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Guidelines on how to excel in Math exams. It highlights the problems hindering students from comprehending Mathematics and proffers solutions to them. It also provides tips on how to prepare for Math exams, including being attentive in class, having regular private study, making good summary sheets, practicing regularly, knowing strengths and weaknesses, giving more preference to Math, taking study breaks, using available campus resources, studying in a convenient environment, and testing oneself with peers and online quizzes. The document also warns against pitfalls to avoid, such as failure to read instructions, failure to understand the language of Math, illegible handwriting, and lack of time consciousness. It concludes with standard Math quiz questions and solutions from the University of Benin, Nigeria.

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Download The Secrets to Math Exam Success and more Summaries Mathematics in PDF only on Docsity! THE SECRETS TO MATH EXAM SUCCESS BY DANIEL O. AMAIZE With [Standard Math quiz questions with solutions] INTRODUCTION Mathematics is not a subject you can pass just by reading through the texts. You must practice problem solving on a regular basis. And you must be acquainted with the requisite formulas to solve problems in Mathematics. Each time I write concerning Math studying tips, I remember my high school mate and friend John Makun. John hated Math and found Math problems as the toughest challenge he will ever face in life. Laughable right? Yeah! John later studied Math in School and he graduated with an upper grade. Because I told him he must fall in love with Math to excel in it, which he did. That is one of the problems that has led many students to fail Mathematics. The lack of interest in the subject kills every zeal to learn Math. And once the willingness to learn is not there, learning cannot take place. So in this write up, am going to highlight some of the problems hindering students from comprehending mathematics. Am also going to outline some guidelines on how to answer Math exam questions without stress. Follow the guidelines in this booklet if you want to to become outstanding in your next Mathematics exams. REASONS WHY STUDENTS FIND IT HARD TO COMPREHEND MATH In the introductory section, I highlighted a few of the problems/hindrances to comprehending Math. Here, we are going to look at the problems in details and also proffer solutions to them. 1. A Lack of Interest And motivation: most times students find it difficult to comprehend subjects in general, the underlying problem could be a lack of interest on the part of the student. Many a time, I have seen students lose interest in a subject because the subject teacher failed to motivate the students. When a serious student finds him/herself in such a situation, the only way to succeed in such scenario is to find a way to motivate self. When I was preparing for my high school final exams, we didn’t have a good Mathematics teacher. But we (me and my Math crew) did not allow that to hinder our successes. We found a way to motivate ourselves. There were others (our peers) who used that as an excuse not to prepare very well for the final exams, because they had a lack of interest in the subject. So before you can succeed in Mathematics, your interest in the subject must be stronger than your excuses. You must find a way to motivate yourself when your school tutors fail to do their jobs. HOW TO PREPARE FOR A MATH TEST/EXAM You must be prepared before taking a test/quiz or writing an exam. There is a saying “He who fails to plan, plans to fail.” If you must pass your next Math quiz/exam, then preparation (planning) is key. The following are some preparation tips which will aid you to pass your next Math test/exam: 1. Be Very Attentive in Class: one of the reasons students fail Math tests/exams is that they are not always attentive in Math class. Math requires much focus and attention which most students don’t often realize. So you’ve got to be very attentive in Math classes in order to grab most of the basic principles which will aid you to pass your tests and exams. Being attentive in Math classes is the first preparation you need to make. 2. Have Your Private Study Regularly: as a preparation for your next Math exam, make sure to study your Math textbooks regularly. Do your Math assignments and try to solve other exercises from the textbooks on your own. Just make sure you solve a few Math problems on a daily basis. Also, try to increase the number of problems you can solve as a measure of your progress. For example, you could improve from solving three problems a day to solving five a day the next week and so on. 3. Make good summary sheets from your study and problems solved: during your study, do well to make a list of important formulas, theorems, rules and laws in Math. Also, make a list of the course objectives for each topic and do well to review the list on a daily basis. 