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St. Patrick College PO. Box 63 Abeokuta Ogun State. 9th June, 2022. DearAdewale, I am very happy to write this letter to you in a most respectful manner, fully conscious of the fact that you are studying well. How is your health and your studies? I hope that everything is running smoothly in your school. Dear friend, it is a thing of joy for me to write this letter to you after one year of silence between two of us. I could recalled that the last time I received your letter was on the 6th of April, 2021. This is not normal considering how closed we are to each other. Dear Ade, I am writing this letter to intimate you of my future career and how it will be a beneficial to my country, Nigeria. I earnestly want to red medicine in the university. I want to be a medical doctor. This is a profession that I like, cherish and have passion for. I always envy medical practitioners because they are well-respected in the society. Though the profession is highly competitive, I have aptitude for science and desire to came for others. As a medical doctor, i shall be beneficial to my country, Nigeria, by helping others in an incredibly significant way. When someone is sick or injured, his or her normal way of life is disrupted, as a doctor I have the incredible opportunity to restore these people's lives to normalcy and even save some from death. Therefore, l being a medical doctor will be extremely rewarding to my country, Nigeria. As a medical doctor, I will have the ability to build meaningful relationships with my patients. By seeing my patients over and over again, I shall be able to build meaningful friendly relationships with them. Again, if l am a medical doctor in the nearest future, I shall learn everything there is to know about the human body. I shall have the opportunity to study and further examine human body with the innovative technology. From the pumping of the heart to drugs that take away pain. to machines that allows me examine human anatomy. Using modern fascinating. Moreover, I want to be a medical doctor so that I can speak to my patients on the need for exercise and physical activities, To inform them about the benefits of exercise for good health. Also to motivate my patients to adopt a better healthy lifestyle and better exercise habits. Furthermore, I want to be beneficial to my country as a medical doctor by providing information about suitable health orientation. Medicine is a notable profession or career. The satisfaction gained from treating a human being is one of the key reasons I have chosen this career. Relieving a patient's pain or bringing a patient back from the verge of death provides enormous gratification that no other profession can equal. In addition, why I want to study medicine is that, I can play an important role in altering societal norms and taboos. For example, I shall educate all members of my country about the dangers of smoking or speak out against certain practices such as open defecation. From here my patients will need my advice and live healthy life. In the same vein, having the opportunity to heal, relieve pain and cure humanity, the credit for a longer lifespan and higher quality of life belongs completely to medical advancement and research. I shall do research as a medical doctor and give the government information on how to prevent outbreak of epidemics and illnesses that would have wiped away people in my country. As a surgeon, shall diagnose complex conditions, perform intricate operation and develop cutting-edge surgical techniques, which is intellectually challenging work for the people of my country. I shall be beneficial in treating debilitating mental health conditions, As part of me helping others in my country recover from illness and lead a healthier lifestyle that can promote quality of life and longevity, I shall build my private hospital and treat patients free of charge. I shall continually seek new methods and medications to treat and improve the overall functioning of the body of the sick in my country. With these and many others that I shall do, I shall be immense benefit to my country Nigeria, If I succeed to become a medical doctor. Thanks and have a nice time till we meet. Greet everybody over there for me. Yours affectionately, Ajanaku

