Simple Maths for AS Biology

1. Simple Maths for AS Biology

2. Bar Charts has categories.

3. Histogram has continuous data and usually no gaps between the categories

4. Line graph • Have a title and use over half the page. • Needs to show trends. • Put the independent variable on the X-axis. • Dependent variable goes on the Y-axis. • Have linear axes that start at the origin 0,0. • Show axis breaks with a jagged line. • Use a sensible scale. • Label axes with EXACTLY what they show and give UNITS. • Plot points with PRECISION.

5. Percentage % Given value x 100 Possible value As with your test results when you calculate your percentage; What you got! x 100 = Percentage Score. Full possible marks Percentages allow comparison of proportions where the total value may vary! One test might be longer than another so possibly more marks are available or one population may be larger than another.

6. % Change Find the difference = Final value – initial value. Difference x 100 = % change. Initial value % change may be an increase or decrease. It can be several hundred % if the final value is much bigger ( or smaller) than the initial value. A minus value is a % decrease and a positive value is a % increase.

7. MEAN and Standard Deviation. • Mean is the type of average used in biology so call it by this name. • Add all the values together then divide by the number of values used. • If there are a number of values contributing to the mean then Standard Deviation (SD) which is the mean variation of points about the mean value can be calculated. • The larger the number of similar values (sample size) the smaller the S.D. • SD gives an idea of the spread of the data; so how varied were the data points that contribute to the mean. • When SD value are taken into account the mean points may indicate overlap. One should question whether they are different!

8. Rate • If you measure the time for something to happen than you can calculate the rate. • E.g. if during an enzyme reaction a measuring cylinder filled with gas in 20s at optimum temperature, but than at 10 degrees lower temperature, takes 40s to fill the measuring cylinder with gas then the first experiment was faster so went at a higher rate. • Repeat the experiment to calculate a mean time.

9. Water displacement or gas syringe.

10. Calculating rate. Start by calculating your mean time. 1/mean time in seconds = Mean Rate. If you have a volume or value use that, otherwise use 1. What is the significance of using 1? You are using it as a whole arbitrary unit. In other words one whole reaction process. It might signify the end point of a completed reaction or in the example one full measuring cylinder/test tube of gas.

11. In our example we have two rates. 1/20 = 0.05 arbitrary units per second Or 1/40 = 0.025 arbitrary units per second. As we have used the same arbitrary units our results are comparable. However we have decimal places to plot – not always easy!

12. Using 1000 instead of 1 removes these decimal points. 1000/20 = 50 arbitrary units (x1000) per second Or 1000/40 = 25 arbitrary units (x1000) per second. As we have used the same arbitrary units for all of our values our results are still comparable but now easier to plot as whole numbers. Now on your Y-axes label you will have to remember to add a multiplication factor (x1000) in the units. As well as calling it a MEAN RATE.

13. Pulse is a measure of HEART RATE. • If you measure pulse then you know how fast the heart is beating. Each time the left ventricle CONTRACTS the blood pressure increases as the blood surges into the aorta and pushes the blood already there forward (Mass flow). • This pressure is referred to as HYDROSTATIC PRESSURE. Each high value is SYSTOLE and lower value (occurring between contractions) is DIASTOLE. • Blood pressure is a result of ventricular contraction.

14. Measuring Pulse • You can easily measure pulse by placing a finger on an artery and noting how frequently the artery bulges over a period of time. • Generally pulse is measure in beats per minute [bpm] or; beats per minute or; beats/min or; beats min-1. • If you measure pulse for a shorter time you will have to use seconds [s]. This can then be converted to bpm. • More accurately measure with a digital pulse meter. The disadvantage of this is that it measures pulse over a set period of time and it may increase or decrease during this time.

15. Magnification and Size. Size of image = Magnification Real object size This is simply a ratio of sizes, so there are no units BUT THE SAME UNITS MUST BE USED IN THE TOP AND BOTTOM LINES OF THE EQUATION. Actually MAG. is a measure of how many times the real thing would fit into the enlargement. Crucial to the calculation is the use of the SAME UNITS for the image and the object. Generally it is easier to convert mm measured (image) into um by MULTIPLYING by 1000.

16. Calculating real object size. IF YOU ARE GIVEN AN IMAGE IT SHOULD EITHER HAVE A MAGNIFICATION OR SCALE BAR. If you are given an Image and MAG and need to calculate the real size then the equation must be rearranged (very simply); Real object size = Image size ÷ Mag. Again the units must be the same for the image and the object.

17. Calculating size from a scale bar. Using Scale Bars is easy as they are just like rulers! • Measure the SCALE BAR using a ruler in millimetres. • Look at the value of the scale bar (given in micrometers) and divide it by the number of mm measured. • This is the value for each mm on the ruler. • Measure the designated distance on the image and multiply the value for each mm by the number of millimetres measured.

18. Advice • Always attempt calculations – they are not that scary and often give EASY marks!!!