5.3.1Tools
Applying General Mathematics in Biology — IB Biology HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 7 of 10
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Section 1 of 5Number Skills
Decimals and fractions
- Decimals and fractions Quantities such as cell size are often decimals or fractions,
- and answers should be given to a sensible number of significant figures.
Ratios
- Ratios A ratio such as 3 : 1 compares quantities, and can be used to scale up expected numbers from a cross.
Percentages
- Percentages A percentage expresses a part as a fraction of 100, for example percentage cover in a quadrat.
Scientific notation
- Scientific notation Very large or small numbers are written as a × 10ⁿ, so 0.000 002 5 m is 2.5 × 10⁻⁶ m.
Estimation
- Estimation Rounding values before a calculation gives a quick check that the final answer is of a sensible size.
Section 2 of 5Averages, Spread and Change
Averages, Spread and Change
Mean, median and mode
- Mean, median and mode The mean is the sum divided by the number of values, the median is the middle value and the mode is the most frequent value.
Range and quartiles
- Range and quartiles The range is the largest minus the smallest value, and quartiles divide ordered data into four equal parts.
Percentage change
- Percentage change Percentage change = (final − initial) ÷ initial × 100, where a negative answer shows a decrease.
Rate of change
- Rate of change Rate = change in quantity ÷ time taken, found from a graph by the gradient of a tangent for curves.
Data types
- Data types Discrete data are counts of separate items, whereas continuous data are measurements that can take any value within a range.
| Data | Type | Example |
|---|---|---|
| Number of leaves | Discrete | 6 leaves |
| Leaf length | Continuous | 7.4 cm |
| Blood group | Categorical | AB |
Section 3 of 5Choosing Statistical Tests
Chi-squared test
- Chi-squared test It compares observed and expected counts in categories, for example offspring phenotypes.
t-test
- t-test It compares the means of two sets of continuous data to decide if they are significantly different.
Correlation
- Correlation The correlation coefficient measures how strongly two variables vary together, but correlation does not prove cause.
Significance
- Significance A probability below 0.05 means the difference is unlikely to be due to chance alone.
Section 4 of 5Worked Example
Question
- The mass of a plant is 5.2 g at the start of an experiment and 6.5 g at the end.
- Calculate the percentage change in mass.
- Change = final − initial = 6.5 − 5.2 = 1.3 g.
- Divide by the initial mass1.3 ÷ 5.2 = 0.25.
- Multiply by 100 to give a percentage: 25%.
Answer The mass increases by 25%.
Section 5 of 5Exam Checklist & Tips
5.3.1 – Key Points for the Exam
- Mean The sum of the values divided by the number of values.
- Percentage change The change as a percentage of the initial value.
- Discrete data Data that can take only separate values, such as counts.
- Continuous data Data that can take any value in a range, such as measurements.
Common Mistakes
- Dividing by the final value instead of the initial value when finding percentage change.
- Applying a t-test to categorical counts.
- Treating a correlation as proof that one variable causes the other.
- Giving answers to too many or too few significant figures.
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