Answers S1S-OC Pre-Calculus B E3710 - AGPerformance Task: Trigonometric Identities

Performance Task: Trigonometric Identities — Cumulative exam Answers

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Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?

Apply the 15% discount first, and the final purchase price is $332.50.

Apply the 15% discount first, and the final purchase price is $340.00.

Apply the $50 off first, and the final purchase price is $332.50.

Apply the $50 off first, and the final purchase price is $340.00.

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What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

As , and as , .

As , and as , .

As , and as , .

As , and as , .

Review the proof of cos(A - B) = cosAcosB + sinAsinB.Step 1: Step 2: Step 3: Step 4: Step 5:Step 6:Step 7:

1 and 1

2 and 1

(cosAcosB)2(sinAsinB)2 and (cos2(A – B))((sin2(A – B))

(cos2A + sin2A)(cos2B + sin2B) and (cos2(A – B))(sin2(A – B))

What is the exact value of tan(195°)?

StartFraction StartRoot 3 EndRoot + 1 Over 1 minus StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot minus 3 Over 3 + StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot minus 1 Over 1 + StartRoot 3 EndRoot EndFraction

StartFraction StartRoot 3 EndRoot + 3 Over 3 minus StartRoot 3 EndRoot EndFraction

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

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 single transformation can be applied to the graph of y = 72 to produce the graph of y = 9 ?

vertical translation

vertical compression

horizontal translation

horizontal compression

Which statement about the polynomial function g(x) is true?

If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

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.

The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube?

3x3 + 18x2y + 36xy2 + 8y3

27x3 + 54x2y + 18xy2 + 2y3

27x3 + 18x2y + 12xy2 + 2y3

27x3 + 54x2y + 36xy2 + 8y3

Suppose . Which value(s) of a would make the composite functions commutative?

any value of a

no value of a

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

1.45 million

3.45 million

40 million

48 million

Which statement is true about the discontinuities of the function f(x)?

There is a hole at x = 2.

There are asymptotes at x = 0 and x = –1.

There are asymptotes at x = 0 and x = –1 and a hole at .

There are holes at x = 0 and x = –1 and an asymptote at x = 2.

On interval 0 ≤ x < 2π, where are the x-intercepts of y = cos(2x)?

StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction

0, π, and 2π

StartFraction pi Over 2 EndFraction, pi and StartFraction 3 pi Over 2 EndFraction

Option

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years

2.0 years

3.1 years

5.0 years

A chemist has 500 mL of a 30% acid solution. She adds x milliliters of a 10% acid solution. Which statement is true about the graph of the function that represents the concentration of the final solution?

The horizontal asymptote y = 30 means that the final concentration will always be less than 30%.

The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.

The vertical asymptote x = 500 means that the volume of the solution will always be greater than 500 mL.

The vertical asymptote x = 0 means that the volume of the solution will always be greater than 0 mL.

The function h(x) = –x5 + 12x is an odd function. Which transformation of h(x) results in an odd function?

h(5 – x)

1 + h(x)

h(x + 8)

–6h(x)

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

(x – 2)(x + 5)(x – 3)

(x + 2)(x – 5)(x + 3)

(x – 2)(x + 5)

(x + 2)(x – 5)

For , which expression is equivalent to ?

StartFraction 1 Over StartRoot 2 (1 + cosine x) EndRoot EndFraction

StartFraction 1 Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction

(StartRoot StartFraction 1 + cosine (x) Over 2 EndFraction EndRoot) (StartFraction 1 Over 1 minus cosine (x) EndFraction)

(StartFraction 1 + cosine (x) Over StartRoot 2 (1 minus cosine x) EndRoot EndFraction) (StartFraction 1 Over 1 minus cosine (x) EndFraction)

Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

f(x) domain: x ≥ 3f–1(x) domain: x ≥ 3

f(x) domain: x ≥ 3f–1(x) range: y ≥ 3

f(x) domain: x ≥ 0f–1(x) domain: x ≥ 0

f(x) domain: x ≥ 0f–1(x) range: y ≥ 0

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Performance Task: Trigonometric Identities — Cumulative exam Answers

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