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Book , Online - Google Books. Rowland, Robert, Milton, Qld. Previous ed. There are three people in particular whom I would like to single out for special mention: Jennifer Nolan, whose support for the Maths Quest project and for me personally has made everything possible; Ingrid Kemp, the newest addition to our team, who has brought a new set of eyes to our project and kept the ball rolling thanks Ingrid; and nally Keith Hartmann, who has tirelessly reviewed all of the new material and has completed all of the answer checking thanks Keith I hope youre enjoying retirement!
Finally, and most importantly, to my family thank you. Without your support this book and online resources would never have been completed. The author and publisher would like to thank the following copyright holders, organisations and individuals for their assistance and for permission to reproduce copyright material in this book. Illustrative material AGL: p. Not to be used for navigation. Rubberball Productions: p. Software The authors and publisher would like to thank the following software providers for their assistance and for permission to use their materials.
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Order forms are available at www. Due to copyright restrictions, the demo version of Cabri Geometry II Plus must not be used in the classroom for presentation on a regular basis. For site licences contact Cabrilog Grenoble-France at sales cabri. Screenshots reproduced throughout with permission from Microsoft. Every effort has been made to trace the ownership of copyright material.
Information that will enable the publisher to trace the copyright holders or to rectify any error or omission in subsequent reprints will be welcome. About the author Robert Rowland has been teaching Mathematics for over 20 years and currently holds the position of Head teacher, Teaching and learning at Ulladulla High School.
He taught at Cabramatta High School from to before taking up his appointment at Ulladulla High School in Robert has successfully taught all levels of Mathematics to Year 12 as well as Computing Studies and Information Processes and Technology. Try the questions below. Thursday 6. Expressing one quantity as a percentage of another. Calculating salary payments Methods of payment A payment received by an employee for doing a job is called income.
There are many different ways people are paid for performing a job. In this section we are going to look at some of these methods of payment: salaries, wages, commission, royalties, piecework and overtime. Salaries Many people employed in professional occupations are paid a salary. Such employees include teachers, lawyers, accountants and some doctors. A salary is a xed amount of money that is paid to employees to do their jobs.
The amount paid does not change, regardless of the number of hours worked. Salaries are usually calculated on an annual basis. A salary is therefore usually stated as an amount per annum, which means per year. Salaries are paid in weekly, fortnightly or monthly amounts. To make calculations about salaries, you will need to remember the following information.
Calculate the amount that Dimitri is paid each fortnight. THINK 1 2. We reverse this calculation when we are given the weekly, fortnightly or monthly pay of a person and are then asked to calculate the annual salary.
Calculate Graces annual salary. To compare a salary payment with other forms of income it may be necessary to calculate the equivalent daily or hourly payment. To do this, we need to know the number of days or hours worked per week. If Charlotte works an average of 42 hours per week, calculate her equivalent hourly rate of pay. THINK 1. Calculate the weekly pay by dividing the salary by Calculate the hourly rate by dividing the weekly pay by A salary is a xed payment made for doing a job.
A salary is usually calculated on an annual basis and can be paid in weekly, fortnightly or monthly instalments. To calculate information about equivalent daily or hourly rates of pay, we need information about the number of days and hours worked by the employee.
Calculate Tonis fortnightly pay. Calculate Rogers weekly pay. Calculate Friedas monthly pay. Calculate Wendys pay if she is paid: a weekly b fortnightly c monthly.
Calculate Darrens fortnightly pay, correct to the nearest cent. Calculate Maxines annual salary. Calculate Thaos annual salary. Calculate Deidres annual salary. If Fiona works an average of 40 hours per week, calculate the equivalent hourly rate of pay. Calculate the hourly rate to which Jades salary is equivalent. Give your answer correct to the nearest cent.
Calculate the number of hours that Henry will need to work each week to earn more money than Garry does. Calculating wages Most people in the workforce earn a wage.
A wage is paid at an hourly rate. The hourly rate at which a person is usually paid is called an ordinary rate. The wage for each week is calculated by multiplying the ordinary rate by the number of hours worked during that week. Calculate Sadiqs wage in a week where he works 38 hours. To compare two peoples wages, we cant just look at the amount of money each receives in a pay packet. We must also consider the number of hours each has worked. Wages are compared by looking at the hourly rate.