4. Practice make perfect: do well to practice the problems you encounter on daily basis until you master the ability to solve them, and do well to verify the solutions. This will give you a good understanding of the question patterns and mode of solution to each of the problems. 5. Know Your Strengths and Weaknesses: do not be afraid of your limits, but know your limits and avoid them. If you must pass your next Math exams, you must know your areas of strength and weaknesses. Develop your areas of strength and put more efforts in improving your areas of weakness. 6. Give more preference to Math: if you must become flawless in solving Math problems, then this should become your priority. Give more attention to Math by spending more time in solving problems in Math compared to other subjects. 7. Take Study Breaks: you should not study Math without taking a break. You cannot afford to overwork your brain without giving it time for a little rest. “All work and no play they say makes Jack dull.” Always give the brain some time off to recharge and assimilate what has been committed to it. During your study breaks, take a walk and some refreshments. You can go back to the difficult problems you could not solve previously after the break. 8. Try Using Available Campus Resources: there are many Math resources available on campus. You can access free online Math tutoring on the Academic support centres. Also, do well to leverage on the Stem Learning Centres and other study groups. 9. Study in a Convenient Environment: distraction is an arc enemy of Math study. If you want your study to be efficient and effective, do well to study in a serene and convenient environment. Avoid noise and every form of distractions during Math study. 10. Test Yourself with peers and online quiz: do not be a master of yourelf but try to compare and contrast your knowledge with your peers. Compete in math quizes in school and in online quiz platforms like Typeform, Wirisquizes and others. REASONS WHY STUDENTS MAY STILL FAIL MATH EXAMS AFTER PREPARING WELL FOR THE EXAMS First things first; before we look into the tips (the dos) on how to pass Math quizzes and exams, let us look at some practices to avoid (the don’ts). Please avoid these pitfalls because they will make you to lose marks and also reduce your chances of passing your next Math test/exams. 1. Failure to Read the Instructions: one of the main reasons many students fail Math quizes/exams is because they don’t read the instructions. It doesn’t matter whether this is intentional or just an oversight, you may fail your next Math quiz or exam if you do not pay attention to the instructions given before attempting to answer the questions. The instructions are the guidelines (more like a manual). Imagine you bought an entirely new device without looking at the manual. You might damage the device if you attempt to operate it with reading through the manual. So for no reason should you fail to read the instructions before answering the questions in your next Math quiz/exam. 2. Failure to Understand the Language of Math: more like other subjects, there is mode of communication in Mathematics. Be sure to understand mathematical statements and sentences. This will help you to understand the questions asked and the required answers tto the questions. 3. Illegible Handwriting: when your handwriting is not clear enough to be read, then the examiner is in trouble. He cannot mark what he cannot read. And it is very easy for an examiner to mark your work wrong if your handwriting is not clear enough to be read. So make sure to work on your handwriting before your next Math quiz/exam. Also, it is good practice to always enclose your final answer in a box to make it obvious and very visible. 4. Time Consciousness: another reason why students fail Math tests/exams is that they are not always conscious of the time allocated for the exam. The purpose of exams is to test the student’s speed and accuracy in applying the principles learnt. So if you must pass your next Math exams, then you have to be very conscious of the time allowed for the exams. So in preparation, test your speed by answering a number of questions in a given period of time. STANDARD MATH QUESTIONS AND ANSWERS [UNIVERSITY OF BENIN-NIGERIA] 1. Solve for a if 27a x 92(a + 3) = (3a)4 Solution This is a question in indices Start by expressing each term the smallest possible base (3): That is; (33)a x (32)2(a + 3) = (3a)4 Simplify all brackets; 33a x 34a + 12 = 34a Apply the multiplication law of indices on the left hand side 3(3a + 4a + 12) = 3(4a) Since both bases are equal, the indice are equal. Thus ; 3a + 4a + 12 = 4a 3a + 4a – 4a = -12 3a = -12 Therefore, y = 8 (since a number base cannot be negative) 5. Find the quadratic equation