5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:5

336 STEP 4. Review the Knowledge You Need to Score High

3. The position function of a particle moving
   on a coordinate line is given ass(t)=t^2 −
   6 t−7, 0≤t≤10. Find the displacement
   and total distance traveled by the particle
   from 1≤t≤4.


4. The velocity function of a moving particle
   on a coordinate line isv(t)= 2 t+ 1
   for 0≤t≤8. Att=1, its position is−4.
   Find the position of the particle att=5.


5. The rate of depreciation for a new piece of
   equipment at a factory is given asp(t)=
   50 t−600 for 0≤t≤10, wheretis
   measured in years. Find the total loss of
   value of the equipment over the first 5 years.


6. If the acceleration of a moving particle on a
   coordinate line isa(t)=−2 for 0≤t≤4,
   and the initial velocityv 0 =10, find the
   total distance traveled by the particle during
   0 ≤t≤4.


7. The graph of the velocity function of a
   moving particle is shown in Figure 14.7-2.
   What is the total distance traveled by the
   particle during 0≤t≤12?

v(t)

v

t

20

10

• 10

(^012) 3 4 5 6 7 8 9 10 11 12
Figure 14.7-2

8. If oil is leaking from a tanker at the rate of
   f(t)= 10 e^0.^2 tgallons per hour wheretis
   measured in hours, how many gallons of oil
   will have leaked from the tanker after the
   first 3 hours?


9. The change of temperature of a cup of
   coffee measured in degrees Fahrenheit in a
   certain room is represented by the function

f(t)=−cos

(

t

4

)

for 0≤t≤5, wheretis

measured in minutes. If the temperature of

the coffee is initially 92◦F, find its

temperature after the first 5 minutes.

10. If thehalf-lifeof a radioactive element is
    4500 years, and initially, there are 100
    grams of this element, approximately how
    many grams are left after 5000 years?


11. Find a solution of the differential equation:
    dy
    dx
    =xcos (x^2 );y(0)=π.


12. If
    d^2 y
    dx^2
    =x−5 and atx=0, y′=−2 and
    y=1, find a solution of the differential
    equation.

Part B Calculators are allowed.

13. Find the average value ofy=tanx
    fromx=
    π
    4
    tox=
    π
    3

.

14. The acceleration function of a moving
    particle on a straight line is given by
    a(t)= 3 e^2 t, wheretis measured in seconds,
    and the initial velocity is

1

2

. Find the
displacement and total distance traveled by
the particle in the first 3 seconds.
15. The sales of an item in a company follow an
exponential growth/decay model, wheretis
measured in months. If the sales drop from
5000 units in the first month to 4000 units
in the third month, how many units should
the company expect to sell during the
seventh month?
16. Find an equation of the curve that has a
slope of
2 y
x+ 1
at the point (x,y) and passes
through the point (0, 4).
17. The population in a city was approximately
750,000 in 1980, and grew at a rate of
3% per year. If the population growth