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

MA 3972-MA-Book April 11, 2018 15:14

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

11. A ball is dropped from the top of a 640-foot
    building. The position function of the ball
    iss(t)=− 16 t^2 +640, wheretis measured in
    seconds ands(t) is in feet. Find:

(a) The position of the ball after 4 seconds.

(b) The instantaneous velocity of the ball at

t=4.

(c) The average velocity for the first

4 seconds.

(d) When the ball will hit the ground.

(e) The speed of the ball when it hits the

ground.

12. The graph of the position function of a
    moving particle is shown in Figure 10.5-4.

1

1

0

2

3

4

234567

s(t)

s

Seconds

Feet

t

Figure 10.5-4

(a) What is the particle’s position att=5?

(b) When is the particle moving to the left?

(c) When is the particle standing still?

(d) When does the particle have the

greatest speed?

Part B Calculators are allowed.

13. The position function of a particle moving
    on a line iss(t)=t^3 − 3 t^2 +1,t≥0 where
    tis measured in seconds andsin meters.
    Describe the motion of the particle.


14. Find the linear approximation of f(x)=
    sinxatx=π. Use the equation to find
    the approximate value of f

(

181 π

180

)

.

15. Find the linear approximation of f(x)=
    ln (1+x)atx=2.


16. Find the coordinates of each point on the
    graph ofy^2 = 4 − 4 x^2 at which the tangent
    line is vertical. Write an equation of each
    vertical tangent.


17. Find the value(s) ofxat which the graphs
    ofy=lnxandy=x^2 +3 have parallel
    tangents.


18. The position functions of two moving
    particles ares 1 (t)=lntands 2 (t)=sintand
    the domain of both functions is 1≤t≤8.
    Find the values oftsuch that the velocities
    of the two particles are the same.


19. The position function of a moving particle
    on a line iss(t)=sin(t) for 0≤t≤ 2 π.
    Describe the motion of the particle.


20. A coin is dropped from the top of a tower
    and hits the ground 10.2 seconds later. The
    position function is given as
    s(t)=− 16 t^2 −v 0 t+s 0 , wheresis measured
    in feet,tin seconds, andv 0 is the initial
    velocity ands 0 is the initial position. Find
    the approximate height of the building to
    the nearest foot.

10.6 Cumulative Review Problems

(Calculator) indicates that calculators are
permitted.

21. Find
    dy
    dx
    ify=xsin−^1 (2x).
    22. Givenf(x)=x^3 − 3 x^2 + 3 x−1 and the
    point (1, 2) is on the graph of f−^1 (x). Find
    the slope of the tangent line to the graph
    off−^1 (x) at (1, 2).