HESI A2 MATH PRACTICE EXAM
The HESI A2 Math Practice Exam provides a full-length simulation of the math portion of the exam. It is designed to help you identify strengths and weaknesses while improving speed and accuracy under test conditions.
Topics Covered
Number Operations
Fractions and Decimals
Ratios and Proportions
Algebra
Measurement and Data
00:00
Add and simplify: 1/3 + 1/4 + 1/5
A.
4/5
B. 13/15
C. 47/60
D. 83/90
Rationale
The sum of 1/3 + 1/4 + 1/5 equals 47/60 when calculated using a proper common denominator approach.
A) 4/5 This choice often comes from a mental shortcut where students attempt to "average" the fractions rather than calculate a true sum. They might incorrectly take the average of numerators (1 + 1 + 1)/3 = 1, and average the denominators (3 + 4 + 5)/3 ~ 4, producing 1/4 and misadjusting to 4/5. Another reason is rounding the decimals of 1/3 ~ 0.333, 1/4 = 0.25, 1/5 = 0.2 -> sum ~ 0.783 and comparing it to a common fraction estimate of 4/5 = 0.8. While close, this is slightly higher and not exact, so 4/5 is an overestimation.
B) 13/15 This option comes from a partial application of the least common multiple (LCM). Some students might take only two denominators into account or miscalculate: for example, they might incorrectly convert 1/3 = 3/15, 1/4 = 5/15, 1/5 = 3/15, summing to 11/15, then miscopy as 13/15. Another source of error is thinking the LCM of 3, 4, and 5 is 15, which is incorrect the correct LCM is 60. Decimal approximation 13/15 ~ 0.866, which is higher than the true sum 0.783, showing this is an overestimate.
C) 47/60 Correct approach: the LCM of the denominators 3, 4, 5 is 60. Convert each fraction: 1/3 = 20/60, 1/4 = 15/60, 1/5 = 12/60. Adding numerators: 20 + 15 + 12 = 47, so the sum is 47/60. Decimal check: 47 ÷60 = 0.783, which matches the sum of the decimals 0.333 + 0.25 + 0.2 = 0.783. This confirms the fraction is exact and properly simplified.
D) 83/90 This arises from an incorrect choice of LCM and miscalculation of numerators. A student might take 90 as the LCM: 1/3 = 30/90, 1/4 = 22.5/90 (impossible to have half a numerator), then round to 23/90, and 1/5 = 18/90. Summing gives 30 + 23 + 18 = 71, sometimes misadded as 83/90. Decimal 83/90 ~ 0.922, far above the correct sum 0.783. This shows an overestimation due to improper fraction conversion and arithmetic error.
Conclusion
The exact sum of 1/3 + 1/4 + 1/5 is 47/60, confirmed by correctly calculating the least common multiple of the denominators, converting each fraction, summing the numerators, and verifying against the decimal sum. All other options result from rounding errors, LCM miscalculations, or incorrect mental shortcuts.
Eighty percent of the class passed with a 75 or higher. If that percent equaled 24 students, how many students were in the whole class?
A.
18
B. 30
C. 36
D. 60
Rationale
If 80% of the class equals 24 students, then the total number of students can be found by dividing 24 by 0.8.
A) 18 This is a common mistake where students take 80% of the given number (24) instead of finding the total. They calculate 0.8x 24 = 19.2 and then round to 18. The logic is reversed€â€they treat 24 as the total instead of the part, so it does not make sense in context.
B) 30
Correct: Total = 24 ÷0.8 = 30. Verification: 30x 0.8 = 24, exactly matching the number of students who passed. This method correctly identifies the whole class from the given percentage.
C) 36 This results from mentally adding 20% to 24 instead of dividing by 0.8. 24x 1.2 = 28.8, which might be rounded to 36 erroneously. Checking: 36x 0.8 = 28.8 ‰ 24, so this overestimates the total students.
D) 60 This is a wild overestimate, possibly from doubling 24 and adding extra arbitrarily. 60x 0.8 = 48, far exceeding 24, so it clearly does not match the problem's condition.
Conclusion
The total number of students is 30, as it is the only number that, when 80% is taken, equals exactly 24. All other options stem from misinterpreting the percentage, improper arithmetic, or arbitrary guessing.
Express 3.08 as a fraction in lowest terms
A.
3 4/5
B. 308/100
C. 3 2/25
D. 3 2/25
Rationale
3.08 = 3 + 0.08 -> 0.08 = 8/100 -> reduce by 4 -> 2/25 -> 3 2/25.
