National 5 Applications Of Maths 2026 | Mock Paper 1

Added: 2026-05-11

[00:00:00]I've got a kind of current maths today on National 5 applications of maths 2026 mock paper one. Cut the sale off Mr Savage, so thank you very much for that.

[00:00:08]And remember we've got a last minute live streams on Thursday at 7:00 p.m.

[00:00:11]for National 5 applications of maths.

[00:00:13]So, members only, £4.99. Get in there for that last minute boost, tips, tricks, and all my predictions. Okay, National 5 applications of maths 2026 mock paper one, question one. Paul baked a cake. In terms of dry ingredients, the recipe Paul used requires flour, sugar, and cocoa in the ratio 6:4:3. Paul used 240 g of sugar. Calculate the total weight of dry ingredients used for the cake. So, I need to identify where sugar is. Well, it's the second one, so four parts are sugar, and we know that four parts equals 240 g.

[00:00:45]So, we can find one part by dividing by four. So, one part 240 / 4 is 60 g. And then we need to find the total weight. So, how many parts have we got? 6 + 4 + 3 parts is equal to 13 parts.

[00:01:04]So, I need to do a sum for 13 parts of 60 times 13. Now, one of the easiest ways to do that is times by 10 and times by three. So, that will give me 600 for times by 10. Then three 60s, three 60s is 18, 180. So, in total, 780 g.

[00:01:28]And we're done there. Clear on maths is published by Leckie, the educational publisher for Scotland. They offer viewers of this channel a massive 50% discount. Just use the discount code [email protected].

[00:01:39]The practice question books go all the way from level three to advanced higher and include National 3, 4, and 5 apps as well. So, you can get any book you need for your studies. These are an excellent resource for 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, at the time you finish a book, you'll be ready for your exams. Usually £9.99, just use the discount code "clear maths" to get 30% off that. Link down below.

[00:02:06]This is a five-mark question for maths 2026, mock paper one, question two.

[00:02:10]Stefano is driving to visit his parents.

[00:02:12]He knows that his car fuel tank can hold a maximum of 64 L when full. Looking at his current fuel gauge, he sees that he's used 24 L since he last fully filled his fuel tank.

[00:02:23]Mark the amount of fuel remaining on the tank.

[00:02:27]Mark the amount of fuel remaining on the tank on the fuel gauge below.

[00:02:31]So, it can fill at 64. We know that. So, we need to know how much each division is worth, so we can count the divisions.

[00:02:39]It goes 1 2 3 4 5 6 7 8. So, to work out one division, I can do 64 / 8, which is 8.

[00:02:48]And it says, "Looking at the current gauge, he sees he has used 24." So, he was full and he's using 24, so that's 8 16 24 will be here. So, we just mark that there with a nice straight line, and we're done there.

[00:03:09]It says, "Stefano drives an average speed of 50 mph. His parents' home is 120 mi away. He is scheduled to arrive at 14:10 plus or minus 15, and he begins his journey at 11:30. Will he arrive on schedule?" So, this is a tolerance question, so we need to write down the max and the min to always get a mark.

[00:03:29]So, the max is found by adding 15 minutes, so that's 14:25.

[00:03:34]And the min is found by taking away 15 minutes, which will be 13:55.

[00:03:42]So, there's the first part of the problem.

[00:03:44]Um it says he's driving 50 mph for 120 mi. So, distance, speed, and time we're doing.

[00:03:52]Distance is speed times time, but we want to work out time, so it's distance divided by speed.

[00:03:57]So, the distance is 120 miles divided by the speed of 50.

[00:04:03]Can simplify that to 12 divided by 5 then and do a bus stop if we have to.

[00:04:09]12 divided by 5 5 and 10 goes 2 2 left over, so we add a decimal point.

[00:04:16]5 * 4 is 20, so we now know it's 2.4 hours. That is a problem cuz that's not a time. So, we can work out how many hours and minutes that is. How do we do the minutes? 0.4 * 60 because there's 60 minutes in an hour. 6 * 4 is 24. 24 men.

