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Quadratics are ubiquitous in mathematics. For the purposes of this piece a quadratic is a realvalued function of the form
,
where such that . There is a little bit more to be said — particularly about the differences between a quadratic and a quadratic function but for those this piece is addressed to (third level: nonmaths; all second level), the distinction is unimportant.
Geometry
The basic object we study is the square function, , :
All quadratics look similar to . If then the quadratic has this geometry. Otherwise it looks like and has geometry
The geometry dictates that quadratics can have either zero, one or two real roots. A root of a function is an input such that . As the graph of a function is of the form , roots are such that , that is where the graph cuts the axis. With the geometry of quadratics they can cut the axis no times, once (like ), or twice.
Here are a number of additional exercises for those who never got them in class:
The following are all of exam level difficulty:
Updated on May 24th 2011.
The results are down the bottom. You are identified by the last three digits of your student number. If there is a zero is means that you did not write down your student number. The results are in alphabetical order but if you are unsure email me and I will tell you what you got.
The scores are itemized as you can see. At the bottom there are some average scores. Finally the last column displays your Continuous Assessment mark for Test 2 (out of 15).
If you would like to see your paper or have it discussed please email me at jippo@campus.ie
St No 
One 
Two 
Three 
Four 
Five 
Six 
/40 
% 
CA/15 

390 
10 
5 
10 
3 
5 
2 
35 
88 
13.2 

000 
10 
5 
10 
3 
3 
4 
35 
88 
13.2 

928 
7 
4 
9 
5 
5 
5 
35 
88 
13.2 

136 
10 
5 
10 
2 
0 
4 
31 
78 
11.7 

669 
10 
5 
8 
3 
1 
0 
27 
68 
10.2 

784 
9 
5 
10 
0 
2 
0 
26 
65 
9.75 

051 
10 
5 
5 
3 
1 
2 
26 
65 
9.75 

817 
9 
5 
5 
3 
0 
2 
24 
60 
9 

417 
9 
5 
4 
3 
2 
1 
24 
60 
9 

933 
9 
2 
10 
0 
0 
0 
21 
53 
7.95 

175 
5 
5 
10 
0 
0 
0 
20 
50 
7.5 

465 
6 
2 
9 
0 
0 
0 
17 
43 
6.45 

000 
9 
2 
2 
0 
0 
0 
13 
33 
4.95 

917 
0 
2 
4 
0 
0 
0 
6 
15 
2.25 

812 
3 
0 
3 
0 
0 
0 
6 
15 
2.25 

828 
2 
1 
5 
0 
0 
0 
8 
20 
3 

163 
5 
4 
5 
3 
0 
4 
21 
53 
7.95 

953 
3 
2 
0 
0 
0 
0 
5 
13 
1.95 

513 
2 
0 
2 
0 
0 
0 
4 
10 
1.5 

000 
2 
0 
0 
0 
0 
0 
2 
5 
0.75 

Ave 
6.5 
3.2 
6.05 
1.4 
0.95 
1 
19 
49 
7.275 

Ave % 
65 
64 
60.5 
28 
19 
24 




The MATH6014 Test 2 will be held at 5 p.m. Tuesday 03/05/11. The test is worth 15% of your final mark. The test will be 50 minutes long and you must answer all questions. The marks each question carries will be stated on the test and I will attach a set of tables.
Sample to be found here.
The results are down the bottom. You are identified by the last three digits of your student number. If there is a zero is means that you did not write down your student number. The results are in alphabetical order but if you are unsure email me and I will tell you what you got.
The scores are itemized as you can see. At the bottom there are some average scores. Finally the last column displays your Continuous Assessment mark for Test 1 (out of 15).
If you would like to see your paper or have it discussed please email me at jippo@campus.ie
St No  1a  1b  2a  2b  3a  3b  %  CA 
784  5  1  15  3  20  20  64  10 
136  15  4  15  15  20  18  87  14 
933  10  0  1  15  20  17  63  10 
0  0  0  0  0  20  0  20  3 
390  13  1  3  8  20  20  65  10 
0  12  4  7  6  20  20  69  11 
828  0  0  0  0  20  0  20  3 
917  0  0  0  0  20  4  24  4 
051  8  4  7  3  20  17  59  9 
918  0  0  0  1  20  14  35  6 
465  2  0  2  3  20  13  40  6 
817  8  0  3  2  10  12  35  6 
162  0  0  3  0  20  19  42  7 
417  15  0  7  12  10  15  59  9 
0  0  0  2  0  20  12  34  6 
953  2  0  1  0  5  3  11  2 
175  0  0  0  0  20  4  24  4 
498  0  0  1  0  10  6  17  3 
812  6  1  0  0  20  14  41  7 
513  5  0  3  0  20  11  39  6 
669  4  10  10  15  20  20  79  12 
928  9  5  6  0  20  18  58  9 
440  0  0  1  0  20  14  35  6 
092  3  0  1  0  5  5  14  3 
163  4  0  0  8  20  12  44  7 
Ave  4.84  1.20  3.52  3.64  17.60  12.32  43.12  6.92 
Ave %  32.27  8.00  23.47  24.27  88.00  61.60 
The first MATH6014 test will be held at 5 p.m. today. The test is worth 15% of your final mark. The test will be 50 minutes long and you must answer all questions. Question 3 is worth 40 marks; Questions 1 and 2 30 marks each. I will put the formula for the roots of a quadratic equation on the paper. Please find a sample here.
Module Description:
More detailed General Information on this module (* not all one hundred percent accurate at time of publication) may be found after the table of contents in this set of incomplete notes:
(last updated 04 May)
February 16
Additional exercises have been added to the section on Basic Algebra (go to the link to the notes above).
Additional exercises are also to be found in the suggested reading.
Past exam papers also comprise additional exercises.
I will strive to include more exercises in future — and will have more algebra exercises in time. I will furnish ye with equation exercises on Friday.
An exam paper from 2007/08:
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