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
A circle has a radius of 2 cm. Using π ≈ 3.14, find its area A.
r = 2 cmπ ≈ 3.14
A = cm²
2.Pre-nursing math (entrance exam)Hard
In a course, homework counts 15%, the midterm 35% and the final exam 50% of the grade. A student scores 97% on homework, 62% on the midterm and 64% on the final. What is the course grade G? Round to one decimal place.
15% · 9735% · 6250% · 64
G = %
3.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A dose calculation for a small injection gives 0.24981 mL. The rule in this exercise is that volumes below 1 mL are rounded to the nearest hundredth of a mL. What value x do you record?
0.24981 mL
x = mL
4.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 1½ cups of tea, 2½ tsp of cough syrup, 1½ tbsp of liquid supplement. Using the equivalents given, find the total oral intake V in mL.
1 cup = 8 fl oz = 240 mL1 tsp = 5 mL1 tbsp = 15 mL
V = mL
5.Reading comprehension (entrance exams)Medium
The river flooded after a week of heavy rain. Water covered the main road, so the town closed it and set up a detour through the hills. What caused the town to close the main road?
ASnow falling during the week
BA traffic accident on the detour
CRepairs being made in the hills
DFlood water covering the main road
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?
AThe author says nothing about the studies.
BA small effect does not make it the only factor.
CThe studies did not look at water.
DWater makes people eat many more calories.
7.Healthcare vocabulary (entrance exams)Medium
Choose the meaning of the word in bold: “Drinking enough fluids helps prevent constipation.”
ADifficulty passing stools
BFrequent, loose stools
CStomach cramps after meals
DPainful urination
8.Healthcare vocabulary (entrance exams)Hard
Which word is closest in meaning to ubiquitous?
AWidespread
BUnique
CDangerous
DInvisible
9.English grammar & language usage (entrance exams)Medium
Which sentence punctuates “however” correctly in the middle of a clause?
AThe test; however, was easier than expected.
BThe test, however was easier than expected.
CThe test, however, was easier than expected.
DThe test however, was easier than expected.
10.English grammar & language usage (entrance exams)Hard
Which sentence uses “not only … but also” with correct parallel structure?
AShe is not only a nurse but also a teacher.
BNot only she is a nurse but also a teacher.
CShe not only is a nurse but also a teacher.
DShe is not only a nurse but also teaches.
11.Human anatomyMedium
Which cranial nerve controls movement of the tongue?
AGlossopharyngeal nerve (IX)
BFacial nerve (VII)
CVagus nerve (X)
DHypoglossal nerve (XII)
12.Human anatomyHard
A tumour at the apex of the lung causes drooping of the eyelid, a small pupil and loss of sweating on the same side of the face. Which pathway is disrupted?
ACervical sympathetic chain
BOculomotor nerve
CParasympathetic fibres of the vagus
DFacial nerve
13.Human physiologyMedium
Which receptors respond mainly to a fall in arterial oxygen levels?
APeripheral chemoreceptors in the carotid and aortic bodies
BStretch receptors in the lungs
CCentral chemoreceptors in the medulla
DBaroreceptors in the carotid sinus
14.Human physiologyHard
Why does breathing 100% oxygen correct hypoxaemia from a true right-to-left shunt only poorly?
AThe shunted blood never comes into contact with alveolar gas
BPure oxygen damages haemoglobin
CThe extra oxygen is all exhaled as CO₂
DShunted blood is already fully saturated
15.Biology for nursing entrance examsMedium
How do bacteria usually reproduce?
ABy budding off viruses
BBy forming seeds
CBy binary fission
DBy meiosis
16.Biology for nursing entrance examsHard
During the Industrial Revolution, soot darkened tree trunks in parts of England, and dark peppered moths became more common than pale ones. What best explains this?
AThe soot settled on the pale moths and slowly turned them dark
BBirds found and ate fewer dark moths on the dark trunks
CThe moths chose to become dark to hide
DDark moths were produced by the polluted air
17.Chemistry for nursing entrance examsMedium
Which coefficients balance __Na + __Cl₂ → __NaCl?
A2, 2, 1
B1, 1, 1
C1, 2, 1
D2, 1, 2
18.Chemistry for nursing entrance examsHard
In the reaction 2Na + Cl₂ → 2NaCl, which substance is the oxidising agent?
ACl₂
BNa
CNaCl
DNa⁺
3Solutions
1.Pre-nursing math (entrance exam)
Answer: A = 12.56 cm²
Perimeter, area and volume: the perimeter is the distance around a shape (rectangle: 2l + 2w). Area is measured in square units: rectangle l × w, triangle ½ × base × height, circle π·r². The circumference of a circle is π·d = 2π·r. Volume is in cubic units: box l × w × h, cylinder π·r²·h. Use the value of π the question gives.
Area
A = 3.14 × 2² = 3.14 × 4 = 12.56 cm²
Answer
A = 12.56 cm²
2.Pre-nursing math (entrance exam)
Answer: G = 68.3 %
Weighted average: when parts count for different percentages, multiply each score by its weight (as a decimal) and add. A plain mean of the scores is only right when every part counts equally.
