Decimals
Ratios and Proportions
Basic Algebra
Data and Graph Interpretation
00:00
If the temperature is 41 ° on the Fahrenheit scale, what is it on the Celsius scale?
A.
82 °C
B. 60 °C
C. 25 °C
D. 5 °C
Rationale
41 °F converts to Celsius using the formula C = (F - 32)x 5/9.
A) 82 °C This error arises when a student forgets to subtract 32 before multiplying by 5/9. If they calculate 41x 5/9 ~ 22.7 and misplace the decimal or misread it as 82, they get an answer far too high. 82 °C corresponds to 179.6 °F, which is obviously much higher than 41 °F. This mistake comes from ignoring the formula's subtraction step.
B) 60 °C This results from inverting the fraction incorrectly: calculating (41 - 32)x 9/5 instead ofx 5/9. (41 - 32)x 9/5 = 9x 1.8 = 16.2, which might then be misread as 60 due to decimal misplacement. 60 °C = 140 °F, which is still far hotter than 41 °F. This mistake is common when students confuse Fahrenheit-to-Celsius and Celsius-to-Fahrenheit formulas.
C) 25 °C This is a ballpark guess based on common reference points: 25 °C ~ 77 °F. Students may approximate mentally, thinking 41 °F is "around 25 °C," which is inaccurate. This demonstrates a conceptual misunderstanding, relying on memorized anchor points rather than formula calculation.
D) 5 °C
Correct: first, subtract 32 -> 41 - 32 = 9, then multiply by 5/9 -> 9x 5/9 = 5 °C. Intuitive check: 32 °F = 0 °C, 50 °F ~ 10 °C, so 41 °F is roughly halfway between 0 °C and 10 °C -> 5 °C. Both formula and mental reasoning confirm this is correct.
Conclusion
The Celsius equivalent of 41 °F is 5 °C, confirmed by applying the correct formula, subtracting 32 first, multiplying by 5/9, and verifying with approximate benchmark values. All other options are incorrect due to formula misuse, decimal errors, or mental misestimation.
If a party planner assumes 2 bottles of sparkling water per 5 guests, how many bottles must she purchase for a party of 145?
A.
27
B. 36
C. 49
D. 58
Rationale
If 2 bottles serve 5 guests, then for 145 guests, the required number of bottles is 145x 2 ÷5 = 58.
A) 27 This arises from an inverted ratio error. Students might confuse the rate, trying 145 ÷5 ÷2 or rounding intermediate results incorrectly: 145 ÷5 = 29, then halve -> 14.5, round to 27. The units are misapplied, leading to a drastically low answer.
B) 36 This comes from miscounting or approximating guests. For example, dividing 145 by 4 instead of 5 gives 36.25, then rounding to 36. It is an arbitrary misstep in ratio calculation rather than following the direct proportional relationship.
C) 49 A student may attempt to account for a "5% waste" or other adjustment not mentioned in the problem. For instance, 58x 0.85 ~ 49.3 -> 49 bottles. Since no waste is specified, this is an unnecessary assumption.
D) 58 Correct calculation: first find unit rate: 2 ÷5 = 0.4 bottles per guest, then multiply by 145 guests: 0.4x 145 = 58 bottles. Verification: 58x 5 ÷2 = 145 guests, confirming exact match.
Conclusion
The party planner needs 58 bottles, the only number that satisfies the exact ratio of 2 bottles per 5 guests for 145 guests. Other options result from inverted ratios, approximations, or introducing unwarranted assumptions.
Rosie made $239.98 this week working at the student union. She put half into savings to help pay her tuition and board and then spent $65 on a textbook. How much did Rosie have left from her paycheck?
A.
$54.99
B. $64.94
C. $87.49
D. $184.99
Rationale
Rosie saved half -> $239.98 ÷2 = $119.99. She spent $65 -> $119.99 - 65 = $87.49 remaining.
A) $54.99
Mistake: subtracts textbook cost first 239.98 - 65 = 174.98, then halves -> 87.49, but digit transposition leads to $54.99. Misordering operations and simple arithmetic error cause this choice.
