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This exam covers some of the techniques seen in the Psychology page on the wiki.

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a) 

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Firstly calculate how much of the grant each patient is given towards the treatment: 

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$\\dfrac{\\var{grant}}{\\var{patients}} = \\text{£} \\var {precround(grant/patients,2)}$ (to 2 decimal places). 

\n

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Then subtract this value from the cost of the treatment to find out how much each patient pays:

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$\\text{£}\\var{cost} - \\text{£}\\var{precround(grant/patients,2)} = \\text{£}\\var{precround(cost - (grant/patients),2)} $ (to 2 decimal places).

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Each person pays £$\\var{precround(cost - (grant/patients),2)}$ for the the treatment. 

\n

 

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b)

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Firstly calculate how much of a loss was made in July:

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The company lost four times more in July than in June: $4\\times -\\text{£}\\var{june} =-\\text{£} \\var{4*june}$

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Total the losses: $(-\\text{£}\\var{june}) + (- \\text{£}\\var{4*june}) +(-\\text{£} \\var{august}) = - \\text{£}\\var{june+4*june+august}$.

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So you need to bid for a grant of £$\\var{june+4*june+august}$.

\n

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You work in a psychologist's office. You are introducing a new treatment for addiction involving hypnotherapy. The cost of the treatment per person is £$\\var{cost}$. You have $\\var{patients}$ patients requiring the treatment. You have a grant for your patients of £$\\var{grant}$. 

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How much will each patient have left to pay towards the treatment providing everyone gets the same share of the grant? (to 2 decimal places)

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You are working for a company that is making losses due to its high standards of patient care. There is the potential for a grant to cover their losses because of the service they provide. In June they made $-$£$\\var{june}$, in July they lost four times what they had in June and in August they made $-$£$\\var{august}$. 

\n

How much grant should you apply for to cover the losses made in these three months?

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some basic calculations on mathematics with positive and negative numbers.

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a) The correct way to calculate the percentage is: $\\dfrac{\\text{recorded}}{\\text{total possible}}\\times100$.

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This is because you want the amount that you recorded as a fraction of the total and then you multiply by 100 to get this as a percentage. 

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b) Using the above formula the correct calculation is $\\frac{\\var{r}}{\\var{t}}\\times 100$, by substituting in the given values. 

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cThen the correct final value is $\\var{precround(r/t*100,1)}$% using the above calculation. We could probably have guessed that this was the correct percentage as ${\\var{r}}$ is less than $\\var{t}$ so it cannot be greater than $100$% and $\\var{r}$ is larger than half of ${\\var{t}}$ so the only probable solution is that $\\var{r}$ is $\\var{precround(r/t*100,1)}$% of $\\var{t}$.

\n

 

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Which of the following is the correct way to calculate the percentage of time spent behaving aggressively?

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$\\dfrac{\\text{recorded}}{\\text{total}}\\times100$

", "

$\\dfrac{\\text{recorded}}{\\text{total}}\\div100$

", "

$\\dfrac{\\text{total}}{\\text{recorded}}\\times100$

", "

$\\dfrac{\\text{total}}{\\text{recorded}}\\div100$

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Which is the correct calculation?

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$\\dfrac{\\var{r}}{\\var{t}}\\times 100$

", "

$\\dfrac{\\var{t}}{\\var{r}}\\times 100 $

", "

$\\dfrac{\\var{r}}{\\var{t}} \\div100$

", "

$\\dfrac{\\var{t}}{\\var{r}}\\div 100$

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Which is the correct answer?

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{precround((r/t)/100,3)}%

", "

{precround((r/t)*100,1)}%

", "

{precround((t/r)*100,1)}%

", "

{precround((t/r)/100,3)}%

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When studying behaviour it can be difficult to write down every behaviour seen continuously. Instead, behaviour “sampling” is used.

\n

You are conducting a pilot study of the social behaviour of guinea pigs in a rehoming centre who have just been introduced. As part of a future study you wish to compare behaviour when they are introduced in a neutral territory to when one of the guinea pigs are in their usual accommodation.

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You are measuring the percentage of time spent behaving aggressively and the percentage of time spent grooming each other. You record either of these behaviours if they are happening on the $5$ minutes mark every $5$ minutes over $3$ hours. You record $\\var{r}$ instances of aggression out of the $\\var{t}$ total possible recording points.

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You have to give out the drugs at a ratio $\\var{a}:\\var{b}$.

\n

There are ($\\var{a}+\\var{b}$) = $\\var{a+b}$ parts in total.

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Divide the $\\var{c} \\text{g}$ by $\\var{a + b}$ to get one part, and multiply by $\\var{a}$ to get the amount of drug A to administer.

