Equations With One Variable - SAT Math
Card 0 of 151
A graph comparing two companies’ growth starts the y-axis at 90 instead of 0. What’s misleading?
A graph comparing two companies’ growth starts the y-axis at 90 instead of 0. What’s misleading?
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It visually exaggerates small differences in growth.
It visually exaggerates small differences in growth.
A headline says 'Study shows pets make people live longer.' What’s the potential error?
A headline says 'Study shows pets make people live longer.' What’s the potential error?
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Correlation ≠ causation; healthier people might be more likely to own pets.
Correlation ≠ causation; healthier people might be more likely to own pets.
A nutrition study finds people who eat more salads have lower BMI. Conclusion: eating salads causes weight loss. What’s the flaw?
A nutrition study finds people who eat more salads have lower BMI. Conclusion: eating salads causes weight loss. What’s the flaw?
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Confounding variable: people who eat salads may also exercise more or have other healthy habits.
Confounding variable: people who eat salads may also exercise more or have other healthy habits.
A poll asks, 'Do you agree that responsible citizens should vote?' What’s the flaw?
A poll asks, 'Do you agree that responsible citizens should vote?' What’s the flaw?
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Leading question wording biases responses toward agreement.
Leading question wording biases responses toward agreement.
A recipe for 4 servings uses 2 cups of rice. How much rice for 10 servings?
A recipe for 4 servings uses 2 cups of rice. How much rice for 10 servings?
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5 cups.
5 cups.
A researcher finds that students who study in groups perform better and concludes that group study causes success. What’s another possible explanation?
A researcher finds that students who study in groups perform better and concludes that group study causes success. What’s another possible explanation?
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Motivated students may be more likely to join study groups (confounding variable).
Motivated students may be more likely to join study groups (confounding variable).
A study shows students who bring laptops to class have lower grades. The article concludes that laptops cause poor performance. What’s the flaw?
A study shows students who bring laptops to class have lower grades. The article concludes that laptops cause poor performance. What’s the flaw?
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Correlation does not imply causation; other factors (e.g., study habits) could explain the result.
Correlation does not imply causation; other factors (e.g., study habits) could explain the result.
Compare: $y = 100 + 10t$ vs. $y = 100(1.1)^t$. Which grows faster for large $t$?
Compare: $y = 100 + 10t$ vs. $y = 100(1.1)^t$. Which grows faster for large $t$?
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$y = 100(1.1)^t$ (exponential).
$y = 100(1.1)^t$ (exponential).
Data: 2, 2, 3, 5, 20. How is it skewed?
Data: 2, 2, 3, 5, 20. How is it skewed?
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Skewed right (outlier high value).
Skewed right (outlier high value).
Data: 20, 25, 30, 35, 40. What is range?
Data: 20, 25, 30, 35, 40. What is range?
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$40-20=20$.
$40-20=20$.
Define a cross section.
Define a cross section.
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A 2D shape created by slicing a 3D figure.
A 2D shape created by slicing a 3D figure.
Define a secant.
Define a secant.
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A line that intersects a circle at two points.
A line that intersects a circle at two points.
Define confounding variable.
Define confounding variable.
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A variable related to both explanatory and response variables that makes it unclear which causes the effect.
A variable related to both explanatory and response variables that makes it unclear which causes the effect.
Define control group.
Define control group.
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A group receiving no treatment or standard treatment for comparison.
A group receiving no treatment or standard treatment for comparison.
Define experiment.
Define experiment.
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Researchers impose treatments to study cause-and-effect relationships.
Researchers impose treatments to study cause-and-effect relationships.
Define lurking variable.
Define lurking variable.
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A variable not included in the study that influences both the explanatory and response variables.
A variable not included in the study that influences both the explanatory and response variables.
Define nonresponse bias.
Define nonresponse bias.
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Occurs when selected individuals do not respond, potentially skewing results.
Occurs when selected individuals do not respond, potentially skewing results.
Define observational study.
Define observational study.
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Researchers observe outcomes without imposing treatments.
Researchers observe outcomes without imposing treatments.
Define parameter.
Define parameter.
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A numerical summary that describes a population.
A numerical summary that describes a population.
Define placebo effect.
Define placebo effect.
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When subjects respond to a fake treatment because they expect an effect.
