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The first GCSE Maths exam is drawing ever nearer. If your students are anything like ours, they will be more than a little fed up of doing past exam papers. And if you are anything like me, you will be sick of marking them. So, I just wanted to remind you of the free Diagnostic Questions GCSE Maths papers we have on the site. These are complete Higher GCSE maths papers, broken down into manageable 20 question quizzes, with the content and challenge matching what students might expect from the actual paper. They are based on past Edexcel papers, but the content makes them suitable for any other awarding body.

The questions themselves have been adapted into an easy-to-use multiple-choice format, so they don’t reflect the actual appearance of the questions in the exam, but will give you familiarity with the content, contexts and skills required. The quizzes also have four extra advantages over traditional paper based exam papers:

1. They will be automatically marked, revealing the exact areas your students and classes need help on
2. The questions are broken down into single steps, revealing the precise concept within a topic that your students are having trouble with
3. Students writing explanations for their answers will test their depth of understanding
4. Students can benefit by reading explanations given by students from all around the world until they find the magic one that makes sense to them.

Let’s take a look at each of these advantages in more detail

1. They will be automatically marked, revealing the exact areas your students and classes need help on

A traditional Question Level Analysis can take ages to complete. With a Diagnostic Questions GCSE Paper, it is done instantly, immediately showing you which questions you need to focus on:

QLA

Automated making is great, but for real depth of knowledge about your students’ levels of understanding, explanations are the key. Each time a student answers a Diagnostic Question they are promoted to give an explanation. You can access these explanations with a click of a button for any troublesome questions, to gain real insight into exactly how deep your students’ levels of understanding are, and the precise nature of their misconceptions:

Explanation 1Explanation 2

2. The questions are broken down into single steps, revealing the precise concept within a topic that your students are having trouble with

What does it mean to say a student can’t do simultaneous equations? If you think about the separate skills required to answer a traditional GCSE Maths exam question on simultaneous equations, the list gets pretty long: manipulating algebraic expressions, collecting like terms, adding and subtracting negative numbers, solving linear equations, substitution into formulae, and more. Two students may score 0 out of 5, or 2 out of 5 on a simultaneous equations questions for very different reasons. It is important to diagnose exactly where in the process the misconception or lack of understanding occurs. Only by knowing the precise skill or concept that the student requires help on, can you work with them to help resolve their misconception.

So, in these Diagnostic Questions GCSE Maths Exam Papers, questions are broken down into single skills or concepts. So, a single question on simultaneous equations becomes:

Simultaneous 1 Simultaneous 2 Simultaneous 3 Simultaneous 4 Simultaneous 5 Simultaneous 6

Combining this with the automated marking, QLAs and student explanations described above allows us to identify exactly where in the process students are going wrong, and thus we can intervene effectively.

3. Students writing explanations for their answers will test their depth of understanding

Scientific studies have consistently shown that explaining answers demonstrate and facilitates a deeper level of learning and understanding than simply giving answers. Just take a look at some of the wonderful explanations given by Year 11 students to the following question on constructions:

Construction

if you imagine a line joining A and B then a perpendicular bisector of this line would show all the points the same distance away from A and B- imagine some points that are the same distance from A and B they would form a line

it can’t be an angle bisector because there’s no angle it can’t be a straight line because that doesn’t solve anything and it can’t be a circle because it says on the line not around the 2 points

Every point on a perpendicular bisector would be the same distance from A and B. You get a good sense of this because the point exactly half way between A and B is on the perpendicular bisector

using compasses to mark the same distance from each point, and marking where the curves cross. drawing a line using these two points creates a perpendicular bisector at equal distances from the two points

If your students are producing these, you can be sure their depth of understanding of constructions is sound.

4. Students can benefit by reading explanations given by students from all around the world until they find the magic one that makes sense to them.

As well as helping out the student who wrote these wonderful explanations, they are also of great benefit to students who read them. When reviewing their answers to a GCSE Maths Diagnostic Questions Quiz, students can read explanations giving by students from all around the world on any question they are unsure of until they find the magic one that makes sense to them.

This is all done with the click of a button:

Substitution

Review 1 Review 2 Review 3

Finally, students can use our new Revision Page (available by clicking “revise Now” on their student dashboard when they login), complete with top-quality videos and follow-up quizzes, to support their independent revision. The topics are automatically arranged in order of importance to each individual student, giving a tailor-made revision programme, all for free.

Revise

I really hope you and your students find this useful, and happy revising!

The Diagnostic Questions GCSE Maths Exam Paper collection  can be found here: https://www.diagnosticquestions.com/Edexcel

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Last week’s question on plotting a Cumulative Frequency Diagram was one of the worst answered questions across the whole of the free daily GCSE Revision Streamto date, with less than 40% of students answering it correctly. This proportion was true across our own Year 11s, despite the fact that we must have covered cumulative frequency diagrams approximately 54 million times over the last few years.

