Let's take a look at how to approach problem-solving questions in GCSE maths.
We'll discuss some general tips for approaching these types of questions, as well as looking at some specific methods that can be used for different question types whilst running through some practice exam questions.
This video is ideal for students who are studying GCSE maths and need help with problem-solving questions.
Math is by its very nature a method to do problem solving and basically every technique that you use in math is going to be doing that. Of course, it's useful to know how to problem solve things. In particular, this will be in the context of things like exam questions, questions or otherwise pieces of information you're given to find an answer. One place I think it's always useful to start is this thing here, the equal sign, which in math does not get enough credit. In my opinion.
The reason why it's two parallel lines like this is because a parallel line is a way of saying that two things are straight, will never intertwine. So it's a way of saying they are the same. So whenever you're doing problem solving, what you're really doing is trying to find something which is the same as something else. And usually in math that involves using multiple techniques. If you could only use it with one technique then it wouldn't really be much good.
So these are applicable to many different techniques. But bear in mind that some of these steps are obviously going to be a lot more involved than others. But having a good framework is always an excellent place to start thinking specifically about, well, let's go for an actual math exam question. We'll go over this little framework which can help you establish how to solve these problems. First of all, trying to get it in terms of something equaling something else and then actually solving it.
So first of all, read the question. I know it seems very obvious, but whenever you're reading a question, particularly in the exam scenario, they're trying to give you all the information they possibly can just in that question. And often that can be a little bit intimidating. What's quite useful is to highlight important information for a start. So in this case, for example, if we were to look for important stuff, highlights would probably be its own little verb right there.
Now, highlighting useful information is useful. What I also find is quite a useful step is to then cross off information as it's used in a question. For example, if you're asked to use a particular set of weights in a question, usually you'll only need to use any one of those weights once. So once you use something, you can then just cross it off once it's already been done. I find that can also reduce the amount of information overload you might be experiencing during exam.
The second thing is thinking about what do you need to do? Again, it seems like a slightly obvious part, but looking to what the question is asking to do can help here. What's your end goal? What's the end objective? Is it to make something equal to something else?
Is it to find an area? Is it to find a weight? Is it to find something measured in pounds? It's useful to think about that critically. What are you going to need to do that?
There's a lot of tools in a mathematician's toolbox and usually questions will give away some piece of information for the topics you'll need. But unfortunately, there isn't really any replacement for just having a good understanding of the math and really thinking about everything. That's really what these problems are trying to do, just to get you to think as much as possible. This third one here is what don't I need? As in what parts of the question are you going to need?
Some parts of the question end up being called upon earlier and then they're not necessarily needed later, whereas other pieces might just sit there for a while and not be used. This is the value of highlighting from earlier and crossing things off as you go, because if by the time you get towards the end of a question you're not entirely sure what to do next, you might want to then look back at the stuff that you've not yet used. Fourth, what math technique should I use? Fairly straightforward, this usually be involved in the question. If it's something to do with angles, then probably using something like trigonometry, whereas if it's something like ratios or simultaneous equations or one of the many other techniques, trying to think of one of those number five, you've done it, you've used the techniques, you've used what you needed and now you need to think, is my answer correct?
Though obviously the answer is hopefully yes. Some questions have got a nice little show that which means you just need to show an answer is equivalent to it. But what this set means is basically engaging in the I want to call it common sense area of your brain, which is thinking about what answer I've actually written down here. Is this something that's reasonable in real life? To be honest, it takes a step of confidence.
That can only really happen when you've got enough practise with maths. If you're somebody who's say, coming from more of like a science background, like physics, and you get a value of a car is equal to 10,000 kilogrammes, it's good to have an idea of, is that reasonable? Is that not reasonable? Is that ten times too big? What could it possibly be?
And the same thing happens in math. If you get an angle, which is something like a few thousand degrees, then something's probably gone wrong in your calculator. And similarly, if you're asked to find out what the circumference of a circle is, which only has a radius of a few centimetres, and you have an answer in miles, again, you've probably got an answer wrong somewhere. This last part here is, have I done everything? This is a bit more important in the sciences and so on, but it's generally things like, have you converted any kind of units that you need to use?
Have you answered in standard form, decimal places to be honest. This last part is usually just involving in making things neat and making sure that your answer is presentable. But it is so important to show that you've understood the process fully. Let's actually apply this stuff in the example. So this is, I'd like to say, fairly typical math question, which I'd like to say this is a fairly typical question, which was mostly on the screen.
