Test Results

First of all results are down the bottom. You are identified by the last four digits of your student number (or five if these four digits are shared by another student). The scores are itemized as you can see. At the bottom there are some average scores.

If you would like to see your paper or have it discussed please email me.

Students with no score were either absent in which case they score zero — or certified absent in which case their marks carry forward to the summer exam.

Solutions and Remarks

Solution are found here.

Question 1 (a) was answered pretty well in general. A number of students made mistakes with their final answer. As the inequality was strict, the endpoints should not have been included in the answers. i.e. the answer to Test 1 B Q. 1(a) was $(-1/8,5/2)$ not $[-1/8,5/2]$. If you are unsure of how these go you were perfectly entitled to write $-1/8 or even “the solution set is all the real numbers between -1/8 and 5/2 not including -1/8 and 5/2“.

Q. 1(b) was easy if you knew the formula for $a^3+b^3$ — which you might have remembered from MS 1001. Take heart if you derived this formula using $(a+b)^3$ or used the factor theorem — you’ve done well. Some people thought they knew the formula but had it wrong — those that worked it out on the spot usually got it right.

Q. 2 OK first of all so many showed brutal exam technique — read the question and answer the question. Most people didn’t answer the first part of Q. 2.

Only five people had the correct definition of continuity at a point $a\in\mathbb{R}$: the simple

$\lim_{x\rightarrow a}f(x)=f(a)$.

Almost everyone else said that a function was continuous if the left and right limits agreed. While this is needed or necessary for the function to be continuous, it is not enough or sufficient. We also need the function to be defined at $a$ — and its value equal to the limit at $a$. Proposition 2.1.3 is an equivalence result — in fact you could define a limit in terms of left-and right- hand limits and then prove that this is equivalent to our definition… but continuity needs a bit more.

Those who gave good geometric definitions were given half the marks.

By and large the rest of Q.2 was answered very well — although if you didn’t score well you may have a critical lack of understanding. Please come to more tutorials and do exercises.

Q. 3 was built to be hard but anyone who learnt their definitions got the first two no problem. Q. 3 (3) was answered very poorly. Remember the definition of a limit — I say the function gets close to $L$ — you say how close — I say as close as you want — then you can say $1/100$ — or any other positive number for that matter. That is why we have to define it in terms of a general $\varepsilon>0$ — it has to get as close as you want — in this case within $1/100$.

If you failed you are going to have to up your game. Do exercises, come to tutorials, ask questions, etc.

 Stud I.D. Q 1(a)/2 Q 1(b)/3 Q 2/4 Q 3/3.5 Mark out of 12.5 Percent 0697 1.5 0 3.5 1 6 48 7109 2 2 5 2 11 88 5149 1.5 0 4 2 7.5 60 6607 2 2 4 2 10 80 4159 2 2 5 3.5 12.5 100 1209 1 2 4 0 7 56 5095 1.5 2 5 2 10.5 84 3269 0.5 0 0.5 2 3 24 5479 2 2 4 2 10 80 2147 1.5 2 4 2 9.5 76 3747 2 0 4 2 8 64 4745 1.5 1.5 4 2 9 72 4229 1.5 0 2.5 1 5 40 9259 1 1.5 4 2 8.5 68 5473 5669 1.5 2 0 0 3.5 28 0663 1.5 0 4.5 2 8 64 6233 2 2 4 2 10 80 0059 1 2 4 1 8 64 2031 1 2 3.5 2 8.5 68 1025 1.5 2 4 1 8.5 68 3481 1.5 0 2.5 2 6 48 5587 0 0 0 1 1 8 7784 1.5 2 4.5 2 10 80 40067 1 0 4 2 7 56 7258 1 2 4 2 9 72 1701 2 2 4 2 10 80 2929 1 0 1 1 3 24 4923 1 0.5 4 2 7.5 60 9663 2 0 0.5 0 2.5 20 1209 2 2 4 3.5 11.5 92 7705 1 2 5 1 9 72 4858 9917 1.5 2 4 1 8.5 68 5527 2 2 4 2 10 80 5251 2 0 4 2 8 64 8745 1 2 4 1 8 64 3031 2 0 0 0 2 16 0543 1 0 3.5 0 4.5 36 7241 1.5 1.5 0 3.5 6.5 52 9415 1 2 4 1 8 64 7197 1.5 2 4.5 2 10 80 4513 1 2 0 0 3 24 0285 2 2 4 3.5 11.5 92 8108 1.5 0 3 1 5.5 44 7327 3327 1.5 2 0 2 5.5 44 4673 1.5 2 4 1 8.5 68 59001 1 1 0 0 2 16 0133 1.5 2 4 1 8.5 68 1915 0 2 4 2 8 64 2430 1.5 2 4 2 9.5 76 3301 2 2 4 2 10 80 8475 0 0 4 1 5 40 8443 1.5 2 4 1 8.5 68 1579 4454 2 2 3.5 2 9.5 76 8299 1.5 1.5 4 0 7 56 3245 2 2 4.5 3.5 12 96 4855 2 2 5 2 11 88 1931 1.5 2 4 1 8.5 68 8159 2 0 4 2 8 64 1678 1.5 0 4.5 1 7 56 3024 9571 1.5 2 5 2 10.5 84 2221 2 2 4 2 10 80 5109 1.5 0 4 2 7.5 60 5026 8577 2 2 4 2 10 80 0395 2 2 4 0 8 64 0492 2 0 4 2 8 64 69001 2 0 2.5 1 5.5 44 0153 1.5 0.5 0 2 4 32 5263 4411 1 0 4 2 7 56 10067 1.5 1 0 1 3.5 28 0684 0 5503 1.5 0 4.5 1 7 56 1947 1 0 2.5 1 4.5 36 Average Marks 1.47 1.23 3.35 1.56 7.50 60.85 Percentages 73.59 61.27 67.04 44.47