by christos nikolaidis solutions · a2+a (a — b) (a + b + l) o ... find the solutions of the...
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![Page 1: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/1.jpg)
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HAEF IB – FURTHER MATH HL
TEST 2
SETS, RELATIONS AND GROUPS
by Christos Nikolaidis
SOLUTIONS Date: 8/12/2017
Questions
Solution
![Page 2: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/2.jpg)
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Solution
![Page 3: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/3.jpg)
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Solution
(a) (i)
A1A1
[8 marks]
![Page 4: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/4.jpg)
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Solution
![Page 5: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/5.jpg)
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5. [Maximum mark: 10]
(d) Using the set Z+ as both domain and codomain, give an example of a surjective
function that is not injective. [3 marks]
Solution
(d) ���� = �1, = 1 − 1, > 1
Surjective as range = codomain
Non-injective as ��1� = 1 = ��2�
![Page 6: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/6.jpg)
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6. [Maximum mark: 12]
Solution
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7. [Maximum mark: 19]
Solution
(ii)
OR the sum of two half-integers is a half integer A1R1
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8. [Maximum mark: 15]
Solution
![Page 9: by Christos Nikolaidis SOLUTIONS · a2+a (a — b) (a + b + l) O ... Find the solutions of the equation aAb = 4Ab , for a #4. (a) ... ¥42 for all correct, Al for 2 correct. .41A1](https://reader031.vdocuments.net/reader031/viewer/2022031110/5babacae09d3f22f738c1a5d/html5/thumbnails/9.jpg)
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