Eduqas / WJEC - GCSE Maths Foundation - May / June 2017 - Paper 1 - Worked Solutions / Walkthrough

Ajouté : 2026-05-14

[00:00:07]So, welcome to my work solutions for the Educas WJC GCSE Foundation from the summer 2017 series, which was actually the first in the current series. But anyway, it's paper one, component one, whatever you want to call it. Let's leave our calculators in a drawer and get on with it. Question one. The table shows some words that may describe the numbers 1 2 8 or 9. And the column for one has been done for you. Let's go for the column two. Is two a prime number?

[00:00:43]It is. It's not odd. It is even. So tick. And it's not square and not cube.

[00:00:50]By the way, each column correct. Give yourself a mark. Any mistake in a column nullifies that column. So unfortunately one mistake per column you score zero out of three. Onto number eight. Prime number it's not odd. It's not even. It most certainly is. And eight is also a cube number. 2 cubed. 2 * 2 * 2 gives you 8. Onto nine.

[00:01:22]Nine is not prime, but it is odd and it's also square. 3 * 3 gives us nine.

[00:01:30]There we go. It's basically two ticks per column. Doesn't always work out like that. So, don't try and look for any patterns and stuff like that. Not worth it. Just go one at a time. Question 2 A.

[00:01:44]Unusual to have these, but it has cropped up a couple of times. Uh, this is now the second time I've done it, Freddy Cass, and I've been working backwards. So, unfortunately, yeah, you got to write the whole thing out. I'm not going to bother. I have done on my uh on my model answers, it is 67.31 is less than.

[00:02:12]Okay, less than, not less than or equal to and no other inequalities. You get a mark for the correct inequality. It's a less than. And then you've got 700. Get your numbers right for the second mark.

[00:02:29]On we go. Part B. Work out the difference. Difference means subtract between the value of the eight and the value of the five. The eight is in the thousand's column.

[00:02:47]The five is next door. It's in the hundreds column.

[00:02:52]We need to subtract. Whether you do it mentally or column, it's entirely up to you.

[00:03:00]But whatever way gets you to 7,500 is a good way of doing it. Number three, got some pictograms.

[00:03:09]Alice asks a group of students, "What's your favorite type of music?" and the pictogram has the results. Now the key you'll notice does not have a number of students. So that's obviously going to be one of the questions. Let's have a read through. 20 students chose pop.

[00:03:32]How can 20 be represented by one full circle, two full circles, and half a circle? Well, that would be 8 + 8 plus half of 8 four. So the key the full circle represents eight students.

[00:03:53]Write down the modal. Modal means most just like mode means most. There are more for rock than any other. Quite right too. How many students answered Alice's question? Let's go back to rock.

[00:04:11]Each full circle is eight. So it's 8 8 and a4 of 8 will be two gives us 26.

[00:04:21]Other music that's eight. 34 of 8 is three twos. Six meaning other is 14.

[00:04:32]You need to add all them up. 26 14 is 40 and the 20 gives us 60.

[00:04:40]Question D. How many more chose rock than other? How many more is another way of saying difference? 26 take away 14.

[00:04:52]You've got four marks for your pictogram work.

[00:04:57]But part E, more but not the same. Draw a bar chart. Take all your numbers from here. 26 for rock, 20 for pop, 14 for other. And when you come to draw a bar chart, what are they looking for for your marks? Well, as you can see, it's worth three. You will get one for your labeling. Both frequency and type of music are absolutely essential. You'll get one mark for the heights being correct.

[00:05:34]So whatever scale you've chosen on your yaxis and I'll come back to that must be applied correctly. And your third tick is for those scales in the axes. So 30 20 and 10. And for your horizontal axis they're not that bothered about how whether you've got gaps or not. Although I think you should have cuz it's discrete data not continuous. They are more bothered if you've got bars of unequal width. So if rock was two bars wide and pop was one and a half and other was one that's just wrong on so many levels. So as you can see I've kept my width to one bar.

[00:06:25]You could have done two. There's enough room for two, but it must be consistent.

[00:06:31]Just like the y-axis must be consistent.

[00:06:35]So, tick for heights, tick for labels, tick for consistency. That'll do for your three.

[00:06:43]Number four, draw two more lines on the diagram. So, the shape has exactly three lines of symmetry. It's a strange way of saying, basically, put the other two lines of symmetry on. So from one corner to another, from one to another. I normally will nag that you should be doing it with a ruler. So I am going to do it. But the mark scheme does actually specify accept good quote good free hand. But for me, I think free hand is bone idle.

[00:07:22]Use a ruler. Why not?

[00:07:26]Part B, Renata says this shape has rotational symmetry order four. Now, she would be correct if it wasn't for the shading. So, words or phrases to the effect that it's actually got order two would be correct. Give yourself a tick.

[00:07:47]Or the shading stops it from having order four. Again, things along those lines. Give yourself the mark 5 a some bog standard angles it's always about 180s and 360s fortunately for this question five they don't ask for reasons so you don't have to give them 5 a angles on a straight line is 180 minus the 124 again do it as mental arithmetic or column subtraction it's up to you as long as You've got 56.

[00:08:26]Whatever method you did worked. Part B.

[00:08:29]Notice it's worth two marks. The idea being they want you to know that 90° is the right angle. And then you need to do 300 minus the two angles. You know, not the one. Whoops. Sorry. 360. You know what I meant. 360 take away the 300 giving you 60.

[00:08:56]I was thinking about one thing writing another. Anyway, no one noticed. 6 a we need to write 5.907 correct to one decimal place.

[00:09:12]The nine is in that position. We only look at the digit immediately after. The seven does not play a part in this. It's a zero. It is not a five or above. Now, I don't like the phrase rounds down. I always avoided it when I was teaching. A five or above rounds up. A four or below levels off. So the 5.9 stays at 5.9 370 the first significant figure means the most important three is the most important.

[00:09:57]The digit immediately after is a seven.

[00:10:02]That's a five or above. So the three must go up to a four. But when you're dealing in large numbers like this, doesn't matter so much when you've got decimals going in significant figures, but that's for another day. You must make sure that you keep the number of the same order. So, because it was 370, your answer needs to be 400.

[00:10:30]And there we go. Part C. The mass of one red apple is 132. Estimate the mass of 38 of these red apples. Each of those numbers needs rounding off. The mark scheme does allow some leeway. I'm going for 38 to become 40 red apples and 132 g to be 130.

[00:11:00]You may have gone down to 100. Mark scheme's fine, but I'll stick with what I've gone for.

[00:11:07]13 * 4 13 doubled and doubled again is 52.

[00:11:15]Two zeros there means 5,200 g.

[00:11:22]Does say in word in bold kilograms.

[00:11:26]Whatever answer you get it must be divided by a th00and to get your third and final mark.

[00:11:36]Number seven, Daniel serves up some fast food. I think we like Daniel. One day he works for 5 hours and earns £3050.

[00:11:47]How much per hour? It's a bus stop.

[00:11:51]£3050 divided by five.

[00:11:58]When you do bus stop with decimals, line up a decimal point in your answer. Fives into three does not go. So fives into 30 is six exactly. Fives into five once no remainder. And fives into naugh is a big no. So Daniel's getting 610 does sound low but don't forget we're in 2026 as I record this. This was 9 years ago now. Yep. Times have changed a bit.

[00:12:28]Part B. In July, Daniel works for a total of 50 hours. How much does he earn? We need to take the 610 and times it by 50. Personally, I think a better way of tsing by 50 is times it by 10 times it by five.

[00:12:55]Times it by 10, you get 61.

[00:13:01]Let's times that by five.

[00:13:04]Again, mental mental multiplication. If you fancy your chances, I'll go for standard. One five is a five. 65s are 30.

[00:13:17]On we go. What we got? Typical. All right. Over-the-top overblown educas.

[00:13:25]Vending machine sells drinks. Each drink costs 50 p.

[00:13:31]All that information is in the sign. We can suck it off. Drinks are 50p and it only accepts those coins. Complete the table. What a mess the table is. But there we go. First line.

[00:13:47]If a 20 p has already been used, there's 30p left. You can already see the other ways. Three 10 has gone. Two 10, two fives has gone. So it's now 110 making 30p and four fives.

[00:14:06]Another way though is also 120 but six fives.

[00:14:14]That's all the options with 50s and 20s.

[00:14:16]We now move on to tens. We've got four 10, 40p. That would need two fives.

[00:14:25]Reduce the tens by one. Increase the number of fives by two. Down by one for the tens. Up by two for the fives.

[00:14:38]Yeah. Mark scheme gives one mark for any three correct rows and two for every row correct.

[00:14:49]Part B. More waffle. But let's not panic. The machine has a display to show how much cash has been put in. It resets the display after each drink is taken.

[00:15:03]So in other words, if I put too much in, the next person doesn't know. Basically, the machine pockets it. Cheap really, but hey, the cash container is emptied every night. And when it's emptied, all those coins are in the machine. Don't read on.

[00:15:24]It's obviously going to ask you to work it out. So 10 50p coins, that's a fiverr.

[00:15:35]15 20p coins. 15 * 2 is 30. So it's going to be 300 p. That's £3.

[00:15:46]3110 PS.

[00:15:50]That's £310.

[00:15:53]And 25ps, that's exactly a pound. We're getting £1210.

[00:16:04]Bit of a weird number, but don't panic.

[00:16:09]It's part of the question. Work out the greatest possible number of drinks that could have been sold. Well, it's 50p a drink. So, each pound gets two drinks. So, £12 will score 24 drinks.

[00:16:32]Okay. Now, the assumption made because it's the maximum. The assumption made is that only one person overpaid because don't forget it tells you it resets after each person. You could have had a person putting 99 p in buys a drink. That 49 p got cancelled for the next person. It wasn't a case that the person after you could pop a penny in and they'd get a drink. Nope. It reset.

[00:17:10]So, our assumption in order for 24 drinks to be sold, it just means that one person overpaid by 10p or two people overpaid by 5p. So, two people put 55p in would be an alternative correct answer.

[00:17:30]comment on the effect that our assumption has. Well, if All right, our assumption means if we were wrong, there'd be fewer drinks sold. Again, if everybody had put in, let's say, 75p, then every two drinks purchased, there's essentially 50p going to waste. So the effect is that the number of drinks sold could reduce, could be lower, can't be more than 24, but could be smaller than 24.

[00:18:11]Anyway, back to normality. 9 a. We've got some calculations of increasingly difficult, but let's get on with it. 4* 9. That's a nice way to start.

[00:18:24]Part B. Fractions of an amount. Take the amount, divide it by the bottom, times it by the top. 8 / 4 is 2 times the top. Six.

[00:18:39]A negative multiplied by a negative is a positive answer. 12 2 with or without the plus sign is correct. And part D, bid mass always applies.

[00:18:56]Cube the number, cube two first. 2 * 2 * 2 is 8. Square the one at the same time or just immediately after, but then add them.

[00:19:10]Mark scheme. Two lines right for a tick.

[00:19:15]Three lines right for two ticks. All four lines right for three ticks. And part B, write down a relationship between the answers to A and B.

[00:19:28]Entirely your choice. You could say 6^ squar is 36 or the square root of 36 is 6. Anything along those lines. All right, on we go.

