Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination Sample Paper. Mathematics

Transcription

1 2015. M25S Coimisiún na Scrúduithe Stáit State Examinations Commission Leaving Certificate Examination Sample Paper Mathematics Time: 2 hours, 30 minutes 300 marks Running total Examination number Centre stamp For examiner Question Mark Total Grade

2 Instructions There are two sections in this examination paper. Section A 200 marks 8 questions Section B 100 marks 3 questions Answer all eleven questions. Write your answers in the spaces provided in this booklet. You may lose marks if you do not do so. There is space for extra work at the back of the booklet. You may also ask the superintendent for more paper. Label any extra work clearly with the question number and part. The superintendent will give you a copy of the Formulae and Tables booklet. You must return it at the end of the examination. You are not allowed to bring your own copy into the examination. You will lose marks if all necessary work is not clearly shown. You may lose marks if the appropriate units of measurement are not included, where relevant. You may lose marks if your answers are not given in simplest form, where relevant. Write the make and model of your calculator(s) here: Leaving Certificate Sample Paper Page 2 of 19 Mathematics

3 Section A 200 marks Answer all eight questions from this section. Question 1 Use your calculator to answer the following. (25 marks) (a) (i) Find 45 36, correct to two decimal places. Answer: (ii) Find the exact value of Answer: (b) John has 42. He spends 4 3 of this money on clothes. Find how much money he has left. (c) The distance from Waterford to Dublin is 165 km. Mary drives from Waterford to Dublin at an average speed of 75 km/h. How long does Mary s journey take? Give your answer in hours and minutes. page running Leaving Certificate Sample Paper Page 3 of 19 Mathematics

4 Question 2 (a) (i) Find 33% of 120. (25 marks) (ii) A coat costs 120. In a sale, the price is reduced by 33%. Find the new price. (b) The price of a camera, including VAT at 23%, is What is the price of the camera excluding VAT? (c) Write 3 6 and without using indices. 3 6 = = Leaving Certificate Sample Paper Page 4 of 19 Mathematics

5 Question 3 (25 marks) (a) Write 6% as a decimal. Answer: (b) A sum of 5000 is invested in a three-year government bond with an annual equivalent rate (AER) of 6%. Find the value of the investment when it matures in three years time. page running Leaving Certificate Sample Paper Page 5 of 19 Mathematics

6 Question 4 (25 marks) Deirdre did a survey of the Leaving Cert students in her school. She asked them what they hoped to do after they leave school. There were 50 students, and the results were as follows: Get a job 6 Go to a third-level college 25 Do a Post-Leaving Cert course (PLC) 7 Other 4 Don t know 8 Deirdre wants to display the results as a pie chart. She works out the percentage for each answer and the number of degrees for each angle. Complete the table below to show these numbers. Give the angles to the nearest degree. The first row is already done. Answer Number of students Percentage Angle for pie chart Get a job 6 12% 43 Go to a third-level college 25 Do a Post-Leaving Cert course (PLC) 7 Other 4 Don t know 8 Total % 360 Use this space for calculations, if you need to. Leaving Certificate Sample Paper Page 6 of 19 Mathematics

7 Use your table to complete the pie chart below. Get a job 12% 43 page running Leaving Certificate Sample Paper Page 7 of 19 Mathematics

8 Question 5 (25 marks) An experiment involves asking two different people the day of the week on which they were born. The outcome is recorded in this form: (day 1, day 2). For example, if both of them were born on a Monday, this is written as (Monday, Monday). (a) Write out three possible outcomes of this experiment. (b) How many different possible outcomes are there? (c) Assuming that every day of the week is equally likely, answer the following. (i) Find the probability that both people were born on a Wednesday. (ii) Find the probability that both people were born at the weekend (Saturday or Sunday). (iii) Find the probability that at least one of them was born at the weekend. Leaving Certificate Sample Paper Page 8 of 19 Mathematics

9 Question 6 (a) The shape shown in the diagram is a square from which a quarter of a disc has been removed. (25 marks) Find the area of the shape, in cm 2, correct to two decimal places. 8 cm 10 cm 10 cm (b) The solid object shown is 35 cm long. Its cross-section has the dimensions of the shape in part (a). Find the volume of the solid, correct to the nearest cm cm page running Leaving Certificate Sample Paper Page 9 of 19 Mathematics

