This video provides comprehensive solutions to the 2026 National 5 Applications of Maths Mock Paper 2, covering key topics including depreciation calculations (using compound interest formula), pie chart construction from survey data, mean and standard deviation calculations, area and volume of composite shapes, bulk purchasing value comparisons, percentage profit calculations, box packing optimization, work rate problems with inverse proportion, critical path analysis for project scheduling, volume of composite 3D shapes, net pay calculations with multiple deductions, scatter graphs with lines of best fit, probability calculations with conditional events, multi-currency exchange rate conversions, and time zone calculations for flight durations.
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National 5 Applications Of Maths 2026 | Mock Paper 2Added:
with African math. Today we're on national 5 application maths 2026 mock paper 2 courtesy of Mr. Sarah. So thank you very much there. And remember we've got our last minute live streams the night before exams this Thursday 700 p.m. for national five apps 88 p.m. for higher apps. Join now members only for £4.99. We'll be going for my last minute tips, tricks, predictions everything and you should see what is coming up in that. It is going to make you feel really confident going into that exam on Friday. Now for this question in this paper, this is a bit of a speedrun. I'm not going to rush through the questions.
But it's quite last minute for us all. I wanted to get stuff out there more important than really going in depth. So in terms of the edit, which takes a lot of time, I will probably skip out some of the edits I would usually do, but I'll make sure that any gaps or anything like that are gone. Let's go. Five applications as 2026 mock paper two.
Question one. Trisha bought a car 3 years ago. cost him £8,200. It decreased in value by 18% find the current value to force two significant figures. So I'll do 100 minus 18 and I calculate for half day. So that's 190 82 and change it to a decimal by dividing by 100. 0.82 it's for 3 years.
So I need to do 8200 * 0.82 cubed because it's depreciation.
Get a calculator in and we get 4521.217 4521.217 two significant figures is here. So it's 4500 pound sign and we're done there. Clever Math is sponsored by Leki, the educational publisher for Scotland. They offer viewers of this channel a massive 30% discount. Just use the discount code clever maths at leiscotland.co.uk.
The practice question books go all the way from level three to advanced higher and include national free four and five apps as well. So you can get any book you need for your studies. These are an excellent resource with questions on every topic and contain work solutions so you can see how the marks are awarded. As you go through the book the questions get increasingly difficult so that by the time you finish the book you'll be ready for your exams. Usually £9.99 just use the discount code clea mask to get 30% off that link down below. Okay, question two for national five application master 2026 mock paper two. A new eco group at a primary school carries out a survey to find out what pupils would like to focus on first as part of their environment friendly agenda. Results are shown. So we got plastic reduction, energy efficiency and biodiversity. We have to do a pie chart.
So to do a pie chart you need your total first. So we can add all them up. 210 + 80 + 160 that's 450. And to get your angle, all you do is take each number, divide by 450 or over 450 and times by 360 because it's 360° in a circle. So there's the sum for the first one, but I'll then do the rest of them separately.
210 / 450 * 360 is 168. And I do the same again. 80 / 450 * 360.
calculator 80 450 360 64 and the last one is 160 450 360 is 128.
So there's our angles. These should all add up to what? 360. So you can do a quick check but then we move on to actually draw the pie chart. So any attractive for this you've already got a little bit done. So I'll just do them in order. So 168. I get my P protractor out. I'm going north in the middle.
Make sure I'm going through that zero. I can make my my protractor a bit smaller if I want. So it's going through the zero, but you get the idea.
So there it is there.
We bit smaller so you can really see it.
So I'm going through my zero and then I need to make sure I go 168. So I'm going through the top zero. So that's the top scale. So I just go down to 160 65 678.
Try to be as accurate as I possibly can.
And if I've done that right, it's about there. So I can now move my tractor out the way, get myself a Google and join it up.
So, being as accurate as you possibly can, but don't worry too much if you're out by a degree or two, as long as you're not out by too much. 168 is there. So, that's the first one done.
The next one was 64 or 128. It's up to you. But you get your protractor, you turn it around again so that it's now along that new line. So, you just need to measure it up, get it really, really nice.
