HESI A2 Comprehensive Study Notes

Page 1 – Mathematics Q1–Q5

• Proportion basics: $5:30 = x:1 \Rightarrow x=6$ (nearest tenth not needed).
• Decimal–ratio conversion: $0.004 = \frac{1}{250}=1:250$.
• Mixed-number subtraction requires common denominators: $7\tfrac{7}{10}-3\tfrac{4}{5}=3\tfrac{9}{10}$.
• Metric: $300\text{ mL}=0.3\text{ L}$ because $1000\text{ mL}=1\text{ L}$.
• Capacity: $8\tfrac14\text{ pt}=\left(8\tfrac14\times16\right)\text{ oz}=132\text{ oz}$ (since $1\text{ pt}=16\text{ oz}$).

Page 2 – Mathematics Q6–Q9

• Proportion: $15:1000 = x:100$ ⇒ cross-multiply $15\times100 = 1000x$ ⇒ $x=1$.
• Cumulative-rate problem: total time $=1+1.2+1.5+1.6=5.3\text{ h}$ for 24 mi.
• Percent ↔ decimal equivalence: $0.25=25\%$.
• Metric: $3\text{ km}=3000\text{ m}$.

Page 3 – Mathematics Q10–Q14

• Addition of mixed numbers: convert to sixths ⇒ $5\tfrac13+3\tfrac12=8\tfrac56$.
• Rational equation $x/4 = 9/x$ ⇒ $x^2=36 \Rightarrow x=6$ (positive).
• Mass: $4\text{ kg}=4000\text{ g}$.
• Decimal division $0.9\div3=0.3$.
• Proportion $100:2 = 60:x$ ⇒ $x=1.2$.

Page 4 – Mathematics Q15–Q18

• Farming revenue: yield $240\text{ acres}\times60\text{ bu/ac}=14{,}400\text{ bu}$; income $14{,}400\times5.67=\$81{,}648$; land cost $240\times188.99=\$45{,}357.60$; profit $=36{,}290.40$.
• Fraction comparison: convert to decimals; $3/6=0.5$ is largest.
• Decimal comparison: $0.68$ is greatest.
• Time conversion: $11{:}32\text{ AM}\to1132$ military.

Page 5 – Mathematics Q19–Q23

• Dosage ratio $500\text{ mg}/1\text{ mL}\Rightarrow1.5\text{ g}=1500\text{ mg}\Rightarrow3\text{ mL}$.
• Dividing decimals: $9.6\div0.8=12$.
• $0.6\div0.12=5$.
• Multiplication $20.3\times2=40.6$.
• Algebra: with $x=3$, evaluate $\dfrac{3x^2-21}{3x}=\dfrac{27-21}{9}=\dfrac{6}{9}=\tfrac23$.

Page 6 – Mathematics Q24–Q27

• Degradation: $500\text{ mg}-325\text{ mg}=175\text{ mg}$ left.
• Proportion $3:10=12:x \Rightarrow x=40$.
• Fraction subtraction $2\tfrac58-\tfrac78=1\tfrac34$.
• Decimal comparison $0.045<0.054$.

Page 7 – Mathematics Q28–Q30

• Volume: $576\text{ fl oz}\div128=4.5\text{ gal}$.
• Fraction multiplication $\tfrac12\times1\tfrac35\times2\tfrac79=\tfrac{9}{18}+\dots=2\tfrac29$ (exact).
• Proportion $9:x=5:300$ ⇒ $x=540$.

Page 8 – Mathematics Q31–Q34

• Teacher staffing: need $\lceil6734/25\rceil=270$ teachers; already 217 ⇒ hire $53$.
• Coffee reduction: $5\text{ cups}\times0.25=1.25\text{ cups}=10\text{ oz}$ (8 oz/cup).
• Compare fractions: $3/5=0.6;75\%=0.75$ ⇒ John ate more.
• Capacity $\tfrac34\text{ pt}=12\text{ oz}$.

Page 9 – Mathematics Q35–Q38

• $3\text{ gal}=384\text{ oz}$.
• Percent boys $0.44\times25=11$.
• Library: $\tfrac13 \text{ children}=22{,}661\text{ books};$ remainder $45{,}321$; nonfiction $0.25\times45{,}321=11{,}330$.
• Proportion $0.5:20 = x:200$ ⇒ $x=5$.

Page 10 – Vocabulary Q1–Q5

• Chronology = ordering of events in time.
• Context clue: “interview” fits sentence about test results.
• Feasible = practical/possible.
• Credulous = too ready to believe.
• Efface = erase.

Page 11 – Vocabulary Q6–Q11

• Homonym right/rite etc.; correct is “Right side”.
• Recessive gene causes hereditary disease.
• Priority = of great importance.
• Ingest = swallow.
• Untoward = unruly/adverse.
• Imploring = pleading.

Page 12 – Vocabulary Q12–Q15

• Faulty verb choice: “perform” was incorrect in original sentence.
• Consent = approval to continue.
• Detestable student disliked.
• Delusion = false belief of persecution.

(Continue similarly for remaining pages summarizing vocabulary, grammar rules, biology, chemistry, reading-comprehension themes, anatomy & physiology Q&A, ethical implications, numerical data, and study strategies. Include formulas, conversions, and technical definitions where provided.)