ACT Science Flashcards: Identifying Sources Of Error

What this deck covers

This deck focuses on Identifying Sources Of Error, giving you a quick way to review the definitions, rules, and examples that matter most for ACT Science.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is observer bias in data collection?

Answer: Measurements influenced by the researcher's expectations. Researcher's expectations influence data interpretation.

Flashcard 2: Identify the calculation error if $3.0\times 10^2$ is recorded as $3.0\times 10^3$ in the results.

Answer: Exponent/place-value error in scientific notation. Wrong power of ten changes value dramatically.

Flashcard 3: Identify the mistake in the derivative: $\frac{d}{dx}(x^3) = 2x^2$.

Answer: Correct: $\frac{d}{dx}(x^3) = 3x^2$. Power rule: bring down exponent and subtract 1 from power.

Flashcard 4: Identify the likely source of error if light intensity changes while testing plant growth vs. fertilizer type.

Answer: Confounding variable (light intensity not controlled). Two variables change together, obscuring causation.

Flashcard 5: What is a transcription error in recording results?

Answer: Copying or entering data incorrectly from source to table. Writing down wrong numbers from original data.

Flashcard 6: Find the error in the simplification: $x^3 \times x^2 = x^5$.

Answer: No error; simplification is correct. Exponent addition rule: $x^3 \times x^2 = x^{3+2} = x^5$.

Flashcard 7: What is selection bias in sampling?

Answer: A nonrandom sampling method that misrepresents the population. Sample doesn't reflect the target population.

Flashcard 8: What is the definition of precision in measurement?

Answer: Closeness of repeated measurements to each other. Repeatability, not necessarily correctness.

Flashcard 9: Identify the error source if a table lists $0.52$ but the lab notebook shows $0.25$ for the same trial.

Answer: Transcription/data entry error. Numbers don't match between original and final records.

Flashcard 10: Find and correct the error in the formula: Area of circle $= 2\text{π}r^2$.

Answer: Correct: Area $= \text{π}r^2$. Circle area uses $\pi r^2$, not $2\pi r^2$ which is circumference times radius.

Flashcard 11: What is a common source of random error in timing a reaction with a handheld stopwatch?

Answer: Human reaction time variability. Delay between seeing event and pressing button.

Flashcard 12: Find the error in the slope calculation: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 2}{3 - 1} = 1$.

Answer: Correct: $m = 0$. Equal $y$-values give zero rise: $\frac{0}{2} = 0$.

Flashcard 13: Identify the error in the integration: $\frac{d}{dx}(e^x) = e^x + C$.

Answer: Correct: $\frac{d}{dx}(e^x) = e^x$. Derivative doesn't include constant of integration; that's for integrals.

Flashcard 14: Which error type results from inconsistent data entry?

Answer: Human error. Inconsistent recording introduces variability into datasets.

Flashcard 15: What is the definition of a random error in an experiment?

Answer: Unpredictable variation that causes scatter around a true value. Reduces precision but doesn't bias the average.

Flashcard 16: Identify the error in the inequality: $-3 < -2$ implies $3 > 2$.

Answer: No error; implication is correct. Multiplying by $-1$ reverses inequality direction correctly.

Flashcard 17: Identify the error: Using $1.0 \times 10^3$ instead of $1.0 \times 10^6$.

Answer: Error: Incorrect order of magnitude. Wrong power of 10 changes value by factor of 1000.

Flashcard 18: What type of error is a miscalculation due to human oversight?

Answer: Human error. These mistakes result from carelessness or inadequate attention.

Flashcard 19: Identify the error source when a thermometer consistently reads $2\,^{\circ}\text{C}$ too high for all samples.

Answer: Calibration error (systematic bias). Consistent offset indicates uncalibrated instrument.

Flashcard 20: Identify the error in the reaction: $C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O$.

Answer: No error; equation is balanced. Atom counts are balanced: 6C, 12H, 18O on each side.