A) 3 8/10
Literal interpretation error: students read ".08" as 8/10 instead of understanding decimal place value (hundredths). 8/10 = 0.8, which is ten times larger than 0.08. Misreading the decimal leads to a gross overestimation.
B) 308/100
Place value misstep: student forgets the whole number 3 and converts the entire number as a single fraction. 308/100 = 3.08, correct numerically but not expressed as a mixed number in lowest terms.
C) 3 4/50
Partial reduction attempt: 8/100 ÷2 = 4/50, but not fully simplified. Further reduction by 2 gives 2/25. Some students stop too early and fail to reduce completely.
D) 3 2/25
Correct and fully simplified mixed number: 0.08 = 2/25, add 3 -> 3 2/25. Decimal check: 3 + 2 ÷25 = 3 + 0.08 = 3.08
Conclusion
The correct fraction is 3 2/25, fully reduced and matching the decimal 3.08. All other options result from misreading decimals, incomplete reduction, or improper fraction form.
Add and simplify: 1/2 + 1/4 + 1/6 =
A.
Nov-24
B. 11-Dec
C. 13-Dec
D. 07-Dec
Rationale
The sum of 1/2 + 1/4 + 1/6 simplifies to 11/12 when all fractions are converted to a common denominator and added correctly.
A) 11/24
This option is incorrect because it arises from miscalculating the least common multiple (LCM). If a student thinks the LCM is 12 but halves it incorrectly during reduction, they might write 11/24.
Decimal check: 11/24 ~ 0.458, far smaller than the true sum ~ 0.917.
Demonstrates misunderstanding of fraction addition and simplification.
B) 11/12
Correct calculation: LCM of 2, 4, and 6 is 12.
Convert fractions: 1/2 = 6/12, 1/4 = 3/12, 1/6 = 2/12.
Add numerators: 6 + 3 + 2 = 11 -> 11/12.
Decimal verification: 1/2 = 0.5, 1/4 = 0.25, 1/6 ~ 0.1667 -> sum ~ 0.9167 -> matches 11/12.
Fully reduced: numerator and denominator have no common factors.
C) 13/12
Incorrect due to adding numerators without a common denominator or misplacing decimal.
Results in an improper fraction greater than 1, while the sum of these fractions is less than 1.
Decimal check: 13/12 ~ 1.083 -> too large.
D) 7/12
Results from misusing LCM or incorrectly reducing fractions.
Decimal check: 7/12 ~ 0.583 -> far below actual sum ~ 0.917.
Conclusion
The correct sum is 11/12. Miscalculations in LCM, numerator adjustment, or decimal errors account for the other options.
In what numeric system does 101 name this amount: 5?
A.
Roman
B. Arabic
C. Decimal
D. Binary
Rationale
The 101 representation corresponds to 5 in the binary system.
A) Roman
Roman numerals: 5 = V -> 101 incompatible.
B) Arabic
Arabic numerals: 5 = 5 -> 101 does not represent 5.
C) Decimal
Decimal: 5 = 5 -> 101 = 101 -> incorrect.
D) Binary
Binary base 2: 101‚‚ = 1x2² + 0x2¹ + 1x2° = 4 + 0 + 1 = 5.
Matches number of blocks exactly.
Conclusion
Binary is the only numeric system that writes 5 as 101.
At Jules's Grocery, Lena bought 6 apples for $5.70. How many did Sarah buy for $3.80?
A.
2
B. 3
C. 4
D. 5
Rationale
To determine how many apples can be bought for $3.80, first calculate the unit price: $5.70 ÷6 = $0.95 per apple. Then divide the available money by the unit price: $3.80 ÷$0.95 = 4 apples.
A) 2
This error occurs when the student halves the money ($3.80 ÷2 = $1.90) and concludes that $1.90 buys 2 apples. This method ignores the actual unit price per apple, leading to underestimation. It reflects misunderstanding of proportional reasoning and unit cost calculations.
B) 3
Some students approximate by multiplying 3x $0.95 = $2.85. They see this as "close enough" to $3.80 and select 3 apples. This demonstrates premature rounding and failure to complete the division correctly, undercounting what can be purchased.
C) 4
Correctly, 4x $0.95 = $3.80, which exactly matches the amount available. This confirms that 4 apples can be purchased without leftover money and represents accurate proportional reasoning.
D) 5
Multiplying 5x $0.95 = $4.75 exceeds the available $3.80. Some may choose 5, thinking it is approximately correct, but this overestimates the quantity that can be bought. This highlights the importance of checking multiplication against the budget constraint.
Conclusion
Only 4 apples can be bought exactly with $3.80. This is verified by calculating the unit price and dividing the total amount by it, ensuring an exact solution.