[00:04:34]So, we now know that it is 2 hours and 24 minutes.

[00:04:39]So, when did they leave?

[00:04:41]11:30. So, we need to add 2 hours 24 minutes on 11:30. So, 11:30 becomes add the 2 hours 12:30 13:30 add the 24 minutes 13:54.

[00:04:59]Funny question is because the minimum is 13:55 and the maximum is 14:25. So, it's scheduled to arrive between these two times, but it doesn't arrive between these two times. It arrives before. So, does it arrive on the in the schedule?

[00:05:15]No. Because 13:54 is less than 13:55.

[00:05:21]That's a width of over range. National 5 application math 2026 mock paper 1 question 3. Nadia purchases two bags of compost for her flower beds. 3/5 of a bag was used in the rose bed, 5/6 was used in the marigold bed. The remaining is used in the petunia bed. Calculate total amount of compost Nadia used in her petunia bed.

[00:05:44]Give your answer as a fraction of a bag.

[00:05:46]So, first of all, we need to add. So, we need to do 3/5 + 5/6.

[00:05:51]Well, make a common denominator, times by 5, then together to get 30, and then do a little cross. 5 3 6s is 18.

[00:05:59]5 5s is 25.

[00:06:01]25 + 18, well, that's 35 43.

[00:06:06]43 out of 30, which is above 30, so she's used a whole bag. So, simplifying that down to 1 and 13/30 left over. So, how much did she use in a petunia bed?

[00:06:19]We need to get back up to a whole bag from 13/30. The easiest way to do that, 30 - 13 is 17 out of 30 left over.

[00:06:28]And we're done there. Nadia's flower beds are in the shape of a rectangle with a semicircle cut out. The outside edge of each flower bed has a decorative railing.

[00:06:37]Calculate the length of decorative railing for one flower bed. So, this is a circumference question. So, start of the exam paper, C is pi d, but this is half a circle, so we're going to use half of that. So, step one was identify the diameter first.

[00:06:52]Diameter goes from the outside of each bit of the circle all the way along here.

[00:06:57]Now, all the way along is 4, but then I need to take off two halves, which is 1.

[00:07:03]So, that diameter is 3 m.

[00:07:06]So, for our circumference, we need to do pi, which is 3.14.

[00:07:13]It should say in the question to use 3.14 if it's non-calculator.

[00:07:17]Times the diameter of 3, but then we need to divide by 2 because it's half a circle. So, a little bit of maths to do.

[00:07:23]3 4s is 12.

[00:07:25]Carry 1.

[00:07:26]3 1s is 3 + 1 is 4. 3 3s is 9. 9.42 / 2 So, 2 into 9 is 4.

[00:07:37]We're 1 left over. 2 7s is 14, and 2 1s is 2. So, the semicircle bit is 4.71 m.

[00:07:45]But, the decorative railing is all the way around the outside. So, I need to add that on to all the way up the sides.

[00:07:51]So, I've got another side of 2.4 here.

[00:07:53]So, it's going to be 2.4, another 2.4, a four, and two 0.5s, plus the 4.71.

[00:08:04]So, I don't know where I'm up. I've got one, and then I've got 10, 17, 18, 19, 20, 21.

[00:08:10]It's 4.25.

[00:08:13]Carry two.

[00:08:14]4 5 6 7 8 9 10 14. So, it's 14.51 m.

[00:08:21]And we're done there. That's the five application marks, 2026.

[00:08:26]Mock paper one, question four. A cinema research group notes the age of A cinema research group notes the age of the first group of people in the screen one.

[00:08:37]The stem and leaf diagram shows the ages noted for the data for today, the median, lower quartile, upper quartile.

[00:08:42]There's two ways to do this. You could list it over data again, or you can count how many there are. Now, you don't usually have to. N equals 15 tells you how many there are. To find the median, which is the middle, you just add one and divide by two.

[00:08:56]So, the middle start comes at eight.

[00:08:58]Now, if that isn't doesn't give you a whole number, then it goes between the two. So, if you got 5.5, you know it's between five and six.