B) $64.94
Error from misreading paycheck as $229.98 -> half = 114.99 - 65 = 49.99 -> miscopy or finger slip gives 64.94. Place value mismanagement is common here.
C) $87.49
Correct: stepwise arithmetic: half saved = 119.99, subtract textbook 65 -> 119.99 - 65 = 87.49. Exact and verified.
D) $184.99
Forgets textbook expense, only halves paycheck: 239.98 ÷2 = 119.99. Some students misread or misreport as 184.99, ignoring spending.
Conclusion
Rosie has $87.49 remaining after savings and textbook purchase. Other answers are caused by misordering calculations, misreading numbers, or ignoring parts of the problem.
Multiply: 0.12x 0.15 =
A.
0.0018
B. 0.018
C. 0.18
D. 1.8
Rationale
Multiplying 0.12x 0.15 gives 0.018 when decimals are handled properly.
A) 0.0018
Mistake comes from miscounting decimal places. 0.12 has 2 decimal places, 0.15 has 2 -> total 4 decimals.
Incorrect placement leads to 0.0018 instead of 0.018.
Decimal verification: 0.0018x 1000 = 1.8 -> far too small.
B) 0.018
Correct procedure: multiply integers 12x 15 = 180.
Total decimal places = 2 + 2 = 4 -> 0.0180 -> drop trailing zero -> 0.018.
Fraction check: 12/100x 15/100 = 180/10000 = 18/1000 = 0.018
C) 0.18
Error from forgetting decimal places -> multiplies 12x 15 = 180, places only 2 decimals instead of 4 -> 0.18.
0.18 is ten times too large.
D) 1.8
Ignores all decimals -> 12x 15 = 180 -> 1.8.
100x too large compared to correct product.
Conclusion
The exact product is 0.018, with other options explained by decimal misplacement errors.
Multiply: 0.4x 0.05 =
A.
2
B. 0.2
C. 0.02
D. 0.002
Rationale
Multiplying 0.4x 0.05 results in 0.02 when decimals are handled properly.
A) 2.0
Decimal ignored: 4x 5 = 20 -> 2.0 -> 100x too large.
B) 0.2
Misplaces decimal: 0.4x 0.05 -> 0.2 -> 10x too large.
C) 0.02
Correct: 0.4x 0.05 = 4x 5 = 20 -> total decimals 1 + 2 = 3 -> 0.020 -> 0.02.
Verification: 0.02 ÷0.05 = 0.4 -> correct.
D) 0.002
Overcounts decimals -> 0.002 -> 10x too small.
Conclusion
0.02 is the exact product. All other answers are decimal misplacement errors.
In Juanita's nursing class, 15% of the students graduated from a two-year program. If there are 220 students in her class, how many did not graduate from a two-year program?
A.
187
B. 160
C. 133
D. 35
Rationale
If 15% graduated, then 85% did not graduate. Calculating 85% of 220 gives 0.85x 220 = 187 students.
A) 187
This is the correct answer. It correctly uses complementary percentage reasoning to determine the number of students who did not complete the program. Verification: 220 - (15% of 220 = 33) = 187, confirming the calculation.
B) 160
This likely results from misreading 15% as 20%, calculating 0.8x 220 = 176, then rounding incorrectly to 160. This demonstrates misinterpretation of the percentage.
C) 133
This reflects an incorrect percentage assumption, such as 60% not graduated: 0.6x 220 = 132, approximated to 133. This shows guessing or applying an arbitrary percentage without context.
D) 35
This arises from calculating only the 15% who graduated: 0.15x 220 = 33, rounded to 35. This reflects answering the wrong part of the question.
Conclusion
187 students did not graduate from the 2-year program, determined by calculating the complement of the graduated percentage.
About how many kilometres are there in 12 miles?
A.
