SAT Math Flashcards - SAT Math
Card 0 of 43
A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
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$h = 10 - 2t$.
$h = 10 - 2t$.
A car travels 180 miles in 3 hours. What is the speed?
A car travels 180 miles in 3 hours. What is the speed?
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60 mph.
60 mph.
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
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The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
A newspaper says, 'A new medicine doubled survival rate—from 1% to 2%.' What’s misleading about that claim?
A newspaper says, 'A new medicine doubled survival rate—from 1% to 2%.' What’s misleading about that claim?
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Relative increase sounds large, but absolute improvement is small.
Relative increase sounds large, but absolute improvement is small.
A person walks 6 miles in 2 hours. How long to walk 9 miles?
A person walks 6 miles in 2 hours. How long to walk 9 miles?
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3 hours.
3 hours.
Definition of a rate.
Definition of a rate.
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A ratio comparing two quantities with different units.
A ratio comparing two quantities with different units.
Definition of unit rate.
Definition of unit rate.
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A rate with a denominator of 1.
A rate with a denominator of 1.
Formula for distance between $(x_1, y_1)$ and $(x_2, y_2)$.
Formula for distance between $(x_1, y_1)$ and $(x_2, y_2)$.
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$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
If 12 workers finish a job in 8 days, how many days for 6 workers (same rate)?
If 12 workers finish a job in 8 days, how many days for 6 workers (same rate)?
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16 days.
16 days.
If 120 miles are driven in 3 hours, what is the unit rate?
If 120 miles are driven in 3 hours, what is the unit rate?
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40 miles per hour.
40 miles per hour.
If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
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$d = 60t$.
$d = 60t$.
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
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Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
If a printer prints 300 pages in 10 minutes, find the rate per minute.
If a printer prints 300 pages in 10 minutes, find the rate per minute.
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30 pages per minute.
30 pages per minute.
If a train travels 240 miles in 4 hours, find speed in km/h (1 mile ≈ 1.6 km).
If a train travels 240 miles in 4 hours, find speed in km/h (1 mile ≈ 1.6 km).
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$240\times1.6/4=96$ km/h.
$240\times1.6/4=96$ km/h.
If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
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$E = 15h + 50$.
$E = 15h + 50$.
If speed = distance/time, find distance when speed = 50 mph and time = 4 hours.
If speed = distance/time, find distance when speed = 50 mph and time = 4 hours.
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200 miles.
200 miles.
What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
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$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
A map has a scale of 1 inch : 10 miles. How many miles does 3 inches represent?
A map has a scale of 1 inch : 10 miles. How many miles does 3 inches represent?
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30 miles.
30 miles.
Definition of a proportion.
Definition of a proportion.
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An equation stating that two ratios are equal.
An equation stating that two ratios are equal.
Definition of a ratio.
Definition of a ratio.
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A comparison of two quantities by division.
A comparison of two quantities by division.
Definition of constant of proportionality.
Definition of constant of proportionality.
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The constant ratio $k$ in $y = kx$.
The constant ratio $k$ in $y = kx$.
Definition of directly proportional relationship.
Definition of directly proportional relationship.
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When one quantity increases, the other increases at a constant ratio ($y = kx$).
When one quantity increases, the other increases at a constant ratio ($y = kx$).
Definition of inverse proportionality.
Definition of inverse proportionality.
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When one quantity increases, the other decreases so that $xy = k$.
When one quantity increases, the other decreases so that $xy = k$.
If $y = \frac{12}{x}$, what is the constant of proportionality?
If $y = \frac{12}{x}$, what is the constant of proportionality?
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12
12
If $y = 4x$, what is the constant of proportionality?
If $y = 4x$, what is the constant of proportionality?
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4
4
If $y$ is directly proportional to $x$, and $x$ triples, what happens to $y$?
If $y$ is directly proportional to $x$, and $x$ triples, what happens to $y$?
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It triples.
It triples.
If $y$ is inversely proportional to $x$, and $x$ triples, what happens to $y$?
If $y$ is inversely proportional to $x$, and $x$ triples, what happens to $y$?
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It becomes one-third as large.
It becomes one-third as large.
Rewrite $\sqrt[3]{x^5}$ using rational exponents.
Rewrite $\sqrt[3]{x^5}$ using rational exponents.
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$x^{5/3}$.
$x^{5/3}$.
Simplify the ratio 12:18.
Simplify the ratio 12:18.
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2:3.
2:3.
Special triangle: ratio for $30^{\circ}$–$60^{\circ}$–$90^{\circ}$.
Special triangle: ratio for $30^{\circ}$–$60^{\circ}$–$90^{\circ}$.
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$1:\sqrt{3}:2$ (short leg : long leg : hypotenuse).
$1:\sqrt{3}:2$ (short leg : long leg : hypotenuse).
Special triangle: ratio for $45^{\circ}$–$45^{\circ}$–$90^{\circ}$.
Special triangle: ratio for $45^{\circ}$–$45^{\circ}$–$90^{\circ}$.
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$1:1:\sqrt{2}$.
$1:1:\sqrt{2}$.
What is the ratio of part to whole if 5 students out of 20 like math?
What is the ratio of part to whole if 5 students out of 20 like math?
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5:20 or 1:4.
5:20 or 1:4.
What property is used to solve proportions?
What property is used to solve proportions?
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Cross-multiplication.
Cross-multiplication.
Why are percentage-based graphs sometimes misleading?
Why are percentage-based graphs sometimes misleading?
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Changing the scale or starting axis at a non-zero value exaggerates differences.
Changing the scale or starting axis at a non-zero value exaggerates differences.
Convert 0.0004640 into scientific notation.
Convert 0.0004640 into scientific notation.
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When written in scientific notation, a number will follow the format 
in which 
is between one and ten and 
is an integer value.
To find 
, take the first non-zero digit in your given number as the ones place. In 0.0004640 this would be the first 4. All subsequent digits fall into the tenths, hundredths, etc. places.
To find 
, we must count the number of places that 
is removed. In 0.0004640, the first digit of 
is in the ten-thousandths place. This indicates that 
will be 
.
Together, the final scientific notation will be 
.
When written in scientific notation, a number will follow the format
To find
To find
Together, the final scientific notation will be
Convert 1.5 meters to centimeters.
Convert 1.5 meters to centimeters.
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150 cm.
150 cm.
Convert 2 feet to inches.
Convert 2 feet to inches.
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24 inches.
24 inches.
Convert 2500 milliliters to liters.
Convert 2500 milliliters to liters.
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2.5 L.
2.5 L.
Convert 3 hours to minutes.
Convert 3 hours to minutes.
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180 minutes.
180 minutes.
Convert 5 minutes to seconds.
Convert 5 minutes to seconds.
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300 seconds.
300 seconds.
Convert 60 mph to feet per second (1 mile = 5280 ft).
Convert 60 mph to feet per second (1 mile = 5280 ft).
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$\frac{60\times5280}{3600}=88$ ft/s.
$\frac{60\times5280}{3600}=88$ ft/s.
Convert 90 km/h to m/s.
Convert 90 km/h to m/s.
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$90\times\frac{1000}{3600}=25$ m/s.
$90\times\frac{1000}{3600}=25$ m/s.
Convert three yards to inches.
Convert three yards to inches.
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To solve this problem, we need to know the conversions between yards to feet, and feet to inches. Write their correct conversions.
Convert three yards to feet.
Convert nine feet to inches.
To solve this problem, we need to know the conversions between yards to feet, and feet to inches. Write their correct conversions.
Convert three yards to feet.
Convert nine feet to inches.