Biology Mathematical Skills Handbook Extract The following pages are extracted from the back of the OCR Biology Mathematical Skills Handbook, which is available for free via OCR Interchange. It is important to be aware of the new DfE mathematical requirements for AS and A Level Biology (listed in appendix 5e of the new AS and A Level specifications). Linked to this, learners are required to recall some formulae (below in Appendix A) and to be able to select and use others (below in Appendix B). We hope you will find this document useful, perhaps as a hand-out for your learners. If you have any comments or suggestions for this resource or the full Biology Mathematical Skills Handbook just let us know positiveaboutpractical@ocr.org.uk Best wishes, Katherine Hands-Taylor and Richard Tateson A Level Biology Subject Specialists © OCR 2015 Version 1.0 GCE Biology 1 Appendix A – Useful formulae for biology As indicated in the specification content and the mathematical appendix, learners should recall the following, Magnification (Bio A 2.1.1, Bio B 2.1.1): Magnificat ion ο½ size of image size of real object Retention Factor (Rf) (Bio A 2.1.2, Bio B 2.1.3): π π = πππ π‘ππππ πππ£ππ ππ¦ π‘βπ π πππ’π‘π πππ π‘ππππ πππ£ππ ππ¦ π‘βπ π πππ£πππ‘ How to calculate rates of reaction - including, o Enzyme rates of reaction (Bio A 2.1.4, Bio B 2.1.3) o Diffusion rates (Bio A 2.1.5, Bio B 2.1.1) o Breathing (Respiration) rate (Bio A 5.2.2, Bio B 4.1.2) o Transpiration rate (Bio A 3.1.3, Bio B 2.2.4) o Rate of photosynthesis (Bio A 5.2.1, Bio B 4.3.1) o Respiration rate (Bio A 5.2.2, Bio B 4.1.1) o Epidemiology –(incidence, prevalence and mortality rates Bio B only 3.2.1) o Reaction times (Bio A 5.1.5, Bio B 5.2.1) Water Potential (Bio A 2.1.5, Bio B 2.1.2): π = ππ + ππ Surface Area to Volume Ratio (Bio A 3.1.1, Bio B 2.2.1): π ππ‘ππ = ππ’πππππ π΄πππ ππππ’ππ Species Richness and Species Evenness (Bio A only 4.2.1): Species Richness (S) can be found by counting the number of individual species found within a sample area. Species Evenness (EH) can be found using the formula, EH ο½ H ln S Where H is Shannon’s diversity index (which will be provided). Genetic Biodiversity (Bio A 4.2.1, Bio B 3.1.3): πππππππ‘πππ ππ ππππ¦ππππβππ ππππ ππππ = ππ’ππππ ππ ππππ¦ππππβππ ππππ ππππ π‘ππ‘ππ ππ’ππππ ππ ππππ The relationship between Heart Rate, Cardiac Output and Stroke Volume (Bio A 5.1.5, Bio B 2.2.1): βππππ‘ πππ‘π = πππππππ ππ’π‘ππ’π‘ π π‘ππππ π£πππ’ππ Respiratory Quotient (RQ) (Bio A 5.2.2, Bio B 4.1.1): π π = πΆπ2 πππππ’πππ π2 ππππ π’πππ Microorganism Population Growth (Bio A only 6.2.1): π = π0 × 2π Efficiency of Biomass Transfers (Bio A 6.3.1, Bio B 4.3.1): ππππππππππ¦ = ππππππ π π‘ππππ ππππππ × 100 ππππππ π πππ‘πππ Mean (not content specific): xο½ ο₯x n Percentage Change (not content specific): πππππππ‘πππ πβππππ = πππ€ ππ’πππ‘ππ‘π¦ × 100 ππππππππ ππ’πππ‘ππ‘π¦ Percentage Yield (not content specific): % π¦ππππ = π΄ππ‘π’ππ π΄πππ’ππ‘ × 100 πβπππππ‘ππππ π΄πππ’ππ‘ Relative uncertainty in a value calculated by difference (not content specific): % π’πππππ‘ππππ‘π¦ = 2 × πππ πππ’π‘π π’πππππ‘ππππ‘π¦ × 100% ππ’πππ‘ππ‘π¦ ππππ π’πππ Temperature Coefficient (Q10) (Bio A only 2.1.4): Q10 ο½ R2 R1 (Where R2 is the rate of reaction at a temperature 10°C higher than R1) Haemocytometer calculations – (Bio B only 2.1.1) Note: See M4.1 for the formulae for circumferences, surface areas and volumes of regular shapes. © OCR 2015 Version 1.0 GCE Biology 3 Appendix B – Formulae that will be provided in the assessments Learners should be aware of the following formulae. They should know how and when to use them. Chi Squared ( fo ο fe )2 fe ο£2 ο½ ο₯ The Hardy-Weinberg Equation p 2 ο« 2 pq ο« q 2 ο½ 1 Simpson’s Index ο¦ ο¦ n οΆ2 οΆ D ο½ 1 ο ο§ ο₯ο§ ο· ο· ο§ ο¨NοΈ ο· ο¨ οΈ Spearman’s Rank Correlation Coefficient rs ο½ 1 ο 6ο₯d 2 n(n 2 ο 1) Standard Deviation sο½ ο₯( x ο x ) 2 n ο1 Student’s t-test – Unpaired tο½ x A ο xB s A2 s B2 ο« n A nB Student’s t-test – Paired tο½ d n 39.7 15 ο½ ο½ 81.79 sd 1.88