AnswersAP Calculus AB - MA5186 AUnit Test

Unit Test — Unit test Answers

20 verified answers
1
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This question is designed to be answered without a calculator.If , then

Question illustration
A
Negative StartFraction 1 Over x cubed EndFraction minus 4 x
Option A
B
Negative StartFraction 4 Over x cubed EndFraction minus 4 x
Option B
C
Negative StartFraction 1 Over x EndFraction minus 4 x cubed
Option C
D
Negative StartFraction 4 Over x EndFraction minus 4 x cubed
Option D
2
Free Preview

This question is designed to be answered without a calculator.An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.Which inequality describes all times t for which the object is traveling toward the right?

A
0 ≤ t < 1.25
B
0 ≤ t < 4.5
C
t > 1.25
D
t > 4.5
3

This question is designed to be answered without a calculator.If y = (x2 + x + 1)(x3 – x – 1), then y’(2) =

A
35.
B
55.
C
90.
D
102.
4

This question is designed to be answered without a calculator.

Question illustration
A
StartFraction 5 Over x EndFraction
Option A
B
StartFraction 5 Over x squared EndFraction
Option B
C
Negative StartFraction 5 Over x EndFraction
Option C
D
Negative StartFraction 5 Over x squared EndFraction
Option D
5

This question is designed to be answered without a calculator.Let Which expression represents f '(x)?

Question illustration
A
StartFraction 3 Over 2 x EndFraction
Option A
B
StartFraction 3 (x squared + 1) Over x squared minus 1) squared EndFraction
Option B
C
StartFraction negative 3 (x squared + 1) Over (x squared minus 1) squared EndFraction
Option C
D
StartFraction 3 (3 x squared minus 1) Over (x squared minus 1) squared EndFraction
Option D
6

This question is designed to be answered without a calculator.A ball is thrown upward into the air so that its height, h, in feet, after t seconds is modeled by the function h(t) = 56t – 16t2. What is the velocity, in feet per second, of the ball after 2 seconds?

A
–32 ft/sec
B
–8 ft/sec
C
24 ft/sec
D
48 ft/sec
7

This question is designed to be answered without a calculator.Use this graph of the derivative of function f.Which of these could be the graph of f?

Question illustration
A
On a coordinate plane, a horizontal line starts at open circle (0, 0) and goes to the left. Another line starts at open circle (0, negative 1) and goes to the right.
Option A
B
On a coordinate plane, a line is horizontal at y = negative 0.5 and then increases from (0, negative 0.5) through (3, 2.5).
Option B
C
On a coordinate plane, a line goes through (negative 4, negative 2) to (0, 0), and then curves up through (3, 3) in quadrant 1.
Option C
D
On a coordinate plane, a line goes through (negative 4, negative 2) to (0, 0), and then curves down through (3, negative 3) in quadrant 4.
Option D
8

This question is designed to be answered without a calculator.

Question illustration
A
2xtan2x
B
2xsecxtanx
C
xsecx(2 + xtanx)
D
x(2secx + xtan2x)
9

This question is designed to be answered without a calculator.A particle travels along the x-axis so that its position, in centimeters, after t seconds is given by the function x(t) = –4t3 – 8t2 + 16t – 64. What is the acceleration of the particle at time t = 1 sec?

A
–52 cm/sec2
B
–40 cm/sec2
C
–24 cm/sec2
D
–12 cm/sec2
10

This question is designed to be answered with a calculator.Use the four functions shown.Which function is differentiable for all values of x over the interval (–5, 5)?

Question illustration
A
I
B
II
C
III
D
IV
11

This question is designed to be answered without a calculator.Let f be a continuous and differentiable function. Use this table of values that represents function f.Which of the following is the best estimate of f '(2) based on this table of values?

Question illustration
A
2
B
8
C
10
D
14
12

This question is designed to be answered without a calculator.Use this graph of function .Which of these is the graph of the derivative of ?

Question illustration
A
On a coordinate plane, a curve goes down through (negative 2, 1), (0, 0), curves down to (2.3, negative 3), and then curves up through (4, 4).
Option A
B
On a coordinate plane, a curve goes through (negative 2, negative 1), (0, 0), curves up to (2.5, 3), and then curves down through (4, negative 4).
Option B
C
On a coordinate plane, a parabola opens up, goes through (negative 1, 0), has a vertex at (negative 1, 0), and goes through (1, 0).
Option C
D
On a coordinate plane, a parabola opens down and goes through (negative 2, negative 2), has a parabola at (0, 1), and goes through (2, negative 2).
Option D
13

This question is designed to be answered without a calculator.The function f is differentiable, and the table below provides data representing f(x). Use the table to determine which graph represents the derivative of f(x).

Question illustration
A
On a coordinate plane, points curve up and down. The first point is (0, 0) and the last point is (7, 7.5).
Option A
B
On a coordinate plane, points curve up. The first point is (0, 0) and the last point is (7.5, 7).
Option B
C
On a coordinate plane, points form a curve that opens down. The first point is (0.5, 0) and the last point is around (6.5, 0.2).
Option C
D
On a coordinate plane, points are clustered near the x-axis.
Option D
14

This question is designed to be answered without a calculator.Let f(x) = 1 − 4x3. What is

Question illustration
A
12x2
B
−12x2
C
12x2 + 12x
D
−12x2 − 12x
15

This question is designed to be answered without a calculator.Which of the following shows a function with a non-differentiable point due to a vertical tangent?

A
On a coordinate plane, a line starts at open circle (negative 1, 2) and decreases through (negative 3, 0). A line starts at closed circle (negative 1, 3) and decreases through (2, 0).
Option A
B
On a coordinate plane, a line decreases through (negative 3, 4) to vertex (negative 1, 2) and then increases through (1, 4).
Option B
C
On a coordinate plane, a curve goes through (negative 4, 4) and decreases to (negative 1, 2), and then curves up through (2, 4).
Option C
D
On a coordinate plane, a curve goes through (negative 2, 1), curves through (negative 1, 2), and then curves through (0, 3) into quadrant 1.
Option D
16

This question is designed to be answered without a calculator.If f(x) = 5(x2 – 1), then

Question illustration
A
0.
B
5.
C
10.
D
20.
17

This question is designed to be answered without a calculator.If y = 8x2 – 4x3, then y’’’ =

A
–24.
B
–8.
C
0.
D
16.
18

This question is designed to be answered without a calculator.Use this graph of function f.For how many values of x is f not differentiable over the interval (–4, 4)?

Question illustration
A
1
B
2
C
3
D
4
19

This question is designed to be answered with a calculator.Let f(x) = (1 − x2)2/3. Which type of non-differentiable point exists at x = 1?

A
cusp
B
corner
C
discontinuity
D
vertical tangent
20

This question is designed to be answered without a calculator.Use the definition of the derivative of function f at x = a.If , then f’(4) =

Question illustration
A
One-third
Option A
B
One-half
Option B
C
2.
D
3.

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