Live Paper 3 November 2017 | Part One | November 2017 | Walkthrough Higher Maths Exam Paper

salam alaikum everyone apologize for the delay welcome everyone so now we are back we have technical issues this lunch time so welcome to our first session in Ramadan and we will review the document from November 3,

2017

and we will do the normal. routine of just reading the entire document and we will identify the easy questions, the medium questions and the difficult questions and then we will come back to them, so question one, the table shows information about the heights of 80 children, so we have a table here where we have Heights the class widths are Z 130 to 140 and so on find the class interval that contains the middle so this is a good start easy type of easy question um Part B draw a frequency polygon for the information in the table, so that's a relatively simple question too, question two in London, a liter of petrol costs 108.9 p.

In New York, a US gallon of gasoline is $2.82 um, so we can see quite a bit of information there and we have conversions where the city is the best value gasoline London or New York, so this This is a medium question, so it could be a complicated question, let's move on to next question three. A bar of gold has a mass of 12.5 kg. The density of gold is 19.3 G per cm cubed. Calculate the volume of the gold bar, so this is a reasonable question. I think it's medium, if not medium. I think this is an easy question.

What topic is it about? You can see we have mass and volume density, so this is density. volume of mass, in fact, I should label this as I go, so I'm going to write here density, volume of mass and the other one was conversions question four, there are only blue pens, green pens and red pens in a box, the proportion of the number of blue pens to the number of green pens is 2:5 the ratio of the number of green pens to the number of red pens is 4:1 there are less than 100 pens in the box what is the greatest possible number of red pens in the box box? we can see that this is, I would say there's a lot of text here, so let's say it's a medium type question and the topic is question five about ratios, find the value of the reciprocal of 1.6, so give your answer as a decimal, a very nice and easy question. there so we can do that, in fact, we could do that right away, so this is what happens while you're reviewing the documents, uh, easy questions that you can ask right away, so reciprocal of a number, I'll actually do that.

I will return to you. I'll do this thoroughly in case you haven't found the reciprocal or have forgotten what the reciprocal is and Part B simply rounds a number The result is 9.8. Write the error interval again. One type of easy questions fall into that category, let's look at the next one now question six here is a rectangle the length of the rectangle is 7 cm longer than the width of the rectangle four of these rectangles are used to make this eight sided shape so you have to here the perimeter of the eight sided shape is 70 CM calculate the area of ​​the eight sided shape so that you have a length of the rectangle is 7 cm longer than the width so you have unknown so a little algebra there, so I would call this a medium type question, if not a difficult question, it may get a little easier as we go, when we come back to it, which is the case that happens sometimes.

Okay, so we have question seven. Calculate 13.8 * 10^7 * 5.4 * 10^ minus 12. Give your answer as an ordinary number. A nice easy question. This is one of the reasons we do this. We identify easy questions. We can accumulate them, so this is question seven. All of these other questions can take a lot of time, but we can get to this, close this question, and then spend a little more time on the other questions. Question eight, just looking. You can see this is a math test, but we have like an English essay here so you can see it automatically. I can label this as medium, but what topic is this?

When a thumbtack is released, it can land tip-down or tip-up. Lucy Mel and Tom each dropped the thumbtack several times. The table shows the number of times the bedbug landed tip-down and the number of times the bedbug landed tip-up for each person. Rachel will drop the thumbtack once whose The result is uh will give the best estimate of the probability of the thumbtack landing so we have probabilities and we have things happening so relative frequency relative frequency the next

part

B Stuart is going to drop the thumbtack two times use all the results in the table to calculate an estimate of the probability that the thumbtack will land pointing up the first time and pointing down the second time, so again we continue with that, so let's say.

A medium type question. question nine Jack bought a new boat for £12,500 the value in pounds of Jack's boat at the end of n years is given by the formula V is equal to 12,000 multiplied by 0.85 to the power of n and at the end of how many years was the value of the boat Jack first was less than 50% of the value of the boat when it was new, so this is a medium type question and has to do with percentages and compound interest. Part B is now a savings account that pays interest at a rate. of r% per year Jack invests £5,500 in the account for a year and at the end of the year Jack pays tax on the interest at a rate of 40%, so continuing with that I would say it is a medium type question, another point.