When subjects respond to a fake treatment because they expect an effect.
Define random assignment.
Define random assignment.
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Assigning subjects to treatments by chance to balance variables.
Assigning subjects to treatments by chance to balance variables.
Define replication in an experiment.
Define replication in an experiment.
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Repeating the study or having many subjects to reduce random variation.
Repeating the study or having many subjects to reduce random variation.
Define residual in regression.
Define residual in regression.
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Residual = observed value − predicted value ($y - \hat{y}$).
Residual = observed value − predicted value ($y - \hat{y}$).
Define response bias.
Define response bias.
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When participants give inaccurate or misleading answers (often due to wording or pressure).
When participants give inaccurate or misleading answers (often due to wording or pressure).
Define statistic (in context of sampling).
Define statistic (in context of sampling).
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A numerical summary calculated from sample data.
A numerical summary calculated from sample data.
Define undercoverage bias.
Define undercoverage bias.
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When some members of the population are inadequately represented in the sample.
When some members of the population are inadequately represented in the sample.
Define voluntary response bias.
Define voluntary response bias.
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Bias from individuals choosing themselves to participate; often those with strong opinions.
Bias from individuals choosing themselves to participate; often those with strong opinions.
Definition of a rhombus.
Definition of a rhombus.
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A parallelogram with four equal sides.
A parallelogram with four equal sides.
Definition of a square.
Definition of a square.
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A parallelogram that is both a rectangle and a rhombus.
A parallelogram that is both a rectangle and a rhombus.
Definition of a trapezoid (US) or trapezium (UK).
Definition of a trapezoid (US) or trapezium (UK).
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A quadrilateral with exactly one pair of parallel sides.
A quadrilateral with exactly one pair of parallel sides.
Describe a skewed-left distribution.
Describe a skewed-left distribution.
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Tail extends to the left (low values).
Tail extends to the left (low values).
Describe a skewed-right distribution.
Describe a skewed-right distribution.
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Tail extends to the right (high values).
Tail extends to the right (high values).
Describe a symmetric distribution.
Describe a symmetric distribution.
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Left and right sides are mirror images.
Left and right sides are mirror images.
Equation of a horizontal line through (0, -4).
Equation of a horizontal line through (0, -4).
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$y = -4.$
$y = -4.$
Equation of a line in standard form.
Equation of a line in standard form.
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$Ax + By = C$.
$Ax + By = C$.
Equation of a vertical line through (5, 0).
Equation of a vertical line through (5, 0).
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$x = 5.$
$x = 5.$
Example of reverse causation.
Example of reverse causation.
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A study finds that happier people exercise more, but it could be that exercise makes people happier, not vice versa.
A study finds that happier people exercise more, but it could be that exercise makes people happier, not vice versa.
Explain what the coefficients A, B, C represent in $Ax+By=C$.
Explain what the coefficients A, B, C represent in $Ax+By=C$.
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$A and B are constants determining slope; C sets intercepts/position.$
$A and B are constants determining slope; C sets intercepts/position.$
Find $\sin(\arccos(3/5))$.
Find $\sin(\arccos(3/5))$.
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$4/5$ (since $\sin^2 + \cos^2 = 1$).
$4/5$ (since $\sin^2 + \cos^2 = 1$).
Find $\tan \theta$ if opposite = 8, adjacent = 15.
Find $\tan \theta$ if opposite = 8, adjacent = 15.
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$\tan \theta = 8/15$.
$\tan \theta = 8/15$.
Find adjacent if $\tan \theta = 3/4$ and opposite = 6.
Find adjacent if $\tan \theta = 3/4$ and opposite = 6.
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$a = 8$ (scale of 3–4–5 triangle).
$a = 8$ (scale of 3–4–5 triangle).
Find missing leg if $c = 13$, $a = 5$.
Find missing leg if $c = 13$, $a = 5$.
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$b = \sqrt{13^2 - 5^2} = 12$.
$b = \sqrt{13^2 - 5^2} = 12$.
Find the intersection (solution) of y = 2x + 3 and y = -x + 9.
Find the intersection (solution) of y = 2x + 3 and y = -x + 9.
