Math with

Mr Hunte

##### Introduction

Persons who are paid a fixed amount each month for their services during that period are said to receive a salary. This amount is called a gross salary. After deductions, such as taxes, the amount the worker receives is referred to as a net salary.

##### Example 1

A teacher is paid an annual salary of $33 360. What is his gross monthly salary?

##### Example 2

The gross monthly salary of an economist is $6 875. Calculate his net annual salary after deductions of $985 were made monthly.

##### OVERTIME

When workers work beyond the number of hours allotted for a basic week they receive overtime pay. The overtime rate is higher than the basic rate and is usually at time and a quarter, time and a half or double time.

##### EXAMPLE 1

In a certain company, all employees work a basic week of 40 hours. Overtime worked from Monday to Friday is paid for at time and a quarter. Overtime worked on Saturday is paid for at time and a half and Sunday overtime is paid for at double time. Given that the basic rate is $15.20 per hour, determine the gross wage for a man who worked 10 hours overtime from Monday to Friday, 3 hours overtime on Saturday and 4 hours overtime on Sunday.

##### WAGES

A wage is money that is paid or received for work or services, as by the hour, day or week.

IMPORTANT TERMS

Basic Rate – Amount paid per hour

Basic week – The number of “normal” hours worked per week.

Basic wage = Basic Rate x Basic Week

##### Example 1

Samuel’s wage for a 35 – hour week is $341.25. Calculate his basic rate.

##### Introduction

Commission is a sum of money that is paid to an employee, usually for selling a certain amount of goods or services. It can be paid as a percentage of the sale or as a flat dollar amount based on the number of sales. Employers often use sales commissions as incentives to increase worker productivity.

##### Example 1

A saleswoman sold $1 050 worth of goods during a certain week. Given that she is paid a commission of 3% on total sales, calculate her commission.

##### Example 2

An agent who sells smart phones is paid a basic wage of $680 per week. Additionally, he is paid a commission of 5% on his sales. In a particular week he made sales totalling $10 875. Determine:

(a) his commission

(b) his gross wage for that week.

##### Example 3

The gross wage for a salesman during a certain week is $1 542.75. If his basic wage is $542.75 and he is paid a commission of 2.5% of the total value of goods sold, calculate:

(a) the commission that he is paid

(b) the total value of the goods sold that week.

##### Introduction

If you initially invest money (the principal), a percentage (the rate of interest) of this investment is added to the principal, on a yearly basis. This allows the investment to grow. There are various methods for determining the amount by which the investment should grow. In this section we will only focus of Simple Interest. This may be the easiest way of determining that amount.

In this section, the formula for Simple Interest is

where I=Amount of Interest, P= Principal (Initial Amount), R=Rate of Interest and T=Time in years

##### Example 1

Mr Mottley invests $15 000 at 4% per annum simple interest for 27 months.

(a) Calculate the amount he received in interest for the 27 – month period.

(b) How much does he have after the 27 months?

##### Example 2

Ricardo invested $2 500 for 9 months at 4% simple interest. Calculate the amount he receives at the end of this period.

##### Example 3

The simple interest on a sum of money invested at 3.5% per annum for 2 years is $168. Determine the amount of money invested.

##### Example 4

Kiara earns $250 after investing $1 000 for 8 years at per annum. Determine the value of R.

##### Example 5

At the end of T years Jacob receives $3 600 after investing $3 000 at 5% per annum simple interest. Calculate the value of T.

## MEASUREMENT

##### Example 1

Determine the size of an interior angle of a regular 15 – sided polygon.

##### Example 2

Each interior angle of a regular polygon is 150°. Determine the number of sides of the polygon.

##### Example 3

Find the value of w.

##### Example 4

The diagram shows part of a regular polygon. The interior angle is (15x+20)° and the exterior angle is x°. Find the number of sides of this polygon.

##### Example 1

Determine the volume and surface area of cube below.

##### Example 2

Determine the volume and surface area of cuboid below.

##### Example 3

For the triangular based prism determine

(i) its volume,

(ii) its surface area.

##### Example 4

Determine the volume, curved surface area and total surface area of the following cylinder.