ACT Science Flashcards: Evaluating Trends And Making Predictions

What this deck covers

This deck focuses on Evaluating Trends And Making Predictions, 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: Identify the trend in data with a bell-shaped curve.

Answer: Normal distribution trend. Data peaks in the middle and tapers at both ends.

Flashcard 2: Which graph best represents a cyclical trend?

Answer: Graph with repeating peaks and troughs. Shows alternating high and low values in regular intervals.

Flashcard 3: What does "inversely proportional" mean for variables $x$ and $y$ in a trend?

Answer: $y=\frac{k}{x}$ for constant $k$. Product $xy$ stays constant.

Flashcard 4: A line passes through $(1,6)$ with slope $m=3$. What is $y$ at $x=4$?

Answer: $y=15$. $y = 6 + 3(3) = 15$

Flashcard 5: Find the prediction: data shows a flat trend line.

Answer: Future values will remain constant. No change in trend means future values stay the same.

Flashcard 6: What is the best definition of extrapolation when reading a graph or table?

Answer: Predicting beyond the measured data range. Extends trend past known data points.

Flashcard 7: What is the definition of a trend in data?

Answer: A pattern or direction of change over time. Shows the general direction data moves as time progresses.

Flashcard 8: What does it mean when data points form a perfect line in a scatter plot?

Answer: Perfect correlation. All points lie exactly on a straight line.

Flashcard 9: Identify the trend: A trend line in a graph is steeply rising.

Answer: Rapid increase. Steep slope indicates fast rate of change.

Flashcard 10: What does a convergence of lines in a multi-line graph indicate?

Answer: Convergence of variables. Multiple trends meet at a common point.

Flashcard 11: Which trend is shown by data forming a straight line?

Answer: Linear trend. Data points align in a straight line pattern.

Flashcard 12: Choose the correct prediction: Data shows a consistent 5% monthly growth.

Answer: Next month: 5% increase. Consistent pattern continues into next period.

Flashcard 13: Find the slope $m$ between $(2,5)$ and $(6,13)$.

Answer: $m=2$. $m = \frac{13-5}{6-2} = \frac{8}{4} = 2$

Flashcard 14: What is a prediction in the context of data analysis?

Answer: An estimate of future data values based on trends. Uses observed patterns to forecast what will happen next.

Flashcard 15: What is the most appropriate data region to use for a short-range prediction from a curve?

Answer: The local region nearest the target $x$ value. Local behavior is most reliable for prediction.

Flashcard 16: A table shows $(x,y)$: $(1,4)$ and $(3,12)$. Predict $y$ at $x=2$ assuming linearity.

Answer: $y=8$. Slope is $4$, so $y = 4 + 4(1) = 8$.

Flashcard 17: What is the term for a sudden change in data not following the overall trend?

Answer: Anomaly. An outlier that doesn't follow the pattern.

Flashcard 18: What type of relationship is indicated by a positive slope in a trend line?

Answer: Positive correlation. Both variables increase together in same direction.

Flashcard 19: Identify the trend: Population decreases from 1,000 to 800 over a year.

Answer: Decreasing trend. Population consistently drops from $1,000$ to $800$.

Flashcard 20: What does a peak in a graph represent for the dependent variable $y$?

Answer: A local maximum value of $y$. Peak is the highest point locally.

Flashcard 21: Find the prediction: data follows a logistic trend.

Answer: Growth will plateau over time. Growth rate will slow and eventually level off.

Flashcard 22: A line passes through $(1,6)$ with slope $m=3$. What is $y$ at $x=4$?

Answer: $y=15$. $y = 6 + 3(3) = 15$

Flashcard 23: What does it mean if a graph shows a nonlinear trend between variables?

Answer: The rate of change varies with $x$. Nonlinear curves have changing slopes.

Flashcard 24: A linear model gives $y=-3x+18$. What is the predicted $y$ at $x=4$?