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$Set equal: 2x + 3 = -x + 9 ⇒ 3x = 6 ⇒ x = 2, y = 7 ⇒ (2, 7).$
$Set equal: 2x + 3 = -x + 9 ⇒ 3x = 6 ⇒ x = 2, y = 7 ⇒ (2, 7).$
Find x-intercept of y = -2x + 10.
Find x-intercept of y = -2x + 10.
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Set $y=0$ ⇒ 0 = -2x + 10 ⇒ x = 5.
Set $y=0$ ⇒ 0 = -2x + 10 ⇒ x = 5.
Find x-intercept of y = 3x - 9.
Find x-intercept of y = 3x - 9.
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$0 = 3x - 9 ⇒ x = 3 ⇒ (3, 0).$
$0 = 3x - 9 ⇒ x = 3 ⇒ (3, 0).$
Find y when x = 4 for y = 2x - 7.
Find y when x = 4 for y = 2x - 7.
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$y = 8 - 7 = 1.$
$y = 8 - 7 = 1.$
For $y = |x - 2|$, what happens if 2 is increased?
For $y = |x - 2|$, what happens if 2 is increased?
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Graph shifts right by 2.
Graph shifts right by 2.
Given y = -2x + 5, find y when x = -3.
Given y = -2x + 5, find y when x = -3.
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$y = 6 + 5 = 11.$
$y = 6 + 5 = 11.$
Given y = -4x + 1, what is y when x = 3?
Given y = -4x + 1, what is y when x = 3?
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$y = -12 + 1 = -11.$
$y = -12 + 1 = -11.$
Given y = (\t$\frac{3}{2}$)x + 6, find x when y = 9.
Given y = (\t$\frac{3}{2}$)x + 6, find x when y = 9.
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$9 = (\tfrac{3}{2})x + 6 ⇒ (\tfrac{3}{2})x = 3 ⇒ x = 2.$
$9 = (\tfrac{3}{2})x + 6 ⇒ (\tfrac{3}{2})x = 3 ⇒ x = 2.$
Graph of $y = |x - 3| + 2$
Graph of $y = |x - 3| + 2$
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V-shape shifted right 3, up 2.
V-shape shifted right 3, up 2.
Graph of $y = |x|$
Graph of $y = |x|$
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A V-shape with vertex at (0, 0).
A V-shape with vertex at (0, 0).
How can you tell from an equation if a line is vertical or horizontal?
How can you tell from an equation if a line is vertical or horizontal?
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If only x appears ($x=\text{constant}$) → vertical; if only y appears ($y=\text{constant}$) → horizontal.
If only x appears ($x=\text{constant}$) → vertical; if only y appears ($y=\text{constant}$) → horizontal.
How do you calculate the range?
How do you calculate the range?
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$\text{Range} = \text{maximum} - \text{minimum}$.
$\text{Range} = \text{maximum} - \text{minimum}$.
How do you test if a graph represents a function?
How do you test if a graph represents a function?
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Use the vertical line test — if any vertical line crosses more than once, it’s not a function.
Use the vertical line test — if any vertical line crosses more than once, it’s not a function.
How does range describe data spread?
How does range describe data spread?
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It measures the total span of the data set.
It measures the total span of the data set.
Identify growth or decay: $y = 200(0.85)^t$.
Identify growth or decay: $y = 200(0.85)^t$.
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Decay (since base < 1).
Decay (since base < 1).
Identify growth or decay: $y = 500(1.02)^t$.
Identify growth or decay: $y = 500(1.02)^t$.
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Growth (since base > 1).
Growth (since base > 1).
If $\bar{x}=70$, $s=8$, what is about 95% range?
If $\bar{x}=70$, $s=8$, what is about 95% range?
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$54$ to $86$ (mean ± 2SD).
$54$ to $86$ (mean ± 2SD).
If $\cos \theta = 12/13$, find $\sin \theta$ (acute).
If $\cos \theta = 12/13$, find $\sin \theta$ (acute).
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$\sin \theta = 5/13$.
$\sin \theta = 5/13$.
If $\frac{x}{y}=\frac{4}{7}$ and $y=35$, find $x$.
If $\frac{x}{y}=\frac{4}{7}$ and $y=35$, find $x$.
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$x=20$.
$x=20$.
If $\sin \theta = 3/5$, find $\cos \theta$ (acute).
If $\sin \theta = 3/5$, find $\cos \theta$ (acute).
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$\cos \theta = 4/5$.
