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
Solve for x: 5x + 6 = 31.
5x + 6 = 31
x =
2.Pre-nursing math (entrance exam)Hard
After a 30% pay rise, a nursing assistant earns $305.5 a week. What was the weekly pay x before the rise, in dollars?
$305.5+30%
x = $
3.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient’s temperature is 101.2 °F. Convert it to degrees Celsius T with °C = (°F − 32) × 5/9. Round to one decimal place.
101.2 °F
T = °C
4.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). A prescription reads 1 tbsp of an oral suspension twice a day for 5 days. Using 1 tbsp = 15 mL, how many mL V are needed for the whole course?
1 tbsptwice a day5 days1 tbsp = 15 mL
V = mL
5.Reading comprehension (entrance exams)Medium
“Old Mr. Hale’s garden was full of weeds, the gate hung from one hinge, and the windows were covered in dust.” What can the reader most likely infer?
AThe house has not been cared for in some time.
BMr. Hale spends every single day working in the garden.
CMr. Hale has just moved into the house.
DThe house was cleaned the day before.
6.Reading comprehension (entrance exams)Hard
The author writes: “Teenagers today spend too much time on their phones. My nephew is always texting at dinner.” What is the main weakness of this argument?
AIt uses a single example to judge all teenagers.
BIt argues that phones are useful for teenagers.
CIt does not say what kind of phone the nephew has.
DIt gives too much data about teenage phone use.
7.Healthcare vocabulary (entrance exams)Medium
Choose the meaning of the word in bold: “The pupils dilate in the dark.”
AStop moving
BChange colour
CBecome smaller
DBecome wider
8.Healthcare vocabulary (entrance exams)Hard
Choose the meaning of the word in bold: “Prophylactic antibiotics were given before surgery.”
AGiven to treat an existing infection
BGiven to prevent disease
CGiven in unusually high doses
DGiven only by injection
9.English grammar & language usage (entrance exams)Medium
Choose the correct pronoun: “Who wants to go first? ___ do!”
AI
BMyself
CMe
DMine
10.English grammar & language usage (entrance exams)Hard
Which revision best eliminates wordiness? “At this point in time, the patient is in a state of recovery.”
AThe patient is now recovering.
BThe patient, at this point in time, is recovering now.
CAt this time, the patient is in a recovery state.
DCurrently at this point, the patient is recovering.
11.Human anatomyMedium
Which superficial vein in the front of the elbow is most often used for venepuncture?
ABrachial vein
BGreat saphenous vein
CMedian cubital vein
DAxillary vein
12.Human anatomyHard
Which structure is found in the posterior mediastinum?
AHeart
BOesophagus
CThymus
DAscending aorta
13.Human physiologyMedium
Which hormonal event triggers ovulation?
AA fall in oestrogen
BA rise in progesterone from the corpus luteum
CA surge of luteinising hormone (LH)
DA surge of prolactin
14.Human physiologyHard
Why does a person with lactase deficiency get diarrhoea and bloating after drinking milk?
AUndigested lactose draws water into the gut and is fermented by colonic bacteria
BLactose damages the villi directly
CLactose is absorbed too quickly and raises blood glucose
DMilk protein triggers an allergic reaction
15.Biology for nursing entrance examsMedium
Which element is found in all amino acids but not in carbohydrates?
ACarbon
BOxygen
CHydrogen
DNitrogen
16.Biology for nursing entrance examsHard
Which change would make diffusion across a membrane faster?
AA lower temperature on both sides
BA larger difference in concentration between the two sides
CA thicker membrane
DA smaller surface area for exchange
17.Chemistry for nursing entrance examsMedium
Which coefficients balance the equation __H₂ + __O₂ → __H₂O?
A2, 2, 2
B1, 1, 1
C1, 2, 1
D2, 1, 2
18.Chemistry for nursing entrance examsHard
Under which conditions does a real gas behave least like an ideal gas?
AHigh temperature and large container
BLow pressure and high temperature
CHigh pressure and low temperature
DLow pressure and low volume of particles
3Solutions
1.Pre-nursing math (entrance exam)
Answer: x = 5
Solving equations: do the same thing to both sides until x stands alone. Undo operations in reverse order: first undo addition or subtraction, then multiplication or division. Clear parentheses with the distributive property, a(x + b) = ax + ab, and collect the x terms on one side. Check the answer by substituting it back.
Subtract 6 from both sides.
5x = 25
Divide both sides by 5.
x = 5
Check
5·5 + 6 = 31
Answer
x = 5
2.Pre-nursing math (entrance exam)
Answer: x = 235 $
Reverse percentages: when a value has already been increased or decreased by a percent, the new value is a percent of the original, not the other way round. After a 20% discount the price is 80% of the original, so original = new price ÷ 0.80. Never add the 20% back on to the new price.