Let’s have a reminder of the question, and a look at how the students answered it:

The majority of incorrect responses by students were split across B and C. We can delve into students’ explanations to discover why.

Answer C
There were two groups of students here – those who had not read the question, and those who have two key misconceptions:

The cost across the x-axis has cumulative values and so median of these values is appropriate to use for the scale. The median of the inequality value 20<£≤40 is 30. The point on the graph must have 30 as it’s x-coordinate. We are told directly that it’s y value is 12 as that is it’s frequency and the label for the y-axis is frequency. The coordinates of the point that would correctly that would represent the highlighted row to draw a cumulative frequency are (30, 12) and the only point with that coordinate is C.”

Because the coordinates are 30 across, because the placement needs to be between 20 and 40, and up 12, which of course is the frequency

because you plot the midpoint and the frequency and on the graph we can see that 12 (frequency) has been plotted and so has 30 which is the mid point.”

Answer B
Here we have students remembering the importance of the upper boundary, but cumulative frequency has been neglected:

Cumulative frequency graphs are always plotted using the highest value in each group of data. This is because the table gives you the total that are less than the upper boundary and the cumulative frequency is always plotted up a graph, as frequency is plotted upwards.”

because in the intervals 20 to 40 you plot the last number = 40 and that is plotted on the x axis while the frequency of 12 is plotted on y.”

On a cumulative frequency curve you use the highest amount so in this example 40 on the x axis then go up the a,punt of the frequency so 12

So, what do we take from this? Well, on the bright side, you can make the case that the presentation of the question is not similar to how students would see it in the exam, so no need to panic. However, we have all seen students make these kinds of mistakes. So, at the very least, I believe it is worth showing this question to your Year 11s and just having a quick discussion about each of the incorrect answers to double-check that their knowledge is secure.

With the GCSE Maths exams getting closer, now is the perfect time to sign your Year 11s students up to the free daily GCSE Revision Stream. Over 20,000 students around the country cannot be wrong :-)

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It has been a dramatic week for Guess the Misconception, upon its return after the Easter break.

Firstly, there has been an outcry, both in my maths department and across the nation as a whole, from teachers asking “why wasn’t 100 one of the answers?” or “what happened to 40?”. This highlights both an inherent problem with multiple choice questions – namely, what happens if the answer a student thinks is correct is not actually one of the given answers? – but also reinforces the importance of students giving explanations to support their answer on Diagnostic Questions. A few of our Year 11s gave explanations such as “I am going for 110, but I reckon the answer is 100 due to alternate angles being equal”. This allowed us to go beyond the data and understand this student’s misconceptions.

Secondly – and possibly even more dramatically – the least popular misconception as voted for by teachers, turned out to be the most popular misconception held by students!

This question in… well, question… on angle facts is one of the most poorly answered across the free daily GCSE Revision Streamto date, with over half of students getting the answer wrong. Let’s take a look at the question, and see the kind of misconceptions that it reveals:

Teachers felt that A would be the most common choice, and indeed this did attract around 30% of incorrect student answers, with explanations revealing misconceptions around straight lines and the type of triangle invovled, such as:

“It’s a as it sits on a straight line and angles on a straight line add up to 180 degrees so if you take it away from 180 take away from 100 it’s left with 80″

“A straight line is 180° And this triangle is an equilateral triangle meaning all angles are the same size, triangle is 180°. 180-100 = 80, meaning the other two angles are also 80°”

But the answer that attracted over 40% of incorrect student responses was D. Can you see why? Let’s read some of explanations from the thousands of students who opted for this to find out:

“Exterior angle on the bottom two corners are 100 degrees, the angle of a straight line is 180 degrees so 180-100=80 times that by two equals 160 and then take 160 from 180 as that’s the angles in a triangle added together and that equals 20″

“This is an isosceles triangle meaning that the 2 bottom angles are equal. So first you have to do 180-100 because angles in a straight line and you get 80. This means the 2 bottom angles are going to be 80 degrees. After to find the top angle I did 80+80 which is 160 and then take that away from 180 and you get 20 degrees.”

“because the angle labelled 100 degrees is on a straight time which sums to 180 and that means the angle beside it is 80 degrees and both bottom interior angles are the same so 80 plus 80 is 160 and all interior angles in a triangle make 180 so you do 180 minus 160 which is 20 degrees.”