To calculate the hourly rate of an employee we need to divide the wage by the number of hours worked. Calculate Georginas hourly rate of pay. Using a similar method we are able to calculate the number of hours worked by an employee, given their wage and hourly rate of pay. The number of hours worked is found by dividing the wage by the hourly rate. In some cases, wages are increased because an allowance is paid for working in unfavourable conditions. An allowance is an additional payment made when the working conditions are difcult or unpleasant.
For example, a road worker may be paid an allowance for working in the rain. In these cases, the allowance must be multiplied by the number of hours worked in the unfavourable conditions and this amount added to the normal pay. For working on wet days he is paid a wet weather allowance of 86c per hour. Calculate Ryans pay if for 12 hours of the week he works in the rain. Calculate the wet weather allowance by multiplying 0. Add the normal pay to the wet weather allowance to calculate the total pay.
This type of allowance is also paid to casual workers. When you are employed on a casual basis you do not receive any holiday pay and you do not get paid for days you have off because you are sick. The casual rate is a higher rate of pay to compensate for this. A wage is money earned at an hourly rate. To calculate a wage we multiply the hourly rate by the number of hours worked during the week.
To calculate an hourly rate we divide the wage by the number of hours worked. To calculate the number of hours worked we divide the wage by the hourly rate. Allowances are paid for working under unfavourable conditions. The total allowance should be calculated and then added to the normal pay.
A casual rate is a higher rate of pay for casual workers to compensate them for having no holidays and receiving no sick leave. Calculate Allans wage in a week where he works 40 hours. Name A. Smith B.
Brown N. Tran A. Milosevic L. Calculate Alicias wage in a week where she works: a 36 hours b 48 hours c Calculate Domonics wage in a week where he works: a 32 hours b 37 hours c Calculate the casual rate earned by casual waitresses. White B. Black C. Green D. Brown E. Scarlet F. When he has to work at heights he is paid a 46c per hour height allowance. Calculate 6 Richards pay in a week where 15 hours are spent working at heights.
Calculate Ingrids pay if she works with toxic substances all week. Find the least time Zhong must work if he is to earn more money than Rema does. Calculate Zoes hourly rate of pay. Computer Application 1 Spreadsheets Throughout this chapter we are going to develop a number of spreadsheets that will calculate wages. Work through the following steps. Open a spreadsheet and enter the following information. This will calculate the wage for Frederick Astini the gure should appear in the cell.
Highlight cells E7 to E11 and select the Fill Down option. The wages for each employee should now be calculated and be formatted as currency. If you now change the hours worked by each employee, his or her gross pay should update automatically.
Calculate Donnas wage. Calculate Debbies hourly rate of pay. Calculate Damiens weekly pay. Calculate Simones fortnightly pay. Calculate Ivans monthly pay. Calculate Pennys weekly pay. Calculate the hourly rate to which her salary is equivalent. Answer to the nearest cent. Commission and royalties Commission is a method of payment used mainly for salespeople. When paid commission, a person receives a percentage of the value of goods sold. A royalty is a payment made to a person who owns a copyright.
For example, a musician who writes a piece of music is paid royalties on sales of CDs; an author who writes a book is paid according to the number of books sold. Royalties are calculated in the same way as commission, being paid as a percentage of sales. In some cases, commission may operate on a sliding scale. This means that the commission rate changes with the value of sales. This type of commission is commonly used in real estate sales. In these examples, each portion of the commission is calculated separately.
The nal commission is the sum of each portion. Calculate the balance of the sale. Calculate 2. Add up each portion to calculate the commission. In some cases, people receive a xed amount called a retainer as well as a commission. This is to ensure that the person earns some money even if no sales are made. To calculate this type of pay, you will need to add the retainer to the commission. In some cases, the commission does not begin to be paid until sales have reached a certain point.
Here the commission is calculated only on sales above this xed amount. A commission is earned when a person is paid a percentage of the value of sales made. Some commissions are paid on a sliding scale. In these cases, each portion of the commission is calculated separately and then totalled at the end. Some commissions are paid together with a xed payment called a retainer. To calculate an employees pay, the xed payment needs to be added to the commission.