[00:19:45]Number machines. Good old fashioned number machines. Non-cal paper. highly likely. Take your time, one step at a time. It's stingy on the marks. And when it's reversed, remember you do the opposite. Anyway, the input is two.

[00:20:01]We subtract four, we get minus two, and we times it by five, -10.

[00:20:10]When the input is 6 and a half, not the easiest, but stick with it. Take away four if you prefer to think of things like this as cash 6 pound50 subtract four 2 pound50 and times it by 51 £1250 mark scheme accepts or 12 and the output is 45. So you must reverse everything you reverse the order and the operation to its inverse. So we start with 45 it's divide by five first of all and instead of subtracting four it's adding four we get 13.

[00:20:59]Bit stingy for one mark but you know we're not the boss are we? Part B different number machine now throwing in some algebra. The input n is always a whole number. Now let's have a think about that. What about three? Add one, we get four. Multiply by two, we get eight.

[00:21:23]Let's try an even number. Four. Add one, we get five. Multiply by two, we get 10.

[00:21:31]Let's see what the question's about.

[00:21:33]Which one of these statements describes the output? Well, as we can see, just by doing a couple of quick goes, we've got two even numbers.

[00:21:45]There we go. All right. Which one of these statements describes the output?

[00:21:51]There we go. It must be even. Show how you decided. Well, let's just look at the final stage. It's been multiplied by two. So, show how you decided. It's that step there.

[00:22:07]words or phrases to the effect that when we've multiplied by two, it will always be a multiple of two. It will always be divisible by two. Anything along those lines, give yourself a tick. Part double I. Write an expression for the output.

[00:22:28]Give your answer in terms of n. So we start with n. We are told to add one.

[00:22:36]Whatever we've got, we are told to double the lot.

[00:22:41]So, we either double the lot with a pair of brackets or we double the n and we double the one. They're the two acceptable answers.

[00:22:56]2 n + 1 is wrong, I'm afraid.

[00:23:01]Number 11. Some coordinates on a grid.

[00:23:05]Okay, great. We've got Aston and abroad.

[00:23:09]We've got a flight path. Write down the coordinates of Aston.

[00:23:14]Must be in brackets. It's one along two up from the origin. That's a nice mark.

[00:23:21]We're told there's a scale. One cm represents 100 kilometers. That means to go from cm to kilometers we are tsing by 100 and dividing by 100 to go in reverse. On average the plane flies 4 km. Let's do the let's measure it first.

[00:23:44]Get your ruler out. Now this is where I must say there's an asterisk on the genuine exam. If you measured Aston to broad, you should get exactly 5 cm. Mark scheme allows 0.2 either way.

[00:24:04]If you've got a certain make or model of printer, and in particular, if your school or college, reduce it to an A5 booklet, your answer will be much smaller. If you've got your own home printer and gone full size, even then it will still be something like 4.64. 6 4.5. I think mine was 4.7, but I'm going to go for the exact answer. Just bear that in mind. Be flexible with your work. Having an odd number, having a weird number here can make the calculations really hard. So, don't be tough on yourself. Anyway, 5 cm means the flight is 500 kilometers.

[00:24:52]The plane flies 4 kilometers 4 kilometers each liter. Well, we need to divide the 500 by 4. You could do bus stop.

[00:25:07]I prefer to go men's arithmetic. Harve it and harve it. Harve it 250. Harve it 125.

[00:25:15]But do be generous with yourself cuz that can be a tough one. If you've got 4.7, that makes that 470.

[00:25:25]That makes your dividing a bit trickier.

[00:25:29]So don't be too hard on yourself.

[00:25:32]Question 12. What we all love wordy waffly algebra. Not.

[00:25:37]Sam thinks of a number. His number is n.

[00:25:40]A, B, and C also think of numbers and they're in the table. Anwin's number is seven less than Sam's number. Using words, complete the following. Be's number four in front of it. We need to spell it out because it says words. Not that, not times four. That's not words, unfortunately.

[00:26:08]We need to put times four or four times.

[00:26:15]Part B. Carl says my number is double Sam's number. Explain why Carl is not correct. Carl, mate, yours is n over two. That means it's half of n or it's n / two. any words or phrases that explain. No, you're not doubling, Carl.

[00:26:40]It's haring. And you'll get the mark.

[00:26:44]David. David's come out of nowhere.

[00:26:46]Where's David come from? His number is nine more than Anwins. So, let's put a + 9 there.

[00:26:56]But we are told to simplify it. The n doesn't simplify with anything, but the minus7 + 9 simplifies to positive2.

[00:27:12]Finally, part D. Andwin's number is 63.

[00:27:18]Okay, let's plunk it in there.

[00:27:22]All right. Andwin's number is 63.

[00:27:28]Find Carl's number.

[00:27:30]Well, Anwin n minus 7. So, n minus 7 equ= 63.

[00:27:40]That means Sam's number, which is n is 63 + 7.

[00:27:50]Sam's is 70.

[00:27:53]We're wanting Carl's.

[00:27:56]Hall's is n divided by two. We've just explained that for part B. We need to take Sam's number and haveve it.

[00:28:10]Whatever we got for Sam's number, even if you didn't get 70, if you've h haveved it, give yourself a mark. But for the perfect answer, you want 35 for your three marks. And thankfully that's over and done with. Next on to question 13. Now if you wanted to approach this one with a trial and improvement technique because you know that the length and the width are obviously four times.

[00:28:43]So you know make up a number. If that's two wrong way around Al. If that's two that's going to be eight. Does it work?

[00:28:51]No. Let's make it bigger. If that's three, that makes that 12. You could do it like that. And absolutely feel free.