What comes to mind is that these questions, when we analyze them, are easy, moderately difficult, it is something relative. What might be easy for me is difficult for you. What is easy for you is difficult for me. And so on. It's a relative thing, the key is what we are doing, after we have done this we will know where to spend our time, what questions once we have accumulated them and then the other questions that we can spend more time on. they question 10 there are only blue chips yellow chips green chips and red chips in a bag a random chip is taken from the bag the table shows the probabilities of getting a blue chip or a yellow chip or a green chip so we have this is a probability table calculates the probability of getting a red counter so this is a reasonable question so initial medium my initial thoughts were medium but it is actually an easy question this is a probability table probability table next

part

B what is ? the fewest possible number of counters in the bag, you have to give a reason for your answer, so again let's call that one which is a little bit more difficult, so let's call it middle question 10 just by looking at it you can see that this is the cumulative frequency, for what it is actually is a reasonable medium/easy topic um I won't ask this question right away because my microphone is um I'm having technical difficulties with the camera so I'll ask this one right at the end in case something happens and the

live

stream ends , so we'll save this one for last.

Question 11, let's go to question 12. You can see only in the diagram. This is a probability tree diagram. There's a lot of information here, so it's average, but sometimes these things seem harder than they are. I would classify it as medium to easy, so we look at this one, the next one we have here is the question in standard form 13 x^2 + 6 x - 7 in the form of this x + a 2 plus b where A and B are integers , so this is a medium easy question, this is the topic of uh, this is completing the full square, completing the square question 14 cone A and cone B are mathematically similar, so you can see here, this is similarity, so which would automatically classify this as a medium question, um, the relationship between the volume of cone A and the volume of cone B is that the surface area of ​​cone A is 297 and that shows that the area of ​​cone B is that, so We are showing things.

So this is similarity question 15. Now show that the equation has a solution between xals a 0 and one. So this is a medium/easy question because we are showing it between these two values. Part B shows that the equation x Cub + 7. x - 5 can be rearranged, so again, this is a medium type question, so this is substitution, backward substitution and 15b is rearrangement, rearrangement, is difficult?, it's easy. I think we're going to put easy in the middle so you can see, even though it's question 15, it's actually very reasonable, we have to prove that, so it gives us the answer, starting with x0 is equal to 1, use iteration, so we have an iteration here three times to find an estimate for the solution of x CU + 7 x so this is a medium type question it's not really difficult it's just a long iteration so this is an iteration let me label it here iteration, let's go to the question on the next page and then to the part uh, part D is there, let's go to the questions, part D, leave me alone. read that by substituting your answer to part C into question medium question 16 the gasoline consumption of a The formula gives a car in liters per 100 kilometers, by the way, there is a lot of information here, so you can automatically label it as medium.

The question is whether it is difficult, so gasoline consumption is equal to 100 times the number of liters of gasoline used divided. by the number of kilometers driven, Nathan's car traveled 148 kilometers correct to three significant figures, so just having something like this here tells me that this has to do with limits, so the car used 11.8 L of gasoline, corrector, three significant figures. Nathan says my car used less. 8 liters of gasoline per 100 kilometers, so this is a limit. Could Nathan be wrong? So we will evaluate that question 17 ABC and ADC are triangles ABC ADC the area of ​​triangle ADC is 56 M squared calculate the length of ab give your answer to correct to a decimal, so we have triangles in an area, however these are not triangles right angle, so we are looking at the area of ​​a triangle and the S and cosine rules, so this is a medium/hard topic, so I have the area of ​​the triangle plus the s cosine rule, so question 17 let's move on to next question 18 here is a graph of speed and time for a train and we have this information: speed is equal to speed and time, calculate an estimate of the distance the train travels. the train traveled in the first 20 seconds use four stripes of equal width, so this is the trapezoid rule, so this is a medium type question, not so difficult, medium/easy, the trapezoid rule, so the Question 18 is surprisingly not a very difficult question at that point Part B is linked to whether it is an understatement or not.

Usually your answer is an underestimation or overestimation of the actual distance traveled, so it depends on that question. 19 towards the end of the article, now prove algebraically that the straight line with the equation x to carry 2 y = 10 is a tangent to the circle with the equation x^2 + y^2 = 2 20, so that's a question difficult, there is a lot of algebra or easy if you like algebra, question 20 a B and C are points, so As you can see in the diagram, you have the circle theorem, so it definitely has something to do with the circle theorem circle. a B and C are points on the circumference of a circle.

The center o a o is the diameter of the circle. Prove that the angle ACB is 90 degrees, so we have proof here, so this is a very difficult topic, medium to difficult or difficult and the last question 21 we can see in the diagram that you have in n om MB and APB are straight lines and is equal to 2 o a m is the midpoint of O So o a is a and so on, you can see these are vectors, since MPN is a straight line, find the value of K, so this is a question difficult, so we won't spend as much time on it.

