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Scientific Skills - Experimental Design and Variables

Grade 10IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Independent Variable (IV): The factor that is deliberately changed or manipulated by the investigator to observe its effect. In a graph, this is typically plotted on the xx-axis.

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Dependent Variable (DV): The factor that is measured or observed in response to changes in the independent variable. It represents the data collected (e.g., volume of O2O_2 gas produced). Plotted on the yy-axis.

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Controlled Variables (CV): Factors that must be kept constant throughout the experiment to ensure a fair test and that any change in the DVDV is solely due to the IVIV.

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Hypothesis: A testable prediction often written in the form: 'If the [IV][IV] is increased, then the [DV][DV] will [increase/decrease] because...'.

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Reliability: The extent to which an experiment yields the same results on repeated trials. This is improved by increasing the number of trials and calculating a mean xˉ\bar{x}.

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Validity: The extent to which the experiment actually measures what it intended to measure, determined by how well variables were controlled and the appropriateness of the method.

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Accuracy and Precision: Accuracy refers to how close a measurement is to the true or theoretical value. Precision refers to how close repeated measurements are to each other.

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Random Error: Unpredictable fluctuations in measurements (e.g., reaction time). Can be reduced by averaging. Systematic Error: Consistent deviations caused by faulty equipment (e.g., a balance not tared to 0.00 g0.00 \text{ g}).

📐Formulae

Percentage Error=∣Experimental Value−Theoretical Value∣Theoretical Value×100%\text{Percentage Error} = \frac{|\text{Experimental Value} - \text{Theoretical Value}|}{\text{Theoretical Value}} \times 100\%

Percentage Uncertainty=Absolute UncertaintyMeasured Value×100%\text{Percentage Uncertainty} = \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \times 100\%

xˉ=∑i=1nxin\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}

Range=xmax−xmin\text{Range} = x_{max} - x_{min}

💡Examples

Problem 1:

A student investigates the effect of temperature (TT) on the rate of reaction between HClHCl and MgMg ribbon. Identify the variables and suggest a controlled variable.

Solution:

Independent Variable (IVIV): Temperature (TT in ∘C^\circ C); Dependent Variable (DVDV): Volume of H2H_2 gas produced per minute (V/tV/t); Controlled Variable: Concentration of HClHCl (mol⋅dm−3mol \cdot dm^{-3}).

Explanation:

To ensure a fair test, factors like the concentration and surface area of MgMg must remain constant so they do not affect the rate of reaction.

Problem 2:

In an experiment to determine the acceleration due to gravity (gg), a student calculates a value of 9.52 m s−29.52 \text{ m s}^{-2}. Given the theoretical value is 9.81 m s−29.81 \text{ m s}^{-2}, calculate the percentage error.

Solution:

Percentage Error=∣9.52−9.81∣9.81×100%≈2.96%\text{Percentage Error} = \frac{|9.52 - 9.81|}{9.81} \times 100\% \approx 2.96\%

Explanation:

The percentage error quantifies the accuracy of the experimental result compared to the accepted scientific constant.

Problem 3:

Explain why a student should perform three trials for each increment of the independent variable in an investigation of Ohm's Law (V=IRV = IR).

Solution:

Performing multiple trials allows for the identification of outliers and the calculation of an average resistance (RR), which improves the reliability of the data.

Explanation:

Single measurements are prone to random errors; averaging multiple trials reduces the impact of these fluctuations.