Psychometric practice

  • Created by: jmf00632
  • Created on: 10-09-19 13:17

A restaurant make a total of 1,000,000 meals using

250,000 kg/ 1,000,000 meals = 0.25 kg per meal

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Bob the builder spent £210,000 on 700,000 kg of ma

210,000/700,000= 0.30 per kg

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browns made 200,000 units in 40,000 labour hours.

40,000/ 200,000=0.2 hrs

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Next paid staff £428,750 for 35,000 hours of work.

FYI - The "per hour" part tells us what we put on the BOTTOM - the 35,000 hours goes last (bottom)

428,750/35,000= £12.25

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The percentage change on a percentage

The interest rate on our bank loan is increased from 10% to 13%. What is the percentage increase on the interest rate?

1. work out the difference - 13-10= 3 

2. Then divide the difference by the starting number which is - 3/10= 0.3

0.3 x 100 = 30 percent

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profit margain (%)

If the sales pice is set at £190 and the company has a target profit margain of 40% what is the maximum target cost that they can afford to incur?

  • The PROFIT MARGAIN is 40%
  • Sales revenue is 100%
  • Therefire 100 - 40 = 60 
  • 190 x 0.6= £114 - THIS IS HOW MUCH IT COST TO MAKE THE PRODUCT 
  • THE 190 IS THE SELLING PRICE 
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finding the selling price

If a company has a target profit maragain of 25% and spends £150 producing a unit what must the selling price be set at?

100- 25 = 75 = 0.75

150/0.75= £200

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markup

if the sales price is set at £190 and the compnay uses a markp of 40% what is the production cost of the product?

  • sales revenue- costs = profit
  • revenue is 140%
  • sales price (revenue from each unit is £190 
  • so to find out the cost:
  • 190/140%  x 100 = 135.71
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markup - DO SKELETON WITH THESE Q

if a company spends £50 producing a unit and sets the price to give a mark up of 25% what will the selling price be?

  • 100 + 25= 125 
  • 150/100X125= 187.50
  • 150X0.25=37.50
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Question 1 - proportion

in a box of 12 chocolates, 12 are made from white chocolate. What propotion of the chocolates are not white? Give your answer as a decimal. 

  • 40-12=28
  • so that means it is 28/40
  • they are both multiples of 4 
  • 28/4= 7 
  • 40/4=10
  • which equals 7/10 and as a decimal that is 0.7
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question 2- travel and expenses

400 employees of the same company claimed travel expenses. They each travelled 15 miles. Company expenses are paid at 30p per mile. How many pounds did this cost the company in total?

  • 400 x 15 x 30 = 180000/100= 1,800
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question 3 - calculating the % of a group

In a football team of 25 players, 5 of the players are above the age of 30. What percentage of the squad is older than 30?

5/25 x 100 = 20

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Question 4- measurments

There were 30 children in a class. 250ml of apple juice was given to each child. How many 1 litre carton of apple juice were needed?

  • first, we need to calculate the volume of apple juice needed. so we do: 30 x 250ml= 7.5 l 
  • so we need 8 cartons
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Question 6 (skipped 5) - distance

Two stuents both attend a sponsored walk to raise money for charity. They each walk 24 miles and are sponsored at 24 pence per mile. How much do they raise in total? Give your answer in pounds and pence. 

2 x 24 x 2 = 1152

add a decimal point so 11.52

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Question 8 (skipped 7) - money conversion

A couple wish to buy £400 worth of dollars for their weekend in New York. At there current rate, yo can buy 1.25 dollars for £1. How many dollars will the couple receive for £400. 

  • So £1 i equivalent to $1.25
  • so the calculation we need to do 400 x 1.25
  • IF YOU ARE DOING THIS WITHOUT A CALCULATOR: 1.25 is 25%. 25% of 400 is 100 
  • so 100 is our increase. so you just do 400 + 400 = 500 
  • so they will get $500 
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Question 10 (skipped 9) - proportion

A car dealership has 42 cars, if 28 of the cars are blue, What proprtion of the cars are not blue? give your answer to 2 decimal places. 

  • 42 - 28 = 14
  • so it is 14/42 
  • they are both in the 2 times table so - 7/21
  • and they are both in the 7 times table so 1/3
  • 1/3 as a decimal is 0.33333
  • however, to get the answer to 2 decimal places 3/1..0000 = 0.33333
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Question 2 (skipped 11) - how long it takes to do

Sarah sends 15 texts in 5 minutes. how long des it take her to sned each text?