So that's how we just went through the entire document and we can see that there are some questions that are easy towards the end of the document and some questions that are much easier towards the end of the document and at the end. At the beginning, you also have some medium questions, so now we can allocate our time and answer accordingly. Before I continue, sometimes questions like this are easy marks to hit, so I'll go off on a tangent. I'm doing something that shouldn't be, but since I'm at it because I won't do this, I won't have time for it, but sometimes I just want to show you marks of easy methods, so let me read this question about OMB and APB are they straight lines or a n or a n om om m b APB a PB so we have those three straight lines an is equal to 20 a so a2n is equal to 2 a n so whatever the double m is is the midpoint of OB so B is there or so that's the midpoint or a a is a so let's label this as a let's a a a this way so a O2 B is B O2 B so let's go this way this is B AP is equal to a scalar quantity Times times AB, so we want to know what AB is a b , so we go from A to B, so we have to follow these arrows, so we go in reverse to a,so it's minus a and then we continue. the path of B, so that's B plus b and that's worth a Mark method on an

exam

, okay, so just doing that to um Or A to O then or B just doing that, that's worth a Mark method, so I thought in quickly I'll show you a nice easy make, okay, let's go through this document where some of our easy questions are.

Okay, so we just looked at the trapezoid rule, so let's start there, so I'll give you a few moments to try this question. So let's try this. Here is a speed and time graph for a train. So you have speed and you have time. We have that information. Calculate an estimate of the distance the train traveled in the first 20 seconds. Use four equal WID stripes. We are going to take an estimate of the distance the train travels in the first 20 seconds. We use four strips, so that's my keyword, so I'm going to take 20 divided by four strips. 20 with 4 gives me five, so I'm going to use five here five seconds I have my first strip, my second strip, my third strip and then my fourth strip, so I have my four strips here, so calculate an estimate of the distance distance, how do I do it?

First we calculate the distance. What does the formula equal? ​​I'm going to write it here just so it separates my exercise speed equals distance divided by time, so I'm calculating distance, distance equals speed, time, so I'll use the formula in case you forget what the trapezoid rule is: velocity times velocity. times, time, so we're working on this area, so let's turn this around. We have our four strips, let's join them together. Okay, so you can see here. I have a triangle, a trapezoid, a trapezoid, a trapezoid, so we need to solve for the areas. Of these, this is a triangle, so what is the height here?

I have to be careful, I can see here that 10 squares make five, so two squares make one unit of speed, so I have four squares here, so this is two, um. If I look closely here, it goes up to five, so it has a height of five for 15 up, this is about 15 16 17 18, so 18 okay, so those are my distances, so I have to calculate the area five and then Multiplied by the height, which is two, so you got half base * height divided two um, the next one here I have again for a trapezoid rule, we add the parallel sides, so we have 2 + 5/2 and then we multiply by our um a plus b so 2 + 5/2 times our width then multiplied by five we have the next one here 10 um 5 + 10/2 times the width five the next one here is 10 and that's 18 so 10 + 18 divided by two and then multiplied by the width which is five and then we put it in a calculator, this comes out as five plus this one comes out as 17.5, this one comes out as 37.5 and the last one comes out as 70 + 37.5 + 70 and that it gives me 130, okay, so my answer is 130 meters, okay, so this is, let's look at Part B, it's your answer to an underestimation or overestimation of the actual distance the train has traveled, so if you look at this it's a curve, so my area here is almost done, so I've included these parts so I can write here about estimate about estimate the area includes a little bit more.

Well, now we have it. I realize it took quite a bit. a little bit of time um so sometimes this happens. I started from the back, let me go back to the front. Okay, so we have the table that shows information about 80 children. This is finding the class interval that um finds the class. interval that contains the median, so we want to find the median of this, so, my steps, I forgot about the steps, so the first step and you can do it slightly differently, so I'll take my total. I'm going to find the middle part, the middle number, the middle number, which is my median and then I'm going to add the frequencies until I get to that, so step two is add frequencies, add frequencies and then step three is I I, I find out the width of my class, okay, divided by two, which gives me 40, okay, and now I have four here, the next one will be 4 + 11 = 15, so I have four plus another 11 values ​​that They give me 15, so it's not like that.

I haven't gotten to 40 yet. it doesn't include my 40th value, let me add the following 15 + 24 15 25 35 49 59 61, so clearly I'm over 40, so this is the width of my class, so M final answer for that, okay, now I need to draw a frequency polygon okay, so how do we draw a frequency polygon and then I just plot them?