[00:29:00]It won't take long. The answer to this one is pretty decent. But because it's always better to have a method that works, for example, for a calc paper, just in case the number is awkward, where it could easily be like a 3.2, and let's be honest, you're almost certainly not going to guess that. Let's do it the algebra way. So basically whatever that distance is there, this distance is four times larger and you multiply the length and the width to get the area. We can now make the statement that the 4x^2 algebra area is equal to the 100 that we're given in the question. dividing both sides by four and hopefully your knowledge of square numbers is enough that x equals 5 which is why as I say wouldn't have taken you long to realize that it'll be five and four times longer will be 20 and 5 20s are 100 so if you've done it that way as long as you've made sure that your answer is x= 5 or width equals five cuz don't forget it does say work out the width not the length and it's the length that's four times that's why we need the shorter side on we go into part B a square has sides of length x so little bit like the one we've just done but now we're talking about perimeter the length of a rectangle is equal to the perimeter of this square. If a square has side lengths x by x by x and x, then its perimeter is x + x + x + x. We have a perimeter of 4x.

[00:31:03]If we've got a rectangle, there's a reason why the bottom half of this page is blank.

[00:31:09]They're welcoming you to draw plenty of diagrams if you need to. The perimeter of this rectangle is 14x. The whole way around is 14. The length of this rectangle is equal to the perimeter.

[00:31:28]Stick the 4x there, which will be repeated on the other side.

[00:31:33]The lengths of the other two, the widths. We're going to need to start with our 14x.

[00:31:40]Subtract these eight x's leaving us with 6x which should be balanced between these two sides. Therefore need h havinging.

[00:31:54]So final answer of 3x. Again you could have brute forced it, guessed it, educated guess and revise it from there.

[00:32:02]And again, mark schemes all over the place with where you get your first mark from, but at the end of the day, as long as you end up with a width of 3x, because notice it uh only wants the expression, that's the final expression. It doesn't matter how you got there. It didn't say using an algebraic approach, which is something that it usually says for things like simultaneous equations towards the end of a paper. If it doesn't say use an algebraic approach, and that goes for part A as well, then you can try and improve it. But most of the time, the algebraic approach will get you straight to the answer that little bit quicker. But if you're not a fan, then you're not a fan.

[00:32:52]On to number 14. Patterns sequences.

[00:32:55]Whenever I see patterns and sequences like this, I don't read the question.

[00:33:01]Not yet. I work out how many sticks are in each pattern. Get them counted up.

[00:33:06]You know, put some notches. Count them all up.

[00:33:11]Make sure make sure you've got them all.

[00:33:13]You'll get 13. There's an extra three on the end. And there's an extra three on the end each time.

[00:33:23]By doing that, it slows you down. You know you're going to need that information. And it now means when it starts talking waffle below, you've got the numbers ready to leap into action.

[00:33:35]Jod has 90 sticks left. So the total of all them is 90. She continues this sequence of patterns starting with pattern number five because we've got those four patterns because we now know it's going up in threes.

[00:33:54]Jod's got 90 sticks left. She uses 25 to make pattern five.

[00:34:04]She's left with 65.

[00:34:07]How many more complete patterns?

[00:34:11]Those of you love your highlighter pens, that's an important word. It's complete.

[00:34:17]We don't care about leftover sticks.

[00:34:20]Can she do pattern six? Well, she had 65.

[00:34:26]The 25, we need to add three to get 28.

[00:34:29]Yeah, she's okay. 28 is not bigger. And she's left with 37.

[00:34:36]The seventh pattern, 37 sticks left over.

[00:34:42]Add three on, 31 sticks used for pattern seven. She's fine, but now she's only got six sticks left over.

[00:34:53]Couple of marks for method, but do be careful how you answer it. It does say in bold, how many more?

[00:35:01]Not what pattern number can she get to.

[00:35:03]So, the answer of seven is wrong. It's how many more complete patterns making the answer three and as I said a couple for your method and when it says you must show your working exactly that the answer of three will I can't remember the exact phrase of the mark scheme must be honest the score of the end result of three I would assume scores zero but at most scores one and you know it's not the most tricky maths in the world you want all three on those questions On to number 15. Pavl has to work out the square root of 484.

[00:35:42]And what's he done in the box? He's h haveved it. Pavl's method is incorrect.

[00:35:47]Absolutely. Any words or phrases to the effect that to find a square root, you don't divide by two. Another way would be Pavon should have been working out a number multiplied by itself gives you 484 and these numbers must words or phrases whatever. All right, it's only worth a mark. You're not there for an essay.

[00:36:14]Part B. Nina works out 0.54 plus.23 + 2. Here's her working. Nah's friend says that her answer is too small. I mean, absolutely right. You could check it. Explain why Nah's friend is correct.

[00:36:32]You could argue, do it by estimating two plus 20 plus 50 is going to be 2.70.

[00:36:42]Certainly more than two. You could go for that. Or you could be a bit more specific in terms of what Nah's done wrong. And that's because Nenah's incorrectly place valued the two in the hundredths column. That two should have been in the same column as the zero. So, couple of ways of going about that all get you the tick. Let's move on.

[00:37:10]Number 16. If you've watched any of these other videos, you'll know my hatred of ratio questions where it's all in words. Get it written out with letters and numbers above and below each other. It is much easier to see. We've got ABC tips. Yeah, who cares? They share the tips in the ratio of the hours they work, right? So, where are the hours?

[00:37:39]Ahmed's five, Blake six, and Kath C is 12.

[00:37:48]Kath's share of the tips is 18.

[00:37:52]You've got to ask yourself, how did we get from Kath's hours to Kath's tips?

[00:37:59]Well, it's either add on half if you want to just do it that way. You add on half for each person, which would mean Blake ends up at 9 because we do 6 + 3 and Amed would be £750 because we add on half. or if you're a multiplier person 1.5. But that's more of the calculator technique where you find your multipliers by dividing and all it we actually answered it already. Work out our med share of the tips.