Answer: $y=6$. $y = -3(4) + 18 = 6$

Flashcard 25: If $y$ is inversely proportional to $x$ and $y=3$ when $x=5$, what is $y$ when $x=15$?

Answer: $y=1$. $k = 15$, so $y = \frac{15}{15} = 1$.

Flashcard 26: What is the role of the y-axis in a graph showing trends?

Answer: Displays the dependent variable. Shows the outcome variable affected by changes.

Flashcard 27: What is the best meaning of "rate of change" on a graph of $y$ versus $x$?

Answer: The slope $\Delta y/\Delta x$. Measures how quickly $y$ changes with $x$.

Flashcard 28: Identify the most defensible prediction method when a graph shows scattered points with a clear overall rise.

Answer: Use the overall trend (best-fit), not extremes. Best-fit line ignores outliers and noise.

Flashcard 29: Predict the outcome: A trend line shows consistent decline in scores.

Answer: Scores will continue to decrease. Downward trend indicates continued decline.

Flashcard 30: If $y$ is inversely proportional to $x$ and $y=8$ when $x=2$, what is $y$ when $x=4$?

Answer: $y=4$. $k = 16$, so $y = \frac{16}{4} = 4$.

Flashcard 31: Identify the trend: Monthly profits remain constant at $500$.

Answer: Stable trend. Profits stay at same level with no variation.

Flashcard 32: A trend decreases from $y=9$ to $y=3$ as $x$ goes from $1$ to $4$. What is the slope?

Answer: $m=-2$. $m = \frac{3-9}{4-1} = \frac{-6}{3} = -2$

Flashcard 33: Which method estimates a value within a series based on surrounding data points?

Answer: Interpolation. Estimates values between known data points.

Flashcard 34: Find the prediction: data follows a logistic trend.

Answer: Growth will plateau over time. Growth rate will slow and eventually level off.

Flashcard 35: What does it mean if error bars for two means overlap substantially on a graph?

Answer: A clear difference is not strongly supported. Overlapping error bars suggest no significant difference.

Flashcard 36: Find the trend: data values oscillate around a mean.

Answer: No trend; data is random. Data fluctuates randomly without consistent direction.

Flashcard 37: What does it suggest if $xy$ is approximately constant across multiple data points?

Answer: $y$ is inversely proportional to $x$. Constant product indicates inverse relationship.

Flashcard 38: What does a positive slope in a line graph indicate about the relationship between $x$ and $y$?

Answer: As $x$ increases, $y$ increases. Positive slope means upward trend.

Flashcard 39: What does a larger absolute slope $|m|$ indicate about the trend's rate of change?

Answer: A faster rate of change. Steeper lines show greater change rates.

Flashcard 40: A linear model gives $y=2x+1$. What is the predicted $y$ at $x=7$?

Answer: $y=15$. $y = 2(7) + 1 = 15$

Flashcard 41: What does a trend line that curves upward indicate?

Answer: Exponential growth. Rate of increase accelerates over time periods.

Flashcard 42: If $y$ is inversely proportional to $x$ and $y=3$ when $x=5$, what is $y$ when $x=15$?

Answer: $y=1$. $k = 15$, so $y = \frac{15}{15} = 1$.

Flashcard 43: Identify the type of trend with periodic fluctuations.

Answer: Cyclical trend. Data repeats in regular cycles over time intervals.

Flashcard 44: What does a peak in a graph represent for the dependent variable $y$?

Answer: A local maximum value of $y$. Peak is the highest point locally.

Flashcard 45: Predict the outcome: A trend line shows consistent decline in scores.

Answer: Scores will continue to decrease. Downward trend indicates continued decline.

Flashcard 46: Which type of prediction is generally less reliable: interpolation or extrapolation?

Answer: Extrapolation is less reliable. Predicting beyond data is riskier.

Flashcard 47: Identify the type of trend: data increases steadily.

Answer: Positive trend. Values consistently rise over time, showing upward movement.

Flashcard 48: What role does extrapolation play in predictions?

Answer: Estimates future data beyond known values. Projects data patterns beyond the observed time range.