Set up the equation
1.3 · x = 305.5
Solve
x = 305.5/1.3 = $235.00
Answer
x = $235.00
3.Nursing math & unit conversions
Answer: T = 38.4 °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
101.2 − 32 = 69.2
Multiply by 5/9
T = 69.2·5/9 = 38.44 ≈ 38.4 °C
Answer
T = 38.4 °C
4.Nursing math & unit conversions
Answer: V = 150 mL
Dimensional analysis: write the given quantity, then multiply by conversion factors written as fractions (for example 60 min/1 h or 1 mg/1000 mcg) so that each unwanted unit appears once on top and once underneath and cancels. When only the wanted unit is left, calculate. Use the equivalents the question gives and round only the final answer.
Volume per dose
1 tbsp = 1·15 = 15 mL
Whole course
V = 15 mL × 2/day × 5 = 150 mL
Answer
V = 150 mL
5.Reading comprehension (entrance exams)
Answer: A · The house has not been cared for in some time.
Why this is the answer
Weeds, a broken gate and dusty windows all point to neglect over time. They contradict the idea of recent cleaning or daily gardening.
Answer
A · The house has not been cared for in some time.
6.Reading comprehension (entrance exams)
Answer: A · It uses a single example to judge all teenagers.
Why this is the answer
One nephew’s behaviour is not enough evidence to judge “teenagers today” as a whole. This is a hasty generalisation.
Answer
A · It uses a single example to judge all teenagers.
7.Healthcare vocabulary (entrance exams)
Answer: D · Become wider
Why this is the answer
To dilate is to widen or open up; pupils dilate to let in more light.
Answer
D · Become wider
8.Healthcare vocabulary (entrance exams)
Answer: B · Given to prevent disease
Why this is the answer
Prophylactic means preventive; prophylactic antibiotics lower the risk of infection after surgery.
Answer
B · Given to prevent disease
9.English grammar & language usage (entrance exams)
Answer: A · I
Why this is the answer
In “I do”, the pronoun is the subject of the verb, so the subject form “I” is needed.
Answer
A · I
10.English grammar & language usage (entrance exams)
Answer: A · The patient is now recovering.
Why this is the answer
“At this point in time” means “now”, and “is in a state of recovery” means “is recovering”. A says the same thing in five words.
Answer
A · The patient is now recovering.
11.Human anatomy
Answer: C · Median cubital vein
Why this is the answer
The median cubital vein crosses the cubital fossa between the cephalic and basilic veins. It is superficial, large and fairly fixed, so it is easy to puncture.
Answer
C · Median cubital vein
12.Human anatomy
Answer: B · Oesophagus
Why this is the answer
The posterior mediastinum contains the oesophagus, descending aorta, azygos veins and thoracic duct. The heart and ascending aorta are in the middle mediastinum; the thymus is in the superior and anterior mediastinum.
Answer
B · Oesophagus
13.Human physiology
Answer: C · A surge of luteinising hormone (LH)
Why this is the answer
Rising oestrogen from the dominant follicle triggers an LH surge from the anterior pituitary, which causes ovulation about a day later.
Answer
C · A surge of luteinising hormone (LH)
14.Human physiology
Answer: A · Undigested lactose draws water into the gut and is fermented by colonic bacteria
Why this is the answer
Unabsorbed lactose acts osmotically, pulling water into the lumen. Colonic bacteria ferment it, producing gas and short-chain fatty acids.
Answer
A · Undigested lactose draws water into the gut and is fermented by colonic bacteria
15.Biology for nursing entrance exams
Answer: D · Nitrogen
Why this is the answer
Every amino acid has an amino group (–NH₂), which contains nitrogen. Carbohydrates contain only carbon, hydrogen and oxygen.
Answer
D · Nitrogen
16.Biology for nursing entrance exams
Answer: B · A larger difference in concentration between the two sides
Why this is the answer
Diffusion is faster with a steeper concentration gradient, a higher temperature, a larger surface area and a thinner barrier.
Answer
B · A larger difference in concentration between the two sides
17.Chemistry for nursing entrance exams
Answer: D · 2, 1, 2
Why this is the answer
2H₂ + O₂ → 2H₂O has 4 H and 2 O on each side. You may change coefficients, never the subscripts in the formulas.
Answer
D · 2, 1, 2
18.Chemistry for nursing entrance exams
Answer: C · High pressure and low temperature
Why this is the answer
At high pressure the particles are close, so their own volume matters; at low temperature they move slowly, so attractions matter. Both break the ideal gas assumptions.
Answer
C · High pressure and low temperature
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.