[00:38:33]He's getting £750 share.

[00:38:37]On we go. The following week the tips total £72.

[00:38:43]We've still got the same three people.

[00:38:46]Let's get that.

[00:38:48]And it says Blake works twice as many as Armed. We don't know how many. A works, but we know Blake B is double and Kath is triple. Now, you could use any other numbers. If Armed was two, that would make Blake four and six. But I would always say, why would you make numbers bigger? If you make numbers bigger, bigger, you're making them trickier. You could use algebra, but again, why would you bother when numbers works a treat?

[00:39:21]The total following week, the tips total 72.

[00:39:27]How much is Blake's share of the tips?

[00:39:30]We're looking at B.

[00:39:32]That's two out of six. two out of the six shares, which is the same as a third. You need to take the 72 pounds and divide it by three. Or if you stuck with two sixs, divide it by six and then multiply by two. Both will work. Both gives the answer 24. And you've bagged your three marks for the ratio work.

[00:40:03]Five in total. Not bad. Number 17, we've got some download dev download buys and downloads. So, nothing illegal from dev.

[00:40:14]The number of tracks he buys in one month, and the approximate prices are shown below. Using the value in the table, calculate an estimate of the mean. This is one of those estimating the mean questions, except they've done the midpoints, the approximate prices for us. You'll be used to seeing Whoops.

[00:40:36]You'll be used to seeing information given in tables and normally the first groups something like 11 to 30 or 10 to 30 or some nonsense like that. And your job is to find the midpoints go halfway between them. That's been done for us. And that's part of the reason why this question is only three marks as opposed to a normal estimating the mean question which is four. So we just have to move to the second step and the second step is multiply the prices in this case by the frequencies.

[00:41:14]70 * 50 75 35 80 * 1 N * 2 pretty nice and 100 * two very nice you've earned a mark for those products we now need to column addition them all or if you pair them up or if you risk it men's arithmetic yeah it's risky Put zero down there. What we got? One. Carry a couple across and all that becomes 810.

[00:41:52]And the final stage of estimating the mean. Divide by how many there are. 5 + 1 + 2 + 2 means we are dividing by 10.

[00:42:04]And I said it before, estimating the mean is normally a paper two topic.

[00:42:10]Normally, you've got a calculator for it. But that doesn't mean it always is exclusive to the calculator paper. If it appears on the non-calc paper, the numbers will be extremely friendly, as evidenced in this question. There's your 81. On we go.

[00:42:30]All of the actual prices paid were rounded up. As we know, most prices end in nines, don't they? It was probably 69 p 79 p and so on. Is the mean price per track higher or lower than your estimate? Because we've used numbers in our calculations that are all higher or above the true value.

[00:43:00]The true mean price would be lower.

[00:43:05]Okay. the true mean price would be lower as the and it says give a reason. If we were doing it properly, the numbers used would be smaller or lower or whatever you want to say.

[00:43:25]Or if you say our numbers were too big, so the true mean is smaller than 81.

[00:43:32]That'll do. Give yourself a tick. On we go. We've got a gate. Diagram shows a rectangular garden A B C D with a gate.

[00:43:42]And that gate must be 2 m. In it goes. The fact that the bottom length there 10 means that the length of the fence along the top 10 minus 2 gives us eight.

[00:44:01]Eight fence, two gate. That'll do.

[00:44:06]Wire fencing costs £32 for a whole 10 m roll. Right, let's stop right there. We need to find the perimeter, but not obviously including the two for the gate. There's five on the left, there's five on the right, there's 10 on the bottom to make 20.

[00:44:29]That means with the eight at the top, we've got the perimeter is 28 m of fence.

[00:44:40]It's £32 for a whole roll. So, we could buy three whole rolls.

[00:44:52]That's first choice. If we buy three whole rolls, we're going to have a bit left over. All right, we're going to have 3 10 30. We don't need the gate.

[00:45:04]That means we do £32* 3 and that would be 96.

[00:45:14]But it does say justify your answer because you've got to investigate the other way. You've got according to the mark scheme at least one more way or at least have a justification that you know that a roll for 10 meters is cheaper. So you've got a choice. You could go for two whole rolls and eight single meters.

[00:45:45]You could go for one whole roll and 18 single meters.

[00:45:51]And if you really want to go, you could go 28 single meters.

[00:45:57]So they are all possibilities.

[00:46:00]But another way of going about it, and by the way, they that' be perfectly acceptable, just a little bit long- winded.

[00:46:09]You can probably guess, by the way, that 96 is going to be the cheapest, but they don't allow that. You've got to have some further justification. I'd also add, look at how much maths we've done.

[00:46:21]Do you really think all the maths I've done so far is going to be worth four marks? No chance. There's got to be more to it. So, a bit of your algebra tech, your exam technique there. So let's look at the other possibility of if you buy 10 m singularly as you can see 10 m singularly would be £45.8 m singularly we can take off £9.

[00:47:01]All right, that would be 36.

[00:47:05]All right, you could have done £450* 8 or done it my way, the buildup technique. But that justification there will be showing you that for example, two hole plus 8 m is really going to be £64 for the two holes plus 36 basically any words, phrases or maths to the justification that it's now getting more expensive. If you wanted to go on further, all right, if you want to go on further, feel free. Like I mentioned, doing 28 single meters, but that's then going too far for four marks. We've now definitely earned three. Let's now make our decision. We've got enough evidence that by dropping the whole rolls, bringing in single bits, it's going up in price. £96 is your cheapest and it's justified and backed up. On we go. Number 19. Amy needs 14 identical pieces of ribbon to gift wrap some presents. Amy has two rolls of ribbon that are the same length. She cuts 10 pieces from the first roll and has none left over. 10 pieces.

