ap precalc mcq
the binomial theorem can be used to expand the polynomial function p is given by p(x)=(x-3)^5. What is the coefficient of the x^3 term in the expand polynomial
(-3)^2 times 10
the figure shows the graph of an exponential decay function f. The coordinates of two of the points are labeled. If y=f(x) what is the y-coordinate of the point on the graph where x=0
40
the function g is given by g(x)=7sin(2x) which of the following is an equivalent form for g(x)
g(x)=14cos x sin x
the polynomial function p is given by p(x)=(x+3)(x^2=2x-15) which of the following describes the zeros of p
p has exactly two distinct real zeros
for the time t hours 0 is less than or equal to t and 2 is greater than or equal to t, the number of people inside a large shopping center is changing at a rte modeled by the function P is given by P(t)=t^3=4t^2+3t+1, where P(t) is measured in hundreds of people per hour. Which of the following gives the time t and reasoning for when the number of people inside the shopping center is at its maximum?
t=1.445 because the rate of change in the number of people inside the shopping center changes from positive to negative
on a given day the number of people in thousands, that have entered a museum is modeled by the function h given by h(t)=4.217tan^-1(0.7t-0.026), where t is measured in hours and 0 is less than or equal to t or 8 is greater than or equal to t. Based on the model at what time t did person number 4000 enter the museum?
t=2.029
the table gives values for a polynomial function g at selected values of x. if a is less than b then g(a) is greater than g(b) for all a and b in the interval 3 is less than x or 7 is greater than x. Which of the following could be true about the graph of g on the interval 3 is less than x or 7 is greater than x
the graph of g is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing
the location of point X in polar coordinates (r,theta) is (1,5pi/6). Which of the following describes the location of the point X in rectangular coordinates (x,y)
(-rad3/2, 1/2)
the polynomial function k is given by k(x)=ax^4-bx^3+15, where a and b are nonzero real constants. Each of the zeros of k has multiplicity 1. In the xy-plane, an x-intercept of the graph of k is (17.997,0) a zero ok k is -0.478-0.801i Which of the following statements must be true?
-0.478+0.801i is a zero of k
A physical therapy center has a bicycle that patient use for exercise. The height, in inches (in), of the bicycle pedal above level ground periodically increases and decreases when used. The figure gives the position of the pedal P at a height of 12 inches above the ground at time t=0 seconds. The pedal's 8-inch arm defines the circular motion of the pedal. If a patient pedals 1 revolution per second, which of the following could be an expression for h(t), the height, in inches, of the bicycle pedal above level ground at time t seconds
12-8sin(2pit)
the table shows the length of high-speed railways, in thousands of kilometers, in a certain country, starting in the year 2010 (t=). A quartic regression is used to model the length of high-speed railways, in thousands of kilometers, is predicted by the model for 2028 (t=18)
127.0
in a certain simulation, the population of a bacteria colony can be modeled by using a geometric sequence, where the first day of a simulation is day 1. The population on day 4 was 4,000 bacteria, and the population on day 8 was 49,000 bacteria. What was the population of the colony on day 6 based on the simulation
14,000
the function f is given f(x)= 2sin(4x)+cos(2x). Using the period of f which of the following is the number of complete cycles of the graph of f in the xy plane on the interval 0 is less than or equal to x and 1000 is greater than or equal to x?
318
the figure shows the graph of a function g in the xy-plane with four labeled points. It is known that a relative maximum of g occurs at A, and the only point of inflection of the graph of g is C. Of the following points at which is the rate of change of g the least
C
the table gives polar coordinates (r,theta) for four selected points.Which of the points lies in quadrant II of the xy plane?
D because from the positive x-axis, 7pi/4 counter clockwise from the origin is in Quadrant IV and the negative radius indicates the opposite direction of the angle from the origin
the function g is given by g(x)=2cos(pix)+1. Which of the following is the graph of g for 0 is less than or equal to x or 4 is greater than x?
a=2, period= equals 2 midline is 1, cosine
at a coastal city, the height of the tine in feet (ft) is modeled by the function h defined by h(t)=6.3(pi/6t)+7.5 for o is less than or equal to t or 12 is greater than or equal to t based on the model which of the following is true
the maximum height of the tide is 13.8 ft
a polynomial function p is given by p(x)=-x(x-4)(x+2) where are all intervals on which p(x) >= 0
(-infinity,-] U [0,4]
a complex number is represented by a point in the complex plane. The complex number has the rectangular coordinates (3,3) which of the following is one way to express the complex number using its polar coordinates (r,theta)
(3rad2cos(pi/4))+ i(3rad2sin(pi/4))
in the xy-plane the graph of a rational function f has a vertical asymptote at x=-5 which of the following could be an expression for f(x)
(x-5)(x-3)/(x-3)(x+5)
the figure shows a circle centered at the origin with an angle of measure theta radians in standard position. The terminal ray of the angle intersects the circle at point P. If tan theta= -3/4, what is the slope of the line that passes through the origin and P?
-3/4
What are all values of theta, for 0<=theta<2pi where 2sin^2 theta=-sin theta
0,pi,7pi/6 and 11pi/6
which of the following graphs could represent these data in a semi-log plot, where the vertical axis is logarithmically scaled
10, 100, 1000
the table gives the weight y in pounds of an animals for selected ages x, in years. A logarithmic regression is used to model these data. What is the weight of the animal, to the nearest pound, predicted by the logarithmic function model at age 4.5 years?
