QTS Numeracy Skills Mental Arithmetic Practice Test 3

[@bencalvert4443]

These questions seem much more complicated than the practice ones provided through the Department of Education. They've really knocked my confidence.

[@garethlewis3023]

Sorry I didn't read this sooner Ben. These are designed to be good exercise and preparation. I can't guarantee they'll be exactly as difficult as your test, not least because everyone is different, but rest assured, almost all of my students thought these were harder than their test (which they all passed). I'm working on a fourth test, which I've made a little easier following feedback from those who've passed their tests.

[@vickytaylor9492]

Passed second time, key is plenty of revision, the QTS book was great and yes times tables - know them off by heart and be able to translate fractions to percentages in your head. Thanks

[@F--B]

Hi Gareth, I passed my test the other day, having used your videos extensively. They're such a useful resource, in addition to the official practice tests. As others have mentioned, they are a tad on the difficult side, but I appreciated the extra challenge. If you ever have a chance to do more, then I'm sure they would be a massive help to many more people - as a skills-test student, the more practice tests you have at your disposal the better. Anyway, thanks for all your time and effort. Do you have a tips jar or anything that I can donate to?

[@Chris-fr8ox]

Gareth, I have a question related to graphs on the QTS test, cannot find the reasons why anywhere. The question is based on a line graph. Along the X-Axis are: Year 1, Year 2, Year 3, Year 4, Year 5, Year 6, Year 7, Year 8 & Year 9. The graph doesn't start until its above the year 2 line. The question asks you to at which point the school makes the most progress, its obvious where it is.. HOWEVER It goes up from the line of year 6 (so i thought that was the answer) the correct answer is 7, but that's where the 'most progress point ends' confused why it is year 7 and not year 6. Hopefully that makes sense! hard to explain on here. (I can email you a screen-grab if that is easier? it won't let me post pictures on the comments here!)

[@olasoi2004]

5. 52*7 = 364 total in 7 coaches 52-8 = 44 number in the 8th coach bcos 8 seats free Add 364 = 44 = 408 total numbers

[@olasoi2004]

11. 3.5 div by 100 moves decimal place 2 places to the left 0.035 ANS

[@nessa945]

olaitan kolawole i hope you are still using this handle can you please help me with mental arithmetic like tricks to solve them quickly I wl give u my number

[@olasoi2004]

6. 21/24 Proportion at or above reading level 3/24=1/8 Proportion below the expected age ANS 1/8

[@StephanieJohnson-gt5ks]

These questions are nothing like the ones on the actual test. They are a lot harder and a few are unrealistic to work out in the time frame mentally. If you want to practise with similar questions to the test, go on the GOV's website practice ones and buy skills test books, which have questions in that someone can read out for you. There's probably 2 questions on this video that are similar to the test. I wouldn't practise using these videos because their ridiculously harder than the actual test.

[@garethlewismathstuition5240]

Hi Stephanie, thanks for the feedback. I agree that the questions are towards the harder end, I've had that feedback from others as well. I would rather it be that way than have people think they were too easy and didn't prepare them for the test. I suggest students use these tests in addition to the resources you mention. I will be uploading a new test soon that is a little easier, based on feedback such as yours, so thank you for adding to that feedback.

[@garethlewismathstuition5240]

Again, really appreciate the feedback. One mark's nothing. Good luck next time. My tip - memorise your times tables off by heart up to 9 x 9.

[@markwhite1689]

His earlier tests were difficult but I feel this is close to the standard.

[@tusonla]

9

[@tosin8082]

Hey thank you for this video. please are able to explain the questions?

[@olasoi2004]

8. Area L xB 6.5m *4.5m =29.25 m2

[@olasoi2004]

4. 27*2 = 54 28*2 = 56 56=54 =110 77/110 *100 = 70% those that failed to gain 100% - 70% = 30%

[@olasoi2004]

2. 36/60 = to Per 3/5 * 20/20 = 60/100 ANS 60%

[@garethlewismathstuition5240]

This is Q1, but otherwise correct. 36/60 is equivalent to 3/5 when simplified, which is equivalent to 60/100, or in other words 60%.

[@babypink001]

Hi. I just wanted to say thank you for your videos. Ive done all 3 of the mental arithmetic tests you created. some of the questions were a bit tricky but ive learnt from my mistakes. I was just wondering, when will you make a 4th video? I'm pretty sure I read in the comments section that you said you were working on a 4th test? Thank you

[@garethlewismathstuition5240]

Hi, thanks for your comment. Yes, I did. I've got pretty much done on my phone, I've just got to remember how to edit it and upload it as I've not done one for a while. Apologies for being slow, I'm tutoring seven days a week at the moment, but I'll have a look and see if I can do something. Thanks for the nudge :-)

[@saharasahaja]

I have my skills test in 11 days! Do you think these tests are still at the same difficulty level of the real tests? I've heard the tests have been made harder!

