sum/count; middle of ordered list; most frequent; max − min
Length, capacity, time
1 km = 1000 m, 1 m = 100 cm, 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5280 ft, 1 gal = 4 qt = 16 cups, 1 h = 60 min
Temperature
°F = °C·9/5 + 32, °C = (°F − 32)·5/9; a change of 1 °C = 1.8 °F
Area
rectangle l·w, triangle ½·b·h, circle π·r²
Perimeter and circumference
rectangle 2l + 2w, circle π·d = 2π·r
Volume
box l·w·h, cylinder π·r²·h; 1000 cm³ = 1 L
Speed
distance ÷ time (time in hours for mph or km/h)
Method
Read the last sentence first: what exactly is asked, and in which unit or form (lowest terms, nearest cent, one decimal place)?
Write the numbers in one form: turn mixed numbers into improper fractions, percents into decimals, and hours and minutes into one unit.
Pick the method: PEMDAS for expressions, a common denominator for adding fractions, part ÷ whole × 100 for percents, cross-multiplying for proportions, inverse operations for equations.
Work one step at a time and write each line down; round only at the very end.
Check the size of the answer with an estimate, and put an equation’s answer back in.
Nursing math & unit conversions
Metric steps
1 kg = 1000 g, 1 g = 1000 mg, 1 mg = 1000 mcg, 1 L = 1000 mL
Weight and length
1 kg = 2.2 lb, 1 lb = 16 oz, 1 in = 2.54 cm, 1 ft = 12 in
Household measures
1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 8 fl oz = 240 mL
Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
Reading comprehension (entrance exams)
Method
Read the question first so you know what you are looking for.
Skim the passage for its topic and main point; the first or last sentence often states it.
Go back to the exact lines that answer the question.
For inferences, choose the option the clues most strongly support, not one that goes further.
For labels and tables, apply every rule that fits the case and do the small calculation carefully.
Healthcare vocabulary (entrance exams)
Method
Read the whole sentence and look for a context clue: a definition, a contrast, an example or a cause and effect.
Split an unfamiliar word into prefix, root and suffix and translate each part.
Read a medical term from the suffix back to the start (hepat-itis: inflammation of the liver).
Put each option into the sentence and check that the meaning still fits.
Choose the meaning used in this sentence, even if the word has another everyday meaning.
English grammar & language usage (entrance exams)
Method
Find the subject and the verb of the sentence before choosing a form.
Strip away phrases (of the …, along with …) and extra people (you and …) to test agreement and pronoun case.
Check each clause: can it stand alone? Join independent clauses with a comma + conjunction or a semicolon.
Check modifiers and lists: the describing phrase next to its word, items in the same form.
For word choice and register, pick the precise, formal and concise option.
Biology for nursing entrance exams
Method
Name the topic of the question: cell parts, transport, division, DNA and protein synthesis, inheritance, biomolecules, microorganisms or experimental design.
Recall the key rule: A–T and G–C, diffusion from high to low, water moves towards more solute, mitosis keeps and meiosis halves the chromosome number.
For crosses, write the parents’ genotypes, list the gametes and fill a Punnett square before counting.
For experiments, label the independent, dependent and controlled variables, and ask whether the evidence supports or only suggests the conclusion.
Check each option against the question asked, not just whether it is a true statement.
Chemistry for nursing entrance exams
Method
Identify what is given and asked: particles, a formula, a state change, a concentration, a pH or a mass.
Use the periodic table: the atomic number gives protons, the group gives valence electrons and the usual ion charge.
Balance equations with coefficients only, element by element, oxygen and hydrogen last.
For amounts, go mass → moles → mole ratio → moles → mass, and for solutions use M = mol/L and C₁V₁ = C₂V₂.
Remember that pH is logarithmic: one unit is a factor of 10.
2Practice problems
1.Pre-nursing math (entrance exam)Medium
The numbers of call-light requests on a unit over 6 nights were 35, 31, 36, 19, 33, 38. What is the median m?
35, 31, 36, 19, 33, 38
m =
2.Pre-nursing math (entrance exam)Hard
Use the order of operations to find the value of x: x = −6² + 5 × 7.
x = −6² + 5 × 7
x =
3.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 101.8 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
101.8 °F
T = °C
4.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes ½ fl oz of juice, 4 tbsp of liquid supplement, 2 tsp of cough syrup. Using the equivalents given, find the total oral intake V in mL.
1 fl oz = 30 mL1 tbsp = 15 mL1 tsp = 5 mL
V = mL
5.Reading comprehension (entrance exams)Medium
“The old lighthouse keeper climbed the 120 steps every evening to light the lamp, even when his knees ached, because ships depended on him.” What motivates the lighthouse keeper?
