- Substitution is where we replace letters in a formula with their values
- This allows you to find one other value that is in the formula

- Write down the
**formula**, if not clearly stated in question **Substitute**the numbers given, using brackets around negative numbers, (-3), (-5) etc**Simplify**any calculations if you can**Rearrange**the formula if necessary (it is usually easier to substitute first)**Work out**the calculation (use a calculator if allowed)

- Formulae for
**accelerating**objects are often used

- The letters mean the following:
*t*stands for the amount of time something accelerates for (in seconds)*u*stands for its initial speed (in m/s) - the speed at the beginning*v*stands for its final speed (in m/s) - the speed after*t*seconds*a*stands for its acceleration (in m/s^{2}) during in that time*s*stands for the distance covered in*t*seconds

- You do not need to memorise these formulae, but you should know how to substitute numbers into them
- You should also understand the difference between initial speed (
*u*) and final speed (*v*)

- You should also understand the difference between initial speed (

(a)

Find the value of the expression when and .

Substitute the numbers given.

Use brackets () around negative numbers that you have substituted so that you don't forget about them.

It is a good idea to show every step of working to make sure that you are following the order of operations correctly.

(b)

The formula is used to find the perimeter, P, of a rectangle of length and width .

Given that the rectangle has a perimeter of 20 cm and a width of 4 cm, find its length.

Substitute the values you are given into the formula.

Simplify.

Subtract 8 from both sides.

Divide both sides by 2.

**TERMS**are separated by + or –- The sign belongs to the coefficient of the term
**after the symbol** - If there is no symbol in front of the first term then this is a positive term

- 2
*x*- 3*y*means +2*x*'s and -3*y*'s

- 2

- The sign belongs to the coefficient of the term
- “
**LIKE**” terms must have exactly the**same LETTERS AND POWERS**(the**COEFFICIENT can be different**)**Examples**of like terms:- 2
*x*and 3*x* - 2
*x*^{2}and 3*x*^{2} - 2
*xy*and 3*xy* - 4(
*x*+*y*) and 5(*x*+*y*)

- 2
**Examples**that are**NOT**like terms- 2
*x*and 3*y*(different letters) - 2
*x*^{2}and 3*x*^{4 }(different powers) - 2
*xy*and 3*xyz*(different letters) - 4(
*x*+*y*) and 5(*x*+*y*)^{2}(different powers)

- 2
- Remember
**multiplication can be done in any order***xy*and*yx*are like terms

- Add the
**COEFFICIENTS**of like terms- If the answer is a positive answer then put "+" in front if there are other terms before it
*x*- 2*y*+ 5*y*=*x*+ 3*y*

- If the answer is a negative number then put "-" in front
*x*- 5*y*+ 2*y*=*x*- 3*y*

- If the answer is a positive answer then put "+" in front if there are other terms before it

- A “coefficient” answers the question “how many?”

For example:

the coefficient of x in 2x^{2} – 5x + 2 is -5

and:

the coefficient of x in ax^{2} + bx + c is b

Simplify .

Reorder the terms so that the 's are together, as are the 's, 's and the constants.

Make sure that you keep the same sign in front of them when you reorder them.

Add the coefficients of the 'like' terms.

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