[00:09:06]So, I know it's the eighth one, so I just count the eighth one. 1 2 3 4 5 6 7 8. There's my median there. 9 192 equals 23. So, 199 equals 19.

[00:09:19]Now, to do your lower quartile, that's the middle of the first half up to nine.

[00:09:23]So, there's 1 2 3 4 5 6 7. So, I just need to go 1 2 3 1 2 3, four in the middle.

[00:09:31]And then, the same with the upper quartile.

[00:09:33]1 2 3 1 2 3, seven's in the middle.

[00:09:39]So now we can do our lower quartile as 14. Our upper quartile is 27.

[00:09:46]Construct a box plot. Now you all use a ruler with this, but for the purposes of the video, I won't because it's very messy. But I will get straight lines. A box plot, you need the lowest number, which is eight. That's where I'm starting. So 5 6 7 8.

[00:10:00]So I draw a vertical line at eight.

[00:10:03]I need the highest number, which is 32.

[00:10:06]So again, 32 is over here.

[00:10:11]And now you need to draw my box around the lower quartiles, 14 and 27.

[00:10:20]So there's my box.

[00:10:22]Going right up there.

[00:10:25]Connect it up.

[00:10:27]Connect it up.

[00:10:29]Using a nice neat ruler, and then finally my median is 19, which is just right here.

[00:10:36]Now use my box up. I'll annotate it so we know exactly what we're talking about. So we'll say that that's the lowest.

[00:10:42]That's the highest.

[00:10:48]Then we've got the median.

[00:10:52]The upper quartile and the lower quartile. Just to be on the safe side.

[00:10:58]Question C, calculate the interquartile range of the ages of the group of people in on screen one. Well, that's just lower upper minus lower.

[00:11:05]So it's upper quartile minus lower quartile.

[00:11:09]27 minus 14.

[00:11:12]That is 13 and we're done there.

[00:11:18]Continuing for question four, a similar research group also noted the ages of the first group of people in on screen two.

[00:11:25]The interquartile range of the ages of the first group in on screen two was nine.

[00:11:32]Make one valid comment compared to the ages of the first to the second. So, interquartile range has got the same statement as standard deviation. It's about how consistent or spread out they are. So, screen one was 13, screen two was nine.

[00:11:48]The ages of the group entering screen two was more consistent is what I usually go for.

[00:12:05]I use more consistent when the number is smaller. So, since nine is less than 13, I'm going to do that there. Now, it's the 5 application of maths 2016 mock paper one question five. Andrew walks his dog up a hill. The hill she uses has the four measurements. The horizontal distance between the top and bottom of the hill is 2 km. I don't think it means it like that, but yes, 2 km long. Right.

[00:12:31]The bottom of the hill is 40 m above sea level. So, I've got to draw the sea in there, I suppose.

[00:12:36]Oh, wait a wee line.

[00:12:37]The bottom of the hill, that's 40 m.

[00:12:41]And the top of the hill is 520 above sea level. So, not an extra 520, but in total it makes 520. So, first step I have to do is 520 minus 40 to get that distance, which is 480.

[00:12:57]So, watch out for that. And then we've got the horizontal or distance which is above the sea.

[00:13:02]And when we connect it up, the horizontal distance was 2 km, but that's different to units to 480 m. So, I make that 2,000.

[00:13:12]And now, start of the exam paper to calculate the gradient. Gradient is vertical over horizontal.

[00:13:21]So, we write that down just from the start of the exam paper. We sub in now.

[00:13:25]480 is vertical, straight up and down.

[00:13:28]Horizontals are going along the way.

[00:13:30]And then, we need to simplify it. So, take the zeros off to start with. It makes good.

[00:13:35]There was lots of ways to simplify it.

[00:13:36]Just try and find numbers that go in.

[00:13:38]You might be able to do it in one go, or you might need to take your time. If you half each number, for instance, you would get 24 over 100.

[00:13:46]If you half again, you would get 12 over 50.

