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Basic Maths

This is the AQA version closing after June 2019. Visit the the version for Eduqas instead .

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Everyone

Rounding off Numbers

Rounding off to Whole Numbers - Examples

2.00001 becomes 2
2.4999 becomes 2
2.5 becomes 3
2.999 becomes 3

BODMAS or BIDMAS

Brackets, Order, Division, Multiplication, Addition, Subtraction
Brackets, Index, Division, Multiplication, Addition, Subtraction

This is all about the order in which you do a calculation.

B Anything inside brackets is always worked out first.
O or I This is for items like X^y or 10³ where y and 3 are the order or index. These are worked out after dealing with anything inside brackets.
D Division and ...
M ... multiplication are done next.
A Lastly addition ...
S ... and subtraction are done.

For example here are two bits of arithmetic with different meanings ...

3 + 2 x 7 = 17 Do the multiplication first and then add three.

(3 + 2) x 7 = 35 The brackets override the rule above so work out the brackets first and then multiply by seven.

Times Tables

Speed up your calculations by learning your times tables.

X	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	98	108	120	132	144

Fractions

Calculate 1/4 + 1/7

Using a calculator with brackets you would enter this ...

1 / 4 + 1 / 7 =

You don't need brackets because the BODMAS rules work without them.

Harder Fractions

Calculate Rt if the formula is this: 1 / Rt = 1 / R1 + 1 / R2

Using a calculator with brackets you would calculate Rt like this ...

1 / ( 1 / R1 + 1 / R2 ) =

Rearranging Formulas

If there are no + or - signs in the formula, re-arranging is easy. Diagonal moves are allowed across the equals sign. This works for most of the formulas for Electronics AS and A2.

Here is an example ...

Powers of Ten

Examples - The powers add up.

10³ x 10⁴ = 10⁷

10^-3 x 10⁴ = 10

10⁰ = 1

10^-3 x 10^-2 = 10^-5

1 / 10³ = 10^-3

Powers of Ten on a Calculator

There seem to be several methods used by different calculator manufacturers to solve powers of 10. Most students should use a low cost scientific calculator. More advanced models can be too hard to use and sometimes are quite non-standard.

Find out how to enter powers of 10 into your calculator. The most obvious way is nearly always wrong! Look for the Exp button. This is the "Times-ten-to-the" button. Look for the +/- button. This is used to enter things like 10^-9. If you use the normal minus button, on many calculators, it won't work. On some calculators the Exp button is labelled x10

Example Calculator Key Presses

If the frequency in Hertz = 1 / (2 π R C), to the nearest Hertz, calculate the frequency if R = 84 kilohms and C = 3 nanofarads.

84 kilohms = 84 x 10³ Ohms

3 nanofarads - 3 x 10^-9 Farads

Here are the calculator key presses for simple scientific calculators ...

1 / ( 2 x PI x 84 Exp 3 x 3 Exp 9 +/- ) =

Your calculator may be different. Learn how to use it! Get help if you need it!

X	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	98	108	120	132	144

X	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	98	108	120	132	144

X	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	98	108	120	132	144