$\cos \theta = 4/5$.
If $\sin \theta = 4/5$, find $\tan \theta$.
If $\sin \theta = 4/5$, find $\tan \theta$.
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$\tan \theta = 4/3$.
$\tan \theta = 4/3$.
If $\tan \theta = 3/4$, find $\sin \theta$ and $\cos \theta$ (acute).
If $\tan \theta = 3/4$, find $\sin \theta$ and $\cos \theta$ (acute).
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$\sin \theta = 3/5$, $\cos \theta = 4/5$.
$\sin \theta = 3/5$, $\cos \theta = 4/5$.
If $\tan \theta = 5/12$, find $\sec \theta$.
If $\tan \theta = 5/12$, find $\sec \theta$.
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$\sec \theta = 13/12$.
$\sec \theta = 13/12$.
If $a:b = 2:3$ and $b:c = 4:5$, find $a:c$.
If $a:b = 2:3$ and $b:c = 4:5$, find $a:c$.
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$a:c = 8:15$.
$a:c = 8:15$.
If $a:b = 3:4$, what is $a:b:c$ when $c=8$?
If $a:b = 3:4$, what is $a:b:c$ when $c=8$?
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$a:b:c = 6:8:8$.
$a:b:c = 6:8:8$.
If $a:b = 3:5$, what is $\frac{a}{b}$?
If $a:b = 3:5$, what is $\frac{a}{b}$?
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$\frac{3}{5}$.
$\frac{3}{5}$.
If $a:b=2:3$ and $b:c=6:5$, find $a:c$.
If $a:b=2:3$ and $b:c=6:5$, find $a:c$.
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$a:c=4:5$.
$a:c=4:5$.
If $Q_1=10$ and $Q_3=22$, find the IQR.
If $Q_1=10$ and $Q_3=22$, find the IQR.
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$22-10=12$.
$22-10=12$.
If $x$ doubles in $xy=k$, what happens to $y$?
If $x$ doubles in $xy=k$, what happens to $y$?
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It halves.
It halves.
If $y = 12$ when $x = 3$, find $k$ in $y = kx$.
If $y = 12$ when $x = 3$, find $k$ in $y = kx$.
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$k = 4$.
$k = 4$.
If $y = 200(0.9)^t$, what happens every period?
If $y = 200(0.9)^t$, what happens every period?
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Value decreases by 10%.
Value decreases by 10%.
If $y = 500(1.05)^t$ and $t$ increases by 1, what happens to $y$?
If $y = 500(1.05)^t$ and $t$ increases by 1, what happens to $y$?
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It increases by 5%.
It increases by 5%.
If $y = a(1+r)^t$, what happens if $r$ is negative?
If $y = a(1+r)^t$, what happens if $r$ is negative?
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It becomes exponential decay.
It becomes exponential decay.
If $y = kx$ and $x = 8$, $y = 24$, find $k$.
If $y = kx$ and $x = 8$, $y = 24$, find $k$.
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$k = 3$.
$k = 3$.
If $y$ varies directly with $x$ and $y=15$ when $x=5$, find $y$ when $x=9$.
If $y$ varies directly with $x$ and $y=15$ when $x=5$, find $y$ when $x=9$.
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$y=27$.
$y=27$.
If 1 gallon = 4 quarts, how many quarts in 3 gallons?
If 1 gallon = 4 quarts, how many quarts in 3 gallons?
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12 quarts.
12 quarts.
If 1 inch = 2.54 cm, how many cm in 10 inches?
If 1 inch = 2.54 cm, how many cm in 10 inches?
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25.4 cm.
25.4 cm.
If 5 workers complete 15 tasks, how many tasks per worker?
If 5 workers complete 15 tasks, how many tasks per worker?
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3 tasks per worker.
3 tasks per worker.
If 8 pencils cost $2, what is the cost per pencil?
If 8 pencils cost $2, what is the cost per pencil?
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$0.25$ per pencil.
$0.25$ per pencil.
If a car travels 150 miles using 5 gallons of gas, find miles per gallon.
If a car travels 150 miles using 5 gallons of gas, find miles per gallon.
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30 mpg.
30 mpg.
If a car travels 300 miles on 10 gallons of fuel, how many gallons for 420 miles?