15 texts in 5 minutes so:

  • 5/15 = 1/3
  • 1/3 x 60=  20 
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To find the median from a graph

  • the median is always given by the formula:
  • N+1/2
  • (for the example in the video) N is 11
  • 11+1 / 2 = 6 = this means that on the graph it will be the SIXTH number. but the answer is NOT 6. 
  • for thi type of question, if you are looking for the median from a graph, you have to count along the axis. so count the 6th number, and for this example, the 6th number of the graph was 10. 
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finding the median in a cumulative frequency graph

  • FInd how many people there are in total - to do that we look for the highest point of the graph. The total for this graph was 100. 
  • then to find the media we divide 100 by 2 which is 50 
  • you find 50 on the cumalitvie frequency graph and then draw across to the line and read off the other axis. - this was 60 
  • the median ws 60 

FYI if a graph isflat then it means that the quantity there is 0. THERE IS NO GROWTH IN THAT PART OF THE GRAPH 

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question 3 video 2

You are asked to stretch a string to extend its length by 40%. The orginial length of the spring was 45 cm. what should the length of the springb be now?

if a 100 percent is 45 cm then 10 percent is 45/100=4.5

so to find 40 percent we have to do 4.5 percent x 4= 18 

so a 40 percent increase will be 45 plus 18= 63cm

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question 9 video 2

A teacher took a group of students to the cinema in france. it cost 160 euros. 

if 1.6 euros is equal to £1, what was the toal entrance cost, in pounds?

  • 1.6 euros =£1
  • what we need to do first, is to turn the 1.6 euros into 160 euros. 
  • 1.6 x 100= 160 
  • 1 x 100 = 100 
  • ttherefore, the entrance fee would be £100
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question 11 video 2

A scool trip was planned at a total cost of £120 per pupil. The accomadation cost two-fifths of the total. What ws the cost of the accomadation per pupii? 

to find two-fifths of a number we - 2/5 x 120 = 48 pounds

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finding a fraction of a number

For example, we are asked to find 3/7 of 182 what we do is:

182 / 7 (the bottom number)

then that answer which is 26 times by the top number (26 x 3) = 78

therefore, 3/7 of 182 is 78

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finding a percentage of a number

what is 80 percent of 30? 

0.8 x 30 = 24

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turning a normal number into a percentage number

for example, a student scored 22 out of 60 on a test. to work this out as a percentage is 22/60  x 100 = 36.6

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question 3 test 3

in a year group of 120 students 15 acheived an A star in GCSE English. What percentage of the group acheived an A star in gcse english?

15/120 = 3/24= 1/8

1/8 as a fraction is 12.5 percent 

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Question 8 test 3

A teacher plans a school trip which includes a 152 kilomatre coach journey in fracne. As an approximate, 8 km, is equal to 5 miles. 

using this approximate, how long is the journey in miles?

152 km   

8km:5miles - so we want to try and get 152 km on this side so we can get the equivalent milage on the right handd side:

so we do 152/8 =  19 which means 19 x 5 = 95 

(if you are not using a calculator, the quickest way to x by 5 is to x by 10 and the divide that anwer by 2

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Ratios

£56.10 is given to two charities x andy in the ratio 2:1. how much money is given to charity x?

1. 2 +1 = 3

56.10/3= 18.7

18.7 x 2 = 37.40

ANOTHER QUESTION TAKEN FROM SURREY PATH FINDER PRACTICE - 

The pie chart shows the sales of CDs, cassettes, videos and DVDs from a music shop during one week.

What is the ratio of the value of cassette sales to DVD sales?

he correct answer is 1:4. To find the answer you have to find the highest value that divides exactly into the value of cassette sales ($400) and DVD sales ($1600). The highest value that divides exactly into these values is 400. 400 divides into the value of cassette sales once and the value of DVD sales four times, giving a ratio of 1:4.

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finding the median in a cumulative frequency chart

divide the total number of pupils by 2

e.g. 30/2=15

you then find 15 on the y axis and draw it up to the line and read the number off the x axis.

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question 23 video 3

A teacher is plannig a bus trp to snowdenia. 