In some cases where a xed payment is made, commission may not be paid on all sales, but rather on a section of sales above a certain point. How much does Ursula receive in commission?
What rate of commission does Asif receive? Who earns the most money? What is the value of Ginas sales? How much should his sales be? Payment by piece Payment by piece, or piecework refers to payment for the amount of work completed. It is commonly paid for jobs such as car detailing and letterbox delivery. The amount earned is calculated by multiplying the rate of payment by the number of pieces of work completed. Calculate what Len earns in an afternoon where he washes 24 cars.
In some cases, piecework is paid for multiples, rather than for single units. For example, for letterbox deliveries you may be paid per deliveries made. Calculate what Holly will earn for a delivery of brochures. Divide by to calculate the number of thousand brochures delivered. Multiply 3.
There are also examples where you will be asked to compare payment by piece with other methods of earning income, in particular, wages. Payment by piece is payment to an employee for the amount of work completed. To calculate the amount to be paid, multiply the number of units of work completed by the amount to be paid per unit. Be careful when pay is calculated for completing or units of work.
You will need to rst divide by this amount. Remember your work on other methods of payment. You will need it to compare payment by piece with them. Calculate the earnings of each person in the group if: a Ryan picked 23 baskets b Summer picked 21 baskets c Seth picked 19 baskets d Taylor picked 18 baskets.
Calculate Natalies earnings for doing 14 baskets of ironing. Calculate Matthews earnings in a week if he mows 9 lawns. If Dean cleans 7 houses, calculate his earnings. Calculate what Barbara will be paid for delivering 15 pamphlets. Calculate the amount each person is paid. Calculate what Raul is paid in a day where he assembles: a toys b toys c toys. Calculate Carolinas earnings for a 4 km delivery.
Calculate the amount Keith will earn for a journey of: a 5 km b Calculate her weekly wage. Calculate Viets weekly wage. Calculate Samanthas weekly pay. Calculate Toms fortnightly pay. Calculate her annual salary.
Calculate Jasons pay for a day in which he picks 43 baskets of fruit. Calculate Julias pay for delivering pamphlets. Working overtime Overtime is paid when a wage earner works more than the regular hours each week. When an employee works overtime a higher rate is paid. This higher rate of pay is called a penalty rate. The rate is normally calculated at either: -time and a half, which means that the person is paid 1 1 times the usual rate of pay, 2 or double time, which means that the person is paid twice the normal rate of pay.
A person may also be paid these overtime rates for working at unfavourable times, such as at night or during weekends.
To calculate the hourly rate earned when working overtime we multiply the normal -hourly rate by the overtime factor, which is 1 1 for time and a half and 2 for double time. Calculate Gustavos hourly rate when he is being paid for overtime at time and a half. To calculate the pay for a period of time worked at time and a half or double time, we -multiply the normal pay rate by the overtime factor either 1 1 or 2 and then by the 2 number of hours worked at that overtime rate.
Calculate the amount Adrian earns for 6 hours work on Saturday, when he is paid time and a half. When we calculate the total pay for a week that involves overtime, we need to calculate the normal pay and then add the amount earned for any overtime.
Calculate Natashas pay in a week where she works 5 hours at time and a half in addition to her regular hours.
THINK 1 2 3. Calculate Natashas normal pay. Calculate Natashas pay for 5 hours at time and a half. Add the normal pay and the time and a half pay together. Some examples will have more than one overtime rate to consider and some will require you to work out how many hours have been worked at each rate. If Graeme works overtime, the rst 6 hours are paid at time and a half and the remainder at double time.
Calculate Graemes pay in a week where he works 45 hours. Calculate the number of hours overtime Graeme worked. Of these nine hours, calculate how much was at time and a half and how much was at double time. Calculate Graemes normal pay. Calculate what Graeme is paid for 6 hours at time and a half. Calculate what Graeme is paid for 3 hours at double time. Calculate Graemes total pay by adding the time and a half and double time payments to his normal pay.
Overtime is paid when you work more than your normal working hours in a week, and you receive a higher rate of pay for the extra hours. Overtime can be paid at: - a time and a half 1 1 times the normal hourly rate 2 b double time twice the normal hourly rate.
