Some non-calculator tips

1. estimate means that an accurate answer is not requred. Decimal numbers are rounded up before worked.

example : 3.1 x 7.9 = 3 x 8 = 2

4.2 x 8.8 4 x 9 3

( which is 3.14) is usually rounded up to 3

example. Give the circumference of a circle of radius 4cm

C = 2r = 2 x 3 x 4 = 24cm

2. Dividing by or 0.5 means multiplying by 2. In the same way dividing by means multiplying by 3

example : 5 = 5 X 2 = 10

12 = 12 x 3 = 36

3. The angle between two consecutive numbers of a clock is 30

example : give the angle between the the two arms of a clock at 2 oclock

Count how many spaces there are between the numbers. In this case there are 2. From 12 till 1 and from 1 till 2.

This means that the angle is 2 x 30 = 60

4. There are no long multiplications and no long divisions in non-calculator. Ususally there is some canelling to be done.

5. Find common factors :

Example : 345 x 25 345 x 20

Take 345 out as common

345 x ( 25 20 ) = 345 x 5 = 1275

6. Special triangles :

These triangles are always right angled :

Therefore if you are given that cos A = , it means that since cos A = ,

Adj = 3 and hyp = 5. Therefore opp must be = 4.

From this we can write that sin A = = and also tan A = =

7. Pack of cards :

There are 52 cards in all and each card is UNIQUE.

There are 13 of each suit, two suits are red, therefore there are 26 RED cards.

Two suits are black, therefore there are 26 BLACK cards.

8. Simultaneous equations are almost always such that when you add them up they give the same number.

Example : 7packets and 3 boxes cost 32.40 whilst 3 packets and 7 boxes cost 17.60. How much does one packet and one box cost together?

7p + 3b = 32.40

3p + 7b = 17.60add them up

10p + 10b = 50divide by the common factor

10

1p + 1b = 5 Answer

9. Changing position of decimal point.

Example : 234 x 567 = 132 678. What is the value of 1326.78 56.7 ?

The one which is not mentioned ( 234 ) leave as it is. The others insert x 10 or x 100 and move the point.

( 567 becomes 56.7 x 10, 132678 becomes 1326.78 x 100)

234 x 56.7 x 10 = 1326.78 x 100

Therefore

234 x 10 = 1326.78

100 56.7

23.4 =1326.78

56.7

10. Always remember these sets of numbers :

a) Square numbers : 1 ,4, 9, 16, 25, 36, 49, 64, 81, 100

b) Cube numbers : 1, 8, 27, 64, 125

c) Prime numbers : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

11. Difference of two squares

3.72- 2.72

Open into brackets

(3.7 2.7)(3.7 + 2.7)

( 1) ( 6.4) = 6.4

For all of these methods above you might be able to find a method which to you makes more sense. Feel free to use it, remember in the non-calculator paper it is the answer only that counts.

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