Express 4/5 as a percent
A.
20%
B. 40%
C. 50%
D. 80%
Rationale
To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For 4/5: 4 ÷5 = 0.8 -> 0.8x 100 = 80%.
A) 20%
This results from inverting the fraction (1/5) -> 0.2 -> 20%. This mistake fails to account for the numerator correctly relative to the denominator.
B) 40%
Some students halve 4/5, misapplying 4 ÷10 or 4 ÷5 ÷2 = 0.4 -> 40%. This shows misunderstanding of percentage conversion.
C) 50%
A common approximation: "about half" -> 4/5 ~ 1 -> 50%. This underestimates the proportion.
D) 80%
Correct calculation: 4 ÷5 = 0.8 -> 0.8x 100 = 80% . This aligns precisely with the fraction-to-percent conversion formula.
Conclusion
4/5 as a percentage is 80%, confirmed by dividing the numerator by the denominator and multiplying by 100, making it the only correct answer.
Convert this military time to regular time: 1530 hours.
A.
3:03 P.M.
B. 3:30 A.M.
C. 3:30 P.M.
D. 12:30 P.M.
Rationale
Military time 1530 represents 15 hours and 30 minutes. To convert to standard time, subtract 12 from hours >12: 15 - 12 = 3. The minutes remain 30 -> 3:30 P.M.
A) 3:03 P.M.
Mistake arises from misreading minutes as 03 instead of 30. The student correctly subtracts 12 for P.M. but misinterprets the minutes, giving 3:03 P.M. instead of 3:30 P.M.
B) 3:30 A.M.
This occurs when the student forgets to subtract 12 from hours greater than 12. They incorrectly assume 15:30 is in the A.M. period, showing a misunderstanding of 24-hour to 12-hour conversion.
C) 3:30 P.M.
Correct conversion: 15:30 - 12 = 3:30 P.M. . Minutes remain unchanged, correctly reflecting afternoon time.
D) 12:30 P.M.
Some students incorrectly take the first two digits as the hour without adjustment: 12:30. This ignores the rule that hours >12 require subtracting 12 to get standard P.M. time.
Conclusion
3:30 P.M. is the unique correct civilian time, obtained by subtracting 12 from the hour component and preserving the minutes.
How many feet are in 6 meters?
A.
1.83 ft
B. 18.48 ft
C. 19.68 ft
D. 18.8 ft
Rationale
To convert meters to feet, multiply the number of meters by the conversion factor: 6x 3.28084 ~ 19.685 ft, rounded to 19.68 ft. This gives the most precise standard conversion.
A) 1.83 ft
This occurs when the student mistakenly inverts the conversion factor, using 1 ft ~ 0.3048 m. Multiplying 6x 0.3048 = 1.8288 ft produces a result far too small. This demonstrates confusion about which unit multiplies to which.
B) 18.48 ft
Some students apply a low-ball multiplier such as 3.08 ft/m instead of 3.28084, yielding 6x 3.08 = 18.48 ft. This underestimates the correct distance due to rounding down the factor.
C) 19.68 ft
Correct: 6x 3.28084 = 19.685 ~ 19.68 . Accurately reflects the standard conversion and aligns with typical rounding practices.
D) 18.8 ft
This error comes from rounding an incorrect multiplier like 3.13 instead of 3.28084. 6x 3.13 ~ 18.78, rounded to 18.8 ft. The result is close but not based on the accurate conversion factor.
Conclusion
19.68 feet is the precise equivalent of 6 meters using the standard conversion 1 m ~ 3.28084 ft.
Subtract: 1.085 - 0.85 =
A.
1
B. 0.935
C. 0.235
D. 0.215
Rationale
Align decimals and subtract: 1.085 - 0.850 = 0.235 .
A) 1.0
Student ignores decimal alignment: 1 - 0 = 1. Misinterpretation of decimal subtraction produces a grossly inflated result.
B) 0.935
Misalignment of decimals: treating 0.85 as 0.085 -> 1.085 - 0.085 = 1.0 -> possibly mis-typed as 0.935. This error shows lack of proper decimal placement.
C) 0.235
Correct decimal subtraction: 1.085 - 0.850 = 0.235 . Fully aligns digits and performs borrowing where necessary.
D) 0.215
Borrowing error: 5 - 0 = 4 misapplied, leading to 0.215. Shows a common digit slip when performing manual subtraction.
Conclusion
0.235 is the exact difference, derived from careful alignment of decimals and proper subtraction.
Divide and simplify: 4 5/8 ÷1 ½
A.
2 5/8
B. 3 23/24
C. 3 1/12
D. 3 ¾
Rationale
Step 1: Convert mixed numbers to improper fractions.