St. Patrick College PO. Box 63 Abeokuta Ogun State. 9th June, 2022. DearAdewale, I am very happy to write this letter to you in a most respectful manner, fully conscious of the fact that you are studying well. How is your health and your studies? I hope that everything is running smoothly in your school. Dear friend, it is a thing of joy for me to write this letter to you after one year of silence between two of us. I could recalled that the last time I received your letter was on the 6th of April, 2021. This is not normal considering how closed we are to each other. Dear Ade, I am writing this letter to intimate you of my future career and how it will be a beneficial to my country, Nigeria. I earnestly want to red medicine in the university. I want to be a medical doctor. This is a profession that I like, cherish and have passion for. I always envy medical practitioners because they are well-respected in the society. Though the profession is highly competitive, I have aptitude for science and desire to came for others. As a medical doctor, i shall be beneficial to my country, Nigeria, by helping others in an incredibly significant way. When someone is sick or injured, his or her normal way of life is disrupted, as a doctor I have the incredible opportunity to restore these people's lives to normalcy and even save some from death. Therefore, l being a medical doctor will be extremely rewarding to my country, Nigeria. As a medical doctor, I will have the ability to build meaningful relationships with my patients. By seeing my patients over and over again, I shall be able to build meaningful friendly relationships with them. Again, if l am a medical doctor in the nearest future, I shall learn everything there is to know about the human body. I shall have the opportunity to study and further examine human body with the innovative technology. From the pumping of the heart to drugs that take away pain. to machines that allows me examine human anatomy. Using modern fascinating. Moreover, I want to be a medical doctor so that I can speak to my patients on the need for exercise and physical activities, To inform them about the benefits of exercise for good health. Also to motivate my patients to adopt a better healthy lifestyle and better exercise habits. Furthermore, I want to be beneficial to my country as a medical doctor by providing information about suitable health orientation. Medicine is a notable profession or career. The satisfaction gained from treating a human being is one of the key reasons I have chosen this career. Relieving a patient's pain or bringing a patient back from the verge of death provides enormous gratification that no other profession can equal. In addition, why I want to study medicine is that, I can play an important role in altering societal norms and taboos. For example, I shall educate all members of my country about the dangers of smoking or speak out against certain practices such as open defecation. From here my patients will need my advice and live healthy life. In the same vein, having the opportunity to heal, relieve pain and cure humanity, the credit for a longer lifespan and higher quality of life belongs completely to medical advancement and research. I shall do research as a medical doctor and give the government information on how to prevent outbreak of epidemics and illnesses that would have wiped away people in my country. As a surgeon, shall diagnose complex conditions, perform intricate operation and develop cutting-edge surgical techniques, which is intellectually challenging work for the people of my country. I shall be beneficial in treating debilitating mental health conditions, As part of me helping others in my country recover from illness and lead a healthier lifestyle that can promote quality of life and longevity, I shall build my private hospital and treat patients free of charge. I shall continually seek new methods and medications to treat and improve the overall functioning of the body of the sick in my country. With these and many others that I shall do, I shall be immense benefit to my country Nigeria, If I succeed to become a medical doctor. Thanks and have a nice time till we meet. Greet everybody over there for me. Yours affectionately, Ajanaku

multiply both sides by the LCM 12 x \(\frac{y+2}{4}\) - 12 x \(\frac{y-1}{3}\) >12 x 1 3[y+2] - 4[y-1] > 12 3y + 6 - 4y + 4 > 12 -y + 2 > 12 -y > 12 - 10 = 2 y < -2

(a) r =\(\frac{9}{7-2x}\) r = \(\frac{5x+1}{7-2x}\) \(\frac{9}{7-2x}\) = \(\frac{5x+1}{7-2x}\) 9x9=(7-2x) (5x +17) 81 = 35x + 119 - 10x\(^2\) - 34x 10x\(^2\) - x - 38 (x -2)(10x+19) = 0 x = 2, x = \(\frac{19}{10}\) x = 2 (b) Let the integers be x and y x:y= 3:4 \(\frac{x}{y}\) = \(\frac{3}{4}\) x = \(\frac{3y}{4}\) 3x + 2y=68 3( \(\frac{3}{4}\)y)+ 2y = 68 \(\frac{9}{4}\)y + 2y = 68 9y + 8y = 272 17y = 272 y= 16 x = \(\frac{3}{4}\) * 16 →12

(a) y =(\(\frac{pr}{m} - p^2r\))\(^{\frac{-3}{2}}\) y = (\(\frac{pr - mrp^2}{m})^\frac{-3}{2}\) y = [\(\frac{m}{pr - mrp^2}]^\frac{3}{2}\) \(y^\frac{2}{3} = \frac{m}{r(p - mp^2)}\) r = \(\frac{m}{y^\frac{2}{3}[p - mp^2]}\) b) Given y = -8, m = 1 p = 3 r = \(\frac{m}{y^\frac{2}{3}[p - mp^2]}\) r = \(\frac{1}{(-8)^\frac{2}{3}[ 3 - (1)3^2]}\) r = \(\frac{1}{(-2)^2[3 - 9]}\) r = \(\frac{1}{[4][-6]}\) = \(\frac{-1}{24}\)