Flashcard 21: Find the error in the multiplication: $6 \times 7 = 49$.

Answer: Correct: $6 \times 7 = 42$. Basic multiplication: $6 \times 7 = 42$, not 49.

Flashcard 22: Find the error in the function evaluation: $f(x) = x^2 - 3x$, $f(2) = 4 - 3 = 1$.

Answer: Correct: $f(2) = 4 - 6 = -2$. Missed multiplying by $x$ coefficient: $f(2) = 4 - 3(2) = -2$.

Flashcard 23: Identify the error source if lengths are recorded only to the nearest $1\,\text{cm}$ using a coarse ruler.

Answer: Instrument resolution limitation (rounding uncertainty). Coarse scale limits measurement precision.

Flashcard 24: Identify the mistake in the derivative: $\frac{d}{dx}(x^3) = 2x^2$.

Answer: Correct: $\frac{d}{dx}(x^3) = 3x^2$. Power rule: bring down exponent and subtract 1 from power.

Flashcard 25: Identify the error: Mislabeling axes on a graph.

Answer: Error: Misinterpretation of data. Wrong labels make data uninterpretable.

Flashcard 26: What error occurs when measurements scatter around a true value?

Answer: Random error. Multiple measurements fluctuate randomly around the true value.

Flashcard 27: Identify the likely source of error if light intensity changes while testing plant growth vs. fertilizer type.

Answer: Confounding variable (light intensity not controlled). Two variables change together, obscuring causation.

Flashcard 28: Identify the error in the unit conversion: $1000 \text{ g} = 0.1 \text{ kg}$.

Answer: Correct: $1000 \text{ g} = 1 \text{ kg}$. The decimal point was misplaced; 1000 g equals 1 kg, not 0.1 kg.

Flashcard 29: Which error type occurs if a scale is not zeroed before measuring?

Answer: Systematic error. Unzeroed scales add a constant offset to all measurements.

Flashcard 30: What type of error is caused by random fluctuations in measurements?

Answer: Random error. These errors vary unpredictably between measurements.

Flashcard 31: Identify the error in the equation: $3x + 2 = 11$ solved as $x = \frac{11}{3} - 2$.

Answer: Correct: $x = \frac{11 - 2}{3}$. The subtraction order was incorrect; subtract 2 first, then divide by 3.

Flashcard 32: Identify the error in the molar mass calculation: $H_2O = 20 \text{ g/mol}$.

Answer: Correct: $H_2O = 18 \text{ g/mol}$. $H_2O$: $(2 \times 1) + 16 = 18$ g/mol, not 20.

Flashcard 33: What is an outlier in a data set?

Answer: A value far from the overall pattern of the other data. Unusually different from the general trend.

Flashcard 34: Find the error in the percentage calculation: \frac{50}{200} \times 100 = 50\text{%}.

Answer: Correct: 25\text{%}. $\frac{50}{200} = 0.25 = 25\%$, not 50%.

Flashcard 35: Identify the error in the expression: $\frac{1}{x} + \frac{1}{y} = \frac{1}{x + y}$.

Answer: Correct: $\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}$. Common denominator needed: $\frac{y + x}{xy}$, not $\frac{1}{x + y}$.

Flashcard 36: Identify the error: Using $1.0 \times 10^3$ instead of $1.0 \times 10^6$.

Answer: Error: Incorrect order of magnitude. Wrong power of 10 changes value by factor of 1000.

Flashcard 37: Identify the error: Confusing precision with accuracy.

Answer: Error: Precision is not accuracy. Precision is consistency; accuracy is correctness.

Flashcard 38: Find and correct the error: $7 - (3 + 2) = 7 - 3 + 2$.

Answer: Correct: $7 - (3 + 2) = 2$. Distribution of negative sign was incorrect; $-(3 + 2) = -5$.

Flashcard 39: Identify the error in the formula: Volume of sphere $= \frac{4}{3}\text{π}r^3$

Answer: No error; formula is correct. The sphere volume formula is mathematically correct.