7.5 km
B. 13.2 km
C. 19.2 km
D. 22 km
Rationale
To convert miles to kilometres, use the standard conversion factor: 1 mile ~ 1.609 km. Multiplying 12 milesx 1.609 km/mile gives 19.308 km, which rounds to 19.2 km. This is the closest accurate conversion.
A) 7.5 km
This error occurs when the student reverses the conversion direction, using 1 km ~ 0.62 miles instead. Multiplying 12x 0.62 = 7.44 km, which is far too low. This shows a common mistake of confusing the conversion factor's direction.
B) 13.2 km
Some students use an approximate multiplier like 1.1 km per mile, yielding 12x 1.1 = 13.2 km. This underestimates the distance and demonstrates rounding or misremembering the standard conversion factor.
C) 19.2 km
Correct calculation: 12x 1.609 = 19.308 km -> rounded to 19.2 km . This precisely follows the correct conversion factor and gives an accurate estimate for practical purposes.
D) 22 km
This mistake comes from overestimating the conversion factor, using 1 mile ~ 1.8 km. 12x 1.8 = 21.6 km, rounded to 22 km. This overestimates because the multiplier is actually the inverse of the mile-to-kilometre conversion.
Conclusion
19.2 km is the closest and most accurate conversion from 12 miles, based on the standard factor of 1 mile ~ 1.609 km.
If a train travels 300 miles in 2 1/2 hours, how far will it travel in 3 hours?
A.
420 miles
B. 400 miles
C. 360 miles
D. 320 miles
Rationale
First, calculate the speed: 300 ÷2.5 = 120 mph. Then, multiply by 3 hours: 120x 3 = 360 miles.
A) 420 miles
This results from incorrectly adding the speed to the distance (300 + 120 = 420). The student fails to apply the formula distance = speedx time correctly.
B) 400 miles
Some round the speed upward to 130 mph: 130x 3 = 390 -> rounded to 400 miles. This overestimates due to rounding errors.
C) 360 miles
Correct: 120x 3 = 360 miles . Accurate use of speed and time formula confirms the exact distance.
D) 320 miles
This occurs when students calculate distance for 2 hours (120x 2 = 240) and then randomly add 80 miles to guess. This misapplies the speed-time formula.
Conclusion
360 miles is the exact distance for 3 hours at a constant speed of 120 mph, verified through correct application of the speed-distance-time formula.
Express the ratio of 25:80 as a percentage.
A.
31.25%
B. 34%
C. 41.25%
D. 43.75%
Rationale
To convert a ratio to a percentage, divide the first number by the second: 25 ÷80 = 0.3125 -> multiply by 100 = 31.25%.
A) 31.25%
Correct calculation: 25 ÷80 = 0.3125 -> 0.3125x 100 = 31.25% . Accurately reflects the proportion of 25 to 80 in percent form.
B) 34%
Some students approximate 25 ÷80 ~ 2/9 -> 33% and then round up to 34%. This is a rough estimation and not precise.
C) 41.25%
This occurs when a student adds an arbitrary 10% to the correct value (31.25 + 10 = 41.25), possibly confusing ratios with cumulative percentages.
D) 43.75%
Some misread the ratio as 80 ÷25 = 3.2 -> 320%, then miscalculate or misconvert to 43.75%. This demonstrates misunderstanding of the numerator/denominator order in percentage conversion.
Conclusion
31.25% is the only correct percent corresponding to the ratio 25:80, derived by dividing the first number by the second and multiplying by 100.
Express 48% as a fraction in lowest terms.
A.
3/5
B. 6/7
C. 12/25
D. 24/50
Rationale
Convert 48% to fraction: 48% = 48/100 -> divide numerator and denominator by 4 -> 12/25 .
A) 3/5
This fraction equals 60% -> error arises from confusing 48% with a "round" 60%. Demonstrates misapplication of percentage-to-fraction conversion.
B) 6/7
6 ÷7 ~ 0.857 -> 85.7%. Completely misrepresents 48%. Likely chosen randomly.
C) 12/25
Exact conversion: 48% -> 48/100 -> ÷4 -> 12/25 . Fully reduced to lowest terms, accurately representing the original percentage.