AA plan to sell the lighthouse
BA sense of duty to the ships
CA wish to exercise his knees
DA fear of being alone at night
6.Reading comprehension (entrance exams)Hard
The author writes: “Studies show that people who drink water before meals eat slightly fewer calories. Therefore, drinking water is the only thing you need to lose weight.” Why is the conclusion not supported?
AWater makes people eat many more calories.
BThe author says nothing about the studies.
CA small effect does not make it the only factor.
DThe studies did not look at water.
7.Healthcare vocabulary (entrance exams)Medium
Choose the meaning of the word in bold: “With the stethoscope, the nurse could discern a faint heart murmur.”
AImagine or invent
BDetect or recognise
CIgnore or dismiss
DTreat or correct with medication
8.Healthcare vocabulary (entrance exams)Hard
Choose the meaning of the word in bold: “On the mental health assessment, the patient’s affect was flat.”
AAbility to remember recent events
BPhysical strength and energy
CLevel of pain reported
DOutward expression of emotion
9.English grammar & language usage (entrance exams)Medium
Choose the correct word form: “She is ___ to peanuts.”
Aallergic
Ballergies
Callergy
Dallergically
10.English grammar & language usage (entrance exams)Hard
Which sentence makes a logical comparison?
AHer salary is more higher than her manager’s.
BHer salary is higher than her manager.
CHer salary is higher than her manager’s.
DHer salary is higher than the manager she works for.
11.Human anatomyMedium
Which cranial nerve supplies the lateral rectus muscle of the eye?
ATrochlear nerve (IV)
BOculomotor nerve (III)
CAbducens nerve (VI)
DOptic nerve (II)
12.Human anatomyHard
After a stroke, a patient speaks fluently but uses meaningless words and cannot understand speech. Where is the lesion most likely to be?
APrecentral gyrus of the non-dominant hemisphere
BPosterior superior temporal gyrus of the dominant hemisphere
CCerebellar hemisphere
DInferior frontal gyrus of the dominant hemisphere
13.Human physiologyMedium
What is anatomical dead space?
AAlveoli that have collapsed completely
BThe volume of the conducting airways where no gas exchange happens
CThe air that stays in the lungs after full exhalation (residual volume)
DThe space between the two pleural layers
14.Human physiologyHard
Why is severe hyperkalaemia dangerous for the heart?
AIt speeds up the SA node until tachycardia causes fainting
BIt depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
CIt hyperpolarises cardiac cells, so they can never fire
DIt blocks the binding of calcium to troponin
15.Biology for nursing entrance examsMedium
A person with blood type AB has both A and B antigens on the red cells. What kind of inheritance is this?
AIncomplete dominance
BComplete dominance of A over B
CSex-linked inheritance
DCodominance
16.Biology for nursing entrance examsHard
Muscle cells use a lot of energy. Which organelle would you expect them to have in large numbers?
AChloroplasts
BLysosomes
CVacuoles
DMitochondria
17.Chemistry for nursing entrance examsMedium
What is the normal boiling point of a liquid?
AThe temperature at which its density is greatest
BThe temperature at which its vapour pressure equals 1 atmosphere
CThe temperature at which its particles stop moving
DThe temperature at which it first starts to evaporate
18.Chemistry for nursing entrance examsHard
Equal masses of sand and water sit in the sun and absorb the same amount of heat. Which warms up more, and why?
ASand, because it has a lower specific heat capacity than water
BBoth warm equally, because they absorbed the same heat
CSand, because it has a higher specific heat capacity than water
DWater, because it has a higher specific heat capacity than sand
3Solutions
1.Pre-nursing math (entrance exam)
Answer: m = 34
Mean, median, mode and range: the mean (average) is the sum divided by the number of values. The median is the middle value once the values are in order; with an even number of values it is the mean of the two middle ones. The mode is the value that occurs most often. The range is the largest value minus the smallest.
Order the values
19, 31, 33, 35, 36, 38
Middle
m = (33 + 35)/2 = 34
Answer
m = 34
2.Pre-nursing math (entrance exam)
Answer: x = −1
Order of operations (PEMDAS/BODMAS): work inside parentheses first, then exponents (powers), then multiplication and division from left to right, and last addition and subtraction from left to right. Multiplication does not come before division, and addition does not come before subtraction: each pair is done in the order it appears. A negative number in parentheses keeps its sign when squared: (−3)² = 9, but −3² = −9.
One operation at a time
−6² means −(6²) = −36: the exponent comes before the minus sign.
x = −6² + 5 × 7
= −36 + 5 × 7
= −36 + 35
Result
x = −1
Answer
x = −1
3.Nursing math & unit conversions
Answer: T = 38.8 °C
Temperature: °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. Subtract 32 before you multiply when going from °F, and add 32 after you multiply when going from °C. A quick check: 37 °C is 98.6 °F, and every 1 °C is 1.8 °F.