10 Question 7 The fare for a taxi journey often depends on the distance travelled. In one such case, for journeys from 1 km to 15 km, the fare, in cent, is given by the following formula: F = D, where F is the fare in cent and D is the distance travelled in km. (25 marks) (a) Complete the table below showing the fare, in cent, for some journeys from 1 km to 15 km. Distance (km) Fare (cent) (b) Draw a graph to represent the taxi fare from 1 km up to 15 km fare in cent distance in kilometres Leaving Certificate Sample Paper Page 10 of 19 Mathematics

11 (c) (i) Mary has to pay for her taxi fare. How far will Mary be able to travel by taxi? (ii) James needs to travel 11 5 km to get to his home. How much will James have to pay if he travels home by taxi? Leaving Certificate Sample Paper Page 11 of 19 Mathematics

12 Question 8 (25 marks) The symbol shown below in Diagram 1 was designed by Gerald Holtom in It later became recognised as an international peace symbol. O c Diagram 1 Diagram 2 The circle c has centre O. Use this fact and the additional information in Diagram 2 to draw the symbol in the space below, using a radius of 6 cm. Leaving Certificate Sample Paper Page 12 of 19 Mathematics

13 Section B 100 marks Answer all three questions from this section. Question 9 An extract from an electricity bill is shown. Some of the numbers are missing, and are labelled (20 marks) A, B, C, D, E, and F. METER NO. METER READINGS ELECTRICITY USED METER READING TYPES PRESENT PREVIOUS kwh Z A 7053 C A A: Actual reading C: Customer reading E: Estimated reading Discount Tariff Urban Day AMOUNT Description Units Rate Standing charge 61 days cent/day B 24 hour units C cent/kwh Direct debit discount 12% CR Total excluding V.A.T. V.A.T. at 13.5% D E PLEASE PAY BY TOTAL Direct Debit 21 Sept 14 F Calculate the missing numbers, and insert them in the table below. A B C D E F page running Leaving Certificate Sample Paper Page 13 of 19 Mathematics

14 Question 10 (30 marks) Liam and Mairéad are two mountaineers descending from two mountains, A and B, in different parts of the country. They set off at the same time and, as they descend, the air temperature rises at a steady rate. They each record the temperature, in degrees Celsius, every hour. Some of their recordings are shown in the table below. (a) Complete the table to show the temperatures they recorded over an 8-hour period. Time Mountain A Liam Temperature ( C ) Mountain B Mairéad Temperature ( C ) (b) Write down the rate at which the temperature recorded by Liam rises every hour. Answer: C/h. (c) How many hours pass until both Liam and Mairéad record the same temperature at the same time? Answer: hours. Leaving Certificate Sample Paper Page 14 of 19 Mathematics

15 (d) On the grid below draw graphs for the air temperatures on Mountain A and Mountain B over the 8 hours that Liam and Mairéad were descending Temperature ( o C) (e) Time (Hours) Write down a formula to represent the temperature recorded by Liam on Mountain A for any given time. State clearly the meaning of any letters used in your formula. page running Leaving Certificate Sample Paper Page 15 of 19 Mathematics

16 Question 11 (50 marks) (a) A pattern for a circuit board was reduced in size using an enlargement by the ray method. Because the pattern was made smaller, the scale factor is less than 1. The diagram below shows the pattern before and after the reduction. image original pattern (i) On the diagram, find the centre of enlargement. (ii) By measurement and calculation, find the scale factor of the enlargement. (iii) The area of the original pattern is 27 cm 2. Find the area of the image. Leaving Certificate Sample Paper Page 16 of 19 Mathematics

17 (b) The circuit board is for an electronic game. The side panel of the game is approximately triangular. The diagram below, not drawn to scale, is for the side panel. The measurements are as shown. 6 cm α 11 cm Find α, correct to the nearest degree. (c) The screen measures 7 cm by 12 cm. Find the length of the diagonal of the screen, correct to two places of decimals. 7 cm 12 cm page running Leaving Certificate Sample Paper Page 17 of 19 Mathematics

18 You may use this page for extra work. Leaving Certificate Sample Paper Page 18 of 19 Mathematics

19 You may use this page for extra work. page running Leaving Certificate Sample Paper Page 19 of 19 Mathematics

20 Note to readers of this document: This sample paper is intended to help teachers and candidates prepare for the examination in Mathematics in June 2015 and in subsequent years. Section A of the examination paper will consist of eight questions, each carrying 25 marks. Section B will consist of two, three, or four questions. These questions will not necessarily carry equal marks. The number of marks for each will be stated on the examination paper. The total number of marks for Section B will be 100. Leaving Certificate Mathematics Sample Paper Time: 2 hours 30 minutes