To calculate the hourly rate when working overtime, multiply the normal hourly rate by the overtime factor. To calculate the pay that is received for overtime, multiply the normal hourly rate by the overtime factor by the number of hours worked at that overtime rate. To calculate the total pay for a week when overtime has been worked, calculate the normal pay and the pay for each overtime rate separately, and add them.
Calculate the amount Reece earns each hour when he is being paid time and a half. Calculate Carmens rate a quantity money by a per hour on a Sunday when she is paid double time.
For working on 1. Calculate 2 Gareths hourly rate of pay on a public holiday. Calculate the total amount Ben will of time earn for an 8-hour shift on Saturday when he is paid at time and a half. Calculate Taylors pay for 6 hours on Sunday when she is paid double time. Nguyen M.
Donnell F. Milosevic J. Carides Y. What will Ernies hourly rate be when he is paid time and a half for overtime? Calculate how much more Stephanie will earn in 8 hours work at time and a half than she would at ordinary rates.
Calculate the number of hours at time and a half that Eric will have to work to earn the same amount of money that he will earn in 9 hours at ordinary rates. Calculate Ricks pay in a week where, in addition to his normal hours, he works 16 4 hours overtime at time and a half.
Calculate Kirstys pay in a week where, in addition to her ordinary hours, she works 4 hours on Sunday, when she is paid double time. Calculate Grants pay for a week where he works 4 hours at time and a half and 2 hours at double time in addition to his regular hours.
Name W. Clark A. Hurst S. Gannon G. Dymock D. Colley 14 multiple choice Jenny is a casual worker at a motel. Jenny works 8 hours on Saturday for which she is paid time and a half. On Sunday she works 6 hours for which she is paid double time. Jennys pay is equivalent to how many hours work at the normal rate of pay?
Any overtime that Patricia does is paid at time and a half. What is the minimum number of hours that Patricia will need to work to earn this amount of money? The rst 4 hours overtime he works each week is paid at time and a half with the rest 17 paid at double time. Calculate Stevens earnings for a week in which he works 43 hours. For the rst 4 hours overtime each week Kate is paid time and a half and the rest is paid at double time.
Calculate Kates pay in a week where she works: a 38 hours b 41 hours c 45 hours. If Zac works more than 8 hours on any one day the rst 2 hours are paid at time and a half and the rest at double time. Calculate Zacs pay if the hours worked each day are: Monday 8 hours Tuesday 9 hours Wednesday 12 hours Thursday 7 hours Friday Computer Application 2 Wages 1. This formula will calculate the gross wage for Frederick Astini. Highlight cells G7 to G11 and choose the Fill Down option to copy this formula to the rest of this column.
Check the functioning of your spreadsheet by changing the hours worked by Frederick Astini to 38 normal hours, 3 hours at time and a half and 4 hours at double time. Now change the hours for the other employees and notice the gross pay changing. Now change the hourly rate of pay for each employee. This will mean that you have copies of both version 1 and 2 of the spreadsheet.
Fixed incomes Many people rely on government allowances for an income. These allowances include the youth allowance, pensions and other welfare benets. Investigating government payments Youth allowance 1 2 3 4 What is the youth allowance? How much is paid per week for the youth allowance?
What conditions are placed on receipt of the youth allowance? What will be the total received by a person after one year of receiving the youth allowance? Compare this with a person who receives the youth allowance. Unemployment benets 6 What is the difference between unemployment benets and the youth allowance?
For example, must they show that they are looking for work. Pensions 11 Name three different types of pension that are paid by the government. Additions to and deductions from gross pay Although we may calculate a persons pay, this is not the amount that is actually received. The amount that we calculate, based on their wage or salary, is called gross pay or gross wage. From your gross pay, several deductions may be made for items such as tax, union fees, private health insurance, superannuation and so on.
The amount left after these deductions have been taken out is called the net pay and it is this amount that you actually receive. To calculate an employees net pay we subtract any deductions from the gross pay. Calculate Roberts net pay. In some cases, you will be required to calculate the size of a deduction based on either an annual amount or a percentage. Calculate how much is deducted from Charissas pay each fortnight for superannuation.