$(\\var{c}\\div\\var{a+b})\\times\\var{a} = \\var{precround((c/(a+b))*a,2)}$g of drug A is given (accurate to 2 decimal places)

\n

\n

", "rulesets": {}, "parts": [{"prompt": "

You have $\\var{c}$g of the drugs to give out.

\n

How much of drug A (in g) is given to the residents?

\n

(Give your answer to 2 decimal places.)

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You work in a care home and you have to ensure that the residents are getting enough drug A and drug B as you are performing an experiment on the effects these drugs have on their moods.

\n

You administer drug A and B at a ratio of $\\var{a}$:$\\var{b}$.

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Calculate separately the percentage of employees who are female and working on the project, and the percentage who are male and working on the project, and add them together.

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1. Females

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{females}% of the department is female and {femaleproject}% of females are working on the project, hence the proportion of workers who are female and working on the project is {femaleproject}% of {females}% of the workers.

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In terms of fractions this is \\[ \\frac{\\var{femaleproject}}{100} \\times \\frac{\\var{females}}{100} = \\frac{\\var{femaleproject*females}}{10000} = \\frac{\\var{depfemaleproject}}{100}\\] of the workers, ie {depfemaleproject}%.

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So {depfemaleproject}% of the departmental staff are working on the project and female.

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2. Males

\n

 

\n

{males}% of the department is male and {maleproject}% of males are working on the project, hence the proportion of workers who are male and working on the project is {maleproject}% of {males}% of the workers.

\n

In terms of fractions this is \\[ \\frac{\\var{maleproject}}{100} \\times \\frac{\\var{males}}{100} = \\frac{\\var{maleproject*males}}{10000} = \\frac{\\var{depmaleproject}}{100}\\] of the workers, ie {depmaleproject}%.

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So {depmaleproject}% of the departmental staff are working on the project and male.

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So the total percentage of departmental staff working on the project is $\\var{depfemaleproject}\\% + \\var{depmaleproject}\\% = \\var{project}\\%$.

\n

 

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What percentage of the department is working on the project?

\n

[[0]] %

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In a certain department, $\\var{femaleproject}$% of the females and $\\var{maleproject}$% of the males are working on a project. $\\var{if(describefemales,females,males)}$% of the department is $\\var{if(describefemales,'female','male')}$.

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Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

\n

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

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a)

\n

There are $10^6 \\mu$m in 1m so when converting $\\var{small}$$\\mu$m to metres we divide by $10^6$:

\n

$\\var{small}$$\\mu$m = $\\var{small/(10^6)}$m.

\n

There are 100cm in 1m, so when converting to cm divide by 100 : $\\var{small/(10^6)}$m = $\\var{small/(10^4)}$cm.

\n

$\\var{small}$$\\mu$m = $\\var{small/(10^4)}$cm.

\n

b)

\n

There are 1000ml in a litre, to convert $\\var{liquid}$ml into litres we divide by 1000.

\n

$\\var{liquid}\\div1000$ = $\\var{liquid/1000}$ L.

\n

c)

\n

There are $10^6\\mu$mol in one mole.

\n

To convert $\\mu$mol into moles you divide by $10^6$.

\n

So $\\var{mol}$$\\mu$mol = $\\var{mol/10^6}$ moles.

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Convert $\\var{small}$ $\\mu$m into cm.

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{((small)/10000)} cm

", "

{((small)/1000)} cm

", "

{((small)/1000000)} cm

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Convert $\\var{liquid}$ ml into litres.

\n

$\\var{liquid}$ ml = [[0]] l

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You need to convert everything into grams:
$\\var{calories}$kg = $\\var{calories*1000}$g
$\\var{vitamins}$g = $\\var{vitamins}$ g
$\\var{prozac}$mg = $\\var{prozac/1000}$g.

\n

You have one bag protein powder = $\\var{calories*1000}$g
You have 2 bags of vitamins = $\\var{vitamins*2}$ g
You have 3 packets of Prozac = $\\var{(prozac/1000)*3}$g
Adding together gives $\\var{calories*1000}\\text{g}+\\var{vitamins*2}\\text{g} + \\var{(prozac/1000)*3}\\text{g} $ = $\\var{calories*1000+vitamins*2 + (prozac/1000)*3} $ g.

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In a health and rehabilitation clinic you are doing a stock check. You have one bag of protein powder weighing $\\var{calories}$ kg, two bags of vitamins weighing $\\var{vitamins}$g each, and three packets of Prozac weighing $\\var{prozac}$mg each.

\n

How much stock do you have in total, in grams?

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Calculations where you need to change the units.

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