[00:48:41]Call it whatever you want.

[00:48:44]I'm going to say that 10 x that's roll one.

[00:48:49]And she has none left over.

[00:48:52]She cuts the remaining pieces from the other roll and has 9 m left over. Well, she wanted 14.

[00:49:03]She's got 10.

[00:49:05]She needs four more.

[00:49:09]And when she cuts four more off, she has another 9 m.

[00:49:17]And that accounts for roll two.

[00:49:21]And we are told in the second line, Amy has two rolls that are the same length. These folks are equal.

[00:49:32]Yeah, it's one of those hidden algebra.

[00:49:35]Set it up yourself and get it solved.

[00:49:39]Let's subtract 4x from both sides.

[00:49:45]And let's divide both sides by six.

[00:49:50]You do end up with 9 / 6 if each piece of ribbon is R. Oh, as you can see, I've used X instead of R. My apologies. Do you know what?

[00:50:02]There we go. Perfect. No one will notice. 9 / 6 cancels down to 3 over2.

[00:50:08]And all these are acceptable answers, by the way.

[00:50:13]Probably the best though is 1.5 m left over. On to number 20.

[00:50:20]We've got a table. And in typical Educas fashion, whenever they display a table, it's probably not a good idea to read the whole table because there's almost certainly too much information. Let's just crack on with the question. What do we care about? Thous per thousand grams is about the most important. show that saturated fat to other fat is 8 to five.

[00:50:48]Well, saturated fat as we can see to other fat.

[00:50:55]So, we've got fat which is saturated is 40 g.

[00:51:02]Now, the common mistake here would be to think it goes 65 in there, but then the answer doesn't work because don't forget 40 is saturated, 65 is total fat. So, you need to do 65 minus 40 to get 25 for the other fat and show that it cancels down. I would always tell the examiner what I'm dividing by.

[00:51:34]We divide both sides by five and we do indeed get the answer that we were told to. Part B. How much salt is there in a 50 g serving of this cereal? Salt is 2 g per thousand.

[00:51:54]2 g in 1,000 g.

[00:52:00]That'll be 1 g.

[00:52:03]In 500 g of cereal, we need 50 g of cereal.

[00:52:10]That's a divide by 10. We do the same to the other side. 1 g divided by 10 is 0.1 or 110th of a gram. But taking your info from the table using some kind of decent approach to get to 0.1 g and you've banked three marks.

[00:52:36]Part C, it's recommended that adults eat no more than 6 g of salt per day. Mina is an adult and eats a 50 gram portion of the cereal. So, she's eating 50 gram portion.

[00:52:53]She's eating 0.1 g of her salt allowance out of the six g allowed. Give your answer as a fraction in its simplest form.

[00:53:09]When you're writing fractions, decimals are a no no. We don't like fractions on top of fractions or in this case decimals on top of fractions. And the best way to get rid multiply the top by 10 and the bottom by 10. And that's as simple as that fraction gets.

[00:53:31]Onto some proper math, some good old algebra. When we are solving, it's all about either do the same to both sides.

[00:53:39]If you've been taught one way or you'll have been told change the sign, change the side. It has become increasingly po popular. A couple of students I'm working with in tutoring, they do trimm lines nowadays and they seem to like it, which it means, for example, you write takeaway two there and then you do it down the middle. Now, if that seems becoming more popular, maybe I'll do that on another video, but for now, I'll just do it the oldfashioned.

[00:54:07]Subtract 3x from both sides so it disappears from the right and 7x becomes 4x. Subtract two from the left so that disappears and two from the right goes down to two.

[00:54:25]Now when we divide both sides by four that's fine. You can leave it as 2 over 4 or a half or 0.5 because mark scheme uses the phrase oe meaning or equivalent.

[00:54:42]Part B, not the friendliest solving, but never mind. Bid mass always applies.

[00:54:48]There's brackets. Get them sorted first, but be careful when you multiply or expand these brackets. That's not a two.

[00:54:57]It's a minus2.

[00:54:59]You've got -2 * x is -2x.

[00:55:04]You've got -2 * - 9 that's positive 18.

[00:55:12]Right hand side 5x doesn't go anywhere as not as did the three didn't go anywhere. Right? Negative x's are always a pain. Let's add two x's to both sides.

[00:55:25]That means they disappear.

[00:55:30]And let's simplify our three and our eight 18 sorry positive 18 into 21.

[00:55:39]And now when we divide both sides by seven, we've got the final answer of three. One for brackets, one for simplifying, collecting like terms or any rearrangement that is good and uh correct. and your final answer. And inequalities, now you've got a choice here, folks, but inequalities with negatives, they are Yeah, I try and avoid. So, I'm going to leave the inequality alone, adding 3x to both sides.

[00:56:14]Inequalities with negative x's, they're just not nice. So, let's do that.

[00:56:20]Subtract one from both sides. There we go. And now divide both sides by three.

[00:56:30]Represent that answer on a number line.

[00:56:33]First of all, you put a circle below on or the preference usually is above the important number. This circle will be an open circle. Don't fill it in because there's no equals to. Less ink means less ink. But be careful. X is on the open side of the inequality. That means X is greater than two. That's why we need the arrow of any length pointing towards the right to make sure you get that mark. Yes, all those three aspects are needed just to pick up one mark. Bit stingy, but there we go. Next, under surveys and questionnaires for number 22. Now, these are always extremely wordy or waffly. And whenever you are asked to criticize, they're always the same criticisms. Not this one though, but mostly you always criticize the sample size or they've asked people on a Monday morning in one place, stuff like that. Actually, that's not the case this time. And this is one of the more rarer ones where as you can see for part I explain why it's a biased question.

