Unit Test — Unit test Answers

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Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

(–1 + i) + (21 + 5i) + 0

–1 + (i + 21) + 5i

(–1 + 21) + (i + 5i)

–(1 – i) + (21 + 5i)

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Which statement about the following equation is true?2x2 – 9x + 2 = –1

The discriminant is less than 0, so there are two real roots.

The discriminant is less than 0, so there are two complex roots.

The discriminant is greater than 0, so there are two real roots.

The discriminant is greater than 0, so there are two complex roots.

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

x2 + mx + m = (x – 1)2

x2 + mx + m = (x + 1)2

x2 + mx + m = (x + 2)2

x2 + mx + m = (x + 4)2

What is the distance from the origin to point P graphed on the complex plane below?

StartRoot 7 EndRoot

StartRoot 29 EndRoot

Which equations can be used to find the lengths of the legs of the triangle? Select three options.

0.5(x)(x + 2) = 24

x(x + 2) = 24

x2 + 2x – 24 = 0

x2 + 2x – 48 = 0

x2 + (x + 2)2 = 100

Solve for in the equation .

x = 6 plus-or-minus 3 StartRoot 10 EndRoot

x = 6 plus-or-minus 2 StartRoot 7 EndRoot

x = 12 plus-or-minus 3 StartRoot 22 EndRoot

x = 12 plus-or-minus 3 StartRoot 10 EndRoot

The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?

The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.

The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

The vertical asymptote x = 0 represents that the cost per person approaches $0 as the number of people increases.

The vertical asymptote x = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

What is the distance from the origin to point A graphed on the complex plane below?

StartRoot 5 EndRoot

StartRoot 13 EndRoot

The table below shows y, the average speed of a cyclist in miles per hour, and x, the time in hours that it takes the cyclist to complete a bicycle tour. Which rational function best models the data in the table?Time, x(hours)Average Speed, y(miles per hour)128166918

Option

Which equation demonstrates the additive identity property?

(7 + 4 i) + (7 minus 4 i) = 14

(7 + 4 i) + 0 = 7 + 4 i

(7 + 4 i) (1) = 7 + 4 i

(7 + 4 i) + (negative 7 minus 4 i) = 0

Solve for in the equation .

x = negative 4 plus-or-minus StartRoot 37 EndRoot i

x = –4 ± 5i

x = 4 plus-or-minus StartRoot 37 EndRoot i

x = 4 ± 5i

Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?

Aiko incorrectly used the commutative property by changing the order of the two complex numbers.

Aiko incorrectly used the associative property by changing the order of the two complex numbers.

Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.

Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.

Use completing the square to solve for in the equation .

x = –1 or 15

x = 1 or 7

x = 4 plus-or-minus StartRoot 41 EndRoot

x = 4 plus-or-minus StartRoot 73 EndRoot

Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.

commutative property

identity property

distributive property

associative property

In which quadrant is the number 6 – 8i located on the complex plane?

III

Which complex number has a distance of from the origin on the complex plane?

2 + 15i

17 + i

20 – 3i

4 – i

Which of the following describes the growth rate of the exponential function in the graph below?

For each x increase of 1, the y increases by a common difference of 3.

For each x increase of 1, the y increases by a common factor of 3.

For each x increase of 1, the y increases by 4 more than the previous increase.

For each x increase of 1, the y increases by doubling and then adding 1.

Which of the following is an example of a complex number that is not in the set of real numbers?

-7

2 + StartRoot 3 EndRoot

4 + 9i

Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2 If the number of employees is an indicator of a successful business, in which company should Ajay invest?

company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year

company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year

company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year

company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year

Which of the following is equivalent to ?

18 – 5i

18 + 5i

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Unit Test — Unit test Answers

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