  • the round trip will be aprox 350 miles
  • the fuel consumption is 32 miles per gallon
  • the fuel is 1.13 per litre. 
  • 1 gallon= 4.546 litres
  • for this kind of question i is good to do a ratio with the information that you have been given. 

32 miles:1 gallon 

£1.13: 1 litre 

1 gallon;4.546 litres

now we can start doing the question:

1. divide both sides by 32 (32 miles: 1 gallon) = 1/32 so one mile = 1/32 gallons 

2. 350 / 32 = 10.9375 grams 

3. now we need to find out how many litres is in 10.9375 gallons. 

  • we do know that 1 gallon is 4.546 litres. 

4. so 10.9375 x 4.546 litres = 49.721875 litres

cost is £1.13 per litre

1.13 x 49.771875 = 56.18571

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question 25 video 3

to find a score as a percentage:

fpr example. 52 out of 80 students got an a star in their eams. what percentage of student got an a sta? 

52/80 = 0.65 0.65 x 100 = 65 percent. 

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distance

A eacher plans a cross country compeition. the course is 3.45 kilometres long. pupils do 3 laps of the course. what is the total distance run by each pupil in kilometrs. 

3.45 km 3 laps 

3.45 x 3 = 10.35

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finding a decimal in a total

0.9 of  a year group of 180 pupilstook part in a school sports day. 

how many pupils did not take part?

0.9 of a year geoup of 180 pupils 

  • 0.9 is is the same as 90 percent. 
  • 0.10 - 0.9=0.1
  • 0.1 x100 =18 
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fractions as decimals

1/4 = 0.25

1/3= 0.3333

2/5= 0.4

3/8= 0.375

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30 percent of 256

0.3 x 256 = 76.8

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finding the mean and range in a table

mean - add up all the figures in that column and dividing by how many there are. 

range - highest - lowest 

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exchange rate

For a school visit to iceland, each of the 25 pupils is allowed to take £40.00 spending money. prior to the visit, the teacher collected the money and exchanged it for iceleand money. 

the exchange rate was 31= 141.50 krona. commission of 1% was charged. 

how much money did each pupil hve after the comission was charged?

1. £40.00 x 141.50 iceland money = 5660 iceland money 

2. comission of 1% = 5560 x 0.99= 5603.4 iceland money 

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when asked for proportion

e.g. proportion of staff days out for prof dev / number of days out for all reasons

25/40=0.65

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last q on video 4

A teacher complies a test with a total of 60 marks. he wants to compare the results with a previos test whose results were out of 75. 

  • how many times bigger is 75 than 60?
  • 75/60= 1.25
  • 60 x 1.25
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percentage change formula

(new value - original value) / original value

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if asked the net increase/decrease or something

What is the net increase or decrease in Tin over the final 3 years?

NOTE TO SLEF-  YOU DONT JUST COUNT 3 YEARS 

YOU ARE COUNTING THE DIFFERENCE SO YOU HAVE TO MAKE SURE THAT THERE IS 3 DIFFERENT TIME FRAMES! E.G 

Year 2  to year 3

Year 3 to Year 4 

Year 4 to year 5 

SEE FOR EXAMPLE YOU HAVE COUNTED 4 DIFFERENT YEARS BUT ONLY 3 DIFFERET TIME SPACES 

For example if you made 210 in year 2 and 50 in year 3 you made a net profit of -160

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if asked the total surface area of a shape or anyt

For example a cube = 4 x 4 x 6 = 96 m 2 (there was 6 sides of the cube)

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A conversion measurement you may need to know

There are 10,000 cm2 in 1 m2,

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Told a percentage and converting it to numbers

we are told that 250 people travel to work in different ways. 21 percent go by car, 12 percent walk e.c.t. So we are asked how many people get to work by walking?

to do this question you simply turn the percentage into a decimal (0.12) and x it by 250 == 30

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volume of a shap

length x base x height

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percentage of a total

total of column divided by overall total x 100 

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putting money as a ratio

bob has £1.50 and david has 2.50. what is the ratio of bobs money to davids money in its simplist form 

  • put into pence 
  • 150:220
  • both multiples of 10 - 15:22 
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surface area

the surface area is the area of all the faces. on a ube there is 6 faces 

formula = l x w 

12 x 12 = 144 

144 x 6 = 864

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volume of a prism

v = s cubed

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