“First work out The angles along the bottom line 180 degrees on a straight line, so 180 – 100 (which is the exterior degree) = 80 so the angle to the bottom right is 80 degrees, as is the one on the left Inside a triangle the angles add to 180 There are already two 80 degrees 80 + 80 = 160 180-160 = 20 degrees”

What do we take from this? Well, as a maths department we were a little shocked firstly at how poorly our Year 11s performed on this question, but also the range of the misconceptions they held. Some teachers decided they were going to show this question at the start of the next lesson and allow students to discuss the answers. Other teachers announced they were doing a full angle facts revision lesson. But all decided that some sort of action was required. This might be the case with your Year 11s as well :-)

With the GCSE Maths exams getting closer, now is the perfect time to sign your Year 11s students up to the free daily GCSE Revision Stream. Over 10,000 students around the country cannot be wrong :-)

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Bearings are the kind of topic that students cannot bear (sorry). The tend to sneak their way into several key topics, most notably angle facts, construction and trigonometry. Hence, if a student’s understanding of bearings is dodgy, then it could jeopardise their chances of success across other areas.

This question is one of the most poorly answered across the free daily GCSE Revision Streamto date, with over half of students getting the answer wrong. Let’s take a look at the question, and see the kind of misconceptions that it reveals:

As predicted by teachers, by far the most popular incorrect answer was C). Why would students go for an answer of 150 degrees? Their explanations are incredibly revealing, suggesting varying levels of understanding of angles, but with once again the common thread being students falling flat due to a misremembered or misunderstood rule for bearings:

“this is because angles on a straight line equal to 180 so we take (180 away from 30) which gives us 150″

“Since the angle in the triangle is 30 degrees. I cant measure the bearing of b from a physically. Because, i know that angles on a straight line add up to 180 degrees. I use this understanding to figure out that the bearing is 150 degrees(0150 degrees)”

“Starting clockwise from north, the angle has to be 360 all the way around. 180 is already shown add the 30 degrees. 180+30=210 360-210= 150 degrees from B to A”

“Bearings always go clockwise, and angles on a straight line add up to 180 degrees. So 180 – 30 will give you the bearing from A to B which is 150 degrees”

It is interesting to note that the answer of 30 degrees cropped up in both answer A) and D), which together accounted for just as many wrong answers as C alone. Where does 30 degrees come from, I hear you ask. Well, in the words of students across the world:

“because it needs to be from north so you put the north line there, this creates a z shape. This means alternate angles are equal”

“Angle on a straight line is 180 and add 30 to find the bearing”

“180 – 30 = 150 150 + 180 = 330 360 – 330 = 30″

“Bearings always have three digits and the angles are on the same line.”

And my personal favourite:“HAVEN’T GOT A CLUE ABOUT BEARINGS MISS!!”

Like the rest of the country, over half our students got this bearings question wrong. How will we deal with this? Well, each week in our Monday Maths Departmental meeting, we discuss a particularly poorly answered question from the free daily GCSE Revision Streamthat all our Year 11s complete. We then show this question to each of our Year 11 classes and discuss not only the correct answer, but some of the best ways of explaining the answer, as well as the reasons behind the wrong answers. Doing this on a regular basis (we hope!), will allow us to focus on the areas that our students need help with in an efficient way, and through discussions lead to a deeper understanding of potentially troublesome topics.

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Last week’s question on the area of a triangle brought up two key, but completely different misconceptions. And the one teachers felt was the most popular was in fact beaten into second place by another nasty one. Let’s have a reminder of the question, and then take a look at those two misconceptions:

Incorrect Answer C

Whilst it is pleasing to note that these students have clearly remembered the important fact that they need to divide the product of the base and the height by two, unfortunately they have chosen the wrong height. That becomes very apparent in their explanations:

I think this is the right answer because you can’t just times them without using a division because that would make a rectangle. I think you times the 8 and 7 because that would make like a parallelogram which fits two triangles in it that’s why you divide it by 2?

Because the formula for the area of the triangle is base x height divided by 2. 7cm is a base, 6cm is a height so the area of the triangle is 6×7 divided by 2.

as its not a right angled triangle you cant use base times height so you have to use base times length divided by 2

8×7 gives the total of the area of a square then divide that by 2 to get the area of a triangle

Incorrect Answer B

Students opting for this one could not resist the temptation to include every single number in their calculation of area:

because to work out an area of a shape you times the length of each side together

Base x Height x width is how u find out the area of an isosceles

It is necessary to include the six as it tells you the height

the other three answers simply don’t have enough information.

What can we learn from this? Well, firstly the specific answer the students give determines the support the support they need. Perhaps students who went for C) need a visual approach as to why the perpendicular height is needed. Whereas the students going for B) are showing a lack of deep understanding of area, and perhaps need to go back to square one. The bottom line is that both answers imply a misremembered or misapplied algorithm, which is one of the most common causes of misconceptions that I see across the website.