I'll just really try my best.
So obviously your lines won't be as thick as this. So you'll be way more accurate than I. But we're doing 68. So 60 65 678 is about here. I'll just go out a little bit because I know that when I do the protractor it's goes too far.
So try to be in line. But obviously on an iPad screen it's not going to be very accurate. It's more about the method rather than me being overly accurate. So and join it up and then you get your pen and there you go. And then the last one we've got to do would have been 128. But what you can actually do because it is the last one is just check that that makes about 128.
So, if I just measure up my protractor now, mine will be out a little bit. So, don't worry too much. I'm not going to redo it just because it's out, but you can see it's in the 120s, which is good enough for an iPad.
So, yeah, I'm quite happy with that. So, I'll get rid of the protractor.
We now need to label it. So, the first bit was plastic reduction.
So, I'll put that there. Plastic reduction.
I'll probably quite often even leave label my angle. So that was 168° or we could put the number of people which was 210 probably a number of people would be best. Then energy efficiency energy efficiency and the number of people there was 80.
And then the last one, biod diversity.
And the number of people there is 160.
Or you could be shading that any have a key to see which each bit is worth. But that's basically as good as you're going to get. You could label your angles if you want.
And that one was at the top.
128, I think. Yeah, 128.
You get the idea, a pie chart. So, we're done there. Question three. Coin records the number of baskets they can score at a basketball court in three minute interval. Find the mean and standard deviation. So, the mean we'll just do by adding. So, it's 6 + 7 + 10 + 9 + 6 + 10 + 8 / 7. I think it is 56 / 7 is 8. So I would usually just write 56 / 7 = 8. Standard deviation start of the exam paper is a formula. I usually use the first version x - xr^ 2 all over n -1 and that's stuck under the square root sign. So you list your numbers.
You've got x 6 7 10 9 and then you've got 6 10 8 and then in the middle is x - xr and then at the end is x - xr squared. So in the middle you take away the mean which was eight. So you get negative numbers sometimes.
10 - 2 is 8. 9 - 8 is 1. 6 - 8 is -2. 10 - 8 is 2. 8 - 8 is 0. You then square them. So if you're doing it in a calculator, take the negative away because 2^ 2 is 4 minus 2 is 4. So you get 4 1 2's is 4 1 4 0. Another quick check you can do is add up the middle. That should come to zero.
2 - 2 0 1 - 1 0 that's zero. Now I do my total. So adding up these numbers 4 5 10 14 18. Now our standard deviation is the square root of 18 over one less than the number of numbers. So we had 1 2 3 4 5 6 7. So it's six.
So in the calculator be careful here.
Square root bracket 18 / 6 close bracket 1.732.
So about 1.73 and we're done there. Now the next bit of the question. Our friend Ryan wants to see how many baskets he can score and under the same conditions. His mean is eight and his stand is 2.4. Make two valid comments between the scores of Quinn and Ryan. So if we look at Quinn, he got a and 1.73.
Take a note of that.
And Ryan has got an A as well and a 2.4 Therefore, on average for the mean their scores are the same A is equal to 8. I could say just to show it. And then the next statement, the next state is about consistency. So the smaller number, more consistent.
Quinn scores were more consistent than Ryan scores.
And you can see why in brackets on the side 1.73 is less than 2.4.
And we're done there. Just make sure you don't mention average when you're talking about consistency. You keep it separate. Five application of math 2026 paper two question one in this mock paper. Diana runs a cafe. She orders a new business card with a logo she has designed. The logo is designed in the shape of a right angle triangle with a quarter circle on top. Calculate the area of the logo. So start of the exam paper. Area of a circle is p<unk> r squ.
However, that's the center. So I need this. So another formula you can use is Pythagoras which is also given like this at the start of the exam paper. So I'm going to use Pythagoras first on triangle. So the first thing I do identify the right angle. If I've got the number opposite the right angle I'm not adding I'm taking away. So I'm going to do let's just call this X to give us something.