Weight each score
0.15 × 97 = 14.55
0.35 × 62 = 21.7
0.5 × 64 = 32
Add
G = 14.55 + 21.7 + 32 = 68.3%
Answer
G = 68.3%
3.Nursing math & unit conversions
Answer: x = 0.25 mL
Rounding: look at the digit just after the place you round to: 5 or more rounds up, 4 or less leaves the digit as it is. Round only the final answer, never the steps. Typical exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops and weights to one decimal place; always follow the rule the question states.
Digit in the hundredths place
0.24981 → 4
Only the next digit decides
0.24981 → 9
9 is 5 or more, so round 4 up.
The digits after it (81) are ignored: round once, never step by step.
Round
x = 0.25 mL
Answer
x = 0.25 mL
4.Nursing math & unit conversions
Answer: V = 395 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
1½ cups = 1.5·240 = 360 mL
2½ tsp = 2.5·5 = 12.5 mL
1½ tbsp = 1.5·15 = 22.5 mL
Add
V = 360 + 12.5 + 22.5 = 395 mL
Answer
V = 395 mL
5.Reading comprehension (entrance exams)
Answer: D · Flood water covering the main road
Why this is the answer
The sentence says water covered the main road, so the town closed it. The word “so” links the cause to the effect.
Answer
D · Flood water covering the main road
6.Reading comprehension (entrance exams)
Answer: B · 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
B · A small effect does not make it the only factor.
7.Healthcare vocabulary (entrance exams)
Answer: A · Difficulty passing stools
Why this is the answer
Constipation means infrequent or difficult bowel movements, often with hard stools.
Answer
A · Difficulty passing stools
8.Healthcare vocabulary (entrance exams)
Answer: A · Widespread
Why this is the answer
Ubiquitous means found everywhere, so widespread is the closest meaning.
Answer
A · Widespread
9.English grammar & language usage (entrance exams)
Answer: C · The test, however, was easier than expected.
Why this is the answer
When “however” interrupts a single clause, it is set off with a pair of commas. A semicolon is used only when “however” joins two independent clauses.
Answer
C · The test, however, was easier than expected.
10.English grammar & language usage (entrance exams)
Answer: A · She is not only a nurse but also a teacher.
Why this is the answer
In A both parts are nouns (a nurse, a teacher). In the other choices the two parts do not match grammatically.
Answer
A · She is not only a nurse but also a teacher.
11.Human anatomy
Answer: D · Hypoglossal nerve (XII)
Why this is the answer
The hypoglossal nerve supplies the intrinsic and most extrinsic tongue muscles. A lesion makes the protruded tongue deviate towards the affected side.
Answer
D · Hypoglossal nerve (XII)
12.Human anatomy
Answer: A · Cervical sympathetic chain
Why this is the answer
This is Horner's syndrome: ptosis, miosis and anhidrosis from interruption of sympathetic fibres, here by an apical (Pancoast) tumour pressing on the sympathetic chain.
Answer
A · Cervical sympathetic chain
13.Human physiology
Answer: A · Peripheral chemoreceptors in the carotid and aortic bodies
Why this is the answer
The carotid and aortic bodies detect low PaO₂ (and also high CO₂ and H⁺). The central chemoreceptors respond to CO₂ but not directly to oxygen.
Answer
A · Peripheral chemoreceptors in the carotid and aortic bodies
14.Human physiology
Answer: A · The shunted blood never comes into contact with alveolar gas
Why this is the answer
Shunted blood bypasses ventilated alveoli and mixes deoxygenated blood into arterial blood. Extra inspired oxygen cannot reach it, unlike in V/Q mismatch or hypoventilation.
Answer
A · The shunted blood never comes into contact with alveolar gas
15.Biology for nursing entrance exams
Answer: C · By binary fission
Why this is the answer
A bacterium copies its circular chromosome and splits into two identical cells. This can happen every 20–30 minutes in good conditions.
Answer
C · By binary fission
16.Biology for nursing entrance exams
Answer: B · Birds found and ate fewer dark moths on the dark trunks
Why this is the answer
Dark moths were better camouflaged on sooty bark, so birds ate more pale moths. Dark moths survived and reproduced more, so the dark allele became more common: natural selection in action.
Answer
B · Birds found and ate fewer dark moths on the dark trunks
17.Chemistry for nursing entrance exams
Answer: D · 2, 1, 2
Why this is the answer
Cl₂ has two Cl atoms, so 2NaCl is needed, which needs 2Na: 2Na + Cl₂ → 2NaCl. Each side has 2 Na and 2 Cl.
Answer
D · 2, 1, 2
18.Chemistry for nursing entrance exams
Answer: A · Cl₂
Why this is the answer
Chlorine gains electrons from sodium (Cl₂ → 2Cl⁻), so it is reduced and acts as the oxidising agent. Sodium loses electrons, is oxidised and is the reducing agent.
Answer
A · Cl₂
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