Maths Questions

Question 1

BIOAVAILABILITY

A 75 year old female is admitted to hospital after suffering from a stroke. She takes digoxin tablets 250mcg OD but is being switched to an equivalent dose of elixir. Each 1ml dose of elixir is equivalent to 0.05mg and the syringe is graduated in 0.1ml increments.
What is the equivalent dose of digoxin elixir 50mcg/ml, in ml? Answer to 1d.p
The bioavailability of digoxin tablets = 0.7
The bioavailability of digoxin elixir = 0.8

Answer 1

Digoxin tabs (X) = F 0.7 (this means 70% of the dose is available)
Digoxin elixir (Y) = F 0.8 (this means 80% of the administered dose is available)
Therefore: 80% of Y = 70% of 250mcg
- Y = (0.7 x 250) / 0.8
- Y = 218.75mcg

50mcg/ 1ml = 218.75mcg / X ml
- X = 4.375
- rounded to 1 d.p = 4.4ml

Question 2

BSA and tablet rounding

A 53 year old woman is due to commence a course of fludarabine. Her oncologist would like to dose her at 40mg/m2 daily for 5 days every 28 days, for 6 cycles. She is 1.72m tall and weighs 87kg.
How many fludarabine 20mg tabs will the patient require for the full 6 cycles?

Answer 2

CLUE: Work out per cycle first and round to appropriate dose

BSA = 2.038

2.038 x 40 = 81.55mg per dose
- this is rounded down to 80mg as the tablets come in 20mg
4 tablets per dose
4x5 = 20
20 x 6 = 120 tablets to complete the course

REMEBER TO THINK PRATICALLY

Question 3

DISPLACEMENT VOLUME

A patient has been prescribed ceftriaxone 1.5g OD by IV infusion to treat an infective exacerbation of COPD.
Ceftriaxone is available as powder for reconstitution, which has a displacement volume of 0.8ml per gram.
How many ml of diluent needed to be added to a 250mg vial to produce a final concentration of 25mg/ml. Answer to 1d.p

Answer 3

Step 1: Calculate the displacement volume of the vial
- DV = 0.8ml per 1g
- therefore 0.2ml is displaced per 250mg

Step 2: Work out the final amount diluent needed
- final conc = 25mg/ml
- therefore for 250mg, we need 10ml
- 10ml - 0.2ml (amount displaced) = 9.8ml

REMEMBER: the question says how much diluent needs to be ADDED
- therefore displacement volume is subtracted from the total amount of diluent
- watch out for when the question says how much should be administered- this is when the amount displaced is added on top of from the amount of diluent

Question 4

DISPLACEMENT VOLUME

Ceftriaxone is available in a vile containing 1g of ceftriaxone powder, which should be reconstituted with 10ml of water for injection. Ceftriaxone powder has a displacement volume of 0.8ml/g.
What volume of reconstituted solution for injection, in ml, should be administered to provide a 500mg dose of ceftriaxone? Give your answer to 1 d.p.

Answer 4

Step 1: Calculate the displacement volume of the vial
- DV = 0.8ml per 1g
- therefore, 0.4ml per 500mg

Step 2: Work out the final amount diluent needed
- 1g in 10ml = 500mg in 5ml
- as 0.4ml is displaced by 500mg, the total volume to provide the full dose of 500mg will be 5ml+0.4ml
- 5ml + 0.4ml = 5.4ml

Question 5

DISPLACEMENT VOLUME

Amoxicillin powder for oral suspension has a displacement volume of 3.6ml/g. Each bottle of amoxicillin should be reconstituted with potable water to a final volume of 100ml with a concentration of 50mg/ml.

What volume of potable water, in ml, should be used to reconstitute the bottle to achieve the required final volume and concentration?