(a) 2x + 40 + 2y + 10 = 180^\circ...(1) 2x + 2y = 130 x + y = 65º 5x - 35 = 2(2y+ 10) ... (2) 5x - 35 = 4y +20 5x - 4y = 55 5x - 4(5-x) = 55 5x - 260 + 4x =55 9x = 315 x = 35^\circ y= 65 - 35 y=30^\circ ∠ABC + [2 x º35 + 40] + [5(35)-350)] + 40^\circ =360º ∠ABC + 110 + 140^\circ+ 40º = 360 ∠ABC + 290^\circ = 360^\circ ∠ABC = 70^\circ

a) m = tan 30º = \(\frac{\sqrt{3}, n = tan 45º = 1 \(\frac{ m - n}{mn}\), = \(\frac{\frac{\sqrt{3}}{3} - 1}{\frac{\sqrt{3}}{3}(1)}\) = \(\frac{\frac{\sqrt{3} - 3}{3}}{\frac{\sqrt{3}}{3}}\) = \(\frac{\sqrt{3} - 3}{3}\) X \(\frac{3}{\sqrt{3}}\) = \(\frac{\sqrt{3} - 3}{\sqrt{3}}\) = \(\frac{\sqrt{3} - 3}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{3 - 3\sqrt{3}}{3}\) = 1 - \(\sqrt{3}\) b) see the diagram above.. Let the number of women wearing both wristwatches and glasses be x 15 - x + x + 10 - x = 20 25 - x = 20 x = 5 Therefore, the number of women wearing wrist watches only = 10 - x = 10 - 5 = 5 and number of women wearing glasses only = 15 - x = 15 - 5 = 10 Pr(both) = \(\frac{5}{20}\) = \(\frac{1}{4}\) = 0.25

(a) x-axis: 2 cm to 2 units or 1 cm to 1 unit y-axis: 2 cm to 10 units or 1 cm to 5 units (b) x = -2, x = 4 (x+2)(x-4) = 0 x\(^2\) -4x + 2x -8 = 0 x\(^2\) -2x - 8 = 0 y = 8 + 2x - x(curve has a max. point) m = -1,n = 2, r =8 (c) P(-5,-27),Q(3,5) Gradient = \(\frac{5+27}{3+5}\) = \(\frac{32}{8}\) = 4 (d) Range: {x:-2 < x < 4)

(a) Total cost 180 x 250 =N45,000.00 Total selling price = 300y + (180-y) x 250 x \(\frac{95}{100}\) 300y + 42750 -237.5y = 62.5y + 42750 Profit = 62.5y + 42750 -4500 7125 = 62.5y - 2250 9375 = 62.5y y = 150 (b)) Profit = \(\frac{x^2}{20} - 33x\) (24x+ 103) 9x - \(\frac{x^2}{20}\) - 103 (ii) Cost = 24(20) +103 = 583.00 Selling Price =33(20) - \(\frac{20^2}{20}\) = 640 Percentage profit = \(\frac{640-583}{583}\) x 100% = 9.78%

(a) 35 + 7.5 + 10 + 15 + 17.5 + x = 100 85 + x = 100. x = 100 - 85 x = 15 items % degree food & drinks 35 \(\frac{35}{100} * 360\) = 126º fuel 7.5 \(\frac{7.5}{100} * 360\) = 27º rent 10 \(\frac{10}{100} * 360\) = 36º building project 15 \(\frac{15}{100} * 360\) = 54º education 17.5 \(\frac{17.5}{100} * 360\) = 63º savings 15 \(\frac{15}{100} * 360\) = 54º (c) income tax = \(\frac{12}{100} * 28,800\) = $3,456.00 Monthly tax = \(\frac{3456}{12}\) = $288.00 (ii) Monthly net salary = \(\frac{1}{12} (288 - 3456)\) = $2,112.00 Amount saved each month = \(\frac{15}{100} * 2112\) = $316.80

xº 0 20 40 60 80 100 120 140 160 180 y 7.0 7.6 7.3 6.1 4.2 1.7 -0.9 -3.4 -5.6 7.0 (b) (C)(i) From the graph, When x is 150^\circ y = -4.6 \pm 0.2 (ii) Range of value of x for which y > is x: 0º \le x \le 113