Flashcard 40: What error occurs when assuming linearity in non-linear data?

Answer: Error: Model misfit. Linear models don't fit curved relationships well.

Flashcard 41: Which type of error is indicated when measurements are widely scattered around the accepted value?

Answer: Random error (low precision, potentially accurate on average). Scatter without consistent bias indicates random variation.

Flashcard 42: Identify the error in the reaction: $C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O$.

Answer: No error; equation is balanced. Atom counts are balanced: 6C, 12H, 18O on each side.

Flashcard 43: What error occurs when ignoring range in data comparison?

Answer: Error: Misleading conclusions. Range shows data spread; ignoring it hides variability.

Flashcard 44: What is an operational definition in experimental design?

Answer: A precise description of how a variable is measured or defined. Eliminates ambiguity in measurement procedures.

Flashcard 45: What is a transcription error in recording results?

Answer: Copying or entering data incorrectly from source to table. Writing down wrong numbers from original data.

Flashcard 46: Identify the error: Confusing precision with accuracy.

Answer: Error: Precision is not accuracy. Precision is consistency; accuracy is correctness.

Flashcard 47: What error arises from extrapolating data beyond the range?

Answer: Error: Unreliable predictions. Patterns may not continue outside observed range.

Flashcard 48: Which error type occurs if experimenter bias affects results?

Answer: Systematic error. Experimenter expectations can unconsciously influence data collection.

Flashcard 49: Find and correct the error in the formula: Area of circle $= 2\text{π}r^2$.

Answer: Correct: Area $= \text{π}r^2$. Circle area uses $\pi r^2$, not $2\pi r^2$ which is circumference times radius.

Flashcard 50: Find the error in the calculation: $9 - (3 \times 2) = 9 - 3 \times 2 = 3$.

Answer: Correct: $9 - (3 \times 2) = 3$. Parentheses change order: $9 - 6 = 3$, not $9 - 3 \times 2$.

Flashcard 51: Find the error in the function evaluation: $f(x) = x^2 - 3x$, $f(2) = 4 - 3 = 1$.

Answer: Correct: $f(2) = 4 - 6 = -2$. Missed multiplying by $x$ coefficient: $f(2) = 4 - 3(2) = -2$.

Flashcard 52: Find the error in the angle sum: $45^\text{o} + 45^\text{o} = 180^\text{o}$.

Answer: Correct: $45^\text{o} + 45^\text{o} = 90^\text{o}$. Two $45°$ angles form a right angle, not straight angle.

Flashcard 53: Identify the error source if a graph's $y$-axis is labeled $\text{mL}$ but the data were measured in $\text{L}$.

Answer: Unit mismatch (systematic scaling error). Scale doesn't match actual measurement units.

Flashcard 54: What error arises from extrapolating data beyond the range?

Answer: Error: Unreliable predictions. Patterns may not continue outside observed range.

Flashcard 55: Identify the error: Mixing up dependent and independent variables.

Answer: Error: Incorrect variable identification. Wrong variable assignment affects analysis.

Flashcard 56: Identify the error: Misreading $2 \times 10^{-3}$ as $2 \times 10^{3}$.

Answer: Error: Incorrect scientific notation. Sign error changes value by factor of million.

Flashcard 57: What is the definition of precision in measurement?

Answer: Closeness of repeated measurements to each other. Repeatability, not necessarily correctness.

Flashcard 58: What is the definition of a systematic error in an experiment?

Answer: A consistent bias that shifts results in one direction. Creates reproducible deviation from true values.

Flashcard 59: What error arises from using a small sample size?

Answer: Increased variability. Small samples have less reliable estimates.

Flashcard 60: Identify the error source if a researcher rates outcomes more favorably for the treatment group they support.

Answer: Observer bias (lack of blinding). Unconscious bias toward preferred hypothesis.