[00:57:52]It's opened with a personal statement.

[00:57:56]So Sasha, whatever her intentions are when you are asking people their opinions, you don't simply offer your own opinion. Your opinion does not matter. It should not come into play. So why is it a biased question? Sasha has given her own opinion. Words or phrases to that effect only worth one mark.

[00:58:18]Don't write three lines. State one other criticism of the question. There's actually a couple I would throw in.

[00:58:27]There are people out there for dietary reasons or whatever. Why is there no zero? There are people who also for dietary reasons. Why is there no greater than six? All right. If you're anything like me, on any given day, you're going to be needing like a 20 option or something like that. But they're the main two options. All right. She hasn't covered all the possible answers she could be faced with, and that is a common criticism. I will say another common one is that groups overlap, but she's actually not done that one. So, as you can see here, her groups don't overlap. Another thing you could have said, by the way, is how on earth do you define pieces of chocolate? All right, I'm not going to mention any brand names here because we all know that big brother's always watching, but as we know, you can have small pieces of chocolate depending on one type of chocolate bar and large pieces of chocolate and so on. So, what's a piece of chocolate? Maybe she should have quantified it in grams a bit more. Words to that effect. But there we go. Sasha stands outside of Super Oh, here we go.

[00:59:38]There we go. I've just said it already.

[00:59:41]I'm going to repeat myself. Reason one, 10 people. Sasha, load of rubbish.

[00:59:48]Absolutely pathetic. No. And as you can see, I didn't know. Yeah. Stands outside his supermarket on a Monday morning.

[00:59:58]Biased. All right. Needs to vary the time and place and so on and so forth.

[01:00:04]you know, you just know it's coming. But let's just move on. Let's not repeat.

[01:00:10]Question 23. As always with these questions, I cheat because there's no way in heck I'm able to do this with my limited electronic pen and so on.

[01:00:21]They're always wordy these, so don't let it over complicate and waffle. At the end of the day, it's constructions.

[01:00:26]You're going to have to construct a perpendicular bis sector or an angle bis sector or both or bits of circles. So scale drawing below shows a lake. Okay, it's a lake. Two small islands at A and B. We're not that interested. Lifeguard at C. Yeah. Swimming is only allowed in the area that is nearer to A than it is to B. Stop right there.

[01:00:57]The only way you can know where is nearer to A than is nearer to B is if you draw a perpendicular bis sector. So you grab your compasses, you set your distance over halfway, metal point on A.

[01:01:15]As you can see, I draw a semicircleish almost. Metal point on B. same kind of semicircleish.

[01:01:25]And then with your ruler, join them up.

[01:01:29]I know mine's what rubbish, but that's the arcs that you should be showing and certainly not rubbing out. As you can see, two ticks for them. One for good construction arcs, one for a good line.

[01:01:43]And I always put a little arrow on cuz let's not forget the question did say nearer to A than B. So we need to be on the left hand side of that line. But where else? It says less than 60 m from C. 1 cm is 10 m. 60 m is 6 cm.

[01:02:08]Grab your ruler and your compass. Set your compasses so that the points are 6 cm apart.

[01:02:17]Metal point on the lighthouse. the lookout, whatever it was on C. You could draw a full circle. As you can see, though, it's a lake, don't forget. So, we're only interested in the area in the lake. All right. Lifeboat, not much use on land. So, there we go. And again, we are looking for inside that circle.

[01:02:42]All right. one mark as you can see for the circle itself. But we're looking for the region which is both inside that circle and to the left hand side of your bis sector. And as you can see, don't take too long to shade it in, folks.

[01:03:01]8 10 lines is enough. That's called shading. And you've banked your mark there.

[01:03:08]Next, vectors look complicated. Don't let them complicate things. They're not as bad as you think. They are posh brackets and a number in front of a bracket just like brackets doubles it, triples it, whatever. So our first job is to take the vector Q and multiply all the numbers by three.

[01:03:36]So the minus4 on top becomes -12.

[01:03:41]The seven on the bottom becomes 21.

[01:03:45]And we need to do P + let's pop P before it.

[01:03:54]And we're going to add them. How do we add vectors? Don't forget, by the way, the top numbers move things left and right. The bottom numbers move things up and down. You can treat them as separate questions. Just read across the top.

[01:04:11]They're called elements. You've got six on top added to a debt of 12.

[01:04:18]Negative numbers says minus 6.

[01:04:22]You've got on the bottom element -1 + 21 goes up to 20. And there we go.

[01:04:34]Part B. Part B is a strange one and is a tricky one. Whereas A is not that bad.

[01:04:40]B, yeah, can catch people out. So, let's build it up. It wants us to start with P. Might be a good idea to write it down.

[01:04:51]And some multiple of Q or let's write Q down.

[01:05:00]And we get 10 over N. Shouldn't really put that line in. That's a big no no. My mistake. They're not fractions and shouldn't be written as such.

[01:05:13]Now you've set it up. Let's work with it. Like I said up here, treat the top numbers as a separate question to the bottoms. So let's just read across the top. I'll do it in red. We've got a six added to -4m.

[01:05:34]So that's - 4 m = 10.

[01:05:40]Well, it's another hidden setup and solve question. Let's add 4 m to both sides.

[01:05:50]Take away 10 from both sides.

[01:05:54]And there we go. Four m is worth a debt of four. 1 m is a debt of one.

[01:06:03]We can now get rid of the M.

[01:06:07]We know it's worth minus one. I'll change color to black. Now we read across the bottom.

[01:06:15]We start with -1.

[01:06:19]We've now got -1 ultiplied by 7, that's - 7, equals the n on the bottom.

[01:06:32]So n is equal to -1 - 7 that's -8.