Answer 5

Step 1: Calculate the displacement volume of the vial
- DV = 3.6ml per 1g
- therefore, 18ml per 5g
- 5g comes from: 50mg/ ml = 5g/100ml

Step 2: Work out the final amount diluent needed
- as the question asks what volume of water should be used to achieve the final volume of 100mls, the DV must be SUBTRACTED
- 100ML - 18 = 82ml

Question 6

VOLUME DISTRIBUTION

An 11 year old girl weighing 34.5kg is prescribed a 7mg/kg loading dose of gentamicin to treat sepsis. The volume distribution for gentamicin in paediatric patients is approximately 0.25l/kg.

Calculate the initial plasma concentration of gentamicin, in mg/L, immediately after the dose is administered.

Answer 6

0.25l/kg x4 = 1L/kg
Therefor, 7 x 4 = 28mg/L
- KG cancels out

Question 7

RFM and MOLES

Sodium chloride has a molecular weight of 58.5g/mol. The amount of sodium chloride contained in a solution can also be expressed in mmol/L.
What is the concentration, in mmol/L of a 0.9% sodium chloride solution? Give your answer to two d.p

Answer 7

0.9% = 0.9g/ 100ml
- therefore, 9g/ 1000ml (1L)

MASS = RFM X Moles

So, 9g/L / 58.5g/mole = 0.1538 mol/L
- = 153.85 mmol/L

Question 8

DISPLACEMENT VOLUME

Answer 8

Step 1: Calculate the displacement volume of the vial
- each 600mg vial has a displacement volume of 0.4ml when dissolved

Step 2: Work out the final amount diluent needed
- volume added: 10ml water for injection
- if the displacement volume is 0.4ml, the total final volume is 10ml + 0.4ml
= 10.4ml

Question 9

Answer 9

Question 10

DISPLACEMENT VOLUME

Answer 10

Step 1: convert target concentration to mg/ml
- 2,000 mcg/ml = 2mg/ml

Step 2: calculate the total amount of dobutamine needed
- target = 2mg/ml
- final bag volume = 500ml

To find the total amount of drug needed, multiply the RQUEIRED conc by the total volume
- 2 x 500 = 1000mg

Step 3: calculate the number of vials needed
- 1000mg / 50mg = 20 vials

Question 11

Question 12

DILUTIONS

Answer 12

STEP 1: Calculate amount of magnesium in the intermediate solution
- 5ml of intermediate solution -> diluted with 55ml of water -> 60ml of a 0.7% solution
- 0.7% = 0.7g in 100ml, but we have 60ml
- (0.7/ 100) x 60 = 0.42g in 100ml of the intermediate solution

STEP 2: Calculate concentration of intermediate solution
- 0.42g in 5ml = 8.4g in 100ml (8.4%)

STEP 3: C1V1=C2V2
- Q asks how much stock is needed
- stock is 30%, we have 300mls of 8.4% intermediate
- 8.4% x 300ml = 30% x X
- X = 84mls

Question 13

INFUSION RATES

Answer 13

Step 1: work out total volume infused
- 0.6g x 30kg = 18g (total dose)
- 10% = 10g/ 100ml therefore 18g = 180ml (total volume infused)

Step 2: Work out the volume infused with the known timings

Step 3: Subtract the known volumes from the total volume

Step 4: Work out how long it will take to infuse the remaining volume with the last infusion rate

Question 15

DILUTIONS

Answer 15

Question 17

Answer 17

23.3ml

Question 19

Answer 19

Step 1: calculate the volume of KCL solution needed
- 2.5g = 2500mg
- 15mg/ 1ml = 2500mg/ X mls
- X = 166.67ml

Step 2: determine the final concentration required and find the total final volume
- 0.2% = 2mg/ml
- total volume = total solute mg)/ desired concentration
- 2500mg/ 2= 1250

1250ml = total final volume
We have 166.67ml of KCL stock
So the amount of 5% gluose added is 1250 - 166.67 = 1083.33ml
= 1.08L

Question 20

Volume distribution and half life

Answer 20

Question 22

Answer 22

Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

Answer 29