When employees take annual leave, they may receive an annual leave loading. Gross pay refers to pay before any deductions are made. Net pay refers to the pay received after deductions have been taken out. Some deductions are calculated on an annual basis and then taken out in equal weekly or fortnightly amounts. Some deductions are calculated as a percentage of gross earnings. When employees take their annual leave a loading is often paid.
Additions to and deductions from gross pay 1. Calculate Trevors net pay each week. Calculate Davids net pay. Belinda is paid fortnightly. Yasmin has her fees for private health insurance deducted from her pay fortnightly. Calculate the amount that should be deducted from her pay each week for union fees. Calculate Dorothys net pay. Calculate the fortnightly payment. Calculate Patricks net fortnightly pay.
Calculate the amount that Sabrina pays in superannuation. Calculate the amount that Arthur has deducted from his salary each fortnight for superannuation. Calculate Rexs weekly superannuation contribution. Calculate Rexs weekly net wage. Calculate the amount that is deducted from Raylenes salary each fortnight for superannuation. Calculate the amount of the deduction made for both union fees and health insurance.
Example a Calculate the amount Liang-Yi will earn in a normal working week. Calculate 2 the holiday loading. Calculate how much health insurance Scott must pay for a 4-week period. Computer Application 3 Wages template 1. Your spreadsheet will now calculate both a persons Gross Pay and Net Pay.
You should now have three versions of the spreadsheet saved. When a spreadsheet is in this form it is called a template. The spreadsheet is now ready to accept new data and make new calculations. Save this version as Wages template. Costs of banking Once we have earned money, we use a bank or similar nancial institution to look after it until we need it. When we deposit money in the bank the bank pays interest on that account.
However, for many accounts where we need instant access to our money, the interest paid is very low and there may be fees associated with using the account. Find three bank accounts into which your pay could be deposited electronically. Answer the following questions about them. For example, do you get a cheque book? What are the charges for exceeding this number of transactions?
Calculate Wendys 2 weekly wage. Calculate Davids fortnightly pay. Calculate Veronicas pay in a week where she assembles 45 radios. Calculate what Christy is paid for deliveries. Calculate what Matthew earns per hour in overtime when he is paid at time and a half. Calculate what Darren will earn in a week where he works 37 hours at ordinary rates as well as 5 hours at time and a half.
Calculate Zelkos net wage. Budgeting Once we have earned money we need to allocate the money to cover our expenses; otherwise, we may spend more than we earn! Allocating money to cover expenses is called making a budget. A budget is divided into two parts: income and expenditure. A budget is balanced when income and expenditure are equal. When designing a budget, it is important to look for all your expenses and set money aside for them.
For example, electricity bills arrive every three months and money should be set aside each week so that when the bill does arrive you have the money to pay for it.
The amount set aside should be based on the normal amount of the bill over a year, with that amount divided into weekly or fortnightly amounts. For bills such as electricity and telephone, an extra amount should be allowed, as you do not know the exact amount of the bill until it arrives. Such an allowance covers the possibilities of a price rise or increased usage. This is not necessary for bills such as council rates or insurance, as these are known in advance.
How much should Ben budget for electricity bills out of each weeks pay? Calculate the total of the previous years bills. Make a practical approximation of the answer. Some bills are calculated over different lengths of time, so the simplest way to develop a budget is to calculate all bills over a year.
Calculate the total annual amount for electricity. Calculate the total annual amount for telephone. Mathematics for Australia 11 — General Mathematics has been designed and written for the Australian Curriculum. This book is recommended for students intending to study General Mathematics in Year … This book covers the Preliminary syllabus for Mathematics and Extension 1.
The extension material The extension material is easy to see as it has green headings and there is green shading next to all extension question and List of Stationery and Equipment Requirements Continued Oxford Insight Mathematics General 11 Preliminary Course Ed.
Mathematics Preliminary Course — 2nd Edition. The extension material The extension material is easy to see as it has green headings and there is green shading next to all extension question and This book has been specifically designed to help Year 11 students thoroughly revise all topics in the Preliminary General Mathematics course and prepare for their class tests, half- … Download as PDF, TXT or read online Download. This book is recommended for students intending to study General Mathematics in Year ….
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