CIRCLES

TOPIC: CIRCLES

Learning Objectives.

1. recognize various parts of a circle.
2. state the properties of chords of a circle.
3. state and apply the property of angles at the centre.
4. state and apply the property of angles in the same segment.
5. recognize the property of angles in a semi-circle.
6. explain the meaning of the concyclic points.
7. state the properties of angles in a cyclic quadrilateral.
8. state the properties of angles in a cyclic quadrilateral.
9. state the definition of a tangent to a circle.
10. recognize the properties of the tangents to a circle.
11. state and apply the alternate segment theorem.

 

Circles

            A circle is a set of ponts in a plane so that they are always at a constant distance rom a fixed point. The fixed point is known as the centre and the distance is known as radius (plural: radii).

Parts of a circle

A circle is a closed curve in a plane such that all points on the curve are equidistant from a fixed point. The given distance is called the radius of the circle.

A chord is a line segment with its end points on the circle and a diameter is a chord passing through the centre.

An arc is a part of the circle. A segment is the region bounded by a chord and an arc of the circle.

A sector is the region bounded by two radii and an arc. It is a part of a circular region bounded by the two radii and the arc subtended by them.

Central Angles

The angle formed by two radii of a circle at the centre is called a central angle. 

In the figure below, <POQ is a central angle. Arc PQ subtends <POQ at the centre. An arc whose measure is 45° subtends an angle 45° of at the centre. Also, <POQ intercepts the arc PQ at the circumference. 

 

The length of an arc is proportional to the measure of the central angle, provided the radius of the circle is not changed. 

Chords of a circle

 A chord is a line segment whose end-points are on the circle. A chord which passes through the centre of the circle is called a diameter.

 

ACCOUNTS

INTRODUCTION TO ACCOUNTS

Meaning of accounts:

Account is a record or statement of money received and paid out, as by bank or business. The part of accounting that is concerned with recording data is known as Book-keeping. In short book-keeping is an art of recording financial business transactions on a set of books in terms of money or money’s worth.


Why do we need to keep business record?        

©      To determine whether the business is making profit or loss

©      To determine the financial strength of the business

©      To enable the Government to assess the reliable tax

                  ©      To enable different stakeholders to make reliable decisions about business e.g.                                          investors, bankers customers, etc.

     Double Entry:

            This is the process of recording business transactions twice. The business transaction means the  transfer or movement of money or goods or services valued in terms of money worth from one      part/person to another. Double entry is principle of accounting. Every transaction involving              money has a two-fold aspect, the receiving of value on the one hand and the giving of the same          value on the other hand. This two-fold nature in all transactions must be recorded in the books          and this gives the term “Double entry book-keeping.” 

Different accounting terminologies.

(1)   Ledger.

-     A ledger is the main book of accounting in which business transactions are recorded in double entry. The ledger contains sections called “Accounts” which contain details of transactions for a specific item.

-         When a business is very small, all the double entry accounts can be kept in one book which is now the ledger. As the business grows it would be impossible just to use one book, as many pages are needed for lot of transactions. This would mean that the book would be too big to handle.

Therefore, transactions should be posted to the ledger book, namely: -

                                                                    i.            Cash account

                                                                  ii.            Capital account

                                                                iii.            Purchases account

                                                                iv.            Sales account

                                                                  v.            Stock account

                                                                 vi.            Various expenses such as Rent, Wages, Salary, etc.

-         Each account should be shown on a separate page.

Main sides of the Ledger

1.      The left hand side, is the side which receive money or money’s worth and is called the debit (Dr) side.

2.      The right hand side, is the side which gives or pay out money or money’s worth and is called credit (Cr) side

Hint: The principle of double entry states that “Every debit entry must have a corresponding credit entry of the same amount and vice versa”

            Columns of the Ledger book

A ledger contains main eight (8) columns of which four (4) columns from the left hand side and four (4) columns from the right hand side as follows: -

Columns of the Ledger and their uses

           a.       Date – This column is used to record the year, month and date transaction took place

       b.    Particulars – This column is used to record short narration of the entry of an account i.e. Purchases, Sales, etc.

           c.       Folio – This column records page of reference in books of accounts.

          d.      Amount – This is the column for recording money received or paid out.

       (1)   Capital – The original fund with which a person enters a business

       (2)   Asset – Anything owned by business, whether cash, goods, furniture, shelves in shop etc.

      (3)   Liabilities – This is an opposite of an asset, and it is anything that the trader owes to someone else. Just the amount of money borrowed from other people or bank. E.g. business borrowed money from bank, shop owner purchased Pepsi from company.

