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

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If (x + k) is a factor of f(x), which of the following must be true?

f(k) = 0

f(–k) = 0

A root of f(x) is x = k.

A y intercept of f(x) is x = –k.

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Mrs. Cho wrote the following problem on the board.Problem: Step 1: Step 2: Step 3: What should Mrs. Cho do next?

Find a common denominator for the two fractions.

Divide the numerator and denominator of the first fraction by x2 and y.

Multiply the numerators, multiply the denominators, and then simplify.

Multiply the first fraction by the reciprocal of the second fraction.

Which graph shows all the values that satisfy

A number line goes from negative 10 to positive 10. An open circle appears at positive 7. The number line is shaded from positive 7 toward positive 10.

A number line goes from negative 10 to positive 10. An open circle appears at positive 7. The number line is shaded from positive 7 toward negative 10.

A number line goes from negative 10 to positive 10. An open circle appears at negative 7. The number line is shaded from negative 7 toward negative 10.

A number line goes from negative 10 to positive 10. An open circle appears at negative 7. The number line is shaded from negative 7 toward positive 10.

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

(1, –3)

(–1, 3)

(1, 3)

(–1, –3)

Riley makes a mistake in step 2 while doing her homework. What was her mistake? Step 1: Step 2: Step 3: Step 4:

She added the two fractions incorrectly.

She used the wrong common denominator.

She did not distribute the negative correctly.

She did not multiply the first fraction by a factor.

Which is a factor of f(x) = 60x4 + 86x3 – 46x2 – 43x + 8? Use the Rational Root Theorem to help you find your answer.

x – 6

5x – 8

6x – 1

8x + 5

What is the factored form of ?

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Which expression is equivalent to (3 + 5i)2?

–16 + 30i

6 + 34i

–16 – 34i

16 + 30i

The graph shows the distance in miles of a runner over x hours. What is the average rate of speed over the interval [9, 11]?

Two-fifths

Five-halves

Carlos graphs the equations and and generates the graph below. Which conclusion is supported by the graph?

The equation has no real solutions.

The equation has one real solution.

The equation has two real solutions.

The equation has four real solutions.

Which solution to the equation is extraneous?

a = –2

a = –2 and a = 4

neither a = –2 nor a = 4

a = 4

Which equation is the inverse of y = x2 – 36?

y = plus-or-minus StartRoot x EndRoot + 6

y = plus-or-minus StartRoot x + 36 EndRoot

y = plus-or-minus StartRoot x EndRoot + 36

y = plus-or-minus StartRoot x squared + 36 EndRoot

A small cube with side length 6y is placed inside a larger cube with side length . What is the difference in the volume of the cubes?

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Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the problem using the zero product property, what do those solutions represent?

two possible “first” integers

two possible “second” integers

the two consecutive odd integers with a product of 255

a possible “first” integer and a possible “second” integer

What are the coefficients for the binomial expansion of (a + b)3?

1, 4, 6, 4, 1

1, 1

1, 2, 1

1, 3, 3, 1

Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make?

She makes a subtraction error.

She makes an error choosing the x-term in the quotient.

She makes a multiplication error.

She makes an error rewriting the problem in long division.

Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

x = –2, x = –4

x = –2, x = 4

x = 2, x = –4

x = 2, x = 4

Which relation below represents a one-to-one function?

A 2-column table has 5 rows. The first column is labeled x with entries 5, 14, 7, 13, 12. The second column is labeled f (x) with entries 26, 197, 50, 170, 197.

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 5, 2, 1, 2, 5.

A 2-column table has 5 rows. The first column is labeled x with entries 7.25, 7.5, 7.75, 8, 8.5. The second column is labeled f (x) with entries 11, 13, 15, 13, 11.

A 2-column table has 5 rows. The first column is labeled x with entries 9, 2, 4, 1, 5. The second column is labeled f (x) with entries 12, 7, 9, 13, 5.

A bungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. Then he falls 64.8 feet before bouncing up again. On his third descent, he falls 43.2 feet before going back up. What is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (Do not include the distance traveled up.)

234.0 ft

253.2 ft

789.8 ft

1,281.8 ft

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?

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Which expression is equivalent to ?

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For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

Which equation represents a graph with a vertex at (1, –6)?

y = 3x2 + 6x – 3

y = 3x2 – 6x – 3

y = 3x2 – 8x – 1

y = 3x2 – 3x – 6

If g(x) is an odd function, which function must be an even function?

f(x) = g(x) + 2

f(x) = g(x) + g(x)

f(x) = g(x)2

f(x) = –g(x)

The formula relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth. What is the length of a pendulum that makes one full swing in 2.2 seconds? Use 3.14 for .

2 feet

4 feet

11 feet

19 feet

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