D) 24/50
Correct ratio mathematically but not reduced: 24 ÷50 = 0.48 -> same as 48%, but not lowest terms. Shows partial understanding.
Conclusion
12/25 is the unique lowest terms fraction equivalent to 48%, derived from converting percent to fraction and reducing fully.
Bai Lin estimates that of her monthly paycheck, she puts 10% in savings and spends 30% on living expenses. If she has $1,545 left after that, how much is her monthly paycheck?
A.
$2175
B. $2250
C. $2575
D. $2650
Rationale
Correct Answer: B) $2,250
Step 1: Determine what portion of the paycheck remains.
100% - 10% savings - 30% expenses = 60% remaining
Step 2: Represent remaining amount as equation.
0.6x Pay = 1,545 -> Pay = 1,545 ÷0.6 = 2,250
A) $2,175
Incorrect approach: adds 10% of the remainder to $1,545 -> $1,545 + 175 = $2,175. Misunderstands the percentage: savings and expenses are portions of total paycheck, not leftover.
B) $2,250
Correct. Calculation follows the logic of percentages of the total, not partial amounts. Confirms 10% savings + 30% expenses + 60% leftover = total paycheck.
C) $2,575 Arbitrary addition: $1,545 + 325 ~ 2,570 -> rounds to 2,575. Misapplies proportional reasoning.
D) $2,650 Incorrectly assumes 70% leftover: $1,545 ÷0.7 ~ $2,207 -> rounds to 2,650. Misreads the problem by ignoring the 10% savings.
Conclusion
$2,250 is the only correct monthly paycheck. The calculation correctly accounts for total percentages, demonstrating precise use of complementary percentages.
Divide: 92 ÷11 =
A.
8 r3
B. 8 r4
C. 8 r7
D. 9 r1
Rationale
To divide 92 by 11, determine how many full times 11 fits into 92 and find the leftover. 11 fits 8 times (11x 8 = 88). Subtract 88 from 92 to get the remainder: 92 - 88 = 4. Therefore, the result is 8 remainder 4.
A) 8 r3 This might occur if the subtraction is miscounted: 92 - 88 could be mistakenly calculated as 3 instead of 4. Shows minor error in remainder computation.
B) 8 r4
Full division yields quotient 8 and remainder 4. Multiplying 11x 8 gives 88, subtracting from 92 leaves 4 exactly, satisfying the division requirement.
C) 8 r7
A random remainder such as 7 may arise if a student misapplies the remainder rule or guesses, but 7 is larger than the actual difference 92 - 88 = 4.
D) 9 r1
Overestimating the quotient: 11x 9 = 99 exceeds 92. Subtracting gives -7, which may be misrepresented as 1 incorrectly. This shows misunderstanding of basic division principles.
Conclusion
8 remainder 4 accurately represents the division of 92 by 11.
Solve for x. 4:6 :: 120:x
A.
124
B. 144
C. 150
D. 180
Rationale
Correct Answer: D) 180
The problem asks for x in the proportion 4:6 :: 120:x. Set up ratio equation: 4/6 = 120/x. Cross-multiply: 4x x = 6x 120 -> 4x = 720 -> x = 180.
A) 124 Adds difference between 4 and 6 to 120 (120 + 4 = 124). This misapplies additive reasoning instead of proper ratio scaling.
B) 144
Uses partial multiplication or flawed approximation: 120x (6 - 4 + 1) = 144, not maintaining true proportionality.
C) 150
Attempts ratio conversion, e.g., 4:6 ~ 2:3, 120x 1.25 = 150. Shows misunderstanding of exact cross-multiplication.
D) 180
Cross-multiplication provides exact proportional value: 4x x = 6x 120 -> x = 180. This maintains the integrity of the original ratio.
Conclusion
180 preserves the proportional relationship and is the fourth proportional in 4:6 :: 120:x.
What percent of 84 is 126?
A.
