kingdom of bahrain نيرحبلا ةكلمم samples/g12_ps_p… · (e) in the formula 1 bahrain...

© 2018 BQA PS12/02E

KINGDOM OF BAHRAIN مملكة البحرين

EDUCATION & TRAINING QUALITY AUTHORITY والتدريب هيئة جودة التعليم

Directorate of National Examinations االمتحانات الوطنية إدارة Grade 12 National Examinations االمتحانات الوطنية للصف الثاني عشر

March 2018 2018س امتحان مار

PROBLEM SOLVING حل المشكالت

Paper 2 Problem Analysis and Solution تحليل وحل المشكالت 2الورقة Duration: 2 hours مدة االمتحان: ساعتان

Write your answer on the answer booklet. .اكتب اإلجابة في كراسة اإلجابة

Additional materials: ruler, pencil, eraser, calculator, answer booklet.

ممحاة، ،مسطرة، قلم رصاص األدوات اإلضافية:

آلة حاسبة، كراسة اإلجابة.

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.

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1 Study the Information below and answer the questions that follow. You should show your working. A travel agency is offering recreational and shopping trips that can be booked for the spring break. The following table illustrates the destination, duration and type of each trip:

Destination Duration (days) Type

Dubai 4 Recreational, Shopping

Kuwait 5 Shopping

Jordan 8 Recreational

Sharm El Sheikh 12 Recreational

Baghdad 10 Recreational

Lebanon 8 Recreational

Jeddah 4 Recreational, Shopping

Salalah 6 Recreational

Abha 7 Recreational

Rabat 12 Recreational

Cairo 12 Recreational

Dammam 2 Shopping

Casablanca 10 Recreational

Doha 8 Shopping

Tunisia 13 Recreational

Sharjah 5 Recreational, Shopping

Abu Dhabi 4 Recreational, Shopping

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The following table illustrates the trip costs per day according to the age group of each person:

Destination

Trip costs per day (BD)

Age group (1) older than

8 years

Age group (2) 3 – 8 years

Age group (3) younger than

3 years

Dubai 31 20 10

Kuwait 18 13 6

Jordan 32 21 10

Sharm El Sheikh 42 29 14

Baghdad 50 35 17

Lebanon 38 25 13

Jeddah 32 19 10

Salalah 31 20 9

Abha 30 18 8

Rabat 41 25 13

Cairo 38 23 12

Dammam 10 6 3

Casablanca 44 28 15

Doha 18 12 7

Tunisia 39 24 12

Sharjah 23 13 6

Abu Dhabi 29 20 10

For example: a person in age group (1) would pay BD 124 to the travel agency for the trip to Dubai.

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Anyone who wishes to travel to any of the available destinations can choose any one of the available departure dates for that trip, provided that they adhere to the trip duration. The trip duration is calculated starting from the departure date. The return date of any trip is therefore the trip duration added to the departure date. The following table illustrates the available departure dates for each destination:

Destination

Departure date (1)

Departure date (2)

Departure date (3)

Dubai 24 January 30 January 5 February

Kuwait 21 January 31 January 5 February

Jordan 23 January 1 February 3 February

Sharm El Sheikh 24 January 25 January 29 January

Baghdad 28 January 31 January 1 February

Lebanon 26 January 27 January 29 January

Jeddah 29 January 6 February 11 February

Salalah 24 January 1 February 5 February

Abha 26 January 3 February 6 February

Rabat 20 January 2 February 7 February

Cairo 23 January 27 January 30 January

Dammam 30 January 6 February 13 February

Casablanca 27 January 2 February 6 February

Doha 22 January 1 February 3 February

Tunisia 25 January 26 January 27 January

Sharjah 31 January 5 February 11 February

Abu Dhabi 28 January 4 February 14 February

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(a) Salah wants to travel to Kuwait with his wife and 6-year-old daughter Reem, through the travel agency. How much will Salah pay the agency? [2]

(b) Sami and Talal are friends. After finishing their first semester exams, they have decided to book a recreational trip through the travel agency for no more than 5 days. How much will Sami and Talal pay in total if they choose the cheapest recreational trip? [2]

(c) The travel agency gives anyone who travels through it a virtual travel number made out of six digits; the first two digits from the left represent the person’s age, the first two digits from the right represent the departure date and the remaining two digits represent the trip duration. For example, the travel number 150429 shows that the person’s age is 15, he is travelling for 4 days and his departure date is the 29th of the month. Majed’s trip cost less than BD 100, and his virtual travel number was X8XXX4. In addition to all the information given so far, what further piece of information would be sufficient to determine Majed’s virtual travel number? [2]

