unit6 compatibility mode

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Section 1: Equations

• If we wish to solve an equation, we must find the value of the letter (usually x ) which satisfies the equation .When the equation is solved, the answer must be checked, by substituting it for x in the original.

Example: x + 9 = 23

Here we subtract 9 from each side ; x + 9 – 9 = 23 – 9

Therefore x = 14

We can check by substituting 14 for x

• Equation which we solve at the same time

in order to find two unknown values are

called simultaneous equations.

• An expression which contains a square as

the highest power or any letter ( x,y,etc )

is called a quadratic. If we say that such

an expression is equal to some value, the

resulting equation is known as quadratic

equation.

Example :

Solve x - 5x +6 = 0 By factorising we get ( x -2 ) ( x – 3 ) = 0 Therefore either x – 2 = 0 so x = 2 or x – 3 = 0 so x = 3

x = 2 or 3

The values for x are the roots of the equation

Practice 1.

1. Find the number when seven times the number is four less than sixty seven. 2. Find the number when twenty-eight is one

more than three quarters of the number. 3. Find the number when five , plus three times

the number. equals forty.

4. Three consecutive odd numbers add up to twenty-seven what are they?

5. Two consecutive even numbers add up to thirty. What are they ?

Section 2: Formulae

• When we have solved particular problem, we can often reduce the method of solving it to a fixed pattern and write down this pattern as a formula which can be used for similar problems.

• For example , the statement Average speed is equal to distance covered divided by the total time taken, can be written as the formula :

S =

• Often we will need to change the subject of a formula. For example, from Boyle's law , we have the formula

P =

• We can change the subject of the formula to v, and the result is V =

T D

v k

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Practice 2

Read out the following formulae :

1.

C = d

6 ) F = (C + 32)

2.

2S = U + V

7 ) V = r h

3. x = a- b

8 ) F =

4.

V = u + at

9 ) E = mc

5.

I =

10) A =



5 9

2



n 2

R MV2

2

100

PRT 2

r



Change the subjects of the above formulae as follows :

1) d = 3) b =

2) V = 4 ) u =

5) P = 7 ) h =

6) C = 8 ) R =

9) m = 10) =

Practice 3

Solve the following :

1. b plus eight equals eleven. 2. Seven b equals forty-two. 3. Two x equals one.

4. Three y plus nine equals twenty –seven. 5. Four y minus eleven equals y plus one. 6. Seven b equals sixteen minus three. 7. Five c plus six equals two c plus twenty-four. 8. Twelve plus four a equals seven a minus twenty one. 9. Twelve minus two b equals four b plus thirty-six. 10. Three x plus five equals two x.

Vocabulary practice Fill in the blank spaces in the following sentences :

1. When we have ______ an equation, we should ________ our answer.

2. The answer is checked by _____for the letter in the original equation.

3. If our answer ________the equation , it is correct.

4. We can use one equation to help us solve another equation. These are called ________ equations.