Inequalities

Solve the expression 3x - 7 < 8.

• First, write down the inequality:
• 3x - 7 < 8

• Then add 7 to both sides, to cancel out the -7:
• 3x < 15

• Next, simplify the inequality by dividing both sides by the number in front of x - in this case 3.
• x < 5

So the inequality in 3x - 7 < 8 is satisfied when x is less than 5. (Note that this does not include 5 itself.)

Ratio's

Write the ratio in its simplest form.

To work this out, look for a number that will divide into and .

divides into both numbers, so can be written as .

You can divide these by , so the simplified ratio is .

No number divides into and exactly, so is the simplest form of the ratio.

 

If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be ( to ).

• If you use litre of orange, you will use litres of water .
• If you use litres of orange, you will use litres of water .
• If you use litres of orange, you will use litres of water .

These ratios are all equivalent:

Both sides of the ratio can be multiplied or divided by the same number to give an equivalent ratio.

Negative number 23/10/15

a) 5 × -4
b) -40 ÷ -8

a) We have +5 and -4. The signs are different, so the answer will be negative. So, +5 × -4 = -20

b) We have -40 and -8. The signs are the same, so the answer will be positive. So, -40 ÷ -8 = 5

brackets anf factorisation 9th/10/2015

Factorise the expression: c²- 3c - 10

Write down the expression: c²- 3c - 10
Remember that to factorise an expression we need to look for common factor pairs. In this example we are looking for two numbers that:

• multiply to give -10
• add to give -3

Think of all the factor pairs of -10:

• 1 and -10
• -1 and 10
• 2 and -5
• -2 and 5

Which of these factor pairs can be added to get -3?
Only 2 + (-5) = -3
So the answer is:
c² - 3c - 10 = (c + 2)(c - 5)

Index Laws 8th Sept

Golden rules of index laws (multiplication):


when the big numbers or letters are the same in a multiplication questions you can just add the powers together.

Task
1) A2 x A5= A7
2) B3 x B8= B11
3) C12 x C6= C18
4) D2 x D100= D102
5) E5 x E5= E10

Golden Rules Of Index Laws (Division):



when the big numbers or letters are the same in a division questions you can just subtract the
powers together

1) A5 / A2= A3
2) B7/ B3=B4
3)C3/C5=C-2
4)66/ 62=64
5)712/73=79