4 5/8Â = 4 + 5/8 = 32/8 + 5/8 = 37/8
1 ½ = 1 + 1/2 = 2/2 + 1/2 = 3/2
Step 2: Divide fractions by multiplying by the reciprocal.
37/8 ÷3/2 = 37/8x 2/3 = 74/24
Step 3: Simplify the fraction.
74/24 ÷2 = 37/12 -> mixed number = 3 1/12
A) 2 5/8Â
Represents 21/8. This is significantly less than 37/12. Likely error: student subtracted denominators instead of multiplying by the reciprocal or misconverted mixed numbers. Shows a misunderstanding of fraction division rules.
B) 3 23/24 This is 95/24 ~ 3.958. It is larger than 3 1/12 (~3.083). The official answer key lists this, possibly as a misprint or miscalculation. Choosing this indicates a misstep in multiplying or simplifying fractions.
C) 3 1/12
Correct. All steps align: proper conversion, reciprocal multiplication, simplification, and conversion back to mixed number.
D) 3 ¾
Represents 15/4 = 3.75. Clearly higher than 3 1/12. Error arises from miscalculating improper fractions or misreading numerators and denominators.
Conclusion
The exact quotient is 3 1/12. Proper fraction handling, reciprocal multiplication, and simplification are essential to arrive at this precise answer.
In one litter of kittens, there were 3 black kittens, 4 gray kittens, and 1 black-and-white kitten. What was the percentage of black kittens in the litter?
A.
50%
B. 48%
C. 37.50%
D. 28%
Rationale
Step 1: Total kittens = 3 + 4 + 1 = 8
Step 2: Calculate percentage of black kittens: 3 ÷8 = 0.375 -> 37.5%
A) 50%
Mistake: ignores the b/w kitten, assumes total kittens = 6 -> 3 ÷6 = 50%. Overestimates the percentage.
B) 48%
Random approximation, perhaps rounding 0.375 incorrectly or assuming 3/7 ~ 0.428 -> 48%. Not precise.
C) 37.5% Exact calculation: 3 ÷8 = 0.375 -> 37.5%. Correctly accounts for total kittens.
D) 28%
Assumes 2/7 ~ 0.285 -> 28%. Miscounts black kittens or misreads total population.
Conclusion
37.5% is the exact proportion of black kittens, derived from correct counting and percentage calculation.
What is 15 percent of 95?
A.
14.25
B. 18.5
C. 24.25
D. 28.5
Rationale
To find 15% of 95, convert 15% to decimal: 0.15x 95 = 14.25.
A) 14.25 Direct multiplication using decimal form of percentage yields 14.25, accurately reflecting 15% of 95.
B) 18.5
May result from using 20% instead: 0.2x 95 = 19, rounded to 18.5. Misreads percentage.
C) 24.25
Incorrect additive method, e.g., adding 10% twice plus 4.25, which does not represent true 15%.
D) 28.5
Takes 30% instead of 15%, doubling the intended percentage.
Conclusion
14.25 is the precise result of calculating 15% of 95.
A census of the village showed a ratio of 2:13 born-and-bred villagers to more recent arrivals. Which of the following is a possible actual number of born-and-bred villagers and more recent arrivals?
A.
35:20:00
B. 55:20:00
C. 62:05:00
D. 70:56:00
Rationale
To check if a pair maintains the ratio 2:13, use cross multiplication: a/b = c/d -> axd = bxc.
A) 32:200
2x 200 = 400, 13x 32 = 416 -> 400 ‰ 416. Ratio not preserved.
B) 50:320
2x 320 = 640, 13x 50 = 650 -> 640 ‰ 650. Ratio not preserved.
C) 56:365
2x 365 = 730, 13x 56 = 728 -> 730 ‰ 728. Ratio not preserved.
D) 64:416
2x 416 = 832, 13x 64 = 832 -> equal. Ratio 2:13 is exactly maintained.
Conclusion:
64:416 is the only pair that correctly maintains the 2:13 ratio.
Multiply: 0.6x 0.06 =
A.
0.0036
B. 0.036
C. 0.36
D. 3.6
Rationale
Multiply decimals: 6x 6 = 36. Original numbers have three decimal places in total (0.6x 0.06 -> one + two), so product = 0.036.
A) 0.0036
Too small by factor of 10; misplaces decimal, counting 4 decimal places.
B) 0.036 Correct placement of decimal yields exact product matching the multiplication.
C) 0.36
Too large by factor of 10; ignores proper decimal counting.
D) 3.6
Way too large; ignores decimals completely.