If a car travels 300 miles on 10 gallons of fuel, how many gallons for 420 miles?
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14 gallons.
14 gallons.
If a car travels at 30 mph, how many feet per second does travel?
If a car travels at 30 mph, how many feet per second does travel?
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30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec
30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec
If a recipe uses 2 cups sugar for 5 cups flour, how much sugar for 15 cups flour?
If a recipe uses 2 cups sugar for 5 cups flour, how much sugar for 15 cups flour?
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6 cups sugar.
6 cups sugar.
If data have $\bar{x}=50$ and $s=10$, what range contains most data?
If data have $\bar{x}=50$ and $s=10$, what range contains most data?
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$40$ to $60$ (within 1 SD).
$40$ to $60$ (within 1 SD).
In $y = a(1 + r)^t$, what does $a$ represent?
In $y = a(1 + r)^t$, what does $a$ represent?
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The initial amount (value at $t = 0$).
The initial amount (value at $t = 0$).
In $y = a(1 + r)^t$, what does $r$ represent?
In $y = a(1 + r)^t$, what does $r$ represent?
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The rate of growth per time period (in decimal form).
The rate of growth per time period (in decimal form).
In $y = a(1 + r)^t$, what does $t$ represent?
In $y = a(1 + r)^t$, what does $t$ represent?
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The number of time periods.
The number of time periods.
Interpret $|a - b|$
Interpret $|a - b|$
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The distance between $a$ and $b$ on a number line.
The distance between $a$ and $b$ on a number line.
Interpret a negative residual.
Interpret a negative residual.
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The actual value is lower than predicted.
The actual value is lower than predicted.
Interpret a positive residual.
Interpret a positive residual.
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The actual value is higher than predicted.
The actual value is higher than predicted.
Perfect square trinomial expansion: $(x - y)^2$
Perfect square trinomial expansion: $(x - y)^2$
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$x^2 - 2xy + y^2$.
$x^2 - 2xy + y^2$.
Perfect square trinomial expansion: $(x + y)^2$
Perfect square trinomial expansion: $(x + y)^2$
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$x^2 + 2xy + y^2$.
$x^2 + 2xy + y^2$.
Reciprocal identity for secant.
Reciprocal identity for secant.
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$\sec \theta = \frac{1}{\cos \theta}$.
$\sec \theta = \frac{1}{\cos \theta}$.
Simplify and solve: $6 - 2(x + 1) \ge 0$.
Simplify and solve: $6 - 2(x + 1) \ge 0$.
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$x \le 2$.
$x \le 2$.
Solve $|2x - 4| = 10$
Solve $|2x - 4| = 10$
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$x = 7$ or $x = -3$.
$x = 7$ or $x = -3$.
Solve $|x - 3| = 7$
Solve $|x - 3| = 7$
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$x = 10$ or $x = -4$.
$x = 10$ or $x = -4$.
Solve $|x - 4| > 2$
Solve $|x - 4| > 2$
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$x > 6$ or $x < 2$.
$x > 6$ or $x < 2$.
Solve $|x + 2| < 5$
Solve $|x + 2| < 5$
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$-7 < x < 3$.
$-7 < x < 3$.
Solve $|x| = -x$
Solve $|x| = -x$
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True for $x \le 0$.
True for $x \le 0$.
Solve $|x| = 5$
Solve $|x| = 5$
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$x = 5$ or $x = -5$.
$x = 5$ or $x = -5$.
Solve $|x| = x$
Solve $|x| = x$
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True for $x \ge 0$.
True for $x \ge 0$.
Solve for $x$: $-2x/5 > 6$.
Solve for $x$: $-2x/5 > 6$.
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$x < -15$
$x < -15$
Solve for $x$: $-3x - 2 \ge 7$.
Solve for $x$: $-3x - 2 \ge 7$.
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$x \le -3$
$x \le -3$
Solve for $x$: $-5x + 3 < 8$.
Solve for $x$: $-5x + 3 < 8$.
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$x > -1$
$x > -1$
Solve for $x$: $\frac{2}{5} = \frac{x}{15}$.
Solve for $x$: $\frac{2}{5} = \frac{x}{15}$.
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$x = 6$.
$x = 6$.
Solve for $x$: $\frac{3}{x} = \frac{6}{12}$.