Common abbreviations used in accounting.

v  b/f        -           Brought forward

v  c/f        -           Carried forward

v  b/d       -           Brought down

v  c/d       -           Carried down

v  Dr        -           Debit

v  Cr        -           Credit  

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EXAMINATION FORMAT

FORM FOUR BASIC MATHEMATICS EXAMINATION FORMAT - 2107

      This is an Official format which was released by National Examination Council of Tanzania (NECTA). It is the outline of all the Questions numbers and from which topics will be taken from.
     Of course this will be very helpful to students who will take serous on it. To have the access to it, just click the link below and it is free to download.

DOWNLOAD 

TRIAL BALANCE

Trial Balance

Objectives.

After studying this sub-topic, you will be able to:

-         State the meaning of Trial Balance;

-         Explain the objectives or purposes of preparing Trial Balance;

-         Prepare a Trial Balance

Meaning of trial balance:

Trial Balance may be defined as a statement which contains balances of all ledger accounts on a particular date. This is also defined as the statement showing a list of debit and credit balances extracted from the ledger prepared at the end of accounting period.

Ledger balances are segregated into debit balances and credit balances. If all accounting entries are recorded correctly and all the ledger balances are accurately extracted, the total of all debit balances appearing in the trial balance must equal to the sum of all credit balances.

Objectives or purposes of preparing a Trial balance

        i.            To check, verify or ensure the arithmetical accuracy of double-entry

      ii.            To help in preparing financial statements

    iii.            Helps in locating errors

    iv.            Helps in comparison

      v.            Helps in making adjustments

Note: Trial Balance is generally prepared at the end of the year. However it can be prepared at any time during the accounting year to check the accuracy of the posting.

How to prepare a Trial balance

a)      Balance each account in the ledger

b)      List the accounts in the order in which they come in the ledger, leaving out the accounts with zero balance.

c)      Fill each account listed with the amount in the appropriate column of the trial balance, “debit” in the ‘Dr’ column and “Credit” in the ‘Cr’ column.

d)     Add up the amounts in both columns and see if the totals balance.

Format of a Trial Balance

TRIAL BALSNCE AS AT ----

Name of account	Dr	Cr
Cash Capital Purchases Sales Expenses	XXX   XXX   XXX	XXX   XXX
	XXXX	XXXX

 

Example.

Mrs. Waka commenced as follows

March 1 Capital in cash Tsh. 260,000

2 Purchased goods for cash Tsh. 70,000

3 Sold goods for cash Tsh. 90,000

7 Purchased goods for cash Tsh. 30,000

13 Bought packing materials Tsh. 5,000

19 Paid transport charges Tsh. 3,500

21 Bought more goods for cash Tsh. 20,000

24 Paid insurances for cash Tsh. 6,000

27 Sold goods for cash 60,000

Open the ledger accounts to record the above information, balance off the accounts and extract the Trial Balance

Solution

CASH ACCOUNT (1)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 1 3 27               April. 1	Capital Sales Sales               Balance	2 4 4               b/d	260,000 90,000 60,000	March. 2 7 13   19   21 24 31	Purchases Purchases Packing materials Transport Charges Purchases Insurances Balance	3 3   5   6 3 7 c/d	70,000 30,000   5,000   3,500 20,000 6,000 275,000
			410,000				410,000
			275,000

 

CAPITAL ACCOUNT (2)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 31	Balance	c/d	260,000	March. 1     April. 1	Cash     Balance	b/d	260,000
			260,000				260,000
							260,000

 

PURCHASES ACCOUNT (3)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 2 7 21 April. 1	Cash Cash Cash Balance	b/d	70,000 30,000 20,000	March. 31	Balance	c/d	120,000
			120,000				120,000
			120,000

 

SALES ACCOUNT (4)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 31	Balance	c/d	150,000	March. 3 27     April. 1	Cash Cash   Balance	b/d	90,000 60,000
			150,000				150,000
							150,000

 

PACKING MATERIAL ACCOUNT (5)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 13 April. 1	Cash   Balance	b/d	5,000	March. 31	Balance	c/d	5,000
			5,000				5,000
			5,000

TRANSPORT ACCOUNT (6)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 19 April. 1	Cash   Balance	b/d	3,500	March. 31	Balance	c/d	3,500
			3,500				3,500
			3,500

 

INSURANCE ACCOUNT (7)

Dr                                                                                                                                                Cr
Date	Particulars	Folio	Amount	Date	Particulars	Folio	Amount
March. 13 April. 1	Cash   Balance	b/d	5,000	March. 31	Balance	c/d	5,000
			5,000				5,000
			5,000

 

MRS. WAKA’S TRIAL BALANCE AS AT 31^ST MARCH

Name of account	Dr	Cr
Cash Capital Purchases Sales Packing materials Transport Insurance	275,000   120,000   5,000 3,500 6,000	260,000   150,000
	410,000	410,000

 

Nyeneu Rahabu Peter