ACT Math Flashcards: Table And Graph Interpretation

What this deck covers

This deck focuses on Table And Graph Interpretation, giving you a quick way to review the definitions, rules, and examples that matter most for ACT Math.

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: Which type of graph is best used to display categorical data?

Answer: Bar graph. Bar graphs effectively compare distinct categories side by side.

Flashcard 2: Identify the type of variation: $y = kx$.

Answer: Direct variation. Direct variation means $y$ is proportional to $x$ with constant $k$.

Flashcard 3: What does a negative slope indicate about the relationship between $x$ and $y$?

Answer: As $x$ increases, $y$ decreases. Negative slope means the line falls from left to right.

Flashcard 4: What is the median of the dataset: 3, 7, 9, 15, 18?

Answer:

1. The middle value when data is ordered from least to greatest.

Flashcard 5: Identify the average rate of change from $(2,9)$ to $(8,-3)$.

Answer: $-2$. $\frac{-3-9}{8-2} = \frac{-12}{6} = -2$

Flashcard 6: Identify the median in the dataset: 1, 3, 3, 6, 7, 8, 9.

Answer: The median is 6. Middle value in ordered list of 7 values.

Flashcard 7: Find the mode in the dataset: 2, 4, 4, 6, 8.

Answer: The mode is 4. Mode is the value that appears most frequently.

Flashcard 8: Identify the symmetry of the function $y = x^2$.

Answer: Symmetric about the y-axis. Even functions satisfy $f(-x) = f(x)$, creating y-axis symmetry.

Flashcard 9: What feature of a line graph shows a decrease in the dependent variable?

Answer: Negative slope. Negative slope indicates the line falls from left to right.

Flashcard 10: What does a positive slope indicate about the relationship between $x$ and $y$?

Answer: As $x$ increases, $y$ increases. Positive slope means the line rises from left to right.

Flashcard 11: Identify the slope of a line through $(2,-1)$ and $(2,5)$.

Answer: Undefined slope. Same $x$-values mean vertical line with undefined slope.

Flashcard 12: If $f(x) = 2x - 1$, find $f^{-1}(3)$.

Answer:

1. Find the input value that gives output 3: $2x - 1 = 3$, so $x = 2$.

Flashcard 13: Calculate the midpoint between points (2, 3) and (4, 7).

Answer: (3, 5). Midpoint formula: $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) = (3, 5)$.

Flashcard 14: Identify $f(3)$ if a table lists $(3, -2)$ as an ordered pair for $(x,f(x))$.

Answer: $-2$. The table directly gives the function value.

Flashcard 15: Identify the slope of a line through $(0,4)$ and $(3,4)$.

Answer: $0$. Same $y$-values mean horizontal line with zero slope.

Flashcard 16: A table shows $x:2,3,4$ and $y:9,12,15$. Identify the rule in slope-intercept form.

Answer: $y=3x+3$. Slope is $3$, $y$-intercept is $3$: $y = 3x + 3$.

Flashcard 17: Determine the range of the dataset: 2, 4, 6, 8, 10.

Answer:

1. Range equals the maximum value minus the minimum value: $10 - 2 = 8$.

Flashcard 18: What is the median of the dataset: 3, 7, 9, 15, 18?

Answer:

1. The middle value when data is ordered from least to greatest.

Flashcard 19: Which graph type is best for showing proportions in different categories?

Answer: A pie chart. Pie charts show how parts make up a whole.

Flashcard 20: What feature of a line graph shows a decrease in the dependent variable?

Answer: Negative slope. Negative slope indicates the line falls from left to right.

Flashcard 21: Which graph best shows a frequency distribution of a data set?

Answer: Histogram. Histograms use bars to display the frequency of data intervals.

Flashcard 22: Identify the missing $y$ value for a linear table: $(1,2)$, $(3,6)$, $(5,\, ?)$.

Answer: $10$. Linear pattern: slope is $2$, so $y = 2 + 2(4) = 10$.

Flashcard 23: Identify the $x$-intercept of the line $y=4x+8$.

Answer: $-2$. Set $y = 0$: $0 = 4x + 8$, so $x = -2$.

Flashcard 24: What does the $y$-intercept represent on a graph of $y$ versus $x$?