X^2 is 4.6^ 2 - 4^ 2. get my calculator.
That's 5.16.
So x is the square t of 5.16.
Again, get the calculator.
2.2715.
So about 2.27 I think would be fine. So that's my length. So now I need to do my area of both my bits.
So let's call that a triangle and a semicircle. One and two for one. It's a quarter circle. So it's a quarter *<unk> * well that's center to outside. So that is going to be 2.27^ 2.
A quarter in the calculator 1id 4 *<unk> * 2.27^ 2 is 4.047. 047 or 4.05. I like 4.047. I don't want to round too much.
Now I'll do two. I'll do my units at the end. Half the base times the height for a triangle.
So a half * 2.27 times the height, which is 4.
1 / 2 * 2.27 * 4 is 4.54.
So now my total area is just the total.
So finally my area equals 4.047 + 4.54 I get 8.587 or 8.6 or 8.59 cm squared. And we're done there. Diana as Kathy serves ice cream in the shape of cones or cups. The shape of a cone is shown. Calculate the volume of one cone.
Start of exam paper. Volume is a third p<unk> r² h for a cone. So that's 1/3 * pi time. Now the radius is half of this. So that's 3.5.
And the height is the height which is 15.
Calculator for that 1 / 3 *<unk> * 3.5^ 2 * 15 1 9 2.422 or about 192.42 or 4 cm and it's cubed for units and that's it. Continued Diana's current supply of ice cream cups closes down.
She must choose a new supplier. She finds free supplies with the following deals. Determine the supply which offers the best deal. So for this type of question, you just need to do A, B, and C. So let's do A first.
100 cups per box, £34 per box. Now here's a special offer. Buy two boxes, get a third half price. You need to work out how many deals they need. So I've got 100 cups per box. So it's 2400 divided by 100 to see how many boxes we need. That's 24. And our deal is two.
and then another box. So that's three.
So the number of deals I need is 24 divided by three which is eight deals.
So cost of one deal is going to be equal to 34 per box 34 * 2 plus get a third of a third off that box.
So to work out a third off I can do a third in my calculator.
£1133.
So 34 minus 1133 2267.
So the cost of that deal is 34 * 2 which is 68 plus 2267 9067 for one deal.
But we said we're going to buy eight of them. 8 * 90.67 67 72536.
So there's deal A.
When I move to build B, 80 cups at 29 per box. Nice and easy. Then I need to do 2400 divided by 80 to see how many I need. So that is 8 is 24 30 30 * 29 all calculator work it's £870 and then we've got deal C 60 cups per box at £26 per box so let's work how many deals we need first 2400 divided by 60 6 fours is 2440 25% discount on total box when you purchase 20 or more boxes. Well, I'm doing 20 or more, so it's just 25% off.
So, it's 26 pound per box. 40 * 26 to start with 1040, but you're getting 25% off. So, you can work out 25% to 1040 and take it away or work out 75% and that will be the answer. So 25% 25 / 100 * 1040 is 260.
Take them away.
1040 minus 260 is £780. So we've got one, two, three answers. Which supplier offers the best deal? The cheapest one.
So a supplier a is cheapest and we're done there. So part D. Last week the Anna had outgoings amount to 1150 and an income to 1350. Calculate percentage profit. So I just need to do the difference over the original time 100us 1150.
Press equals 180 over 1150 * 100 gives me about 15.65%.
And we're done there. Okay. Question five. A furniture retailer sells ready assemble furniture and it's packed into boxes. So it's a box packing question.
The dimensions of each box and internal dimensions of the truck are shown. The boxes must be aligned in the same direction. Calculate the maximum number of boxes that fit in a truck. So the boxes have to be aligned this way up. So that is my limiting factor. The height has to be fixed. So if I write down the height first for height, we've got 310.
And then we can do length and bread. Say we'll call it.
So that's fixed. So option one, the height is 310 / 40 on the other box.
Let's call the length 700 divided by the length on the box, which is 130. And the breadth is 280.