[00:13:49]And I can keep halving if they're both even. So, if I half again, 6 and 25. And no number goes into 6 and 25. So, that's the answer. So, we're done there. Now, it's the 5-minute maths, 2026 mock paper one, question six. A local youth group take part in an orienteering activity.

[00:14:07]The group leave the start point and trek on a bearing of 55° for 350 m to A.

[00:14:14]From A, they trek on a bearing of 165° for 52 m to B. Construct a scale drawing, 1 cm is 50 m. So, I need to work out my distances first. 350 / 50 Well, that is seven.

[00:14:33]So, that's going to be 7 cm.

[00:14:35]And then, 525 / 50. Well, that's a little bit harder.

[00:14:40]So, 50 goes into 500 10 times. There'll be 25 left over, which is half of 50.

[00:14:46]So, it's 10.5 cm. And this is a protractor question, so we need a protractor and a ruler.

[00:14:53]I'll try my best to do this one here, but it's quite difficult. But, I have got myself a protractor, so let's see how we go with this.

[00:15:00]So, first of all, most people's protractors won't look like this.

[00:15:05]You need to get it vertical first.

[00:15:08]So, you can actually use it.

[00:15:10]And then, you measure it. From the middle, goes on the start bit, through zero, and we're going to measure around 55°.

[00:15:19]So, 55° will be about there.

[00:15:23]So, we mark that as our place, maybe just a dot.

[00:15:30]Uh now it's stuck to my thing because it's So, maybe I can just do that and do that. And then that means I can get rid of this protractor.

[00:15:41]So, we just delete it in there.

[00:15:43]And now I've got my mark. So, we get our ruler. We turn it around so that it's measuring around the correct way. We make sure we're going through zero.

[00:15:53]Measuring right up through that as accurate as you possibly can.

[00:15:57]You want it to be 7 cm.

[00:16:00]So, you get your thing and do seven.

[00:16:04]Now, I'll not be massively accurate on here. I'm going to be honest with you, but you'll get the idea of how to do it.

[00:16:08]So, once you've done that, we just mark on what we've done.

[00:16:12]That was the 350 m.

[00:16:16]And that was taking me from A to A. So, we're now at A.

[00:16:21]Next step is we need a new vertical line. So, you get your ruler cuz there won't be one drawn for you.

[00:16:27]You get it as nice and vertical as you possibly can.

[00:16:31]And you just draw at the end of that a new north line.

[00:16:35]Label it north and start again.

[00:16:38]From checkpoint A, we go 165.

[00:16:43]So, I get my protractor back.

[00:16:47]165 is what I need. I'm just going to zoom out a little bit so we can see.

[00:16:51]So, turn that around. Now, if it's below 180, you're good to go. But if it goes above 180, then you need to turn that around and add on the extra. And what you have to do when that happens is you draw your north down the way and go around. So, let's say it was 220 for instance just to show you this. If I wanted to go 220, I would draw that down and then I would go an extra 40 cuz 180 + 40 is 220. And I would join it up to there. But, for this question, we're good to go.

[00:17:20]So, turn that line to north again.

[00:17:24]Straight through the zero, being as accurate as you possibly can, and it wants us to go 165.

[00:17:31]165 is down here, 160, cuz I'm through this one, outside scale.

[00:17:36]165 would be about there. So, again, I just mark that on. I'm trying to be accurate.

[00:17:46]It'll be easier but if I try and mark it too much, what happens is it gets marked onto the actual picture, so when I get rid of it, it's gone. See? So, that I need to be careful with that. But, you don't have to be careful with that.

[00:17:57]We're measuring the line that's 10.5.

[00:17:59]So, again, it's for my new position.

[00:18:03]Starting at zero.

[00:18:07]Through there.

[00:18:10]I think that's good.

[00:18:12]All the way down.

[00:18:14]I think it's about where we left off, 10.5.

[00:18:20]Here you go. Mark.

[00:18:24]10.5 is about there.

[00:18:27]Oh, I went too far, but you get the idea.