(d) It was noticed that there was a high demand on the trip to Dammam. In the last trip, there were 24 travellers of different age groups, and the agency achieved financial return of BD 450 from that trip. If more than 18 travellers of age group (1) were in that trip and the number of travellers of age group (2) exceeded the number of travellers of age group (3). What was the number of travellers of age group (1)? Show your working. [3]

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(e) Mohammed is a teacher in a governmental school. He wants to

take advantage of his spring break and to travel through the travel agency. Mohammed will choose the cheapest trip, where he travels before the end of January, and returns after 6th of February. How much will Mohammed pay for his trip? [3]

(f) A company wants to benefit from the travel agency offers to

award its distinguished employees; Ahmad, Ali and Yusuf, each travelling to a different destination for recreation. Ahmad will depart first, then Ali and then Yusuf, but all of them will return on the same date. The company will pay the travel agency a total amount of BD 1248. What is Ali’s destination? [3]

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2 Study the information below and answer the questions that follow. You should show your working. Speed Car Company has the following offers for renting cars:

Car category

Total cost (BD) according to the rental period

One day Three days One week

Small 7.000 19.000 43.500

Mid-size 11.000 32.000 72.000

Large 13.000 38.500 89.500

The company possesses 12 small cars, 5 mid-sized cars and 8 large cars. The maximum seating capacity is 4 persons for the small car, 5 persons for the mid-sized car and 7 persons for the large car. The company also offers chauffer service that costs BD 10 per day per car. If a car is returned before the named rental period ends, the company transfers the customer to the best offer that covers the period of the rent. Before the remaining amount is returned to the customer, only BD 1.500 is deducted as management fees, bearing in mind that the rent is paid in advance. For example: if a customer rents a car for three weeks but returns it after 9 days, the company changes the rental plan to one week, one day, one day and returns the remaining amount to the customer after deducting BD 1.500 from it.

(a) A tourism office needs a group of cars; 4 small cars for three days and 8 large cars for one week. How much will the tourism office pay Speed Car Company, if the tourism office has decided to rent the cars from them? [1]

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(b) Khalid rents a large car annually for 78 consecutive days from Speed Car Company and since he is a regular customer, the company offers him an additional percentage reduction on the car he rents. What is the additional percentage reduction the company offers Khalid that makes the rental cost for his large car BD 798? [2]

(c) During New Year’s Eve celebrations, Speed Car Company generated its highest possible revenues for December 31st. What was the total revenues that the company generated that day? [2]

(d) On a visit to Bahrain, Jaber was not sure about the duration of his stay, but he knew that it would exceed 30 days. Therefore, he decided to rent a small car daily from another company for BD 6.500 per day. After his trip ended, he met a marketing agent for Speed Car Company, who told Jaber that if he had used a car from Speed Car Company for the same period, which would have involved renting the car for a longer period and returning it before the rental period ended, he would have saved BD 11. How many actual days did Jaber use the car he rented from the other company? [3]

(e) In the Formula 1 Bahrain Grand Prix, a team will need 15 cars for two days to transport 75 of its workers both days. Hence, the team decided to benefit from the offers of Speed Car Company and rent at least two cars from each of the three categories. They will not use the chauffeur service. What is the smallest amount the team could pay Speed Car Company? Explain your answer. [3]

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(f) Because the employees of Speed Car Company faced problems

in implementing a complicated renting system, the company manager decided to cancel all the current offers and replace them with a new system that includes only the car’s rental cost per day for each of the three car categories. In order not to affect the revenues too much, the manager determined the car’s rental cost per day for each of the three categories in a way that the difference between the cost of the old offers, per day, per three days and per week, and the new system for the same periods is no more than BD 2, either higher or lower. The car’s rental cost per day is a whole number of dinars for each of the three categories.

(f1) Specify the new system, determining the cost per day for each of the three car categories. [2]

(f2) A Ministry is accustomed to renting a group of cars from one of the categories from Speed Car Company for consecutive days for a particular period yearly. When the human resources manager heard of the new system, he called the company to inquire about how much more or less the Ministry will pay for renting according to this system. Speed Car Company told him that his Ministry will save BD 23 per car. List three possibilities that could explain how the Ministry could save BD 23 per car, determining the car category and the number of rental days. [2]

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3 Study the Information below and answer the questions that follow. You should show your working. Electricity and Water Authority, abbreviated EWA, installs to every new customer a meter for reading electricity consumption and another meter for reading water consumption. The reading of the meter when first installed is zero and thereafter it is the accumulated number of units consumed.

EWA has three different tariffs A, B and C for the consumption of electricity and water during a month. Both of the tariffs A and B apply for a domestic consumption, while the C tariff applies for a non-domestic consumption. Tariff A applies to a domestic consumption for a citizen holding a single account only as shown in the table below.