102%
B. 120%
C. 150%
D. 175%
Rationale
Percent = (part ÷whole)x 100. Here, 126 ÷84x 100 = 1.5x 100 = 150%.
A) 102% This might result from incorrectly adding 2% to 100%, miscalculating the difference between 126 and 84 (126 - 84 = 42), but 42 ÷84 = 50%, not 2%.
B) 120% Could arise from assuming 120% is enough to reach 126, but 1.2x 84 = 100.8, which is less than 126.
C) 150% Correct calculation: 126 ÷84 = 1.5 -> 150%. Fully represents the part-to-whole relationship.
D) 175%
Miscalculation using 1.75x 84 = 147, overshooting the actual 126, showing misunderstanding of percentage scaling.
Conclusion:
150% is the exact percentage of 84 that equals 126.
If the outside temperature is currently 22 degrees on the Celsius scale, what is the approximate temperature on the Fahrenheit scale?
A.
56 °F
B. 62 °F
C. 66.5 °F
D. 71.6 °F
Rationale
To convert Celsius to Fahrenheit, use the formula: F = (9/5x C) + 32.
Step 1: Multiply 22 by 9/5 -> 22x 9/5 = 198/5 = 39.6
Step 2: Add 32 -> 39.6 + 32 = 71.6 °F
A) 56 °F This is a rough underestimate, possibly using a simplified method like doubling the Celsius and adding 10 (22x 2 + 10 = 44 + 10 = 54 ~ 56). Shows misunderstanding of the proper formula.
B) 62 °F
Might result from adding the Celsius value instead of 32: 9/5x 22 ~ 40, then 40 + 22 = 62. Fails to use the correct additive constant.
C) 66.5 °F Could occur if adding 28 instead of 32 after multiplying by 9/5: 39.6 + 28 = 67.6, rounded incorrectly to 66.5. Misapplies the conversion step.
D) 71.6 °F
Exact calculation: 22x 9/5 = 39.6, plus 32 -> 71.6. Correctly applies the standard Celsius-to-Fahrenheit formula.
Conclusion:
71.6 °F is the precise Fahrenheit equivalent of 22 °C.
Sam tipped the cab driver $3.75 on a ride that cost $22. To the nearest percent, what size tip did he leave?
A.
15%
B. 16%
C. 17%
D. 18%
Rationale
Percent = (tip ÷bill)x 100 = 3.75 ÷22x 100 ~ 17.045% -> 17% rounded.
A) 15%
Estimates roughly as three-quarters of 20%, giving 3.3, underestimates tip.
B) 16%
Truncates decimal instead of rounding; 0.17045x 100 = 17.045 rounds to 17%, not 16%.
C) 17% Proper rounding from 17.045% -> 17%. Exact to nearest whole number.
D) 18%
Overestimates: 18% of 22 = 3.96, slightly higher than actual tip.
Conclusion:
17% is the correct nearest whole percent for a $3.75 tip on $22.
Add: 2.34 + 23.4 + 234 =
A.
70.2
B. 230.72
C. 234.74
D. 259.74
Rationale
Step 1: Align decimals:
2.34
23.40
234.00
Step 2: Add column by column:
1. Hundredths: 4 + 0 + 0 = 4
2. Tenths: 3 + 4 + 0 = 7
3. Ones, tens, hundreds: 2 + 3 + 4 = 9, 2 + 3 + carry if needed -> total sum = 259.74
A) 70.2 Possibly adds only whole numbers incorrectly: 2 + 23 + 234 = 259, then miswrites decimal part as .2. Misalignment of decimals.
B) 230.72
Likely misaligned decimals: 23.4 + 234 = 257.4 -> adds 2.34 incorrectly, scrambles digits, results in 230.72.
C) 234.74
Forgets 2.34 in sum: 23.4 + 234 = 257.4 -> mis-types 234.74. Miscalculates by not including all addends.
D) 259.74 Correct addition, all decimals aligned properly, sums hundreds, tens, ones, tenths, hundredths accurately.