[00:18:31]And that is a position B.

[00:18:35]So, we've went to position B for 525 m this time.

[00:18:42]And we're now there.

[00:18:46]So, if the construction scale drawn on the LCA course, we've done that. Part B, the group then returned to the start from trade point B. Use your scale drawing to determine the distance and bearing. So, we've got two things, distance and bearing. Let's do the distance first, cuz that's easier. We'll get our ruler.

[00:19:01]We'll find our zero.

[00:19:07]We'll measure that line.

[00:19:10]So, my zero is there. Where's the start?

[00:19:13]I'm getting about 10.5, maybe 10.6.

[00:19:16]Let's call it 10.6 for my one. You could even join that up, by the way, if you wanted to.

[00:19:21]And then measure the line.

[00:19:23]But yeah, I'm getting 10.6.

[00:19:25]So, let's just take a note of that. 10.6 cm times by 1 to 50. So, I need to times by 50.

[00:19:37]So, that's 106 * 5. 5 * 6 is 30. 5 * 0 is nothing + 3. 5 * 1 is 5. 530 m. And now I need the bearing. So, to get the bearing, you need to have another north line.

[00:19:51]There's actually two ways to do it. I'm going to show you both ways. See which one you prefer.

[00:19:57]The first way to do this is draw another north line as normal.

[00:20:02]Get your protractor back in. And measure how far around it is from north all the way until you get here. Now, the problem is I'm going to go past 180. So, if that happens, you can extend your north line down using a ruler.

[00:20:19]Get your protractor.

[00:20:22]Turn it around so it's the other way.

[00:20:24]And go right in the middle. So, you're going down through that new zero.

[00:20:29]And measure up to that line. So, if you measure up to that line, if I zoom in a little bit, you should be able to see around 120, 121 2 3 4 5. 125 almost exactly. But then that's added on to 180 because you go around 180 first. So, it's 180 + 125.

[00:20:49]So, hopefully that makes sense. 180 + 125. I'll just get rid of that.

[00:20:56]So, 180 + 125 That's 180, 280, 305 degrees.

[00:21:06]530 m. And we're done there. Now, there was one other way you could have done the bearing part, and it's you could measure round to here, and when once you know that, that means that these two add up to 180, so you just take away from 180 to get that angle, and then take away from 360. That seems probably an odd way to do it.

[00:21:23]Let's see how accurate we are.

[00:21:26]Cuz Mr. Sears done this, he got 306° and 515.

[00:21:30]I got 530° and 305. So, I'm a little bit out with my distance, which I'd expect on an iPad, but my degrees was actually quite good, so I'm quite happy with that. You'll be allowed out a little bit, but you need to be as accurate as you're supposed to be. And on paper, you'll be much more accurate than me doing it on an iPad, okay? That's the five application of maths 2016 mock paper one question seven. Christine works in a dairy. She earns £14 per hour. She's paid time and a half.

[00:21:56]In September, she worked 110 hours plus some overtime.

[00:22:00]For overtime, it's time and a half.

[00:22:02]In September, she paid a total of 124.39 in deductions. Her net pay was 1625.61.

[00:22:09]Calculate the number of hours Christine worked overtime in September. So, it's a working backwards question overtime this one, which is a little bit tricky. So, if we've got our net pay, what she gets paid in terms of what she earns is before deductions, so I need to actually add on 124.39 to get back to what she had before we took anything off. So, 9 + 1 is 10, 6 7 8 9 10 again.

[00:22:35]5 9 10. And this would probably be a grade A question. 2 4 5 6 and 1 is 7 1.

[00:22:41]So, she was actually paid 17.50.

[00:22:46]So, now she worked 110 hours plus some overtime.

[00:22:53]We need to work out the overtime, but we already know she paid 110 hours, so 110 * 14 I can work out to see how much that comes to.

[00:23:01]So, I can times do the same trick. Times by 10 first to get 1,100 and then times by four. Four nothings is nothing.

[00:23:08]That's 440.

[00:23:10]1,100 1540.