Answer: The value of $y$ when $x=0$. Where the line crosses the vertical axis.

Flashcard 25: Calculate the midpoint between points (2, 3) and (4, 7).

Answer: (3, 5). Midpoint formula: $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) = (3, 5)$.

Flashcard 26: What is the independent variable on a typical graph of $y$ versus $x$?

Answer: $x$ (horizontal axis). The input variable that can be controlled.

Flashcard 27: Which graph type is best for comparing multiple datasets?

Answer: A grouped bar chart. Shows multiple categories side by side for comparison.

Flashcard 28: Identify the y-intercept in the equation $y = 3x + 7$.

Answer: The y-intercept is 7. The constant term in slope-intercept form $y = mx + b$.

Flashcard 29: What does a line of best fit indicate in a scatter plot?

Answer: It indicates the general direction or trend of the data. Best-fitting line shows overall pattern in data.

Flashcard 30: What is the formula for the slope of a line given 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 any two points on the line.

Flashcard 31: Identify the y-intercept of the line $y = -5x + 4$.

Answer:

1. In slope-intercept form $y = mx + b$, the constant term is the y-intercept.

Flashcard 32: What does an undefined slope indicate about a line on a coordinate plane?

Answer: The line is vertical. Infinite slope means no horizontal change occurs.

Flashcard 33: Identify the line equation form for a vertical line through $(4, 3)$.

Answer: $x = 4$. Vertical lines have constant x-coordinates and undefined slope.

Flashcard 34: What graph is most appropriate for showing trends over time?

Answer: Line graph. Line graphs connect data points to show changes over time periods.

Flashcard 35: Determine the y-intercept of the quadratic $y = x^2 - 4x + 4$.

Answer:

1. Y-intercept occurs when $x = 0$: $y = 0^2 - 4(0) + 4 = 4$.

Flashcard 36: Calculate the sum of the y-coordinates for points (3, 5) and (4, 9).

Answer:

1. Add the y-coordinates: $5 + 9 = 14$.

Flashcard 37: Which data measure is least affected by extreme values?

Answer: Median. Median is resistant to outliers, unlike mean which is affected by extremes.

Flashcard 38: What does a line of best fit indicate in a scatter plot?

Answer: It indicates the general direction or trend of the data. Best-fitting line shows overall pattern in data.

Flashcard 39: Determine the y-intercept of the quadratic $y = x^2 - 4x + 4$.

Answer:

1. Y-intercept occurs when $x = 0$: $y = 0^2 - 4(0) + 4 = 4$.

Flashcard 40: What is the correlation coefficient range?

Answer: -1 to 1. Correlation coefficients measure linear association strength from -1 to 1.

Flashcard 41: Which data measure is least affected by extreme values?

Answer: Median. Median is resistant to outliers, unlike mean which is affected by extremes.

Flashcard 42: What is the average rate of change of $f$ from $x=a$ to $x=b$?

Answer: $\frac{f(b)-f(a)}{b-a}$. Total change in output divided by change in input.

Flashcard 43: What does slope $m=0$ indicate about a line on a coordinate plane?

Answer: The line is horizontal. Zero slope means no vertical change occurs.

Flashcard 44: Identify the outlier in the dataset: 5, 7, 8, 9, 50.

Answer: The outlier is 50. Value significantly different from other data points.

Flashcard 45: What does the $y$-intercept represent on a graph of $y$ versus $x$?

Answer: The value of $y$ when $x=0$. Where the line crosses the vertical axis.

Flashcard 46: What is the distance formula between points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Pythagorean theorem applied to coordinate differences.

Flashcard 47: Identify the $y$-intercept of the line $y=3x-7$.

Answer: $-7$. In $y = mx + b$ form, $b$ is the $y$-intercept.

Flashcard 48: Identify the quadrant where point $(-3, 4)$ is located.

Answer: Quadrant II. Quadrant II contains points with negative x and positive y coordinates.

Flashcard 49: Which graph type is best for comparing multiple datasets?

Answer: A grouped bar chart. Shows multiple categories side by side for comparison.

Flashcard 50: What does it mean if a line passes through the origin on a $y$ versus $x$ graph?

Answer: The $y$-intercept is $0$. The line passes through point $(0,0)$.