Flashcard 49: Predict: If a trend shows consistent growth, what is expected next?

Answer: Continued growth. Consistent upward pattern will likely continue.

Flashcard 50: Which graph best represents a positive trend?

Answer: Graph with an upward slope. Shows data values rising consistently from left to right.

Flashcard 51: What is the purpose of a trend line in data analysis?

Answer: To show the general direction of data. Summarizes overall data movement for easy interpretation.

Flashcard 52: Which option best describes a "best-fit" trend line used for prediction?

Answer: A line representing the overall pattern of data. Minimizes distance to all data points.

Flashcard 53: What is the term for predicting future values based on current trends?

Answer: Extrapolation. Extends a trend beyond known data points.

Flashcard 54: What is the best definition of interpolation when reading a graph or table?

Answer: Predicting within the measured data range. Uses existing data to estimate between points.

Flashcard 55: Identify the prediction: data shows a consistent linear decline.

Answer: Future values will continue to decrease. Extends the declining pattern into future time periods.

Flashcard 56: Find the prediction: data shows exponential growth.

Answer: Future values will increase rapidly. Accelerating growth rate will continue into the future.

Flashcard 57: Identify the trend in data with a bell-shaped curve.

Answer: Normal distribution trend. Data peaks in the middle and tapers at both ends.

Flashcard 58: What is the slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Rise over run between two points.

Flashcard 59: A curve is concave down over an interval. What happens to the slope as $x$ increases in that interval?

Answer: The slope decreases. Concave down curves flatten as $x$ increases.

Flashcard 60: Identify the dependent variable on a standard graph when making predictions from trends.

Answer: The variable on the $y$-axis. Dependent variable responds to changes.

Flashcard 61: Identify the prediction: a dataset has a strong correlation.

Answer: Predictions are likely to be accurate. Strong correlations enable reliable future value estimates.

Flashcard 62: Data show $y$ changes from $20$ to $26$ when $x$ changes from $10$ to $13$. Predict $y$ at $x=15$ linearly.

Answer: $y=30$. Slope is $2$, so $y = 26 + 2(2) = 30$.

Flashcard 63: Predict the next value: A trend shows doubling each time, current value $3$.

Answer: $6$. Doubling pattern: $3 × 2 = 6$.

Flashcard 64: Identify the trend: Sales increase from 100 units to 500 units over 5 months.

Answer: Increasing trend. Sales rise consistently from $100$ to $500$ units.

Flashcard 65: What type of trend is shown by seasonal data changes?

Answer: Seasonal trend. Data follows predictable patterns based on time of year.

Flashcard 66: Identify the dependent variable on a standard graph when making predictions from trends.

Answer: The variable on the $y$-axis. Dependent variable responds to changes.

Flashcard 67: What is the slope formula for two points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Rise over run between two points.

Flashcard 68: Identify the trend in data with a constant rate of change.

Answer: Linear trend. Data changes by the same amount in each time period.

Flashcard 69: What does a flat line in a trend graph typically indicate?

Answer: No change or stable trend. Values remain constant with no increase or decrease.

Flashcard 70: Identify the trend: Data points cluster tightly around a positive slope line.

Answer: Strong positive trend. Close clustering shows strong linear relationship.

Flashcard 71: Which trend is shown by a diminishing rate of growth?

Answer: Logistic trend. Growth rate slows as values approach a maximum limit.

Flashcard 72: What does an R-squared value close to 1 indicate?

Answer: Strong correlation between variables. Variables move together very predictably and reliably.

Flashcard 73: Choose the word that best labels predicting $y$ at $x=12$ when data only cover $x=0$ to $x=10$.

Answer: Extrapolation. Predicting outside the data range.

Flashcard 74: Identify the independent variable on a standard graph when making predictions from trends.

Answer: The variable on the $x$-axis. Independent variable is controlled or varied.

Flashcard 75: Identify the trend: Population decreases from 1,000 to 800 over a year.

