billy Maths
Microsoft Word - MATH 1151 Semester I Supplemental Exam 2020.docx 1 Programme Code: DT6522, DT6524 Module Code: MATH1151 CRN: 29247, 29365 TECHNOLOGICAL UNIVERSITY DUBLIN CITY CAMPUS _____________ Programme Code: DT6522, DT6524 Programme Title: Access Foundation Programme International Foundation Programme Year 1 ______________ SEMESTER 1 SUPPLEMENTAL EXAMINATIONS 2019/20 ______________ Module Title: Intermediate Mathematics 1 Internal Examiner: Dr. Theresa Hedderman-Bowe Dr. Qi Wang External Examiner: Sriyani Jayaweera David McCann Exam Duration: 3 hours Instructions: Answer all the questions for full marks Special Instructions/Handouts: Use of non-programmable calculators is allowed Use of mathematical tables and formulae book is allowed 2 QUESTION 1 (100 marks) (a) Simplify: 3! 15+ 7 − 4+ 3(4!) (6 marks) (b) Find: (i) The LCM of 6, 7 and 13 (6 marks) (ii) The HCF of 32 and 56 (6 marks) (c) Perform the following calculations: (i) Increase 56 by 36% (4 marks) (ii) Decrease 789 by 13% (4 marks) (iii) Increase 152 by a factor of 4 (4 marks) (iv) Decrease 78 by a factor of 3 (4 marks) (d) Patrick is travelling from Dublin to Dundalk by train. The train journey takes 1 hour 45 mins. It takes 35 minutes to get from Connolly station to Gormanstown station. It takes 1/5 of the total time to get from Gormanstown station to Laytown station. And 30% of the total time to get from Laytown station to Drogheda station. How long does it take to get from Drogheda to Dundalk station? (12 marks) (e) A certain mobile phone company is offering a deal to its domestic bill paying customers. The offer is 225 free texts and 300 minutes of free calls to any network anytime in Ireland for €75 per month. Additional texts messages cost 8 cent per message and phone calls cost 25 cent per minute. Calculate the following monthly bills: (i) 150 texts and 325 minutes of calls for the month of April (10 marks) (ii) 5 hours and 30 minutes of calls and 11 texts each to 23 people for the month of May (10 marks) (iii) For the month of June an average of 20 minutes of calls and 35 texts per day were sent (10 marks) (f) A toy store owner is buying game consoles. Xbox comes in 8 per box, PS4 comes in 12 per box and Nintendo Switch comes in 18 per box. 3 (i) What is the smallest number of Xbox consoles the owner can order where there is an equal number of all three consoles ? (12 marks) (ii) The store owner wants to have at least 80 Nintendo Switches but also wants to have an equal number of all consoles. How many boxes of each console must be ordered to achieve this? (12 marks) QUESTION 2 (100 marks) (a) Factorise the following algebraic expressions by grouping: (4 marks each) (i) 2?? − ?? + 12?? − 6?? (ii) 6?? + 3?? + 4?? + 2?? (iii) 5?? + 2?? − 6?? − 15?? (iv) −4?? + 28?? + 3ℎ? − 21ℎ? (b) Solve the following simultaneous equations: (6 marks each) (i) ? + 7? = 17 2? − 4? = −2 (ii) −3? + 6? = 9 −4? − 4? = −36 (c) Simplify each of the following using the rules of indices and logarithms: (4 marks each) (i) 132 × 138 (ii) !!! 511 (iii) log2 10 - log2 2 (iv) log3 6 log3 5 (d) A tennis match in Wimbledon costs €50 for a premium ticket and €20 for a standard. For the women’s final 14,800 people were recorded as present at the match. The total money earned from ticket sales was €323,000. How many of each type of ticket were sold? (12 marks) (e) In a construction company workers fall into four categories. These are plumber, electrician, carpenter and painter as shown in the table below. 