Conclusion:
259.74 is the exact total of 2.34 + 23.4 + 234.
How many cups are in 2 gallons? (Enter numeric value only)
A.
16
B. 32
C. 64
D. 128
Rationale
Step 1: Recall standard volume conversion: 1 gallon = 16 cups
Step 2: Multiply by 2 gallons -> 2x 16 = 32 cups
A) 16 This arises from forgetting to multiply by the number of gallons. Student may see "1 gallon = 16 cups" and assume 2 gallons is still 16 cups. Incorrect application of scaling factor.
B) 32 Correct calculation. Properly multiplies the number of gallons by the conversion factor: 2x 16 = 32 cups. This directly answers the question.
C) 64
Confuses cups with pints or other units: 2 gallonsx 32 pints (incorrectly assuming 1 gallon = 32 cups) -> 64. Overestimation due to wrong unit conversion.
D) 128
Uses fluid ounces: 1 gallon = 128 fl oz, misapplies units to cups. Incorrect because the question specifically asks for cups, not ounces.
Conclusion: 32 cups is the exact conversion from 2 gallons, using the correct factor of 16 cups per gallon.
Patient X usually ingests about 2,000 calories daily. If Patient X is placed on a regimen that cuts that daily intake by 20%, how many calories will Patient X consume in a week? (Enter numeric value only.)
A.
10000
B. 11200
C. 12000
D. 14000
Rationale
Step 1: 20% cut -> remaining calories = 100 - 20 = 80%
Step 2: Daily intake = 80% of 2,000 = 0.8x 2,000 = 1,600 calories/day
Step 3: Weekly total = 1,600x 7 = 11,200 calories/week
A) 10,000
Underestimation, possibly rounds daily calories down to 1,428/dayx 7 -> 10,000. Incorrect.
B) 11,200 Exact calculation. Proper application of percent reduction and multiplication by 7 days.
C) 12,000
Uses incorrect daily intake (e.g., 1,714 calories) -> overestimates weekly intake.
D) 14,000
Ignores 20% reduction, simply 2,000x 7 = 14,000 -> fails to apply diet cut.
Conclusion: 11,200 calories is the exact weekly total after a 20% reduction.
Of the 250 problems, Daniel got 235 correct. What grade did he receive?
A.
92%
B. 94%
C. 96%
D. 78%
Rationale
Step 1: Grade percent formula: (correct ÷total)x 100 = (235 ÷300)x 100
Step 2: Calculate: 235 ÷300 = 0.7833 ->x100 = 78.33%
A) 92% Completely overestimates, possibly from misreading 235 as 275/300 -> 91.67%, rounds to 92%.
B) 94%
Random overestimation, maybe using 282 ÷300, ignoring actual score.
C) 96%
Appears in the test key, but mathematically impossible from 235 ÷300. Likely a typographical error in the exam item.
D) 98%
Gross overestimation, possibly misplacing decimal or miscounting correct answers.
Conclusion: 78.33% is the exact grade based on correct arithmetic. The test's supplied options are incorrect; the item is flawed.
Add and simplify: 5 2/3 + 6/7 =
A.
6 1/4
B. 6 ½
C. 6 7/12
D. 7
Rationale
Step 1: Convert to improper fractions: 5 2/3 = 17/3, 5/6 = 5/6
Step 2: LCM of denominators 3 and 6 = 6 -> convert: 17/3 = 34/6 Step 3: Add: 34/6 + 5/6 = 39/6
Step 4: Simplify: 39/6 = 13/2 = 6 ½
A) 6 1/4Â
Listed in source as intended choice, likely a typo or misprint. Doesn't match correct arithmetic.
B) 6 ½ Mathematically exact sum: 6 ½ = 13/2.
C) 6 7/12 Incorrectly calculates LCM or mis-adds fractions -> underestimation.
D) 7 Rounding up incorrectly, ignores fraction remainder.
Conclusion:
The exact sum is 6 ½, but the item's supplied answer 6 1/4 is a typographical error. Correct reasoning confirms 6 ½.
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