So divide that by the 90. And remember with these ones, you need to round down cuz how many can fit in? So 310 divided by 40 is 7.75. So you just 7 700 divided by 130 5.38. So just five and 280 / 90 is 3.11. So just three. So for option one it's 7 * 5 * 3. he times them together at the end which is 105. But that's not a lonely option because option two the height has to stay the same. So we keep that is fixed but we can just switch out the other two. So you still start always 700 and 280 but you just switch the 130 and the 90. So that becomes 90 here and 130 there. You don't even need to think about it really. You just do it. So 700 / 90 is 7 and rounding down 280 / 130 is 2. So for option two it's 7 * 7 * 2 which is 98. So the max is equal to 105 and we're done there.
Furniture retailer offers to send a team of workers to assemble furniture for a fee. A customer takes this offer due to the large amount of furniture to be assembled. A team of three could take 9 hours. A customer pays extra for an additional worker. All workers are the same way. Start at 9 and take 25 minutes for lunch. Determine the time we finish assembling all the furniture. So this is where it's inverse proportion. when usually you would divide 9 by three to find one worker. But since work's been done, to find one worker, you do the opposite. So one worker is 9 * 3, which is 27 hours, which makes sense. It take longer. Then I'm adding in an extra worker. So I've got four workers now. So I take my 27 and divide by four. That's a calculator job.
6.75 hours. But I need to have hours and minutes to be to use time. So that's 6 hours into times of 75. I just change that by times by 60 45 men.
So that's to start with. But then you take a 25 minute lunch break. So I need you to add 25 minutes.
So that's four 6 hours 45 55 05 10 7 hours 10 minutes. So since it takes 7 hours and 10 minutes, just double check. 6 hours 45, 6 hours 50, 7 hours 10. If we start at 0900, then I need to add 7 hours + 10 minutes.
9 + 7 is 16. So you could leave your answer as 1610 or 410 p.m.
Either of them are fine. And we're done there.
Alistister is going to furnish his new bedroom with furniture from the retail, but decides to ask his friends to help assemble. The table shows a list of tasks and times taken. So, this is going to be one of these precedence tables. We need to use this table to fill in the box. We've already got a done for us.
So, we look for the next none. This one has got none next to it and it's C. So, C is two. And then we continue through there. We need to look for after a and c Let's just look for after a first. After a is B, which is six.
So it looks like the way this has been drawn, B and C lead in up here. So just watch out for that one. We've got lots of options for B and C. So the easiest way to do it is either to guess it or to actually try and work. And I usually just like to guess it then go back and if it doesn't work. So very quickly, if I just put D and E on the top, then after D and E is F and after F is G and after G is M. So that's actually worked. And if that hadn't worked, I would just quickly delete it and go back and put it on the bottom. So now I can put my timings in.
D and E is 20 and 16.
My F is two.
My G is one.
My M at the end is three. And then I'll go back and do after B and C again.
So after B and C, I've got H and I.
So that must go there for six and 18.
After H, well, we've got some sort of J coming in at some place after I is J. So since after I is J, these two are actually going the wrong way. So H and I have to switch places. So I can just delete. So I can go I and H. So you see, you make a mistake, you just go back and fix it. So I was 18 and H was six.
And now I've got after I is J, which is six.
And then after giant H it will have to say is K which is three and after K is L which is five and then we're back to after G and L. So we've done it. Fantastic.
Calculate the minimum time required to complete the job. So we need to find the critical path it's called. So critical path we need to find the longest path.
Now remember things that are happening simultaneously you take the longest of.
So, it's 8 A, then B, and then I've got a choice between this way.
So, I can go that way or I can go that way. And you might just have to check the longest between them is 20. 20 + 2 + 1 22 23. I can ignore that because it's at the end. 18 + 6. So 18 + 6 here is J happening at the same time as I H. H is after B and C. K is after H and J. So H has to have happened but I need to have done I. So it's 18 22 23 24 25 30.
So I think you need to go that way because it's longer than going 20 22 23.
So it's a b i is the longest between h i and h. Then I need to do j then k then l m adding all them up.