Flashcard 51: What is the meaning of a data point $(x,y)$ on a graph of $y$ versus $x$?

Answer: When $x$ equals the first value, $y$ equals the second. The input value determines the output value.

Flashcard 52: What is the dependent variable on a typical graph of $y$ versus $x$?

Answer: $y$ (vertical axis). The output variable that responds to input changes.

Flashcard 53: What is the definition of a histogram?

Answer: A histogram is a bar graph representing the frequency distribution of data. Shows frequency distribution using adjacent bars.

Flashcard 54: What is the dependent variable on a typical graph of $y$ versus $x$?

Answer: $y$ (vertical axis). The output variable that responds to input changes.

Flashcard 55: What does a positive slope indicate about the relationship between $x$ and $y$?

Answer: As $x$ increases, $y$ increases. Positive slope means the line rises from left to right.

Flashcard 56: A table shows points $(1,4)$ and $(4,10)$. Identify the slope.

Answer: $2$. $m = \frac{10-4}{4-1} = \frac{6}{3} = 2$

Flashcard 57: What does it mean if a graph is decreasing on an interval?

Answer: As $x$ increases, $y$ decreases. The function has negative slope on that interval.

Flashcard 58: A table shows points $(1,4)$ and $(4,10)$. Identify the slope.

Answer: $2$. $m = \frac{10-4}{4-1} = \frac{6}{3} = 2$

Flashcard 59: What is the mode of the data set: 8, 8, 9, 10, 10, 10?

Answer:

1. The mode is the value that appears most frequently in the dataset.

Flashcard 60: A line increases $12$ units in $y$ while increasing $3$ units in $x$. Identify the slope.

Answer: $4$. $m = \frac{\Delta y}{\Delta x} = \frac{12}{3} = 4$

Flashcard 61: Identify the x-intercept in the equation $y = -2x + 10$.

Answer: The x-intercept is 5. Where the line crosses the x-axis when $y = 0$.

Flashcard 62: What is the definition of a histogram?

Answer: A histogram is a bar graph representing the frequency distribution of data. Shows frequency distribution using adjacent bars.

Flashcard 63: What is the interquartile range of the dataset: 1, 3, 5, 7, 9, 11?

Answer:

1. IQR is $Q_3 - Q_1 = 9 - 3 = 6$ for this ordered dataset.

Flashcard 64: Identify the symmetry of the function $y = x^2$.

Answer: Symmetric about the y-axis. Even functions satisfy $f(-x) = f(x)$, creating y-axis symmetry.

Flashcard 65: Find the slope of the line passing through points (2, 3) and (4, 7).

Answer: The slope is 2. Using slope formula: $\frac{7-3}{4-2} = \frac{4}{2} = 2$.

Flashcard 66: What is the interquartile range of the dataset: 1, 3, 5, 7, 9, 11?

Answer:

1. IQR is $Q_3 - Q_1 = 9 - 3 = 6$ for this ordered dataset.

Flashcard 67: Identify the slope of the line represented by the equation $4x - 2y = 8$.

Answer:

1. Rearrange to $y = 2x - 4$; the slope is the coefficient of $x$.

Flashcard 68: What is the standard deviation a measure of in a data set?

Answer: Data dispersion. Standard deviation quantifies how spread out data points are from the mean.

Flashcard 69: Identify the value of $x$ when $y=0$ for the line $y=-2x+6$.

Answer: $3$. Set $y = 0$: $0 = -2x + 6$, so $x = 3$.

Flashcard 70: What is the average rate of change of $f$ from $x=a$ to $x=b$?

Answer: $\frac{f(b)-f(a)}{b-a}$. Total change in output divided by change in input.

Flashcard 71: What does the correlation coefficient indicate?

Answer: It indicates the strength and direction of a linear relationship between variables. Ranges from -1 to 1, measuring linear association.

Flashcard 72: Identify the $x$-intercept of the line $y=4x+8$.

Answer: $-2$. Set $y = 0$: $0 = 4x + 8$, so $x = -2$.

Flashcard 73: Calculate the average rate of change of $y = x^2$ from $x=1$ to $x=3$.