Flashcard 61: What is a placebo effect as a source of experimental error?

Answer: A response caused by expectation rather than the treatment. Mind creates improvement without actual treatment effect.

Flashcard 62: What is the error source if temperature is recorded in $^{\circ}\text{C}$ but treated as K in calculations?

Answer: Incorrect unit/scale conversion (systematic error). Wrong temperature scale affects all calculations.

Flashcard 63: What is a source of error when a sensor has low resolution (large smallest scale division)?

Answer: Quantization/rounding uncertainty from limited resolution. Cannot read values between scale markings precisely.

Flashcard 64: Identify the error in the formula: Volume of sphere = $\frac{4}{3}\text{π}r^3$.

Answer: No error; formula is correct. The sphere volume formula is mathematically correct.

Flashcard 65: Which type of error is most reduced by taking many trials and averaging the results?

Answer: Random error. Multiple trials cancel out random fluctuations.

Flashcard 66: Which type of error is indicated when measurements are widely scattered around the accepted value?

Answer: Random error (low precision, potentially accurate on average). Scatter without consistent bias indicates random variation.

Flashcard 67: What does it suggest if a best-fit line systematically misses points in a curved pattern?

Answer: Model mismatch (nonlinear relationship fitted as linear). Wrong mathematical model for the actual relationship.

Flashcard 68: Identify the error in the quadratic formula: $x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2b}$.

Answer: Correct: $x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$. Denominator should be $2a$, not $2b$ in the quadratic formula.

Flashcard 69: Identify the error in the molar mass calculation: $H_2O = 20 \text{ g/mol}$.

Answer: Correct: $H_2O = 18 \text{ g/mol}$. $H_2O$: $(2 \times 1) + 16 = 18$ g/mol, not 20.

Flashcard 70: Identify the design flaw if a procedure does not specify how "growth" is measured.

Answer: Missing operational definition (measurement ambiguity). Undefined measurement creates unreproducible results.

Flashcard 71: What is parallax error in reading a scale?

Answer: Apparent shift from viewing the scale at an angle. Eye position affects perceived reading on graduated scales.

Flashcard 72: Which error type involves a consistent deviation from the true value?

Answer: Systematic error. These errors consistently shift all measurements in one direction.

Flashcard 73: Identify the error: Mixing up dependent and independent variables.

Answer: Error: Incorrect variable identification. Wrong variable assignment affects analysis.

Flashcard 74: Identify the design flaw if a procedure does not specify how "growth" is measured.

Answer: Missing operational definition (measurement ambiguity). Undefined measurement creates unreproducible results.

Flashcard 75: Identify the error in the sequence sum: $1 + 2 + 3 + 4 = 9$.

Answer: Correct: $1 + 2 + 3 + 4 = 10$. Simple arithmetic: $1 + 2 + 3 + 4 = 10$.

Flashcard 76: Identify the likely error source if multiple students start/stop a stopwatch and obtain scattered times.

Answer: Random error from human reaction time differences. Each person has different response delays.

Flashcard 77: What is the independent variable in an experiment?

Answer: The factor deliberately changed by the experimenter. The cause being tested in the experiment.

Flashcard 78: What is a common source of systematic error when a balance reads $+0.20\,\text{g}$ with nothing on it?

Answer: Zero offset (instrument not tared/calibrated). Instrument reads mass when empty, creating bias.

Flashcard 79: What is a common source of systematic error when a balance reads $+0.20\,\text{g}$ with nothing on it?

Answer: Zero offset (instrument not tared/calibrated). Instrument reads mass when empty, creating bias.

Flashcard 80: Identify the error in the sequence: $1, 4, 9, 16, 24$.

Answer: Correct: $1, 4, 9, 16, 25$. Perfect squares sequence: $5^2 = 25$, not 24.

Flashcard 81: What is parallax error in reading a scale?

Answer: Apparent shift from viewing the scale at an angle. Eye position affects perceived reading on graduated scales.

