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

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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?

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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).

What is the difference?

StartFraction x squared + 4 x minus 1 Over x (x + 2) EndFraction

StartFraction x squared + 4 x + 1 Over x (x + 2) EndFraction

StartFraction 4 Over negative 1 (x squared + x minus 2) EndFraction

StartFraction x squared + 6 x + 1 Over x (x + 2) EndFraction

What is the solution set of the quadratic inequality

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Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

f(x) =

The center of an earthquake was detected along the Pacific Rim. Geologists determined that the distance the seismic waves traveled is represented by r = 15sin(θ), where r is in miles. Which graph represents the distance the waves traveled?

On a polar coordinate plane, a circle goes through (15, 0) and (15, StartFraction pi Over 2 EndFraction)

On a polar coordinate plane, a circle goes through (30, 0) and (30, StartFraction pi Over 2 EndFraction).

On a polar coordinate plane, a circle goes through (0, 0) and (3, StartFraction pi Over 2 EndFraction).

On a polar coordinate plane, a circle goes through (0, 0) and (25, StartFraction pi Over 2 EndFraction).

Review the graph of z2.

Which sequence explains a geometric method of determining ?

Plot 2 + 2i. Scale by . Rotate 45° clockwise.

Plot 3 – 17i. Scale by . Rotate 45° clockwise.

Plot 2 + 2i. Scale by . Rotate 45° clockwise.

Plot 3 – 17i. Scale by . Rotate 45° clockwise.

Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?

(16, positive infinity)

(Negative 16, positive infinity)

(Negative infinity, 16)

(Negative infinity, Negative 16)

Juan jogs each day from his house to a local park, and then he jogs back along the same route. On his way to the park, he averages 4 miles per hour. On his way home, he averages 6 miles per hour. If the total trip takes hours, which equation can be used to find x, the distance in miles from Juan’s house to the park? Distance (mi)Rate (mi/hr)Time (hr)Trip to Parkx4 mph Trip to Homex6 mph

StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1

StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 and one-half

4 x + 6 x = 1 and one-half

4 x + 6 x = 1

The graph represents the fees in thousands of dollars, y, depending on the amount invested in millions, x, with one financial investment firm.

[0, 5)

[1, 5)

[0, 20)

[1, 20)

The height of a tennis ball tossed into the air is modeled by h(x) = 40x – 16x 2, where x is elapsed time in seconds.During what time interval will the tennis ball be at least 15 feet above the ground?

x > 0.5 seconds and x > 2.04 seconds

x > 0.5 seconds and x ≤ 2.04 seconds

x ≥ 0.5 seconds and x > 2.04 seconds

x ≥ 0.5 seconds and x ≤ 2.04 seconds

Functions f(x) and g(x) are composed to form . If , what is the value of a?

–1

–2

–4

Which graph represents the polar curve r = 1 + sin(θ)?

On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, negative 2). It has a cardioid at (0, 0).

On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, 2). It has a cardioid at (0, 0).

On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (negative 2, 0). It has a cardioid at (0, 0).

On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (2, 0). It has a cardioid at (0, 0).

Which expression is equivalent to the following complex fraction?

StartFraction (y + 1) (y minus 1) Over y squared EndFraction

StartFraction y + 1 Over y minus 1 EndFraction

StartFraction y minus 1 Over y + 1 EndFraction

StartFraction y squared Over (y + 1) (y minus 1) EndFraction

What is the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i?

root 5

i root 5

11i

Which expression is equivalent to ?

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If what is the value of w in terms of x and y?

w = StartFraction x minus 3 y Over 3 EndFraction

w = StartFraction x minus 3 y + 1 Over 3 EndFraction

w = x minus 3 y + 1

w = StartFraction x + 1 Over 9 y EndFraction

The relationship between voltage E, current I, and resistance Z is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of the circuit?

4 – i

4 + i

8 + i

8 + 7i

What property is used in the second step of solving the inequality below?______Given_________________________Multiplication Property

Identity Property

Addition Property

Multiplication Property

Transitive Property

Which graph shows the solution set of ?

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For the expression , which sum represents the correct form of the partial fraction decomposition?

StartFraction A x + B Over 3 x squared minus 4 EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction

StartFraction A Over 3 x squared minus 4 EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction

StartFraction A x + B Over (3 x squared minus 4) squared EndFraction + StartFraction C x + D Over (3 x squared minus 4) squared EndFraction

StartFraction A Over (3 x squared minus 4) squared EndFraction + StartFraction B Over (3 x squared minus 4) squared EndFraction

Which transformations to the graph of y = ex would result in the graph of y = ex + 34 – 27?

translation of 34 units right and 27 units up

translation of 34 units right and 27 units down

translation of 34 units left and 27 units up

translation of 34 units left and 27 units down

A party planner is going to use an arch of balloons for a parade of recent graduates. The estimated curve the balloons will create is modeled by the function given in the table, where x represents the distance in feet along the ground from the start and f(x) represents the height in feet above the ground.

no, because the width of the arch is 8 feet

yes, because the width of the arch is 9.6 feet

no, because the maximum height of the arch is 8 feet

yes, because the maximum height of the arch is 9.6 feet

Which graph includes a function, its inverse, and a dashed line that verifies the relationship?

Option

Which graph shows the solution set of ?

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The function W(t) = 40e–0.35t models the healing of a wound after t hours, where W(t) represents the wound area in square millimeters. What relationship do W(t) and t have?

when t = 0, W(t) > 40

when t = 0, W(t) < 40

when t > 0, W(t) > 40

when t > 0, W(t) < 40

How many liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin? Round the answer to the nearest hundredth if necessary. Original (L)Added (L)New (L)Amount of Glycerin0.96x0.96 + xAmount of Solution12x12 + x

0.18 liter

1.14 liters

1.92 liters

2.10 liters

The table shows several points for function j(t).

A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries negative 1, negative 2, negative 10, negative 250.

A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.

A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.

A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 8, 10, 17.

Consider the graph of f(x) = 5x 6 – 5x 5 – x 4.

One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than x less-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

One-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot less-than-or-equal-to x less-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

x less-than one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot

x less-than-or-equal-to one-half minus StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot and x greater-than-or-equal-to one-half + StartFraction 3 Over 10 EndFraction StartRoot 5 EndRoot