Solve for $x$: $\frac{3}{x} = \frac{6}{12}$.
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$x = 6$.
$x = 6$.
Solve for $x$: $2 - 4x > 10$.
Solve for $x$: $2 - 4x > 10$.
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$x < -2$
$x < -2$
Solve for $x$: $3x - 5 > 10$.
Solve for $x$: $3x - 5 > 10$.
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$x > 5$.
$x > 5$.
Solve for $x$: $7x + 2 \le 16$.
Solve for $x$: $7x + 2 \le 16$.
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$x \le 2$.
$x \le 2$.
Solve for $x$: $8x - 7 \ge 17$.
Solve for $x$: $8x - 7 \ge 17$.
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$x \ge 3$
$x \ge 3$
Solve for $x$: $x/4 - 3 < 2$.
Solve for $x$: $x/4 - 3 < 2$.
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$x < 20$.
$x < 20$.
Solve for x: 3(2x - 5) = 9.
Solve for x: 3(2x - 5) = 9.
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$6x - 15 = 9 ⇒ 6x = 24 ⇒ x = 4.$
$6x - 15 = 9 ⇒ 6x = 24 ⇒ x = 4.$
Solve for x: 5x + 8 = 23.
Solve for x: 5x + 8 = 23.
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$x = 3.$
$x = 3.$
Solve for x: 7 - 4x = 15.
Solve for x: 7 - 4x = 15.
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$-4x = 8 ⇒ x = -2.$
$-4x = 8 ⇒ x = -2.$
Solve for x: 8x - 3 = 5x + 9.
Solve for x: 8x - 3 = 5x + 9.
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$3x = 12 ⇒ x = 4.$
$3x = 12 ⇒ x = 4.$
Solve for x: 9x - 7 = 2x + 14.
Solve for x: 9x - 7 = 2x + 14.
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$7x = 21 ⇒ x = 3.$
$7x = 21 ⇒ x = 3.$
Solve system: y = 3x + 2 and y = x + 8.
Solve system: y = 3x + 2 and y = x + 8.
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$3x + 2 = x + 8 ⇒ 2x = 6 ⇒ x = 3, y = 11 ⇒ (3, 11).$
$3x + 2 = x + 8 ⇒ 2x = 6 ⇒ x = 3, y = 11 ⇒ (3, 11).$
What are the steps to find equation of a line given two points.
What are the steps to find equation of a line given two points.
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- Find slope; 2) use point-slope form; 3) simplify to desired form.
- Find slope; 2) use point-slope form; 3) simplify to desired form.
What do the edges of the box represent?
What do the edges of the box represent?
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The first and third quartiles ($Q_1$ and $Q_3$).
The first and third quartiles ($Q_1$ and $Q_3$).
What do the ends of a boxplot’s whiskers represent?
What do the ends of a boxplot’s whiskers represent?
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The minimum and maximum data values (excluding outliers).
The minimum and maximum data values (excluding outliers).
What does a larger range indicate?
What does a larger range indicate?
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Greater variability in the data.
Greater variability in the data.
What does a smaller IQR indicate?
What does a smaller IQR indicate?
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Data are more tightly clustered around the median.
Data are more tightly clustered around the median.
What does the line inside the box of a boxplot represent?
What does the line inside the box of a boxplot represent?
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The median.
The median.
What is a common flaw in voluntary online polls?
What is a common flaw in voluntary online polls?
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Responses are self-selected, creating strong bias and unrepresentative samples.
Responses are self-selected, creating strong bias and unrepresentative samples.
What is sampling bias?
What is sampling bias?
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When a sample systematically favors certain outcomes or groups.
When a sample systematically favors certain outcomes or groups.
What is the definition of a function?
What is the definition of a function?
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A relation in which each input has exactly one output.
A relation in which each input has exactly one output.
What is the definition of variance?
What is the definition of variance?
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Average squared deviation from the mean.
Average squared deviation from the mean.
What is the difference of squares identity?
What is the difference of squares identity?
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$a^2 - b^2 = (a + b)(a - b)$.
$a^2 - b^2 = (a + b)(a - b)$.
What is the standard form of a line?
What is the standard form of a line?
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$Ax+By=C$, where A, B, and C are integers and A ≥ 0.
$Ax+By=C$, where A, B, and C are integers and A ≥ 0.