5345
the function C models the cost, in dollars, for producing x items and is is given by C(x)=1000+bx/x, where b is a constant, It is known that the cost is $115 to produce 10 items and $65 to produce 20 tems. What is the average rate of change of C as x changes from x=30 to x=40
=$-.83 per item
a portion of the graph of the polar function r=f(theta) where f(theta)=2-4 cos theta, is shown in the polar coordinate system for a is less than or equal to theta and b is greater than or equal to theta. If o is less than or equal to a and b is greater than a and 2pi is greater than b, which of the following are the values for a and b?
a=0 and b= pi/3
the function f is defined by f(x)=asin(b(x+c)+d) for constants a,b,c and in the xy plane the points (2,2) and 94,4) represent a minimum value and a maximum value, respectively on the graph of f. What are the values of a and d?
a=1 and d=3
a large wheel of radius 2 feet is rotated at a constant rate. The figure provides a representation of the wheel in the xy plane with the direction of rotation indicated. At time t=0 minutes, the wheel begins to rotate. Point P on the wheel is at the "start" position in the figure. At the time t= 20 minutes, 120 rotations of the wheel have been completed, and P is in the same position as it was at time t=0. A sinusoidal function is used to model the y-coordinate of the position of P as a function of time t in minutes. Which of the following functions is an appropriate model for this situation
f(t)=2sin(12pit)
in the xy-plane, the graph of a rational function f has a hole at x=2. Input values of f sufficiently close to 2 correspond to output values arbitrarily close to 6. Which of the following could define f(x)
f(x)=(x-2)(x+4)/(x-2)(x-1)
in the xy-plane, the graph f which of the following functions has a vertical asymptote at x=3pi/4
f(x)=cot(x+pi/4)
the table shows values fro a function g at selected values of x. Which of the following claim and explanation statements best fits these data?
g is best modeled by a quadratic function, because the change over consecutive equal-length input-value intervals is constant
the amount of water used each day in an office building, measured in hundreds of gallons, is modeled by the function g is defined by g(t)=5sin(0.8(t+2)) +25, for integer values of t with 0 is less than or equal to t or 365 is greater than or equal to t. Using actual data over time, it was determined that the model underestimates the amount of water used each day by 800 gallons. Based on this information, which of the following functions is a better model for the amount of water used each day, measured in hundreds of gallons?
h(t)=5sin(0.8(t+2)) + 33
in the xy-plane the function h, given by h(x)=3^(x+2), is a horizontal translation of the exponential function f, given by f(x)=3^x. Which of the following is an equivalent form for h(x) that expresses h as a vertical dilation of f?
h(x)=9 times 3^x
the function f is given by f(x)= 5x^6-2x^3-3 which ofthe following describes the end behavior of f
lim f(x) x->-infinity =infinity and lim f(x) x->infinity= infinity
let x and y be positive constants. which of the following is equivalent to 2lnx-3lny
ln(2x/3y)
two function models k and m are constructed to represent the sales of a product at a group of grocery stores/ Both k(t) and m(t)represent the sales of the product, in thousands of units, after t weeks for this greater than or equal to 2. If k(t)=14=2.885ln t and m(t)=-t+14, what is the first time t that sales predicted by the logarithmic model will be 0.1 thousand units more than sales predicted by the liner model?
t=4.324
the rate of people entering a subway car on a particular day is modeled by the function R where R9t)=0.03t^3-0.846t^2+6.587t+1.428 for 0 is less than or equal to t or 20 is greater than or equal tp t. R(t) is measured in people per hour and t is measured in hours since the subway began service for the day. Based on the model, at what value of t does the rate of people entering the subway car change from increasing to decreasing
t=5.505
the function of f is given by f(t)=e^t, and the function g is given by g(t)=7ln t. If the function h is given by h(t)=f(g(x)) which of the following is an expression for h(t) for t is greater than 0
t^7
for 0 is less than or equal to t and 16 is greater than or equal to t, the rate at which customers arrive at a restaurant on a given day is modeled by the function R, where R(t) is measured in customers per hour and t is measured in hours since the restaurant opened. The function R is increasing for 0 is less than t or 4 is greater than t, and 8 is less than t and 12 is greater than t, and R is decreasing for 4 is less than t and 8 is greater than t and 12 is less than t and 16 is greater than t. The function N models the total number of customers who have arrived at the restaurant since it opened, up to time t. Which of the following could be the graph of y=N(t) for 0 is less than or equal to t and 16 is greater than or equal to t?
the graph starts at 0, the the first curve is increasing concave down, the last curve is increasing concave up
a regression model S is constructed for a data set. The residuals from the regression are plotted and labeled. Based on the vertical axis of the residual plot (not shown), point A is located at 1.3 and point B is located at -2.5. Which of the following statements is true about the model and the estimates produced by the model that correspond to A and B
the model produces an underestimate at A and an overestimate at B. Based on the absolute values of the residuals, there is a greater error in the model with B than with A
the figure shows the graph of the polar function r=f(theta), where f(theta)= 4cos (2theta) in the polar coordinate system for less than theta or pi/2 is greater than or equal to theta, the portion of the given graph that remains consists of two pieces. One of those pieces is the portion of the graph in quadrant I from C to E. Which of the following describes the other remaining piece
the portion of the graph in Quadrant III from E to D
the function k is given by k(theta)=2sin theta. What are all values of theta, for 0 is less than or equal to theta or 2pi is greater than theta, where k(theta)=-1
theta=7pi/6 and theta=11pi/6