[01:06:40]So as I say don't be scared of vectors although I would argue part B is very very tricky and certainly going to put people off but do not give up on vectors if a quest part B is a very rare style of question. Part A is much more popular. Get used to that bit and you're going to have some results in the future.

[01:07:02]On to number 25. Again, typical educas.

[01:07:06]Don't read the entire information. No, no way. There's only going to be a few bits of information on that table that we care about. So, let's read the question and see which we do care about.

[01:07:22]Riley is planning to send two laptops to James using this delivery service. Guess the laptops are to be sent. Full insurance.

[01:07:31]So there's no option there. Full insurance. Oh, it's all full insurance.

[01:07:37]Not that important. Then each laptop is worth £700 and has a mass of £1,250.

[01:07:47]Correct. To the nearest 50. Well, that means we've got two laptops.

[01:07:54]So before we read on, that means if each laptop is worth £700, it's going to be £1,400 price of the laptops and 2,500 g for the weight in total if we send them together. More on that in a sec. Riley says the delivery charge is more than 20. James says you can send it for less than 20. Let's see how they can both be correct. So, let's look at what Riley is saying.

[01:08:36]Let's see where we can get a cost of more than 20. Riley to make it cost more because obviously in real life it's usually cheaper to try and send stuff together. So Riley is probably going to be sending them separately. That means 1,250 g. We can't do the,000 gs. That's a no.

[01:09:02]Not enough. Got to be less than. So for Riley, we will send them separate.

[01:09:12]It means they're going to come under the seven, sorry, the 1,750 grams. And because we want full insurance, it's going to cost us £13 each because as our £700 and that covers £750. So separate will be £750 insurance.

[01:09:37]It's £13 doubled.

[01:09:42]So Riley says over 20. It's actually 26.

[01:09:47]Let's look at James.

[01:09:50]Send them together.

[01:09:55]If we send them together, this 25,500 now kicks into play.

[01:10:04]We can now read across that as we know we are going to need to insure them £1,400.

[01:10:13]It's that price there, not £1550.

[01:10:16]Wrong column. It's the £1,500. We're going to need £1750.

[01:10:24]That's your lot. So send together is going to be simply £1750.

[01:10:35]As you can see it does say to oh I thought it says answer box at the bottom. Explain how the how by the way is met by that separate and together.

[01:10:50]And we've said it clearly show all your working and state any assumptions. Well, again, the assumptions are there.

[01:10:57]We might want to just clarify that for James.

[01:11:04]Let's add in £1,500 insurance. And for Riley, it's £750 insurance for both. Probably should have put that in, but there we go. Onwards.

[01:11:23]ven diagrams.

[01:11:25]There's 20 people in this ven diagram.

[01:11:28]13 swim in the sea. Now that's the whole circle. So I'm going to the total of these two dots is 13. Could be like 13 and n 12 and one. Who knows?

[01:11:43]17 to the funf fair. Same principle.

[01:11:49]All right. 17 go to the funf fair. We don't know where to put could be 17 n 161 don't know two don't do either there there is at least one we know so two people don't do anything that means these three numbers are going to need to add up to 18 as it stands they add up to 30 which is 12 too big we can't have people magicking out of nowhere. 12 too big simply means 12 do both.

[01:12:29]It means 12 + 1 gives us the 13 swimmers and 12 + 5 give us the 17 funf fairer.

[01:12:40]Part B. A person is chosen at random.

[01:12:42]Find the probability that this person swims in the sea and goes to the funfair. That's the intersection.

[01:12:51]of people who do both. Which means our answer is 12 out of 20 or any simplified version of that. Find the probability that this person either swims in the sea or goes to the funf fair but does not do both.

[01:13:12]There's swims in the sea. Theirs goes to the funf fair. They're the people that do it separately.

[01:13:20]If you've added them together, whatever numbers you may have, you get a mark.

[01:13:25]But it boils down to 6 over 20 or any cancel down equivalent of number 27. And finally, explain why triangle BDF is equilateral.

[01:13:44]Long- winded this one. Now I have written it out in full on my worked answers. So if you want to go and see my model solution as always go to the website click on a few things click on a couple of things link below have a look.

[01:13:59]But here's a quicker way. Now the first thing I would say is because you are told it's a regular hexagon all these sides are the same. A B= B C= C D= D E= E F= F A. All of those are the same.

[01:14:23]And because it's a regular hexagon, the sum of the angles at each bit is 720.

[01:14:35]meaning that there there that there all those angles are 120.

[01:14:48]All right.

[01:14:49]From there what we've got going on if you look at each triangle this is congruency.

[01:14:58]So I can say that triangle F A B triangle D E F and triangle B C D are congruent thanks to side angle side and if they're congruent it means that the third that they are also all equal.

[01:15:28]And that's one way of going about it.

[01:15:31]I'll quickly mention another way once you've got the idea that it's a regular hexagon. By the way, get that 120 in there.

[01:15:46]Once you've got that 120, realizing hopefully that the white triangles are isoclesles, you can then say that each of these angles is 30 30 30 30.

[01:16:06]And what does that mean? Well, if the whole lot there is 120 and the two little bits are 30, then that bit in the middle, that's 60, that's 60, and that's 60. Again, that's a different way. You don't have to go down the side angle side route, the congruency route. You can go down the angle route. Neither way are particularly nice, but that's why it's question 27, folks. It's designed to sit there, keep people thinking right until the final whistle. Anyway, there's the paper one done. Overall, I thought there was quite a few wordy waffly question. I don't like how they do all these. Quite a few wordy waffly questions going over the top. As always with Educas, if you can get beyond the words and concentrate on the maths, it's a quite fair paper.

[01:17:06]The the actual difficulty level reasonably fair. Anyway, well beyond time for me to shut up. Hope that's helped. See you on the next one. Tara.