Answers S1S-OC Pre-Calculus A E3700 - AGUnit Test

Unit Test — Cumulative exam Answers

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At which x-value does the cosine function attain a maximum value?

x = 0

x = StartFraction pi Over 2 EndFraction

x = 1

x = StartFraction 3 pi Over 2 EndFraction

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The acceleration y, in meters per second squared, of an object after x seconds is given by y = .During the first 10 seconds, over which intervals is the acceleration increasing?

(2, 6)

(4, 8)

(0, 2) and (6, 10)

(0, 4) and (8, 10)

The total number of degrees, D, in an n-sided polygon is given by the formula When Janelle solves for n, she gets . Sophie solved the same equation for n and got an equivalent equation. Which of the following could be Sophie’s equation?

n = StartFraction D Over 360 EndFraction + 2

n = StartFraction D Over 180 EndFraction minus 2

n = D minus 178

n = D minus 182

What is the product of 65(cos(14°) + i sin(14°)) and 8(cos(4°) + i sin(4°))?

73(cos(18°) + i sin(18°))

73(cos(56°) + i sin(56°))

520(cos(18°) + i sin(18°))

520(cos(56°) + i sin(56°))

Let csc(x) = , where . Which ratio has a value of ?

cos(x)

sin(x)

sec(x)

cot(x)

Review the graph.

The period of the graph is

The amplitude of the graph is 2 units.

The domain of the graph is the set of x-values from –3 to 3, inclusive.

The graph represents a reflection over the x-axis of the function y = 3sin(2x).

If the function y = sin(x) is transformed to y = sin(2x), how does the graph change?

It is stretched vertically.

It is compressed vertically.

It is stretched horizontally.

It is compressed horizontally.

For the complex number z = , what is arg(z)?

150°

210°

240°

330°

Maddie converts z = 8(cos(300°) + isin(300°)) into rectangular form z = a + bi and determines that a = 4 and b = .Which statement identifies whether her values for a and b are correct?

Both values a and b are correct.

Both values a and b are incorrect.

The value of a is correct, but the value of b is incorrect.

The value of a is incorrect, but the value of b is correct.

What is the additive inverse of the complex number –12 + 4i?

–12 – 4i

–12 + 4i

12 – 4i

12 + 4i

Amanda has a job that pays $35 per hour for the first 40 hours worked each week, plus 1.5 times this hourly rate for work done over 40 hours. Suppose Amanda works 50 hours this week. How much will she earn before taxes?

$1,575

$1,750

$1,925

$2,625

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function g–1(x)?

no restriction on the domain of g(x); inverse is g–1(x) =

domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =

Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t is the time in seconds. For which interval of time is the height of the ball less than 17 feet?

mc022-1.jpg

mc022-2.jpg

mc022-3.jpg

mc022-4.jpg

Determine if the given function has any points of discontinuity. Explain your reasoning.

There is a point of discontinuity at x = b because the denominator has the factor x – b.

There are points of discontinuity at both x = – b and x = b because the numerator has factors of x + b and x – b.

There is a point of discontinuity at x = -b only because the factor of x – b is common to both the numerator and denominator.

There is a point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator and factors out.

A segment in the complex plane has a midpoint at 7 – 2i. If the segment has an endpoint at 11 – 3i, what is the other endpoint?

–10 –2i

3 – i

9 – 2.5i

18 – 4i

Which expression is equivalent to ?

(StartFraction 1 over 32 EndFraction (cosine ( StartFraction pi over 5 EndFraction) plus i sine (StartFraction pi over 5 EndFraction))

(StartFraction 1 over 32 EndFraction (cosine (pi) plus i sine (pi))

(StartFraction 1 over 10 EndFraction (cosine ( StartFraction pi over 5 EndFraction) plus i sine (StartFraction pi over 5 EndFraction))

(StartFraction 1 over 10 EndFraction (cosine (pi) plus i sine (pi))

Consider the function f(x) = . What transformation results in g(x)?

Translate units left and 7 units up.

Translate units right and 7 units up.

Translate units left and 7 units down.

Translate units right and 7 units down.

Consider the function f(x) = |x|. Let g(x) = |–4(x – 7)|.Which shows the graphs of f(x) and g(x)?

On a coordinate plane, y = g (x) opens up and goes through (negative 3, 4), has a vertex at (negative 2, 0) and goes through (0, 7). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).

On a coordinate plane, y = g (x) opens up and goes through (6, 4), has a vertex at (7, 0) and goes through (8, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).

On a coordinate plane, y = g (x) opens down and goes through (6, negative 4), has a vertex at (7, 0) and goes through (8, negative 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).

On a coordinate plane, y = g (x) opens up and goes through (negative 8, 4), has a vertex at (negative 7, 0) and goes through (negative 6, 4). Y = f (x) opens up and goes through (negative 4, 4), has a vertex at (0, 0), and goes through (4, 4).