So let's use our process we just talked about. So I was going to read the question once, then we'll go through and highlight it. In Mrs Abernathy shop, five apples cost £3 in the same shop. Two apples and two bananas cost £1.50. How much would one apple and three bananas cost?
Let's go through and highlight all the information that's involved here. Okay, so we'll highlight what seems to be the useful information for a start. So, first of all, we've got five apples. They cost £3 in the same shop. So that's sort of letting us know the context of the question.
Two apples, two bananas cost £1.50. And then lastly, how much would one apple and three bananas cost? As far as frivolous information goes, the fact that the shop is owned by the lovely Miss Abernathy isn't really relevant, nor is it really relevant as a shop. In many ways, we only really care about the information we've been given, which is about apples and bananas. So it's again going to set this out in a way that we can actually use mathematically, because we're probably going to need to use some kind of simultaneous equation.
Simultaneous equations always end up appearing and if you have two sets of equations or two pieces of information. But in order to make this mathematical, we should probably try and abstract the information. And that's kind of doing one of those steps that we talked about before, where we're trying to think about what mathematical terms and what are going to be useful. So in this case, it might be useful just because maybe we're feeling a bit lazy to end up writing apples as A and bananas as B. And then, like I mentioned, right, start, we want to try and make something with an equal sign.
Now, eventually, our final result, as we can see here, is going to be one A plus three B equals onet. That's our final result. So for that, we need to know what is A than what is B. We're just going to tuck that way down here for now and we'll come back to it later. So we know that five A is equal to £3.
Now, this has been written as 3.0. You've got two options here and this is where I'd like to demonstrate that in maths, you really do have options when it comes to how you think about things best. If you'd rather think about that as a decimal value and have £3.0, that's absolutely fine. Alternatively, you could write this as 300 pennies. It doesn't particularly matter just as long as you're consistent.
This is one of those things about consistency amounts. There is a element of flair and individuality when it comes to it. It's not just one method over and over. So just for the sake of argument, though, I'm going to keep this in terms of pounds, because probably what most people would do. Then we've got two apples and two bananas, end up costing 150.
So I'll write that as 1.50. Now we need to get A and or B on it. And this is where we use the power of the equal sign. There's a couple of ways that you can end up doing simultaneous equations. We could multiply both of these sides by sorry, multiply this one down here by 2.5, which would make it all equal to five A.
However, what I tend to do is make things equal to one quantity first. That can make our lives easier. So A is going to be equal to three over five, which in this case is £0.6. So that's £60. Okay?
And then we can substitute that down here. We know what one apple costs. And now for bananas, we'd say that, well, we know what A is. So two A. So two times 0.6 plus two multiplied by the banana, one is going to be equal to 151.50.
So at this point, that means we've got one two plus two B equals 150. So that means that two B is equal to 0.3. So B is equal to zero point 515 P. So we've got this piece of information here and let's cross it off as we go. We've used five apples.
We've used the fact that cost £3. We've used two apples, two bananas costing £1.50. That kind of clears up this top line, really. And now if we for every reason we're kind of getting a little bit stuck here, maybe there's a secondary part of the question. We now know these values.
So now we need to figure out how much would one apple and three bananas cost? Okay, so let's put this in. In which case, so one A is equal to, in this case, 0.63. B would be the equivalent of three times 0.5. So in this case, that would be 0.6 plus 00:45 equals 1.5.
Okay, so there's our answer. Let's go through the is this correct stage? So, number one, does that seem like a reasonable value? Well, we've got something in value of one, which is about right, by the look of it. Five apples is quite expensive.
Apples are more expensive than bananas. We didn't get a value like £10. That'd be quite unreasonable. That thing is fine. But the other thing I've just alluded to there is we are missing something, which is we need to give a value in pounds at the end because we picked pounds at the start.
We need to have pounds here, okay. Because this is an actual cost. Because if we were working in pennies and said, we'd write 105 pennies, and you can do either one of these. These are equivalent. One thing which is worth remembering is that the people who are marking your exams or your tests or whatever, they do also have a brain, allegedly.
And that means that they can actually cheque a lot of the results that you're interested in. So they know what 105 pence is compared to £1 and five pence. Okay? So looking at it, this all seems fairly reasonable. Now, if we wanted to, we could then substitute this back in to see if we got something else.
But at that point, we just be reverse engineering one here. That's more easy to do when you've got something like, say, dividing by an answer, multiplying by something, and then you know that you've got a definite answer to work with. That's a very brief overview of the way that you go through some of these regular problems, and hopefully that's been useful to you guys. So in which case I'll speak to you guys at some other point, hopefully, and best of luck doing your maths in the future.
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