Answer:

1. Average rate of change: $\frac{f(3)-f(1)}{3-1} = \frac{9-1}{2} = 4$.

Flashcard 74: What is the percent change from $A$ to $B$?

Answer: $\frac{B-A}{A}\times 100\%$. Difference divided by original, times 100.

Flashcard 75: What does a correlation coefficient of 0 indicate?

Answer: No correlation. A correlation of 0 means no linear relationship exists between variables.

Flashcard 76: Determine the y-intercept in the function $f(x) = 4x - 5$.

Answer: The y-intercept is -5. The constant term when $x = 0$.

Flashcard 77: A line increases $12$ units in $y$ while increasing $3$ units in $x$. Identify the slope.

Answer: $4$. $m = \frac{\Delta y}{\Delta x} = \frac{12}{3} = 4$

Flashcard 78: Determine the y-intercept in the function $f(x) = 4x - 5$.

Answer: The y-intercept is -5. The constant term when $x = 0$.

Flashcard 79: What graph is most appropriate for showing trends over time?

Answer: Line graph. Line graphs connect data points to show changes over time periods.

Flashcard 80: Identify the midpoint of the segment with endpoints $(1,7)$ and $(5,3)$.

Answer: $\left(3,5\right)$. $\left(\frac{1+5}{2}, \frac{7+3}{2}\right) = (3,5)$

Flashcard 81: What type of chart is useful for showing parts of a whole?

Answer: Pie chart. Pie charts visually represent proportions of a total as sectors.

Flashcard 82: Identify the outlier in the dataset: 5, 7, 8, 9, 50.

Answer: The outlier is 50. Value significantly different from other data points.

Flashcard 83: If $f(x) = 2x - 1$, find $f^{-1}(3)$.

Answer:

1. Find the input value that gives output 3: $2x - 1 = 3$, so $x = 2$.

Flashcard 84: Given points (2, 3) and (2, 7), what is the slope of the line?

Answer: Undefined. Vertical lines have undefined slope due to division by zero.

Flashcard 85: Determine the range of the dataset: 2, 4, 6, 8, 10.

Answer:

1. Range equals the maximum value minus the minimum value: $10 - 2 = 8$.

Flashcard 86: What does an undefined slope indicate about a line on a coordinate plane?

Answer: The line is vertical. Infinite slope means no horizontal change occurs.

Flashcard 87: What is the slope formula between 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 88: Calculate the sum of the y-coordinates for points (3, 5) and (4, 9).

Answer:

1. Add the y-coordinates: $5 + 9 = 14$.

Flashcard 89: What is the formula for the slope of a line given 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 any two points on the line.

Flashcard 90: What does the $x$-intercept represent on a graph of $y$ versus $x$?

Answer: The value of $x$ when $y=0$. Where the line crosses the horizontal axis.

Flashcard 91: Identify the value of $x$ when $y=0$ for the line $y=-2x+6$.

Answer: $3$. Set $y = 0$: $0 = -2x + 6$, so $x = 3$.

Flashcard 92: What is the primary use of a scatter plot?

Answer: To show the relationship between two variables. Points plotted to reveal correlations between variables.

Flashcard 93: Determine the mode in the dataset: 3, 3, 6, 9, 9, 9.

Answer: The mode is 9. Value 9 appears three times, more than others.

Flashcard 94: Identify the distance between $(0,0)$ and $(6,8)$.

Answer: $10$. $\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = 10$

Flashcard 95: What does slope $m=0$ indicate about a line on a coordinate plane?

Answer: The line is horizontal. Zero slope means no vertical change occurs.

Flashcard 96: What is the definition of standard deviation?

Answer: Standard deviation measures the amount of variation or dispersion in a dataset. Quantifies how spread out data values are.

Flashcard 97: What is the percent change from $50$ to $65$?

Answer: $30\%$. $\frac{65-50}{50} \times 100\% = 30\%$

Flashcard 98: Find the range in the dataset: 2, 8, 10, 15, 24.

Answer: The range is 22. Maximum minus minimum: $24 - 2 = 22$.

Flashcard 99: What is the slope formula between 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 100: Identify the range in the dataset: 4, 7, 9, 10, 15.

Answer: The range is 11. Range equals maximum minus minimum: $15 - 4 = 11$.