[00:23:13]So, whatever the difference between 1750 and 1540 is is how much overtime money she was paid. So, 1750 - 1540 being very neat.

[00:23:25]That's 210.

[00:23:28]210 overtime.

[00:23:31]How much overtime How much is she paid for overtime? Time and a half. So, not 14 for overtime it's always a half more.

[00:23:40]Times it by 1.5.

[00:23:42]That's 21. You can work that out by times by 1.5 or just adding on a half of 14.

[00:23:48]So, that means I need to divide by 21 and we get 10 hours.

[00:23:54]And we're done there. That's the five abacus maths 2016 mock paper one question eight. A fizzy drink company surveyed 20 of its own employees on how they would rate the quality of the drink that their company produces. The results are displayed in the table below. Five people said excellent, 13 very good, two good, zero poor. The company uses results to claim that 90% of the people rated the quality of their drink to be very good or better. Well, isn't 90% at least 13 + 5 is 15 870. Yeah, it's it's probably above 90. What what's wrong with that? Well, the simplest explanation you can say is it's biased.

[00:24:26]They were own employees which means they're predisposed to say the drink at my company is better. So, it's bias.

[00:24:36]Okay, moving on.

[00:24:38]The company then surveyed a random selection of the general public. That's better.

[00:24:42]On how they would rate the quality of the drink that the company produces. The results are displayed in a pie chart below. Love pie charts.

[00:24:49]The company claim that based on our survey at least 60% of the public quality to be very good or better. Is that correct? So, I need to work out does this pie chart give me 60% for very good or better? I've only got fractions in decent I've only got the angles to deal with, so I can only use them. So, very good is 2128.

[00:25:12]And I suppose excellent as well could be included. So, 8 and 2 is 10, 7 8 9 10, and 2. 200°.

[00:25:22]But, a pie chart is out of 360. So, I now get a fraction. So, that's the the method. And all I need to do now is change this fraction, I see all I mean it may be tricky, to a percent. So, easiest way to do that is let's take the zeros off.

[00:25:40]And then let's see if it simplifies. So, two goes into that 10 times, and then that's 18.

[00:25:46]Two goes into 10 five times, and two 18s is nine. So, I've got this fraction 5/9.

[00:25:52]So, an awkward one. So, there's no choice but to divide.

[00:25:56]So, I'm going to do 9 5 / 9.

[00:26:00]9 into 5 does not go. Add as many zeros as you want.

[00:26:04]Add a five.

[00:26:05]9 fives is 45. Add a five. 9 fives is just going to keep going like that.

[00:26:10]0.555. As soon as you start repeating yourself, you stop. As soon as you start repeating yourself, you stop.

[00:26:17]Sorry. Anyway, 0.555.

[00:26:20]To change that to a percent, you times by 100. So, it's going to be 55.555 forever or about 55.6%.

[00:26:31]So, did is the company's claim correct?

[00:26:34]No, 55.6 is less than 60%, and we're done there.

[00:26:41]So, just a note on this, there are other ways to do this question. I'm going to show you what Mr. Sailor came up with in his marking scheme.

[00:26:47]Mr. Sailor said that you could do calculate 6% as an angle which is 216. So, 60% of 360 and then see well, 200 is less than 216. So, that's one way to do it if you preferred. Or you could do 5/9.

[00:27:05]And 60% you could say is 3/5 and then compare them and say well, you've got 15/27 and 15/25 making the same numerators instead of the denominators for change. And that means that you can see that one's more than the other. But, either way, that's how you could do it.

[00:27:20]It's been quite a math. It's been quite a math today we did National 5 Applications of Maths 2026 mock paper one courtesy of Mr. Sira. Hopefully, you found that useful. Grab it on my website, download it, give it a go. And remember, last minute live streams Thursday 7:00 fit Remember, last minute live streams Thursday 7:00 p.m. You need to jump on that. It's going to go for all my predictions, tips and tricks, and all good to know questions for the National 5 Applications of Maths exam. Let's do this. £4.99. Join now.