Subtract 32
101.8 − 32 = 69.8
Multiply by 5/9
T = 69.8·5/9 = 38.78 ≈ 38.8 °C
Answer
T = 38.8 °C
4.Nursing math & unit conversions
Answer: V = 85 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
½ fl oz = 0.5·30 = 15 mL
4 tbsp = 4·15 = 60 mL
2 tsp = 2·5 = 10 mL
Add
V = 15 + 60 + 10 = 85 mL
Answer
V = 85 mL
5.Reading comprehension (entrance exams)
Answer: B · A sense of duty to the ships
Why this is the answer
He climbs despite pain “because ships depended on him”, which shows a strong sense of responsibility or duty.
Answer
B · A sense of duty to the ships
6.Reading comprehension (entrance exams)
Answer: C · A small effect does not make it the only factor.
Why this is the answer
The studies show only a small effect. Claiming water is the only thing needed for weight loss ignores diet, exercise and other factors.
Answer
C · A small effect does not make it the only factor.
7.Healthcare vocabulary (entrance exams)
Answer: B · Detect or recognise
Why this is the answer
To discern is to notice or recognise something that is not obvious.
Answer
B · Detect or recognise
8.Healthcare vocabulary (entrance exams)
Answer: D · Outward expression of emotion
Why this is the answer
In mental health, affect is the observable expression of emotion; a flat affect shows very little emotional expression.
Answer
D · Outward expression of emotion
9.English grammar & language usage (entrance exams)
Answer: A · allergic
Why this is the answer
“Allergic” is the adjective that describes the subject. “Allergy” is the noun, as in “She has a peanut allergy.”
Answer
A · allergic
10.English grammar & language usage (entrance exams)
Answer: C · Her salary is higher than her manager’s.
Why this is the answer
“Her manager’s” means “her manager’s salary”, so salary is compared with salary. B and C compare a salary with a person, and D uses a double comparative.
Answer
C · Her salary is higher than her manager’s.
11.Human anatomy
Answer: C · Abducens nerve (VI)
Why this is the answer
The abducens nerve (VI) supplies lateral rectus. A lesion stops the eye moving outwards and causes horizontal double vision.
Answer
C · Abducens nerve (VI)
12.Human anatomy
Answer: B · Posterior superior temporal gyrus of the dominant hemisphere
Why this is the answer
This is Wernicke's (receptive) aphasia, caused by damage to Wernicke's area in the posterior superior temporal gyrus. Broca's area in the inferior frontal gyrus causes non-fluent aphasia.
Answer
B · Posterior superior temporal gyrus of the dominant hemisphere
13.Human physiology
Answer: B · The volume of the conducting airways where no gas exchange happens
Why this is the answer
Anatomical dead space (about 150 ml) is air in the nose, trachea and bronchi. It is moved with every breath but never reaches the alveoli.
Answer
B · The volume of the conducting airways where no gas exchange happens
14.Human physiology
Answer: B · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
Why this is the answer
High extracellular potassium makes the resting potential less negative. Many fast sodium channels then become inactivated, slowing conduction and risking fatal arrhythmias.
Answer
B · It depolarises cardiac cells, inactivating sodium channels and causing arrhythmias
15.Biology for nursing entrance exams
Answer: D · Codominance
Why this is the answer
The Iᴬ and Iᴮ alleles are codominant: neither masks the other, and both antigens appear. The O allele (i) is recessive to both.
Answer
D · Codominance
16.Biology for nursing entrance exams
Answer: D · Mitochondria
Why this is the answer
Active muscle needs a lot of ATP, so muscle cells are packed with mitochondria, where aerobic respiration takes place.
Answer
D · Mitochondria
17.Chemistry for nursing entrance exams
Answer: B · The temperature at which its vapour pressure equals 1 atmosphere
Why this is the answer
A liquid boils when its vapour pressure equals the surrounding pressure. The normal boiling point is measured at 1 atm (sea-level pressure), which is 100 °C for water.
Answer
B · The temperature at which its vapour pressure equals 1 atmosphere
18.Chemistry for nursing entrance exams
Answer: A · Sand, because it has a lower specific heat capacity than water
Why this is the answer
For the same energy and mass, the temperature rise is inversely related to specific heat. Water's specific heat is much higher than sand's, so the sand warms more. This is why beaches get hot faster than the sea.
Answer
A · Sand, because it has a lower specific heat capacity than water
This is independent practice material. ExamProblems is not affiliated with or endorsed by the organisation that runs this exam, and the exam name is used only to describe the content. HESI is a trademark of Elsevier, which is not affiliated with ExamProblems and does not endorse it or vouch for its accuracy.