Edexcel Mathematics: Core C1 6663 17th May 2017 [Exam Discussion]

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Take your time. Do not rush.

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Read the questions carefully. Answer the questions that have been given to you, not the questions you hoped to see. If underlining key words helps you to focus your mind, then do this. For example, don't find the tangent if the question asks for the normal.

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Differentiation is used to find the gradient at any point of a curve.

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Integration is the opposite to differentiation. When you integrate, remember to include the constant of integration.

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If you get stuck on a question, don't panic. Sit back, breathe and read the question again. Think: what information have I been given; what do I need to get to? For example, are you told the number of roots/intersection points for a function and need to show an inequality? The discriminant might be a good thing to consider because it involves an inequality itself.

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Make links when reading a question. If you read the words 'gradient', 'tangent', 'normal', etc., when looking at a question involving curves, it probably will involve differentiation.

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When working out the equation of a straight line, you need two bits of information: a point the line goes through and its gradient. Make sure you have both of these. If you don't have these, find them out!

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If there is a tricky coordinate geometry question asking you to find the area of something, draw a diagram (if one isn't given) or study the diagram if one is given. Consider how you can perhaps deconstruct the shape into ones whose areas are easier to find. Find/write down any important lengths - these will usually gain you marks. Think of formulae you know and whether they may be relevant/useful.

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For recursive relations, look out for patterns. If you have to calculate a sum that has a small upper limit, write out the terms and then do substitution. Writing out what the sum means shows understanding and will usually give you marks. If the limits seem odd, i.e. the lower limit is not 1 or the upper limit is a big number like 100, perhaps you'll need to think a bit more. For larger upper limits, you are not expected to list out all of the terms and add them. You may be expected to notice a pattern. Alternatively, if the quantity inside the sum is different to original sequence, perhaps you can manipulate your original sequence in some way to get your summand.

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For sequences and series, those worded problems are usually quite simple. However, students seem to get lost and not isolate the key information. Ask yourself: what is the context, what is my first term, what is my common difference; am I working out a sum of terms or am I working at a specific term (and which formula should I thus be using?)?

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Always use the information you are given. If you are asked to find something or show a result out of seemingly nowhere, convince yourself that all of the information you need is in front of you: read it carefully and, once again, try to isolate key words and make links.

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Check your answers make sense. If a straight line is positive for $x>0$ and you find that at $x = 2$, the line has $y$ coordinate $<0$, then something has gone wrong.

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Check your working as you go along. After a few lines, stop, read the question again, read your working again, checking for any silly errors, and continue. Checking your working as you go along is more likely to help you identify errors than at the end, where you may be rushing or reading your work at a 'glance'.

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Curve sketching: show all of the information they have asked in the question. Students forget to give intersection points, or equations of asymptotes, and lose unnecessary marks. Read the question and answer it. Remember a curve crosses the $y$ axis when $x = 0$ and it crosses the $x$ axis when $y = 0$.

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For asymptotes, make sure your curve looks like it is approaching the asymptote. To find asymptotes, consider what will make the equation 'blow up', so the speak. Division by 0 is a key one: what values of $x$ and $y$ will result in division by 0? These will be your asymptotes because your curve simply cannot take these values. For example $y = \frac{1}{x+2}$. If $x = -2$, you would have division by 0, so there is an asymptote there. If $y = 0$, you'd require division by 0, so that must also be an asymptote.

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When transforming graphs, I used to remember the transformations in two ways. If I have $y = f(x)$ and my transformation is inside the bracket, i.e. $y = f(x+a), y=f(ax)$, then the transformation affects the $x$ coordinates and does the opposite to what you think it'd do, i.e. $y=f(x+3)$ takes 3 away from $x$ coordinates, rather than adding 3 to them and $y = f(3x)$ divides the $x$ coordinates by 3, rather than multiplying them by 3. If the transformation is outside the bracket, then it affects the $y$ and does exactly what you think it would do. This is a bit hand-waivey, but it is a nice way to remember it.

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Understand function notation and its link to transformations. If you are given the curve $y = f(x) = x^3 + 2$ and want to find the curve that results from translating the curve + 3 units parallel to the x-axis, then you work out $f(x-3) = (x-3)^3 + 2 = ...$, as I'm sure you can expand and find.

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Don't overdue it tonight. Just go over key ideas, make sure you really understand the basic ideas and keep asking 'why'.