> | greater than (e.g. 3 > 2); |
≥ | greater than or equal to (e.g. a ≥ 4 means that the quantity a may take the exact value 4 or any value larger than 4); |
< | less than; |
≤ | less than or equal to. |
Physical quantity | Name of unit | Symbol for unit |
---|---|---|
length | metre | m |
time | second | s |
mass | kilogram | kg |
temperature | kelvin | K |
amount of substance | mole | mol |
electric current | ampere | A |
luminous intensity | candela | cd |
prefix | symbol | multiplying factor | |
tera | T | 10^{12} | = 1000 000 000 000 |
giga | G | 10^{9} | = 1000 000 000 |
mega | M | 10^{6} | = 1000 000 |
kilo | k | 10^{3} | = 1000 |
- | - | 10^{0} | = 1 |
milli | m | 10^{−3} | = 0.001 |
micro | μ ^{*} | 10^{−6} | = 0.000 001 |
nano | n | 10^{−9} | = 0.000 000 001 |
pico | p | 10^{−12} | = 0.000 000 000 001 |
femto | f | 10^{−15} | = 0.000 000 000 000 001 |
Equation | Step 1 | Step 2 | Solution | |
---|---|---|---|---|
a. | 2x – 1 = 7 | 2x – 8 | x = 4 | |
b. | 5x – 8 = 2 | 5x = 10 | x = 2 | |
c. | 3x + 8 = 5 | 3x = –3 | x = –1 | |
d. | 3x – 8 = 5x – 20 | –8 = 5x – 3x – 20 | 12 = 2x | x = 6 |
e. | 3(x + 1) = 9 | 3x + 3 = 9 | 3x = 6 | x = 2 |
f. | 23 – x = x + 11 | 23 = 2x + 11 | 2x = 12 | x = 6 |
g. | 2(x – 3) – (x – 2) = 5 | 2x – 6 – x + 2 = 5 | x – 4 = 5 | x = 9 |
h. | 4x = 60 | x = 15 | ||
i. | x = 1.2 | |||
j. | 5m + 3m = 30 | m = 3.75 | ||
k. | 7x – 4x = 56 | x = 18.7 (to 1 decimal place) |
2y = x + 7 | subtract 7 from both sides | 2y − 7 = x + 7 − 7 | So, 2y − 7 = x |
y = x + 2 | subtract 2 from both sides | y − 2 = x + 2 − 2 | So, y − 2 = x |
So, 2y – 7 = y – 2 | deduct y from both sides | 2y – y – 7 = y – y – 2 |
So, y – 7 = –2 | add 7 to both sides | y – 7 + 7 = –2 + 7 |
(a) | y = x + 10 | 3y = 2x + 5 |
(b) | y = 4x | y = 3x + 5 |
(c) | y = 7x + 4 | 3y = x + 7 |
(d) | y = 2x + 4 | 3y = x + 7 |
Equations | Step 2: solve for x | Step 3: solve for y | Solution | ||
---|---|---|---|---|---|
(a) | y = x + 10 | y = x + 10 | x = –25 | ||
3y = 2x + 5 | 3x + 30 = 2x + 5 | y = –25 + 10 = –15 | y = –15 | ||
x = –25 | |||||
(b) | y = 4x | 4x = 3x + 5 | y = 4x = 20 | x = 5 | |
y = 3x + 5 | x = 5 | y = 20 | |||
(c) | y = 7x + 4 | y = 7x + 4 | y = 7x + 4 | x = –0.25 | |
3y = x + 7 | 21x + 12 = x + 7 | y = –1.75 + 4 = 2.25 | y = 2.25 | ||
20x = –5 | |||||
x = –0.25 | |||||
(d) | y = 2x + 4 | y = 2x + 4 | y = 2x + 4 | x = –1 | |
3y = x + 7 | 6x + 12 = x + 7 | y = –2 + 4 = 2 | y = 2 | ||
5x = – 5 | |||||
x = –1 |
1. | Sin 0° |
2. | Cos 0° |
3. | Sin 10° |
4. | Cos 10° |
5. | Sin 25° |
6. | Cos 25° |
7. | Sin 45° |
8. | Cos 45° |
9. | Sin 70° |
10. | Cos 70° |
11. | Sin 90° |
12. | Cos 90° |
Angle/degrees | Sine | Cosine |
---|---|---|
0 | 0 | 1 |
10 | 0.1736 | 0.9848 |
25 | 0.4226 | 0.9063 |
45 | 0.7071 | 0.7071 |
70 | 0.9397 | 0.3420 |
90 | 1 | 0 |
‘Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.’ (George Boole, 1815–1864)
1 | H | H | H |
2 | H | H | T |
3 | H | T | H |
4 | H | T | T |
5 | T | H | H |
6 | T | H | T |
7 | T | T | H |
8 | T | T | T |
Measurement | Cell constant/nm |
1 | 2.458 |
2 | 2.452 |
3 | 2.454 |
4 | 2.452 |
5 | 2.459 |
6 | 2.455 |
7 | 2.464 |
8 | 2.453 |
9 | 2.449 |
10 | 2.448 |
Measurement | Cell constant/nm |
1 | 2.458 |
2 | 2.452 |
3 | 2.454 |
4 | 2.452 |
5 | 2.459 |
6 | 2.455 |
7 | 2.464 |
8 | 2.453 |
9 | 2.449 |
10 | 2.448 |
x_{i}/nm | d_{i}/nm | d_{i}^{2}/10^{–5} nm^{2} |
2.458 | 0.0036 | 1.296 |
2.452 | –0.0024 | 0.576 |
2.454 | –0.0004 | 0.016 |
2.452 | –0.0024 | 0.576 |
2.459 | 0.0046 | 2.116 |
2.455 | 0.0006 | 0.036 |
2.464 | 0.0096 | 9.216 |
2.453 | –0.0014 | 0.196 |
2.449 | –0.0054 | 2.916 |
2.448 | –0.0064 | 4.096 |
Measurement | Diameter/mm |
1 | 1.09 |
2 | 1.00 |
3 | 1.25 |
4 | 1.24 |
5 | 1.29 |
6 | 0.89 |
7 | 1.09 |
8 | 1.14 |
9 | 1.22 |
10 | 1.01 |
number of flowers | 4 | 7 | 8 | 9 | 10 |
number of plants | 1 | 4 | 3 | 1 | 1 |
Recovery place | Distance from nest site/km | Number of birds recovered |
Shetland (Lerwick) | 49 | 8 |
Shetland (Foula) | 77 | 5 |
Fair Isle | 114 | 5 |
Orkney | 157 | 2 |
Sule Skerry | 248 | 3 |
Summer Isles | 382 | 1 |
St Kilda | 529 | 2 |
Cape Clear | 1114 | 1 |
South Africa (Durban) | 10568 | 1 |
Instead a slightly different formula is used, namely: