5.3.1Tools
Applying General Mathematics in Biology — IB Biology SL Revision Notes & Topical Questions
5 min read 6 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 6Everyday Calculations
Fractions and decimals
- Fractions and decimals Convert a fraction to a decimal by dividing the numerator by the denominator, for example 3/8 = 0.375.
Percentages
- Percentages A part is converted to a percentage by dividing by the whole and multiplying by 100.
Ratios
- Ratios Ratios compare quantities, such as cell volume to surface area, and are simplified by dividing by common factors.
Reciprocals
- Reciprocals Rate can be found as 1 ÷ time when time is measured for a fixed change to occur.
Approximation
- Approximation Rounding values or making estimates helps check that an answer is sensible.
Section 2 of 6Averages and Spread
Averages and Spread
Mean
- Mean The sum of all values divided by the number of values, sensitive to outliers.
Median
- Median The middle value of ordered data, a better measure when there are outliers.
Mode
- Mode The most common value, useful for categories.
Standard deviation
- Standard deviation Measures how far values are spread around the mean;
- a smaller value means data are more tightly clustered.
Standard error and IQR
- Standard error and IQR Standard error estimates the reliability of the mean, and the interquartile range gives the spread of the middle half.
Section 3 of 6Scale, Magnification and Rates
1
Magnification equals the size of the image divided by the actual size of the object, using the same units.
2
Scientific notation writes numbers as a × 10ⁿ, where a lies between 1 and 10 and n is a whole number.
3
Rate of change equals the change in the dependent variable divided by the change in the independent variable.
4
Percentage change equals (final value − initial value) ÷ initial value × 100.
5
Direct proportionality gives a straight line through the origin, while inverse proportionality gives a curve.
Section 4 of 6Relationships
Positive correlation
- Positive correlation As one variable increases, the other also increases.
Negative correlation
- Negative correlation As one variable increases, the other decreases.
Percentage difference
- Percentage difference Compares two values with their mean, and is used where neither value is the starting point.
Frequency
- Frequency Number of times a value occurs, often shown as a histogram.
Section 5 of 6Worked Example
Question
- A cell in a micrograph measures 45 mm across.
- Its actual diameter is 0.15 mm.
- Calculate the magnification.
- Magnification = image size ÷ actual size.
- Both lengths are in millimetres, so no conversion is needed.
- 45 ÷ 0.15 = 300.
Answer The magnification is ×300.
Section 6 of 6Exam Checklist & Tips
5.3.1 – Key Points for the Exam
- Mean The arithmetic average of a set of values.
- Standard deviation A measure of spread of data around the mean.
- Magnification Image size divided by actual size.
- Percentage change Change as a percentage of the initial value.
- Rate of change Gradient of a graph, change in y divided by change in x.
Common Mistakes
- Using the median when the mean is requested, or the reverse.
- Measuring image size and actual size in different units when calculating magnification.
- Calculating percentage change relative to the final value instead of the initial value.
- Writing scientific notation with a coefficient outside 1 to 10, such as 25 × 10⁻⁶.
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