Mathematical Applications (200 marks)
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1 2015. AP8S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Applied 2015 Mathematical Applications (200 marks) Time: 2 hours General Directions 1. Write your EXAMINATION NUMBER in this space: 2. Write all answers in the boxes or spaces in this answerbook. 3. Show all necessary work in the space provided. 4. Calculators may be used. 5. Answers involving money should be given correct to the nearest cent, unless otherwise indicated. ATTEMPT QUESTION ONE AND THREE OTHER QUESTIONS. ALL QUESTIONS CARRY EQUAL MARKS. For the Superintendent only Centre Stamp For the Examiner only Question 1 2 Cumulative check 3 Running total 4 Disallowed 5 = Total Total Mark
2 Question 1. (a) Calculate 215, correct to two decimal places. (b) A house originally priced at is reduced by 5%. What is the new selling price of the house? (c) An injection uses 15 cm 3 of medicine. How many such injections can be got from 1 8 litres of medicine? (d) What measurement is the arrow pointing to? 4 0 cm 5 0 cm (e) Given an exchange rate of 1 = 0 79 sterling, convert 150 to sterling. Leaving Certificate Applied 2015 Page 2 of 11 Mathematical Applications
3 (f) Calculate (g) A regular hexagon has side of length 7 25 cm. Find the perimeter of the hexagon. (h) I lodged three cheques for 34 32, and in the bank. How much in total did I lodge? (i) What is the difference between the largest and the smallest of the following numbers: 0 034, 0 403, 0 304, 0 430, (j) A letter is chosen at random from the word ALGEBRA. What is the probability the letter chosen is an A? page running Leaving Certificate Applied 2015 Page 3 of 11 Mathematical Applications
4 Question 2. Research Element Question on Enterprise (a) The final accounts for a mini-company are shown below. Final Accounts of THE OLD SCHOOLHOUSE POSTCARD COMPANY on 31 May 2006 Shares Summary Number of shares issued Income Each student gets 14 free shares Expenditure Each student buys a further 6 shares at a reduced price of 10 cent each Each student sells 5 further shares at the full price of 20 cent each TOTAL SHARES ISSUED Purchases Summary 1050 Blank 2 cent each Ink for printer TOTAL PURCHASES Sales Summary 1000 cards sold at 15 cent each Revenue from advertising TOTAL SALES GRAND TOTALS ON 31 MAY (i) Fill in the three missing details on the Final Accounts above. Leaving Certificate Applied 2015 Page 4 of 11 Mathematical Applications
5 (ii) Calculate the total profit of the company on 31 May 2006, the final date. (iii) Calculate the Final Share Value of the company. Final Share Value = Total profit Total number of shares issued (iv) A teacher bought five shares in the company. Calculate the profit the teacher made. (b) A carpenter prices a job: Labour costs: 495 Materials cost: 278. VAT is charged at 21%. Calculate the total cost of the job. page running Leaving Certificate Applied 2015 Page 5 of 11 Mathematical Applications
6 Question 3. (a) The average monthly temperature for Malta is recorded on the following table: Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temp( C) (i) Draw a trend graph to represent this information. (ii) Calculate the average temperature for June, July and August. (iii) Convert the temperature for July from degrees Celsius to degrees Fahrenheit, using the formula: 9 F = C Leaving Certificate Applied 2015 Page 6 of 11 Mathematical Applications
7 (b) The following is from the Bus Timetable between Dublin and Belfast: ROUTE 41a 41b 41c Dublin (Busáras) dep Dublin Airport dep. 1320P 1415P 1505P Newry (Buscentre) arr. 1430D 1525D 1615D Banbridge (War Memorial) arr. 1450D 1545D 1635D Sprucefield (Shopping Centre) arr. 1510D 1605D 1655D Belfast (Glangall Street) arr P : Pick-up stop only. D : Drop-off stop only. (i) At what time does the 41c bus arrive in Belfast? (ii) How long does it take the 41a bus to reach Belfast from Dublin? (iii) The distance from Dublin to Belfast is 170 km. D Find the average speed of the 41a bus, using the formula S =. T page running Leaving Certificate Applied 2015 Page 7 of 11 Mathematical Applications
8 Question 4. (a) (i) In the box below, construct a rectangle 8 cm long and 3 cm wide. (ii) The rectangle you have drawn in part (i) is a scaled diagram of a car parking space. The scale is 1:200. Calculate the actual measurements of the car parking space. Actual length: Actual width: (iii) What is the area of the car parking space? Give your answer in m 2. Leaving Certificate Applied 2015 Page 8 of 11 Mathematical Applications
9 (iv) Tarmacadam costs per square metre. Find the cost of tarmacadam for the car parking space. (v) VAT is added to the cost of the tarmacadam. Find the percentage rate of VAT that is being used. (b) A sphere has a diameter of length 5 cm. Calculate the volume of the sphere, taking π = Volume of Sphere = 4 π r cm page running Leaving Certificate Applied 2015 Page 9 of 11 Mathematical Applications
10 Question 5. (a) (i) Write out the list of all possible two-digit numbers that can be made using the digits: 2, 3, 4. One possible number is 42. These two-digit numbers are used on raffle tickets. The tickets are placed in a bag. (ii) One ticket is chosen at random. What is the probability that the number on the ticket chosen is an odd number? (iii) This ticket is replaced, and a ticket is again drawn at random. What is the probability that the number on the ticket chosen is less than 40? Leaving Certificate Applied 2015 Page 10 of 11 Mathematical Applications
11 (b) Michelle has a gross salary of per year. (i) Tax is paid at 21%. Calculate Michelle s gross tax. (ii) Michelle has a tax credit of 3340 per year. How much tax does she pay? (iii) The Universal Social Charge (USC) is calculated using the following chart. Fill in the missing details to calculate Michelle s USC. Income % USC USC % % Earnings over % Total USC payable page running Leaving Certificate Applied 2015 Page 11 of 11 Mathematical Applications
12 Note to readers of this document: This paper is intended to help teachers and candidates prepare for the June 2015 examination in Mathematical Applications. Questions 1, 3, 4, and 5 have been taken from the 2013 examination. Question 2 has been taken from the 2006 examination, when the Research Element Topic was also Enterprise. Leaving Certificate Applied 2015 Mathematical Applications Time: 2 hours
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