4 (i) Express the number of workers in each category as a percentage of the total number of workers in the company. (10 marks) (ii) With construction projects increasing next year, the company have decided to increase the work force by 14%. How many electricians will have to be taken on? Give your answer to the nearest whole number. (6 mark) (iii) What will be the total number of workers next year after the additional workers are hired? Give your answer to the nearest whole number. (6 mark) (f) Calculate the following amounts: (i) How much will be earned in interest on an investment of €876 left sitting in an account for 9 years at 4% simple interest? (6 marks) (ii) A car loan was taken out for €24,500 over 5 years at 6% which is compounded annually. How much interest will the borrower pay? (16 marks) QUESTION 3 (100 marks) (a) Graph the following on a number line: (4 marks) { x | -2 < x ≤ 9, x ∈ r } (b) solve the following algebraic equations for x: (4 marks each) (i) 5(2 + x) + 3(5x + 4) – 2x + 14 (ii) 4x +16 = 30 – 3x (c) solve the following quadratic equations by factorisation or by using the quadratic formula (the ‘–b’ formula) and state whether the quadratic has real roots or not. (8 marks each) category number of students plumber 29 electrician 35 carpenter 31 painter 26 5 (i) x2 + 9x + 18= 0 (ii) 12x2 - 10x - 5 = 0 (iii) 2x2 – 12x - 9 = 0 (d) in an election, candidate a got 65% of the total valid votes. if 21% of the total votes were declared invalid and the total numbers of votes is 463,000, find the number of valid votes polled in favour of candidate a. (10 marks) (e) max scored 6 marks more than what he did in the previous examination in which he scored 30. maria scored 30 marks more than she did in the previous examination in which she scored 60. who showed less improvement? (i) by what percent did max do better in the second exam compared to the first? (8 marks) (ii) by what percent did maria improve on the second exam compared to the first? (8 marks) (iii) how much better did maria do compared to max? (8 marks) (iv) how many more marks did max need so that his level of improvement equalled maria’s? (10 marks) (f) tina has a gross yearly income of €54,200. she has a standard rate cut off point of € 22,000 and a tax credit of € 3,080. the standard rate of tax is 22% of income up to the standard rate cut off point and 41% on all income above the standard rate cut-off point. calculate: (i) tina’s gross tax for the year (5 marks) (ii) tina’s net tax paid for the year (5 marks) (iii) the total usc tina must pay (5 marks) (iv) tina’s net pay per year (5 marks) usc rates end of paper income rate first €10,036 2% next €5,980 4% on the balance 7% 6 math1151 — intermediate mathematics — useful formulae international foundation programme / semester 1 access foundation programme 2017–2018 rules of indices a p⇥ aq = ap+q a p a q = ap�q � a p � q = ap⇥q a 0 = 1 a �p = 1 a p a p q = q p a p a 1 q = q p a (ab)p = apbp ✓ a b ◆ p = a p b p quadratic formula ax 2+ bx+ c = 0 =) x = �b± p b 2�4ac 2a financial mathematics compund interest : f = p(1+ i)t amortisation (loans) : r = a i(1+ i)t (1+ i)t �1 rules of logs a x = y () log a y = x log a (ax) = x log a x+ log a y = log a (x⇥ y) log a x� log a y = log a x y ! log a � x q � = q � log a x � log a 1 x ! = � log a x log a x log a b = log b x number sets n naturals = {0, 1, 2, 3, 4, 5, 6, · · · } z integers = x="" ≤="" 9,="" x="" ∈="" r="" }="" (b)="" solve="" the="" following="" algebraic="" equations="" for="" x:="" (4="" marks="" each)="" (i)="" 5(2="" +="" x)="" +="" 3(5x="" +="" 4)="" –="" 2x="" +="" 14="" (ii)="" 4x="" +16="30" –="" 3x="" (c)="" solve="" the="" following="" quadratic="" equations="" by="" factorisation="" or="" by="" using="" the="" quadratic="" formula="" (the="" ‘–b’="" formula)="" and="" state="" whether="" the="" quadratic="" has="" real="" roots="" or="" not.