What’s wrong with comparing raw counts from groups of different sizes?
What’s wrong with comparing raw counts from groups of different sizes?
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The groups’ totals differ; comparison should use proportions or percentages.
The groups’ totals differ; comparison should use proportions or percentages.
When solving Ax + B = Cx + D, what’s the first algebraic step?
When solving Ax + B = Cx + D, what’s the first algebraic step?
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Combine like terms: bring x-terms to one side and constants to the other.
Combine like terms: bring x-terms to one side and constants to the other.
Which equation produces an extraneous solution when squared?
Which equation produces an extraneous solution when squared?
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Any equation involving radicals (e.g., $\sqrt{x+1} = x$).
Any equation involving radicals (e.g., $\sqrt{x+1} = x$).
Which functions are symmetric about the origin?
Which functions are symmetric about the origin?
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Odd functions such as $y = x^3$ or $y = \sin x$.
Odd functions such as $y = x^3$ or $y = \sin x$.
Which functions are symmetric about the y-axis?
Which functions are symmetric about the y-axis?
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Even functions such as $y = x^2$ or $y = |x|$.
Even functions such as $y = x^2$ or $y = |x|$.
Which measure of center best represents skewed data?
Which measure of center best represents skewed data?
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The median.
The median.
Which measure of center best represents symmetric data?
Which measure of center best represents symmetric data?
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The mean.
The mean.
Why can a confounding variable create false association?
Why can a confounding variable create false association?
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It affects both variables, making it appear one causes the other.
It affects both variables, making it appear one causes the other.
Why can self-reported data be unreliable?
Why can self-reported data be unreliable?
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Participants may exaggerate, forget, or misunderstand the questions.
Participants may exaggerate, forget, or misunderstand the questions.
Write an equation for:
'A car loses $1200 in value per year starting from $18,000.'
Write an equation for:
'A car loses $1200 in value per year starting from $18,000.'
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$V = 18000 - 1200t$.
$V = 18000 - 1200t$.
Write an equation for:
'A runner starts 100 meters ahead and runs 8 m/s.'
Write an equation for:
'A runner starts 100 meters ahead and runs 8 m/s.'
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$d = 8t + 100$.
$d = 8t + 100$.
Write an equation for:
'A savings account grows by 2% monthly from $1000.'
Write an equation for:
'A savings account grows by 2% monthly from $1000.'
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$A = 1000(1.02)^t$.
$A = 1000(1.02)^t$.
Write an equation for:
'Membership increases by 200 members per quarter from 1000.'
Write an equation for:
'Membership increases by 200 members per quarter from 1000.'
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$M = 1000 + 200t$.
$M = 1000 + 200t$.
Write an equation for:
'The bacteria count triples every hour, starting at 100.'
Write an equation for:
'The bacteria count triples every hour, starting at 100.'
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$N = 100(3)^t$.
$N = 100(3)^t$.
Write an equation for:
'The balance decreases by 3% each year from $10,000.'
Write an equation for:
'The balance decreases by 3% each year from $10,000.'
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$B = 10000(0.97)^t$.
$B = 10000(0.97)^t$.
Write an equation for:
'The number of subscribers increases by 500 per month, starting at 2000.'
Write an equation for:
'The number of subscribers increases by 500 per month, starting at 2000.'
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$S = 2000 + 500t$.
$S = 2000 + 500t$.
Write an equation for:
'The temperature drops 4° each hour from 70°.'
Write an equation for:
'The temperature drops 4° each hour from 70°.'
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$T = 70 - 4t$.
$T = 70 - 4t$.
Write an equation for:
'The value of a car decreases by 15% each year from $20,000.'
Write an equation for:
'The value of a car decreases by 15% each year from $20,000.'
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$V = 20000(0.85)^t$.
$V = 20000(0.85)^t$.
Write the piecewise definition of $|x|$.
Write the piecewise definition of $|x|$.
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$|x| = \begin{cases} x, & x \ge 0 \\ -x, & x < 0 \end{cases}$.
$|x| = \begin{cases} x, & x \ge 0 \\ -x, & x < 0 \end{cases}$.
Zero-product property.
Zero-product property.
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If $ab = 0$, then $a = 0$ or $b = 0$.
If $ab = 0$, then $a = 0$ or $b = 0$.