[@olasoi2004]

7. 30km v= 45km/h v=d/t so t= d/v 30km/45km/h = 2/3 hrs 2/3*60 = 40 minutes must multiply by 60 to change to minutes ANS 40 min.

[@natashawarwick5883]

Thanks for the help on this answer. I have been stuck in it for ages.

[@olasoi2004]

4. 100 /7 = 14.29 pupils 14 groups 0.29 are humans so must form another group 14 groups plus an extra one ANS 15 groups

[@garethlewismathstuition5240]

This is about Q3 rather than Q4. The 14.29 figure you refer to is the number of groups rather than pupils. Fourteen groups of seven pupils makes 98, and so the other two pupils must form an extra group to make 15 groups in total.

[@sarahaminah81]

Hi everyone, I'm struggling to work out question 12! Any ideas? Thanks!

[@FELKADEL]

1=5/8 120 times 5/8=75miles

[@saharasahaja]

Many thanks, I can see that now

[@olasoi2004]

3. 170 * 0.30 170 *30 = 510 so moving decimals 170 * 30 = 51.0

[@or8duckk]

Please could you explain this a bit more?

[@ministryoftruth8499]

Jess Telford Question 2: What is 170 multiplied by 0.3? Step 1: realize that 0.3 = 30% (multiplication of whole numbers by decimals = calculating percentages). So, the question is equivalent to 'What is 30% of 170?' Step 2: 10% of 170 is? 170/10 = 17 Step 3: 30% of 170 is 3*17 = 51. So, 170*0.3 = 51. EDIT: This was the fastest way I found to work out this solution. It's worth to keep in mind, different people might be faster using different approaches.

[@ragpot]

Q7 - 30 KM and 45 KPH - what is the logic approach to this - is it that 45mph is 3/4 of 60mph (assuming 60mph = 30 minutes) therefore 30/3 then x4 = 40minutes?... or is there a more sensible approach?

[@ragpot]

or is it 30/45 = 2/3 = 40/60 = 40 minutes?

[@garethlewismathstuition5240]

You can use proportional reasoning here. i.e. If travelling at 45km/h you would travel 45km in one hour. Then for example, you can say that because 30km is 2/3 of 45km, travelling at the same speed, it would take 2/3 of the time, in other words 2/3 of an hour, which is 40 minutes.

[@garethlewismathstuition5240]

Alternatively, you could use the relationship (Average) Speed = Distance/Time (Elapsed) This is often abbreviated to S = D/T Any formula of that form can be rearranged in the same ways: The numerator (in this case D) is always equal to the product of the other two quantities. So, D = S x T The other two quantities I would describe as something like "interchangeable denominators" - you can swap them round. So S = D/T means T = D/S No matter where you encounter these formulas, the rules are the same. For example, in Physics: Current = Voltage/Resistance I = V/R (I is often used rather than C to denote current) The numerator equals the product of the other two quantities (so V = I x R) and the denominators are interchangeable (so R = V/I). In Geometry: Area of a rectangle = Length x Width A = L x W The numerator equals the product of the other two quantities, so in this relationship, A must be the numerator when you rearrange it, and the other two quantities are interchangeable denominators, so: L = A/W and W = A/L If dealing with Unit Costs: Total Cost = Unit Cost x Number of units T = U x N Again, T is the product of the other two quantities, so it must be the numerator when the formula is rearranged, and U and N must be interchangeable denominators, so: U = T/N and N = T/U Hope that helps.

[@howjamieson123]

Can you explain Question 3? 15 groups would only be enough for 105 pupils?

[@garethlewismathstuition5240]

+Howard Jamieson Fifteen groups is enough for 100 pupils too. Some of the groups will have fewer than seven pupils. We need 15 groups because 14 groups would only have space for 98 pupils (14 x 7).

[@lucijecurri7423]

GREAT!!!!!!

[@fatimab6006]

hi for question 8 ive ended up with 292.5 could you show me where ive gone wrong plz

[@garethlewismathstuition5240]

+Fatima B Area of a rectangle = length x width. 4.5 x 6.5 = (45 x 65)/100. It looks like you divided by 10 instead. This is where estimation is very useful. The result of 4.5 x 6.5 should be between 4 x 6 and 5 x 7 (i.e. between 24 and 35). This enables you to reject answers like 292.5 immediately as being much too big, and is particularly handy for the QTS Skills Test, because it is very punishing. Unlike in GCSE Maths, in the QTS Test, if you make one mistake like yours above, even though you may have got 99.9% of the question correct, you will get no marks for that question. This is at it should be though; I wouldn't want a nurse, say, to get 99.9% of a calculation correct and then inject me with a - possibly fatal - dose of a drug that is ten times bigger than it should have been.

