مملكة البحرين KINGDOM OF BAHRAIN هيئة جودة التعليم والتدريب EDUCATION & TRAINING QUALITY AUTHORITY إدارة اﻻمتحانات الوطنية Directorate of National Examinations اﻻمتحانات الوطنية للصف الثاني عشر Grade 12 National Examinations امتحان مارس March 2019 2019 حل المشكﻻت PROBLEM SOLVING الورقة 2 تحليل وحل المشكﻻت Paper 2 Problem Analysis and Solution مدة اﻻمتحان: ساعتان Duration: 2 hours اكتب اﻹجابة في كراسة اﻹجابة. .Write your answer on the answer booklet اﻷدوات اﻹضافية: مسطرة، قلم رصاص، ممحاة، ,Additional materials: ruler, pencil, eraser calculator, answer booklet. آلة حاسبة، كراسة اﻹجابة. Read these instructions first: Use a blue pen only. Follow the instructions on the answer booklet provided. Answer all questions. The use of calculators is permitted. The total number of marks for this paper is 50. This document consists of 14 printed pages and 2 blank pages. © 2019 BQA PS12/02E 2 1 Study the information below and answer the questions that follow. You should show your working. Mohannad owns a goldsmith’s workshop in the Kingdom of Bahrain, and sells his jewelry via his website. Once the customer selects a piece of jewelry and pays its price electronically, the piece is delivered to him free of charge within the Kingdom. Gold comes in different karats; each referred to by a whole number smaller than or equal to 24, indicating the percentage of pure gold present. The most famous karats are: 24 k, 21 k and 18 k. 24 k is 100% pure gold, whereas the remaining karats are mixed with other metals such as copper, zinc and silver in certain percentages determined by the karat. For example: the percentage of pure gold in 18 k gold is 18 out of 24, which equals 75% (18 ÷ 24 × 100%). Jewelry stores add an additional cost to customers per gram of gold known as “manufacturing charge”. This is an amount determined by the labour required to manufacture the piece of jewelry. Mohannad has three types of jewelry available at his workshop; they are known as simple, elegant and heavy. The table below shows the options he offers his customers for a piece of jewelry in terms of karat, weight and manufacturing charge. Weight of the piece of Manufacturing charge per jewelry (gram) gram (BD) Karat Simple Elegant Heavy Simple Elegant Heavy 18 8 – 9 10 – 11 13 – 14 4 6 8 21 7 – 9 10 – 12 13 – 15 6 8 11 For example: all 21 k heavy pieces of jewelry in Mohannad’s workshop weigh 13 to 15 grams and have a manufacturing charge of BD 11 per gram. Gold prices change from day to day and there is no fixed price for a gram of gold of any karat. The price of a gram of gold for a given karat is calculated using the following formula: Price of a gram of gold for a given karat = the price of a gram of 24 k gold × the percentage of pure gold in the relevant karat The price of a piece of jewelry, on the other hand, is calculated using the following formula: Price of a piece of jewelry = (the price of a gram of gold for the relevant karat + manufacturing charge per gram) × the weight of the piece in grams © 2019 BQA 3 (a) What is the percentage of other metals in a gram of 21 k gold? [1] (b) A female customer bought a piece of 21 k gold jewelry weighing 7.2 gram from Mohannad’s website. The price per gram of 24 k gold on the day of purchase was BD 14.400. How much did this customer pay Mohannad? [2] (c) Mohannad repurchases his gold jewelry pieces if the customers wish to sell them, and sends a representative to the relevant customers to collect the piece of jewelry. The repurchase price is determined by the weight of the piece only, without the manufacturing charge, and based on the price per gram of the relevant karat on the day of repurchase. A customer bought a piece of jewelry from Mohannad’s website. The price per gram of 24 k gold on the day of purchase was BD 14.200, and the customer sold the piece back to Mohannad after one month when the price per gram of 24 k gold was BD 13.400. What is the highest loss the customer may have incurred in the process of purchasing and selling the piece? [2] (d) During the last year, the price per gram of 24 k gold varied between BD 13.200 and BD 19.400. (d1) A customer sent Mohannad an e-mail complaining about non- delivery of his piece of jewelry despite receiving a confirmation of the payment via the website during last year. The customer told Mohannad that his piece of jewelry weighs 10.4 gram, and that he paid an exact amount of BD 262. Mohannad discovered that the customer was planning a fraud. Explain how Mohannad was able to discover that. [2] (d2) During the last year, the friends Hamad and Hassan bought a