have you just sat the test?I'm due to sit it on saturday and this has just thrown me off :(

I’m glad you asked this question. Sorry it’s taken me so long to reply, I wasn’t aware of all the comments until now, but hopefully this will be useful for many other students. Trigonometry students often tell me that in their classes at school, they’re given a right-angled triangle, and usually only given only one of the other angles. Trig Ratios (sin, cos and tan) are part of a bigger subject, Trigonometry, which includes everything to do with measuring triangles. Pythagoras’ Theorem is part of Trigonometry, but also, so is the fact that the sum of the interior angles of a triangle is 180 degrees. This fact is key to answering your question. If you are studying Trig Ratios, you will likely already know that the sum of the interior angles of a triangle is 180 degrees. In a right-angled triangle, one of the three angles is 90 degrees, so the other two always add up to 90 degrees. That means that you never know only one of the other two angles. If I only tell you that one of the other two angles is 80 degrees, you still know that the other one must be 10 degrees. Similarly, if I only tell you that one of the other angles is 40 degrees, you still know that the other one must be 50 degrees. In every Trig Ratios question where you’ve been given a right-angled triangle and been told one of the other angles, you have always known the other one, you’ve just ignored it. So if you’re told both angles, just ignore one of them. Cross it out of you like, and then it turns into one of the questions you’re familiar with. Hope that helps.

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

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.

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.

Thanks for taking the time to say so, Louise. Hope you passed?

Daisy Doo €200/ 1.25 = £160 £160 - £100 = £60 £60 x 1.2 = €72

Aw thank you went the wrong way with multiplying first!

@@jezeldjones should it not be £60 x 1.25 = €75

No, 26 miles there and 26 miles back means two journeys of 26 miles per day. Over five days that means 10 journeys of 26 miles, a total of 260 miles. She estimates using 0.1L of fuel per mile, so 26L in total. Each litre costs £1.30 so the cost in pounds is 1.30 x 26. To calculate 1.30 x 26, I'd suggest splitting the 1.30 into one unit and three tenths. One times 26 is 26, a tenth of 26 is 2.6, so three tenths of 26 is 3 x 2.6, which is 7.8. So the total cost is 26 + 7.8 = £33.8 (On reflection, that's probably a bit difficult compared to the actual test you'll face, but hopefully good exercise)

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 :-)

Hi Jack, I think you're right. The 4th test will be a bit easier, but I still think it's good exercise which is the main thing. And it also allows lots of other people to comment, so you can see what they think. If they're all saying the same, chances are you're right, I guess. I'd rather you found the real thing easier than you find this easy and then get a nasty surprise in the real thing.

Yeah - I totally agree. I passed both my tests first time and I honestly believe they were much easier than even the practice tests that the DfE offer. Either way, Gareth, thanks for these as I know it probably took a long while to orchestrate.

Thanks for taking the time to say so. Yes, it did take a while to think about how difficult the questions should be and what sort of mix, and to work out how to edit it and create a KZbin channel etc, but it's great to hear positive feedback such as yours and to know I've created something useful for people across the country. I've had people contact me from Bradford, Hull, Walsall, London and who knows where else - I really wasn't expecting my amateur videos to get 40,000 views or whatever it is now.

do you really think they're easier than the practice tests? lol.. I sat my Literacy and was done in 15 mins mind, and passed, was easy, but have worried so much about the numeracy that I have postponed it for two weeks! If it's easier, I might just go and give it a go this week!! :)

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.

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.

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

9

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

where from the 60 percent

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

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

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.

Please could you explain this a bit more?

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.

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%.

They're in the description (click show more) but I've copied them here too. Answers: 1. 72 Euros (1:00) 2. 65% (2:25) 3. £16,500 (3:10) 4. 11/40 (4:21) 5. 14:56 (5:30) 6. 60 (6:53) 7. 252 (7:32) 8. £52 (8:31) 9. 85 miles (9:40) 10. 10 lessons (10:37) 11. £33.80 (11:55) 12. 125 miles (13:22)

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.

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

Lovely to hear. That's my intention; rather than to try and create something comprehensive, to fill the gaps that I see. Thanks for the encouragement, it helps motivate me to do more.

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

Many thanks, I can see that now

Correct. There is more than one way to work out those calculations without a calculator, for example: 480 x 25p = 120 x 4 x 25p = 120 x 100p = 120 x £1 = £120 £120/5 = 2 x £120/10 = 2 x £12 = £24.

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

You're welcome. Thanks for taking the time to say so. A "thumbs up" will help others to find the video as well.