Conclusion:
0.036 is the exact product of 0.6x 0.06.
Multiply and express 1 2/3x 3 ½ in lowest terms
A.
3 2/3
B. 4 2/3
C. 5 2/9
D. 5 5/6
Rationale
Step 1: Convert mixed numbers to improper fractions: 1 2/3 = 5/3, 3 ½ = 7/2
Step 2: Multiply fractions: 5/3x 7/2 = 35/6
Step 3: Convert to mixed number: 35 ÷6 = 5 remainder 5 -> 5 5/6 = 5 5/6
A) 3 2/3 Possibly adds whole numbers incorrectly: 1x 3 = 3, then tries fraction multiplication 2/3x ½ = 1/3 -> 3 2/9 ~ 3 2/3. Misapplies fractional multiplication rules.
B) 4 2/3 A low estimate, possibly dividing numerator incorrectly or miscalculating improper fraction conversion.
C) 5 2/9 Likely multiplies incorrectly: e.g., 5/3x 4/3 = 20/9 = 2 2/9 -> mislabels as 5 2/9. Demonstrates confusion with proper fraction multiplication.
D) 5 5/6 Correctly converts mixed numbers -> improper fractions -> multiplies -> converts back to lowest terms mixed number. Matches exact calculation.
Conclusion:
5 5/6 is the exact product of 1 2/3x 3 ½.
A plan for a house is drawn on a 1:40 scale. If the length of the living room on the plan measures 4.5 inches, what is the actual length of the built living room?
A.
45 ft
B. 15 ft
C. 12 ft
D. 12 ft
Rationale
A scale of 1:40 means 1 inch on the drawing represents 40 inches in reality.
Step 1: Multiply 4.5 inches by 40 -> 4.5x 40 = 180 inches
Step 2: Convert inches to feet -> 180 ÷12 = 15 feet
A) 45 ft This arises from mistakenly using a 1:10 scale: 4.5x 10 = 45. Overestimates the real length because the scale factor was not correctly applied.
B) 15 ft Exact calculation using the 1:40 scale: 4.5x 40 = 180 in -> 180 ÷12 = 15 ft. Correct application of scale conversion and unit conversion from inches to feet.
C) 12 ft Likely a subtraction or rounding error: the student calculates 15 - 3 = 12. Shows misunderstanding of scale multiplication.
D) 12 ft Same miscalculation repeated. Incorrectly reduces 15 ft to 12 ft without reason.
Conclusion:
15 feet is the exact real length represented by 4.5 inches at a 1:40 scale.
Callie makes 2% interest quarterly on a deposit of $100. After a year, about how much is in her account?
A.
$102
B. $104
C. $106
D. $108
Rationale
Step 1: Quarterly compound interest formula: Final Amount = Principalx (1 + rate per period)¿
Step 2: Principal = 100, rate per quarter = 0.02, periods n = 4
Step 3: Calculate: 100x (1.02)´ = 100x 1.08243216 ~ 108.24
A) $102
Takes only a single quarter or miscalculates the compounding. Underestimates the effect of 4 quarters.
B) $104
May use simple interest incorrectly: 100x (1 + 0.02x 4) = 100x 1.08 = 108, slightly off, rounds down.
C) $106
Likely uses approximated growth per quarter, underestimating compounding effect.
D) $108 Accurate approximate rounding of $108.24 to nearest whole dollar. Fully accounts for quarterly compounding.
Conclusion:
After 4 quarters at 2% compounded, $108 is the closest approximation of the final amount.
Multiply: 10.6x 0.3 =
A.
3.08
B. 3.18
C. 3.8
D. 3.88
Rationale
Step 1: Ignore decimals initially: 106x 3 = 318
Step 2: Count total decimal places: 10.6 has 1 decimal, 0.3 has 1 decimal -> total = 2 decimal places
Step 3: Place decimal: 318 -> 3.18
A) 3.08 This could result from miscalculating 0.6x 0.3 = 0.18, then writing 3.08 instead of adding correctly to 3.0. Shows a digit slip error.
B) 3.18
Exact calculation: 10x 0.3 = 3.0, 0.6x 0.3 = 0.18 -> 3.0 + 0.18 = 3.18. Perfectly aligns decimals and multiplication.
C) 3.80
Likely from misaligning decimal places, adding incorrectly, or confusing multiplication with addition. Overestimates result.
D) 3.88
Random addition of digits, e.g., 3.18 + 0.7 ~ 3.88. Illustrates misunderstanding of decimal multiplication.
Conclusion: 3.18 is the exact product of 10.6x 0.3, correctly accounting for decimal placement and multiplication steps.
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