number of pieces of gold jewelry from Mohannad’s website. Hamad bought a number of identical pieces of 21 k gold, and Hassan bought a number of identical pieces of 18 k gold on the same day, which differ than Hamas’s pieces of jewelry in terms of type and manufacturing charge. The total weights of their pieces of jewelry were equal, and they paid the same amount of money. What was the price per gram of 24 k gold on the day on which the two friends bought their jewelries? Explain your answer. [2] © 2019 BQA [Turn over 4 (e) The chairwoman of a women’s association wanted to buy pieces of gold jewelry to honour the members of the association on the Bahraini Women’s Day. She decided that each head of committee receives an identical piece of jewelry at 11.5 gram of 21 K gold and that each member of a committee receives an identical piece of jewelry at 8.5 gram of 18 K gold. The association has more than one committee and all committees have the same number of members. The chairwoman bought the pieces of gold jewelry from Mohannad’s website and paid BD 1530.500. The price per gram of 24 k gold on the day of purchase was BD 12. How many pieces of jewelry did the chairwoman buy? [3] (f) Al-Saeed Jewelry Store requests some pieces of gold jewelry from Mohannad’s website every year. The total weight of the pieces of jewelry requested is 450 gram divided equally between 18 k and 21 k, then equally divided between the three types of simple, elegant and heavy jewelry pieces of each karat. The store owner sent Mohannad an e-mail expressing his desire to obtain the same total weight in the upcoming year under the same terms; with the addition of another karat value for the same three types of simple, elegant and heavy jewelry pieces. The store owner realizes that Mohannad would only accept to manufacture gold jewelries of a new karat value if: • The percentage of pure gold is higher than 62.5%. • The manufacturing charge per gram for the new karat value of all three types is higher than that of 18 k gold and lower than that of 21 k gold, and is in whole dinars. Mohannad approved the store owner’s request and stated that the initial total cost will be BD 8500 based on the current price per gram of 24 k gold which is BD 15. Determine the new karat value requested by the owner of Al-Saeed Jewelry Store, specifying the manufacturing charge per gram of all three types of jewelry pieces: simple, elegant and heavy, for this new karat value. [3] © 2019 BQA 5 BLANK PAGE © 2019 BQA [Turn over 6 2 Study the information below and answer the questions that follow. You should show your working. Bahrain Bus Company manages the transportation through all main locations in Bahrain. The schedule below gives the daily destination routes of the buses, starting from the first station to the last station on each route. In addition, it gives the first three and the last three departure times from the first station on the route according to the day of the week. The remaining departure times from the first station are uniformly scheduled at a fixed interval of 15, 20, 30, or 60 minutes depending on the route. As an example, the buses of the A1 Route are scheduled to depart regularly from Isa Town every 15 minutes from 05:00 onwards, so on a daily basis, the 4th bus leaves Isa Town at 05:45, the 5th bus at 06:00 and so on. “A” Route A1 Route: Isa Town Salmaniya Manama Muharraq Airport 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 05:00 05:15 05:30 22:00 22:15 22:30 15 minutes A2 Route: Airport Muharraq Manama Salmaniya Isa Town 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 05:00 05:15 05:30 22:00 22:15 22:30 15 minutes “U1” Route (Loop) Isa Town Sanad Alba Riffa University Isa Town 1st 2nd 3rd Last Bus Bus Bus Bus Sun. every to 05:00 05:30 06:00 21:30 22:00 22:30 30 minutes Thu. Fri. every and 05:00 06:00 07:00 20:00 21:00 22:00 60 minutes Sat. © 2019 BQA 7 “X2” Route X2A Route: Manama City Centre Budaiya 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 05:10 05:30 05:50 21:50 22:10 22:30 20 minutes X2B Route: Budaiya City Centre Manama 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 04:55 05:15 05:35 21:35 21:55 22:15 20 minutes “X3” Route X3A Route: Budaiya Jidhafs Central Market Manama 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 05:05 05:25 05:45 21:45 22:05 22:25 20 minutes X3B Route: Manama Central Market Jidhafs Budaiya 1st 2nd 3rd Last Bus Bus Bus Bus every Daily 05:00 05:20 05:40 21:40 22:00 22:20 20 minutes “M2” Route (Loop) Muharraq Samaheej Hidd Arad Airport Muharraq 1st 2nd 3rd Last Bus Bus Bus Bus Sun.