="" (8="" marks="" each)="" category="" number="" of="" students="" plumber="" 29="" electrician="" 35="" carpenter="" 31="" painter="" 26="" 5="" (i)="" x2="" +="" 9x="" +="" 18="0" (ii)="" 12x2="" -="" 10x="" -="" 5="0" (iii)="" 2x2="" –="" 12x="" -="" 9="0" (d)="" in="" an="" election,="" candidate="" a="" got="" 65%="" of="" the="" total="" valid="" votes.="" if="" 21%="" of="" the="" total="" votes="" were="" declared="" invalid="" and="" the="" total="" numbers="" of="" votes="" is="" 463,000,="" find="" the="" number="" of="" valid="" votes="" polled="" in="" favour="" of="" candidate="" a.="" (10="" marks)="" (e)="" max="" scored="" 6="" marks="" more="" than="" what="" he="" did="" in="" the="" previous="" examination="" in="" which="" he="" scored="" 30.="" maria="" scored="" 30="" marks="" more="" than="" she="" did="" in="" the="" previous="" examination="" in="" which="" she="" scored="" 60.="" who="" showed="" less="" improvement?="" (i)="" by="" what="" percent="" did="" max="" do="" better="" in="" the="" second="" exam="" compared="" to="" the="" first?="" (8="" marks)="" (ii)="" by="" what="" percent="" did="" maria="" improve="" on="" the="" second="" exam="" compared="" to="" the="" first?="" (8="" marks)="" (iii)="" how="" much="" better="" did="" maria="" do="" compared="" to="" max?="" (8="" marks)="" (iv)="" how="" many="" more="" marks="" did="" max="" need="" so="" that="" his="" level="" of="" improvement="" equalled="" maria’s?="" (10="" marks)="" (f)="" tina="" has="" a="" gross="" yearly="" income="" of="" €54,200.="" she="" has="" a="" standard="" rate="" cut="" off="" point="" of="" €="" 22,000="" and="" a="" tax="" credit="" of="" €="" 3,080.="" the="" standard="" rate="" of="" tax="" is="" 22%="" of="" income="" up="" to="" the="" standard="" rate="" cut="" off="" point="" and="" 41%="" on="" all="" income="" above="" the="" standard="" rate="" cut-off="" point.="" calculate:="" (i)="" tina’s="" gross="" tax="" for="" the="" year="" (5="" marks)="" (ii)="" tina’s="" net="" tax="" paid="" for="" the="" year="" (5="" marks)="" (iii)="" the="" total="" usc="" tina="" must="" pay="" (5="" marks)="" (iv)="" tina’s="" net="" pay="" per="" year="" (5="" marks)="" usc="" rates="" end="" of="" paper="" income="" rate="" first="" €10,036="" 2%="" next="" €5,980="" 4%="" on="" the="" balance="" 7%="" 6="" math1151="" —="" intermediate="" mathematics="" —="" useful="" formulae="" international="" foundation="" programme="" semester="" 1="" access="" foundation="" programme="" 2017–2018="" rules="" of="" indices="" a="" p⇥="" aq="ap+q" a="" p="" a="" q="ap�q" �="" a="" p="" �="" q="ap⇥q" a="" 0="1" a="" �p="1" a="" p="" a="" p="" q="q" p="" a="" p="" a="" 1="" q="q" p="" a="" (ab)p="apbp" ✓="" a="" b="" ◆="" p="a" p="" b="" p="" quadratic="" formula="" ax="" 2+="" bx+="" c="0" =)="" x="�b±" p="" b="" 2�4ac="" 2a="" financial="" mathematics="" compund="" interest="" :="" f="P(1+" i)t="" amortisation="" (loans)="" :="" r="A" i(1+="" i)t="" (1+="" i)t="" �1="" rules="" of="" logs="" a="" x="y" ()="" log="" a="" y="x" log="" a="" (ax)="x" log="" a="" x+="" log="" a="" y="log" a="" (x⇥="" y)="" log="" a="" x�="" log="" a="" y="log" a="" x="" y="" !="" log="" a="" �="" x="" q="" �="q" �="" log="" a="" x="" �="" log="" a="" 1="" x="" !="�" log="" a="" x="" log="" a="" x="" log="" a="" b="log" b="" x="" number="" sets="" n="" naturals="{0," 1,="" 2,="" 3,="" 4,="" 5,="" 6,="" ·="" ·="" ·="" }="" z="" integers="">