Mean = \(\frac{\sum fx}{ \sum f}\) = (3x2) +(4x6) + (5x5) + (6x) + (7x6) + (8x9) + (9x8) + (10x5) \div (2 + 6 + 5 + x + 6 + 9 + 8 + 5) 7 = (291 + 6x) \div (41+x) 7(41+x) = 291 + 6x 287 + 7x = 291 + 6x x = 4 (b) Age(x in yrs) No.of child Fx\(^2\) 3 2 18 4 6 96 5 5 125 6 4 144 7 6 294 8 9 576 9 8 648 10 5 500 Σf = 45 Σfx\(^2\) = 2401 Standard deviation = \(\sqrt \frac{196}{45} = \sqrt 4.3555\) = 2.087

(a) ∠XYZ = \(\frac{1}{2}\) (146) = 73º ∠OZX = 34º ∠OZY = 73 - 34 ∠OYZ = ∠OZY = 39 (b) x = y - 7 42 + 38 + 57 + x + x + y + 2x - 15 + 3x - y = 360 122^\circ+7x = 360^\circ 7x = 360º - 122 = 238^\circ 7x = 238º x = 34 : 34 = y - 7 34 + 7 = y 41 = y

9(a)(i) p = \(\frac{1}{4}\), p = 1 - \(\frac{1}{4}\) p = \(\frac{3}{4}\) = \(\frac{3}{64}\) = 0.04687 ≈ 0.05 (ii) p(winning all) = \(\frac{3}{4}\) * \(\frac{3}{4}\) * \(\frac{3}{4}\) = \(\frac{27}{64}\) = 0.422 (iii) p(winning two) = (\(\frac{3}{4}\) * \(\frac{3}{4}\) * \(\frac{1}{4}\)) + (\(\frac{3}{4}\) * \(\frac{1}{4}\) * \(\frac{3}{4}\)) + (\(\frac{1}{4}\) * \(\frac{3}{4}\) * \(\frac{3}{4}\)) = \(\frac{9}{64}\) + \(\frac{9}{64}\) + \(\frac{9}{64}\) = \(\frac{27}{64}\) = 0.4218 = 0.42 (b) Volume of a cone = 1/3\pir\(^2\)h 1200 = \(\frac{1}{3}\) * \(\frac{22}{7}\) * r\(^2\) * 24 r\(^2\) = \(\frac{1200 * 3 * 7}{22 * 24}\) r\(^2\) = \(\frac{25200}{528}\) r\(^2\) = 47.727 r = \(\sqrt 47.727\) r = 6.9085cm Volume of a cone with same radius and height 84cm: v = \(\frac{1}{3}\) * \(\frac{22}{7}\) * (6.9085)\(^2\) * 84 = \(\frac{1}{3}\) * \(\frac{22}{7}\) * 47.727 * 84 volume = 4200cm\(^3\)

209 = 2 * \(\frac{22}{7}\) * \((\frac{7}{2})^2\) + 2 * \(\frac{22}{7}\) * \(\frac{7}{2}\) * h 209 = 77 + 22h 132 = 22h h = 6cm (b) tan 43º = \(\frac{h}{y}\) 0.9125y = h ...[i] tan 38º = \(\frac{h}{y+19}\) 0.7813(y+19) = h ...[ii] 0.7813(y+19) = 0.9125y 0.7813y + 14.8447 = 0.93257 14.8447 = 0.1512y y= 98.1792 = 98.2m h = 0.9325 x 98.1792 = 91.55 =91.6m