Question paper. Mathematics Level 2. Building a garage. Name. Date. General instructions

Transcription

1 Question paper Building a garage Name Date General instructions Answer all the questions. Read each question carefully. Show all your working out. You can use a calculator. To answer the questions in this paper you will need to look at the source documents. 1 of 16

2 Task 1: Planning the project Building a garage Planning the project Martin is going to build a garage on the side of his house. He s made three different scale drawings of garages that he d like to build. Martin has estimated the cost of the materials for the garage to be: Material Cost Concrete for flooring 11 per square metre Concrete blocks for walls 15 per square metre Roof covering 1,250 per roof Roof structure 200 for single or dual pitched roofs only Garage doors The labour costs will be similar for all three of the options. They will cost around 7,000. Notes: Martin will only have to build three walls of his garage, since the fourth is provided by the wall of the house. For all three options, Martin will use concrete blocks to build the walls of the garage. These will be 2.4m high. 1 foot = 30.48cm You need to use the information you have been given to decide which of the options Martin should build. To answer the following questions you need to Martin s scale drawings in the source documents. 2 of 16

3 Task 1: Planning the project 1. Plan how to solve this task. Write down your plan, including the steps you will use. 2. Carry out your plan to investigate the options. Show your working. You should check your work as you go along. Write down one of your calculation checks in the space given. 3 of 16

4 Task 1: Planning the project Check: 4 of 16

5 Task 1: Planning the project 3. Complete this table to present your results and compare the costs of the options. You may not need to use all of the rows and columns. 4. Decide which of the options Martin should build. Give a reason for your choice. 5 of 16

6 Task 1: Planning the project 5. You need to review how well you did the task. Think about How your plan and methods worked How sensible your answers were Anything you found difficult Any other information that you would have liked Things you might do differently if you had to tackle a similar problem. Explain three of the most important points. 6 of 16

7 Task 1: Planning the project To answer the following question you need to use the Planning permission leaflet and Martin s scale drawings in the source documents. 6. Does Martin need planning permission for his garage? Explain your answer and show your working out. 7 of 16

8 Task 2: Finding a builder Finding a builder Last year Martin bought a shed from a company that supplies and builds outbuildings, including garages. He was pleased with the service and the quality of the job they did, so he contacts them to get an estimate. With the costs of materials and labour to build the garage, the company gives Martin an estimate of 9,832. This includes VAT at 20%. As Martin is an existing customer, they offer him a discount on his garage of 5% of the net price (that is, the price without VAT). 7. How much will Martin now pay for his garage, including VAT? 8 of 16

9 Task 2: Finding a builder Martin knows the company isn t the cheapest around, but he is confident they will do a good job. However, if the company is charging a lot more than the average price for a garage he will look elsewhere. He also looked at customer ratings for each company (1 is a low rating and 5 is a high rating). Here are results of Martin s research. Company Price ( ) Rating (out of 5) Do Everything 10,400 5 Outbuildings for All 8,600 4 Brasenose Gardens 11,800 3 Green Hall Garden Centre 9,300 3 Markham Builders 9,700 4 F & B 4,200 2 Home & Garden 8,600 2 P.J. Britwell 9,800 5 Tadley Construction 7,500 1 Glebe Builders 10,200 4 Broadway Prefabrication 7,200 3 Parkway Buildings 11,000 4 Martin wants to see if there is a relationship between the price that a company charges and its customer rating, so he s drawn some graphs. To answer the following questions you need to use the Price and customer ratings graphs in the source documents. 9 of 16

10 Task 2: Finding a builder 8. Which graph is best for showing if there is a relationship between the price and customer rating? Explain your answer. 9. Based on this graph, what type of relationship, if any, if there between price and the customer rating? 10 of 16

11 Task 2: Finding a builder Here are the results of Martin s research again. Company Price ( ) Rating (out of 5) Do Everything 10,400 5 Outbuildings for All 8,600 4 Brasenose Gardens 11,800 3 Green Hall Garden Centre 9,300 3 Markham Builders 9,700 4 F & B 4,200 2 Home & Garden 8,600 2 P.J. Britwell 9,800 5 Tadley Construction 7,500 1 Glebe Builders 10,200 4 Broadway Prefabrication 7,200 3 Parkway Buildings 11, What is the range of the prices? 11 of 16

12 Task 2: Finding a builder 11. Martin wants to work out the average price of a garage. What is the best type of average to use? Explain your answer. 12. Using this type of average, what is the average price of a garage? 12 of 16

13 Task 2: Finding a builder 13. Should Martin accept the deal? Explain your answer. 13 of 16

14 Task 3: Paying for the garage Paying for the garage Martin is paying for the garage with his savings and a loan from the bank. He is going to take a 5,000 loan and pay it back over five years. The annual interest rate is 5.2%. He wants to work out how much the loan will cost him overall. He can work out how much he has to pay back using the following formula: m=p 1+ r 100 n m is the total amount he has to pay back p is the amount he borrowed r is the interest rate n is the length of the loan in years Note: in this equation the variable n is a power. A power is a number multiplied by itself. This table shows some examples: 14. How much will Martin pay back in total? 4² 4 4 = 16 4³ = = = 1, of 16

15 Task 3: Paying for the garage 15. How much will Martin pay back each month? The monthly payment isn t quite enough to pay back the full loan. He has to pay a few pence extra on his final payment. 16. What will his final payment be? 15 of 16

16 Task 3: Paying for the garage 17. Choose one of your calculations from Task 3 to show a check. Check it by a different method to the one you used originally. The calculation I am going to check is in (select one): Question 14 Question 15 Question 16 Check: Save this document on your computer before you complete it. Have a look at the answer sheet for this paper to check your answers. 16 of 16