8 + 6 + 18 + 6 + 3 + 5 + 3 is 49 minutes.
And we're done there.
of so I put it in the wrong place but 49 men right for added safety Alistister purchases a stack of rubber wedges for feet these wedges are in the pack eight of them the dimensions are shown calculate the total volume so volume this wedge is like a prism we call that we need the surface area time the area of the face times the length so I can split this up into shapes so if I imagine I just go there I've then got a rectangle in the bottom I'll call this one and in a triangle. So, let's just draw out a rectangle as a sketch and a triangle is a sketch. The rectangle is 87 long and it's 12 high. The triangle, well, that's where it gets tricky. I need to take off this 27 here. So, 87 - 27 is 60 long. And the height, I've go 32 to the top, but minus 12. So, actually only 20. So, that's a little bit trickier. Then I do the area of them. 87 * 12. And then for the other one, a half the base times the height for a triangle.
So that's 10 44 and the other one is 600. Adding them together, you get 1644. But that's just the area. So then I need to times by the depth. The depth is 25. So the volume now I've done it in millimeters. So I'll show you how to convert it if you end up doing that because it's easy to miss the question at the start.
That's 41 1 0 0.
So that's millime cubed. And I only want centime cubed, not millime cubed.
So one the way to imagine this is if I had a cube 1 millimeter how many millimeters on a centime is 10.
I have 10 either side 10 by 10 by 10 is a th00and so I need to divide by a th00and to get back to centimeters cubed or you times all of them divide everything by 10 to start with before you start. I'm just going to divide by a th00and.
So that equals 41.1 cm cubed. But that's only for one of them. We've got 8. So 8 * 41.1. And you could have divided by,000 at any point.
That's 328.8 cm cubed.
And we're done there. Five applications of maths 2026 mock paper two question six Archie's annual salary is 53560 national insurance calc four deductions calculate Archie's annual national insurance so it's a a band so I start with that band where the wage is over 5270 so I do 5270 minus 12570 * 0.08 08 or 8 divided by 100. But that's the first one. The second one is above. So I do 53 560 minus the 50 270 and that's at 2%. And then I just add them together. So let's do the first one.
5270US 12570 * 08 is 3016.
53560US 5270 * 0.02 is 6580.
Add them together and you get 3081.8.
So8 is the national insurance.
Archie pays 9.1% of his annual salary pension. His annual tax is this. He's paid in 52 weekly installments.
Calculate the net pay for weekly. So 9.1% and you do 9.1 / 100 times his salary which is 53560 or you can times by 0.091 which I'll just type in the calculator.
That's the same as dividing by 100.
That's 487396.
So that's the pension. So I take the annual salary to get the net. I take away the pension.
I take away the national insurance 308180 and I take away the tax.
So calculator for that 4873.96 minus 3081.80 minus 8461.94 is 37142.3 but I want it as a weekly. There's 52 weeks in a year. So for a week I divide by 52 and you get an answer of 714.275 or 714.28 and we're done there. Great. Question six. Archer works for and analyzes in stocks and question six continued. The company Archer works for analyzes stocks and shares. Arch analyst potential ration stocks for different companies.
The table below gives the price per shen pounds and for two companies and with the on the grid draw a scatter graph. So we just plot the points. So just check your axis place for Chandler against Angus. So 4880 4620.
Now it's going up in twos. So 48.80 will be here. And then we need to go 4620 which is going up in twos as well.
So you just put a little dot or a cross and do another one. 5340 and 4860.
5340 is up there.
And 4860.
So 5340.
Can't even see it.
48.6.
There's the next one. Hopefully 4740.
4620.
There's that one. 51 and 4640.
There's that one.
5380. 4840.
4840.
I think that's that one. 4840 5160 and 4760.
That will be here and 4980 4680 that'll be there. So there you go. What a scatter graph. Draw a line of best fit. So that's when you just get your G and you try and make sure you're going.
It doesn't have to go through as many points as long are equidistant. It doesn't have to go through zero or this bit. So, as best you possibly can, every answers will be slightly different.