Answer: Decreasing trend. Population consistently drops from $1,000$ to $800$.

Flashcard 76: Use a linear trend through $(2,7)$ and $(8,19)$ to predict $y$ at $x=5$.

Answer: $y=13$. Slope is $2$, so $y = 7 + 2(3) = 13$.

Flashcard 77: Find the prediction: trend analysis shows strong seasonality.

Answer: Future values will follow seasonal patterns. Seasonal cycles will repeat in predictable patterns.

Flashcard 78: Identify the trend: Sales increase from 100 units to 500 units over 5 months.

Answer: Increasing trend. Sales rise consistently from $100$ to $500$ units.

Flashcard 79: Which trend suggests constant acceleration in data?

Answer: Quadratic trend. Rate of change increases steadily over time periods.

Flashcard 80: Identify the trend: data points form a U-shape.

Answer: Quadratic trend. Data follows a parabolic curve pattern over time.

Flashcard 81: Which trend describes data that spikes and then levels off?

Answer: Logarithmic trend. Rapid initial growth followed by gradual leveling off.

Flashcard 82: What does a convergence of lines in a multi-line graph indicate?

Answer: Convergence of variables. Multiple trends meet at a common point.

Flashcard 83: What does a scatter plot with no discernible pattern suggest?

Answer: No trend. Data points show no clear relationship or direction.

Flashcard 84: Find the slope $m$ between $(1,10)$ and $(5,2)$.

Answer: $m=-2$. $m = \frac{2-10}{5-1} = \frac{-8}{4} = -2$

Flashcard 85: What does a trend line with zero slope indicate?

Answer: No change in data over time. Data remains constant with no upward or downward movement.

Flashcard 86: What does a negative slope in a trend line typically indicate?

Answer: Negative correlation. One variable decreases as the other increases.

Flashcard 87: Predict the next value: If a trend shows halving each time, current value $8$.

Answer: $4$. Halving pattern: $8 ÷ 2 = 4$.

Flashcard 88: Identify the independent variable on a standard graph when making predictions from trends.

Answer: The variable on the $x$-axis. Independent variable is controlled or varied.

Flashcard 89: Which trend is shown by data forming a straight line?

Answer: Linear trend. Data points align in a straight line pattern.

Flashcard 90: Identify the type of trend: data follows a repeating pattern.

Answer: Cyclical trend. Data repeatedly rises and falls in predictable intervals.

Flashcard 91: Predict the next value: Trend shows values increasing by $2$ each time, current $10$.

Answer: $12$. Adding $2$ to current value: $10 + 2 = 12$.

Flashcard 92: Choose the word that best labels predicting $y$ at $x=6$ when data cover $x=0$ to $x=10$.

Answer: Interpolation. Predicting within the data range.

Flashcard 93: What is the term for a sudden change in data not following the overall trend?

Answer: Anomaly. An outlier that doesn't follow the pattern.

Flashcard 94: Predict: If a trend shows weekly sales doubling, what is next if $100$ this week?

Answer: $200$. Doubling pattern: $100 × 2 = 200$.

Flashcard 95: What does it suggest if $\frac{y}{x}$ is approximately constant across multiple data points?

Answer: $y$ is directly proportional to $x$. Constant ratio indicates direct relationship.

Flashcard 96: Find the prediction: data shows a flat trend line.

Answer: Future values will remain constant. No change in trend means future values stay the same.

Flashcard 97: What type of trend is shown by seasonal data changes?

Answer: Seasonal trend. Data follows predictable patterns based on time of year.

Flashcard 98: What does a negative slope in a line graph indicate about the relationship between $x$ and $y$?

Answer: As $x$ increases, $y$ decreases. Negative slope means downward trend.

Flashcard 99: What is the most appropriate data region to use for a short-range prediction from a curve?

Answer: The local region nearest the target $x$ value. Local behavior is most reliable for prediction.

Flashcard 100: What does a flat line in a trend graph typically indicate?

Answer: No change or stable trend. Values remain constant with no increase or decrease.