SAT
Use function notation for the moment an event happens.
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At the start
A bake sale starts at 10:00 a.m.
R(m) is the amount, in dollars, raised m minutes after 10:00 a.m.
R(m) = 0.04m² + 3.5m + 85
m = 0
R(0)
A later moment
The amount raised 20 minutes after the bake sale starts.
m = 20
R(20)
Work these three in a session.
A robotics competition starts at noon.
P(t) is the number of points a team has earned t minutes after noon.
P(t) = 0.002t³ − 0.15t² + 4t + 12
Which choice represents the number of points when the competition starts?
P(0) is correct because:
The competition starts at noon.
t is the number of minutes after noon.
t = 0
P(12) is incorrect because it uses the 12 in the equation. The start is noon, so t = 0.
The equation does not need to be solved.
Answer: B. P(0)
A swimming race starts at 9:00 a.m.
D(m) is the distance, in meters, a swimmer has traveled m minutes after 8:00 a.m.
D(m) = 0.0003m³ − 0.02m² + 1.7m + 25
Which choice represents the distance when the race starts?
D(60) is correct because:
The race starts at 9:00 a.m.
m is the number of minutes after 8:00 a.m.
9:00 a.m. is 60 minutes after 8:00 a.m.
m = 60
D(9) is incorrect because it uses the 9 from 9:00 a.m. The input counts minutes.
The equation does not need to be solved.
Answer: D. D(60)
V(y) is the value, in dollars, of a painting y years after 2010.
The painting was purchased at an auction in 2006.
V(y) = 2400(1.03)y + 860
Which choice represents the value when the painting was purchased?
V(−4) is correct because:
The painting was purchased in 2006.
y is the number of years after 2010.
2010 − 2006 = 4
y = −4
V(2006) is incorrect because it uses the calendar year 2006. The input counts years after 2010.
The equation does not need to be solved.
Answer: A. V(−4)
Try these five on your own.
The main stage at a music festival opens at 4:00 p.m.
N(h) is the number of people on the festival grounds h hours after noon.
N(h) = 15h³ − 36h² + 180h + 950
Which choice represents the number of people when the main stage opens?
N(4) is correct because:
The main stage opens at 4:00 p.m.
h is the number of hours after noon.
4:00 p.m. is 4 hours after noon.
h = 4
N(0) is incorrect because it is noon. The main stage opens 4 hours later.
The equation does not need to be solved.
Answer: C. N(4)
A model rocket is launched.
H(s) is the height, in meters, s seconds after the rocket is launched.
The parachute opens 3 seconds after launch.
H(s) = −4.9s² + 78s + 6
Which choice represents the height when the parachute opens?
H(3) is correct because:
The parachute opens 3 seconds after launch.
s is the number of seconds after the rocket is launched.
s = 3
H(78) is incorrect because it is the coefficient of s in the equation. The parachute opens at s = 3.
The equation does not need to be solved.
Answer: A. H(3)
A town fair started in 1890.
A(y) is the attendance y years after 1900.
A(y) = 0.8y³ + 37y² + 418y + 1624
Which choice represents the attendance when the fair started?
A(−10) is correct because:
The fair started in 1890.
y is the number of years after 1900.
1900 − 1890 = 10
y = −10
A(−1624) is incorrect because it uses the constant 1624 from the equation.
The equation does not need to be solved.
Answer: B. A(−10)
School starts on September 1.
B(d) is the balance, in dollars, of a lunch account d days after August 1.
B(d) = 0.02d² − 3.25d + 48
Which choice represents the balance when school starts?
B(31) is correct because:
School starts on September 1.
d is the number of days after August 1.
September 1 is 31 days after August 1.
d = 31
B(48) is incorrect because it is the constant in the equation. School starts on day 31.
The equation does not need to be solved.
Answer: D. B(31)
A marathon starts at 7:30 a.m.
W(t) is the amount of water, in liters, remaining at a station t minutes after 7:00 a.m.
W(t) = 240(0.985)t + 0.02t
Which choice represents the amount of water remaining when the marathon starts?
W(30) is correct because:
The marathon starts at 7:30 a.m.
t is the number of minutes after 7:00 a.m.
7:30 a.m. is 30 minutes after 7:00 a.m.
t = 30
W(730) is incorrect because it writes 7:30 as 730. The input counts minutes after 7:00 a.m.
The equation does not need to be solved.
Answer: C. W(30)
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