[@staceysmail7214]

please could you explain question 10?

[@garethlewismathstuition5240]

+stacey Smail 1.4 EUR: 1GBP means 140 EUR: 100GBP (exchange £1 one hundred times). Similarly 1.3EUR: 1GBP means 130 EUR: 100GBP. The extra amount in Euros is 140 - 130 = 10 EUR.

[@julianbaker6479]

I got 72mph on question 12. Seem to be 3 short! So....if 10k=6m and 100=60m to get to 120 do I not use 60(for the 100) and 6x2(for the 20) 12+60=72. I know that 5km is equal to 3m but they are asking for 120 (HELP!!)

[@garethlewismathstuition5240]

Hi Julian, there's nothing wrong with your method or calculation, except for the fact that the question specifically asks you to use a different approximation instead of the one that you used. It says 1km = 5/8 mile in the question, which is equivalent to saying 8km = 5miles. Your approximation of 10km = 6miles is a valid one in general, just not for this question, because it specifically requested otherwise. The QTS test tends to use the approximation I gave, but in any case, it's particularly important to note small details such as this because the test is harsh in this regard; one small detail incorrect and you lose the mark for the question.

[@nanammieh5974]

can you explain question 7 please

[@KikiEmmons]

Hey, I did: 45km = 60 mins 90km = 120 mins 30km = 40 mins Hope that helps!

[@garethlewismathstuition5240]

+KikiEmmons Thanks. That reasoning is fine. There are alternatives too. An average speed of 45km/h means that 45km would take 60 minutes. You can then deduce how long it would take to travel other distances by using proportional reasoning. i.e. going twice as far (for example) would take twice as long. There are many ways of doing this. Kiki multiplied by 2 and then divided by 3. One alternative is to divide by 3 first and then multiply by 2. So, 45km takes 60 mins 15km takes 20 mins (I've divided both the distance and time by 3) 30km takes 40 mins (I've multiplied both the distance and time by 2) You could even multiply directly by 2/3 (but there's no need to do this): i.e. 45km takes 60 mins 30km is 2/3 of 45km, so it will take 2/3 of an hour, in other words 40 minutes. ***With calculations involving time, beware that unlike a lot of other measures, time has not been decimalised, so there aren't for example 100 minutes in an hour.***

[@garethlewismathstuition5240]

An alternative to the above is to use the formula "Average Speed = Distance / Time". Rearranging the formula to make time the subject gives a formula for time of "Time = Distance/Speed". So the time taken (in hours) is 30/45. Simplifying that fraction (divide the numerator and denominator both by 5 and then both by 3 for example) gives 2/3. Two-thirds of an hour is twice as much as one third of an hour, and one third of an hour is an hour divided into three equal parts. If you divide an hour into three equal parts, that's 20 minutes each, so 2/3 of an hour is twice that, 40 minutes. Hope that helps.

[@MollyLovesToasters]

Can you explain question 9? I have got 209 but you have got 207

[@garethlewismathstuition5240]

Hi +Molly Craney sorry it's taken me a while to see your question: 40% of the 345 pupils walk, which is 138 of them. The remainder do not walk, which is 345 - 138 = 207. There are a few ways to calculate the 40%. For example: 10% = 34.5 40% = 4 x 34.5 = 2 x 2 x 34.5 = 2 x 69 = 138.

[@lucijecurri7423]

IF I find 1.5hours is 1hour 30 mins Hence 0.66 is 66*6=39.6 ~40 mins (2d.p)

[@garethlewismathstuition5240]

1.5 hours = 1hr 30 mins = 1 1/2 hrs = 3/2 hr ("three halves of an hour"). 2/3 hr ("two thirds of an hour") = 40 minutes precisely. HTH

[@lewisforbes2218]

where do you find the answers??

[@rupjjel3580]

Lewis Forbes x

[@devonjohnson2688]

answers?!

[@clincpb8903]

Answer 10 should be 14 euros not 10 ??

[@garethlewismathstuition5240]

100GBP x 1.4 = 140EUR (Post Office) 100GBP x 1.3 = 130EUR (Airport) So the difference is 10 EUR Hope that helps.

[@olasoi2004]

9. 40% walk 345 Do not walk 60% 345 10% 34.5 60% 34.5 * 6 = 207.0

[@godfather3984]

where from the 60 percent

[@garethlewismathstuition5240]

The percentages for walking and not walking must make 100% in total, so if 40% walk, the remaining 60% don't walk.