I think that looks quite reasonable. It could be moved in a little bit, but I'm fine with that. Use your line of best fit to estimate the price of stock when the price of Angus is 47. Angus is up the top. So, you can just measure along to here, measure down to there, and get 50.8.
So £5080 and we're done there. Your answers might be slightly different for each of that for that question depending on how you plot it.
The social committee archery works for runs a lottery at the end of the month.
The lottery consists of a draw of 23 balls numbered 1 to 23 and a draw of four number balls are drawn and not replaced. These numbers are 6 7 11 19.
If the bonus ball is drawn, calculate the probability the ball is greater than 17. Well, we had 23 balls to start with.
A number over 17 has been drawn, which is one. So, I've now got the number of balls bigger than 17, 18, 19, 20, 21, 22, 23. There usually be six, but I've now only got five left.
And how many balls have been drawn?
Well, I had 23 to start with. I took away four. So, it's five out of 19.
And we're done there. National five application math 2026 mock paper two question seven. Sophia is a travel blogger. Last month she's in Belgium.
She £1,600 for a trip and she's changed it to euros. She stayed seven nights.
The room weight was 9500 a night. She spent 644 and other expenses. She then changed it all to Danish. Calculate how many Danish she received. So I'm going to have to change it into euros first.
So 1,600 * 1.15 is the euro exchange rate.
That's €1840.
Now we need to work out how many euros she let spent. So her room weight was 95 per night.
Stay for seven nights. So times that by seven 665 is what you spent and 644. So I need to take away 6 65 and take away 644 to see how much he's got left.
1840 - 665 - 6 44 I think it was is 541.
And now we need to go to koner. Now you can't go straight to kroner because this exchange rate tables for pounds. So I need to go back to pounds then forward to kroner. The quick way to do that 531 divided by the euro rate to go back to pounds times by the chrono rate.
So you can do it in one go if you want to do it in two goes just to be on the safe side. 46174 I'll just do it in one.
So you got 461.74 and then times by 8.59 is 396635 Danish. Now that is rounded to two decimal places cuz money always is.
Okay. Continued. Last week, Sophia flew from Dublin to Jakarta via Amsterdam.
She got on the aircraft at 16 1850 Dublin time. She got off the aircraft in Jakarta at 2110 V time. She was on the aircraft for 16 hours 40 minutes.
Amsterdam's an hour ahead of Dublin.
Jakarta is 6 hours ahead of Amsterdam.
How long was stop in Amsterdam? So, let's start. This is quite complicated sometimes, but we're in Dublin time at 18:50.
Forget the Jakarta now. She was on the aircraft for 16 hours 40 minutes. So let's add on that 16 hours 40 minutes.
So to add 16 hours, the easiest way to do it is to add 12 hours first cuz that takes you to 650. So if I add the 12 hours first, I'm on 650.
And then I've got 4 hours left. So 6:50 7 8 9 10. And then 40 minutes 10:50 becomes 11:30. So it's 11:30 in the morning.
But that's still dub one time.
She got off Jakarta at 2110.
So I need to find out for Jakarta what time that is in Dublin time or what time Dublin time is in Jakarta time which might be easier. So starting at Dublin time, Amsterdam's an hour ahead.
So 12:30 and that's going to be Amsterdam. EMS I'll display and then Jakarta 6 hours ahead again of Amsterdam. So another six becomes 12 1 2 3 4 5 630.
I'll do that in 24 time cuz that one is 13 14 15 16 17 1830.
That's Jakarta time or Jakarta. Not Jakarta.
So at 1830, which means since she got off the aircraft at 2110, I need to work out the difference. So to go to 2110, which is still the same time frame. Now 18 1920 is 2 hours. 30 to 10 minutes is 40 minutes. 2 hours 40 minutes is how long the stop was in Amsterdam. That's the time it's missing.
So we're done there. It's been Mr. from Grand Maths and today we have done national five applications maths 2026 mock paper 2 cut of Mr. Sarah, remember last minute live stream Thursday 700 p.m. You need to get on this for all my tips, predictions. Link, join now.
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