Tariff A for domestic consumption

Electricity (units in kwh) Water (units in m3)

Consumed units Fees Consumed units Fees

Level Range Fils/unit Level Range Fils/unit

1 0 - 3000 3 1 0 - 60 25

2 3001 - 5000 9 2 61 - 100 80

3 Over 5000 16 3 Over 100 200

Tariff B applies to a domestic consumption for a resident or other accounts of a citizen as shown in the table below.

Tariff B for domestic consumption




1 0 - 3000 6 1 0 - 60 80

2 3001 - 5000 13 2 61 - 100 200

3 Over 5000 19 3 Over 100 300

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Tariff C applies to a non-domestic consumption as shown in the table below.

Tariff C for non-domestic consumption




1 0 - 5000 16 1 0 - 450 400

2 5001 - 250000 19 2 451 - 1000 500

3 250001 - 500000 21 3 1001 - 1500 750

4 Over 500000 29 4 Over 1500 1200

As an example, a customer who has an account under tariff A and consumed 4000 units of electricity then he would pay BD 18 (3000 × 0.003 + 1000 × 0.009) for this consumption. EWA issues a bill sent to the customer on the first day of the next month, which includes a fixed charge in addition to the charges of their consumption of electricity and water. EWA fixed monthly charges are BD 2 for tariff A, BD 3 for tariff B and BD 5 for tariff C.

(a) The consumption of a customer for the last month was 2500 units of electricity and 65 units of water. What was the billed amount if his account followed tariff B? [2]

(b) A customer received a bill of BD 32.700 for the month of May for a domestic consumption of electricity not exceeding 5000 units. If during that month water was not consumed, which tariff did his account follow? Explain your answer. [2]

(c) A customer had one domestic account under tariff B and another non-domestic account under tariff C. During his one month vacation, water was not used by either of the accounts and their electricity consumption did not exceed 3000 units. However, the customer received bills for the same amount for both accounts. If the consumption of electricity under the non-domestic account was 190 units, how many units were used by the domestic account? [2] ]

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(d) The residents of a compound of 10 villas, all of which consumed more than 60 units of water, paid a total of BD 45 for the consumption of water during a month. Six of the villas had a tariff A account, while the other four villas had a tariff B account. The average consumption of water used by villas under tariff A was 70 units. What was the average consumption of water by the villas under tariff B? [2]

(e) A customer chooses EWA Automatic billing system to pay the bills of his domestic account under tariff A. On the 1st of March, the bill of his account was issued and an amount of BD 9.375 was deducted from his bank account. An EWA staff member incorrectly inputted the reading of the electricity meter into the computer, but only for the 1st of February reading. The error has now been recognised and EWA appreciates that the bills issued on the 1st of February and the 1st of March were both wrong. The table below shows the correct electricity and water meters readings.

Date Meter readings

Electricity Water

1st of January 8594 400

1st of February 11094 465

1st of March 17094 520

(e1) What was the incorrect reading of the electricity meter at the 1st of February that was inputted into the EWA computer? [2]

(e2) How much credit or debit should EWA now post to the account of this customer upon recognition of the error? Specify whether the amount is credited or debited to the customer’s account. [3]

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(f) The government has decided to support the local industrial sector. An industrial plant can choose only one from either an electricity support programme or a water support programme. Through the electricity support programme, the range of each level of the number of consumed units is increased by 20% and the fees are reduced by 5%, while for the water support programme, the range of each level of the number of consumed units is increased by 30% and the fees are reduced by 15%.

Last year, a small factory had an average consumption per month of electricity and water for two periods as stated in the following table:

Period

Average consumed units per month

Electricity Water

January - August 100000 1300

September - December 245000 1100

Based on the average consumptions of the small factory for the last year, which government support programme is the best for it for the next year? Explain your answer. [4]

(g) A customer has a domestic account under tariff A and his billed amount was BD 11.000 in December 2015, while his billed amount was BD 45.700 in August 2016. In December 2015, he consumed not less than 2500 units of electricity and not less than 45 units of water. In August 2016, his consumption of electricity was exactly twice as much as it was in December 2015 and his consumption of water was exactly three times as much as it was in December 2015. The number of units of electricity and water consumed are whole number.

How many units of water did he consume in August 2016? [3]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (BQA) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.

© 2018 BQA

PS12/02E

March 2018

2018امتحان مارس

PROBLEM SOLVING حل المشكالت

Paper 2 Problem Analysis and Solution ليل وحل المشكالتتح 2الورقة

kingdom of bahrain نيرحبلا ةكلمم samples/g12_ps_p… · (e) in the formula 1 bahrain...

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