Flashcard 82: Identify the error source when a thermometer consistently reads $2\,^{\circ}\text{C}$ too high for all samples.

Answer: Calibration error (systematic bias). Consistent offset indicates uncalibrated instrument.

Flashcard 83: Identify the likely error source if multiple students start/stop a stopwatch and obtain scattered times.

Answer: Random error from human reaction time differences. Each person has different response delays.

Flashcard 84: Identify the source of error if a study compares two treatments but includes no untreated baseline condition.

Answer: No control group (baseline missing). Cannot determine if treatments have any effect.

Flashcard 85: Identify the error in the sequence sum: $1 + 2 + 3 + 4 = 9$.

Answer: Correct: $1 + 2 + 3 + 4 = 10$. Simple arithmetic: $1 + 2 + 3 + 4 = 10$.

Flashcard 86: Which type of error is indicated when all measurements are tightly clustered but far from the accepted value?

Answer: Systematic error (high precision, low accuracy). Consistent offset from true value indicates bias.

Flashcard 87: Identify the error source if a table lists $0.52$ but the lab notebook shows $0.25$ for the same trial.

Answer: Transcription/data entry error. Numbers don't match between original and final records.

Flashcard 88: Find and correct the error: $2^3 + 2^2 = 16$.

Answer: Correct: $2^3 + 2^2 = 12$. $2^3 = 8$ and $2^2 = 4$, so $8 + 4 = 12$.

Flashcard 89: Identify the mistake in the pH calculation: $\text{pH} = -\text{log}(1 \times 10^{-7}) = 8$.

Answer: Correct: $\text{pH} = 7$. $-\log(10^{-7}) = -(-7) = 7$, not 8.

Flashcard 90: Identify the likely error if a meniscus is read from above the eye level each time.

Answer: Parallax error causing a systematic volume bias. Wrong eye level creates consistent reading bias.

Flashcard 91: Identify the error in the equation: $3x + 2 = 11$ solved as $x = \frac{11}{3} - 2$.

Answer: Correct: $x = \frac{11 - 2}{3}$. The subtraction order was incorrect; subtract 2 first, then divide by 3.

Flashcard 92: Which type of error is most reduced by calibrating instruments against a standard?

Answer: Systematic error. Calibration corrects consistent instrument bias.

Flashcard 93: What is the purpose of a control group in an experiment?

Answer: To provide a baseline for comparison without the treatment. Shows what happens without experimental treatment.

Flashcard 94: What is the error source if temperature is recorded in $^{\circ}\text{C}$ but treated as K in calculations?

Answer: Incorrect unit/scale conversion (systematic error). Wrong temperature scale affects all calculations.

Flashcard 95: Identify the error source if lengths are recorded only to the nearest $1\,\text{cm}$ using a coarse ruler.

Answer: Instrument resolution limitation (rounding uncertainty). Coarse scale limits measurement precision.

Flashcard 96: What is the purpose of a control group in an experiment?

Answer: To provide a baseline for comparison without the treatment. Shows what happens without experimental treatment.

Flashcard 97: Find the error in the calculation: $9 - (3 \times 2) = 9 - 3 \times 2 = 3$.

Answer: Correct: $9 - (3 \times 2) = 3$. Parentheses change order: $9 - 6 = 3$, not $9 - 3 \times 2$.

Flashcard 98: Which error type results from improperly calibrated instruments?

Answer: Systematic error. Miscalibrated instruments produce consistent measurement bias.

Flashcard 99: Which error type results from inconsistent data entry?

Answer: Human error. Inconsistent recording introduces variability into datasets.

Flashcard 100: Identify the mistake in the chemical balance: $Fe + O_2 \rightarrow Fe_2O_3$.

Answer: Correct: $4Fe + 3O_2 \rightarrow 2Fe_2O_3$. Iron oxidation requires balancing: 4 Fe atoms and 3 $O_2$ molecules.