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Unit Test Answers | LAUSD-Algebra II A Prescriptive - Summer | Revolt

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Answers LAUSD-Algebra II A Prescriptive - SummerPerforming Operations with Complex Numbers

Unit Test Answers

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

A

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

B

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

C

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

D

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

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A

m greater-than StartFraction 25 Over 3 EndFraction

Option A

B

m less-than StartFraction 25 Over 3 EndFraction

Option B

C

m less-than StartFraction 49 Over 12 EndFraction

Option C

D

m greater-than StartFraction 49 Over 12 EndFraction

Option D

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

A

I

B

II

C

III

D

IV

Which equation is the inverse of y = 9x2 – 4?

A

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction

Option A

B

y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot

Option B

C

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction

Option C

D

y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds

Option D

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

A

x2 + mx + m = (x – 1)2

B

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

C

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

D

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

Which pair of complex numbers has a real-number product?

A

(1 + 2i)(8i)

B

(1 + 2i)(2 – 5i)

C

(1 + 2i)(1 – 2i)

D

(1 + 2i)(4i)

What is the additive identity of the complex number 14 + 5i?

A

14 – 5i

B

0

C

1

D

–14 – 5i

Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.

A

x = –7 or x = 6

B

x = –7 or x = –6

C

x = –6 or x = 7

D

x = 6 or x = 7

Use completing the square to solve for in the equation .

Question illustration

A

x = –1 or 15

B

x = 1 or 7

C

x = 4 plus-or-minus StartRoot 41 EndRoot

Option C

D

x = 4 plus-or-minus StartRoot 73 EndRoot

Option D

Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.

A

x = –8 or x =

Option A

B

x = or x =

Option B

C

x = or x =

Option C

D

x = or x =

Option D

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

A

1

B

–1

C

i

D

–i

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

A

y = 9 (x + one-half) squared minus thirteen-fourths

Option A

B

y = 9 (x + one-half) squared minus 1

Option B

C

y = 9 (x + one-half) squared + five-fourths

Option C

D

y = 9 (x + one-half) squared minus five-fourths

Option D

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

A

6 units left and 9 units down

B

6 units right and 9 units down

C

6 units left and 9 units up

D

6 units right and 9 units up

What is the domain of the function ?

Question illustration

A

x greater-than-or-equal-to negative 5

Option A

B

x greater-than-or-equal-to 2

Option B

C

x greater-than-or-equal-to 5

Option C

D

x greater-than-or-equal-to 10

Option D

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

A

StartRoot 1 plus-or-minus StartRoot 159 EndRoot i Over 8 EndFraction

Option A

B

StartRoot 5 plus-or-minus StartRoot 153 EndRoot i Over 8 EndFraction

Option B

C

StartRoot 5 plus-or-minus StartRoot 103 EndRoot i Over 8 EndFraction

Option C

D

StartRoot 1 plus-or-minus StartRoot 153 EndRoot Over 8 EndFraction

Option D

Solve for in the equation .

Question illustration

A

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

Option A

B

x = –4 ± 5i

C

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

Option C

D

x = 4 ± 5i

Solve for in the equation .

Question illustration

A

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

Option A

B

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

Option B

C

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

Option C

D

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

Option D

Which equation represents a graph with a vertex at (–3, 2)?

A

y = 4x2 + 24x + 38

B

y = 4x2 – 24x + 38

C

y = 4x2 + 12x + 2

D

y = 4x2 + 16x + 13

Which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p + qi)i

A

p = 3, q = 7

B

p = –3, q = 7

C

p = 3, q = –7

D

p = –3, q = –7

Which equation is the inverse of ?

Question illustration

A

y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction

Option A

B

y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

Option B

C

y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

Option C

D

negative (x minus 4) squared minus two-thirds = negative 6 y + 12

Option D

Which function has the domain ?

Question illustration

A

y = StartRoot x + 11 EndRoot + 5

Option A

B

y = StartRoot x minus 11 EndRoot + 5

Option B

C

y = StartRoot x + 5 EndRoot minus 11

Option C

D

y = StartRoot x + 5 EndRoot + 11

Option D

What is the absolute value of the complex number ?

Question illustration

A

StartRoot 14 EndRoot

Option A

B

3 StartRoot 2 EndRoot

Option B

C

14

D

18

What is the value of ?

Question illustration

A

–3 + 6i

B

3 + 6i

C

5 + 5i

D

5 – 5i

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

A

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

B

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

C

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

D

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

Which equation has a graph that lies entirely above the x-axis?

A

y = –(x + 7)2 + 7

B

y = (x – 7)2 – 7

C

y = (x – 7)2 + 7

D

y = (x – 7)2

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