whose roots are such that one of the roots is 1 3 while the other is two-third the value of the first root. Solution Let the two roots be α and β. Then, β = 2 3 α (because one root is two-thirds the other root) So if α = 1 3 , then β = 2 3 * 1 3 = 2 9 The general format of a quadratic equation is; x2 – (sum of roots)x + product or roots = 0 x2 – ( 1 3 + 2 9 )x + ( 1 3 * 2 9 ) = 0 x2 –( 3 + 2 9 ) + ( 2 27 ) = 0 x2 – ( 5 9 )x + ( 2 27 ) = 0 27x2 - 15x + 2 = 0 6. Find the roots of the polynomial x3 – 8x2 + 19x – 12 = 0. Solution Test for factors of x3 – 8x2 + 19x – 12. Let f(x) = x3 – 8x2 + 19x – 12 F(1) = (1)3 – 8(1)2 + 19(1) – 12 = 1 – 8 + 19 + 12 = 0 Thus, x – 1 is a factor of x3 – 8x2 + 19x – 12 We can get the other factors by dividing x3 – 8x2 + 19x – 12 by x – 1 as follows: x2 - 7x + 12 x – 1 x3 – 8x2 + 19x – 12 -(x3 – x2 - 7x2 + 19x – 12 - (7x2 + 7x - (12x – 12 -(12x – 12 Thus; x3 – 8x2 + 19x – 12 = (x – 1) (x2 - 7x + 12 ) x2 - 7x + 12 = x2 - 3x – 4x + 12 = (x2 - 3x) – (4x + 12) = x(x - 3) – 4(x - 3) = (x - 3) (x - 4) Thus; x3 – 8x2 + 19x – 12 = (x – 1) (x - 3) (x - 4) If (x – 1) (x - 3) (x - 4) = 0, Either x – 1 = 0, x – 3 = 0 or x – 4 = 0 Therefore, x = 1, 3 or 4 7. Find the equation of the straightline passing through point P(3, 4) and perpendicular to the line 4x + 3y + 6 = 0. Solution If 4x + 3y + 6 = 0 y = − 4𝑥 3⁄ – 2 the slope of this line is − 4 3⁄ . So any line perpendicular to this should have a slope of 3 4⁄ . Therefore the equation of the line passing through point (3, 4) and perpendicular to this line should be: (y – 4) = 3 4⁄ (𝑥 − 3) 4(y – 4) =3(x – 3) 4y – 16 = 3x – 9 Therefore, the equation is 4y – 3x – 7 = 0 8. Given that f(t) = 2t4 – 10t-3 + 8y2 + 12, find f1(-2). Solution First differentiate f(t) f(t) = 2t4 – 10t-3 + 8y2 + 12 f1(t) = 𝑑𝑦 𝑑𝑡 = 8t3 + 30t-4 + 16t = 8t3 + 30 𝑡4 + 16t substitute t = -2 f1(-2) = 8(-2)3 + 30 (−2)4 + 16(-2) f1(-2) = 8(-8) + 30 16 + 16(-2) f1(-2) = -64 + 15 8 + -32 therefore f1(-2) = - 753 8 or - 94 1 8 9. A piece of land is in the shape of the curved surface of a cone. Calculate the curved surface area of the land if the cone has a base diameter of 24units and a vertical height of 5units. [π = 3.142] Solution r = d/2 = 24/2 = 12 h = 5 l = √𝑟2+ ℎ2 = √122+ 52 = √144 + 25 = √169 = 13 curved surface area of a cone = πrl = 3.142 * 12 * 13 Therefore, the curved surface area = 490.088squ. units 10. If 8 workmen could do a job in 40 days and they all work at the same rate, how many workmen are required to do a job thrice larger than the first in 10 days? Solution If 8 workmen could do a job in 40 days If the job is three times large, 1 workmen will be able to do the job in: 8 * 40 days = 320 days Number of workmen required to do the job in 10 days = 320 10 = 32 If the job is thrice larger than the first, then the number of workmen required 10 read the Guardian, 30 read the Tribune while 10 people read all three news papers. If 15 people read the Guardian and the Daily news papers, 12 read Tribune and the Guardian while 18 people read the Dailys and Tribune, how many people read at least two news papers? Solution D = 40 G = 50 U = 120 17 5 33 8 2 10 T = 30 From the Venn Diagram above: Daily Newspaper only = 40 – (8 + 5 + 10) = 40 – 23 = 17 Gaurdian Newspaper only = 50 – (5 + 10 + 2) = 50 – 17 = 33 Tribune Newspaper only = 30 – (8 + 10 + 2) = 30 – 20 = 10 At least two Newspapers means that: either they read all three or any two Newspapers = DnGnT or DnG or DnT or GnT = 10 + 8 + 5 + 2 Therefore number of people reading at least two Newspapers = 25 people 15. The number of books n, sold by a bookstore is partly constant and partly varies inversely as the price p, of a book. 80 books were sold when the price of a book was $500 and 50 books were sold when the price of a book was $700. Find the number of books sold when the price of a book is $100. Solution n α k + 1 𝑝 n = k + 𝑐 𝑝 (where k and c are constants) when n = 80 and p = $500; 80 = k + 𝑐 500 500 * 80 = 500 * k + 500 * 𝑐 500 40000 = 500k + c ------------------------------- (1) When n = 50 and p = 700; 50 = k + 𝑐 700 50 * 700 = 700 * k + 700 * 𝑐 700 35000 = 700k + c ------------------------------- (2) Subtracting (2) from (1) gives 5000 = - 200k k = 5000/-200 k = -25 from (1): 40000 = 500 * -25 + c 40000 = -12500 + c c = 40000 + 12500 c = 52500 n = 52500 𝑝 – 25 (relationship) when p = 100 n = 52500 100 – 25 n = 525 – 25 Therefore n = 500 16. Find the inverse of the Matrix below. A = 2 −3 1 1 3 5 −2 1 4 Solution det (A) = 2(12 – 5) - -3(4 - - 10) + 1(1 - - 6) = 2(7) + 3 (14) + 1(7) = 14 + 42 + 7 det (A) = 63 AT = 2 1 −2 −3 3 1 1 5 4 det (Ai) = | 3 1 5 4 | | −3 1 1 4 | | −3 3 1 5 | | 1 −2 5 4 | | 2 −2 1 4 | | 2 1 1 5 | | −1 2 3 1 | | 2 −2 −3 1 | | 2 1 −3 3 | det (Ai) = 7 −13 18 14 10 9 7 8 9 adj (A) = 7 −13 18 14 10 9 7 8 9 * + − + − + − + − + adj (A) = 7 13 18 −14 10 −9 7 −8 9 A-1 = 1 det(𝐴) * adj (A) = 1 63 7 13 18 −14 10 −9 7 −8 9