Question

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 and one-half years?
$2,500
$9,159
$22,827
$23,791



Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?

x2 + 4x – 15; 3 feet
x2 + 4x – 15; 6 feet
2x2 + 8x – 30; 6 feet
2x2 + 8x – 30; 12 feet



Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.

What expression represents the profit?

27x – 650
27x + 390
33x – 650
33x + 390




What is the quotient?

x + 5 )4x2 + 14x − 9

4x + 6 +
4x + 6 −
4x − 6 +
4x − 6 −



Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?

The difference has 3 terms and a degree of 6.
The difference has 4 terms and a degree of 6.
The difference has 3 terms and a degree of 7.
The difference has 4 terms and a degree of 7.



What is the polynomial 3y2 + (y + 7)2 – 15 after it has been fully simplified and written in standard form?

4y2 + 34
3y2 + y + 34
4y2 + 14y + 34
4y4 + 34




The equation T squared = A cubed shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?
k Superscript one-third
k Superscript one-half
k Superscript two-thirds
k Superscript three-halves




What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3
7y2 + 8xy – 3
7y2 + 4xy + 3
7y2 + 8xy + 3




The volume of a rectangular prism can be found by multiplying the base area, B, times the height.



Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it?

4 m squared + 25 n squared; a perfect square trinomial
4 m squared + 25 n squared; the difference of squares
4 m squared minus 20 m n + 25 n squared; a perfect square trinomial
4 m squared minus 20 m n + 25 n squared; the difference of squares




Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?
Negative 4 x Superscript 4 Baseline y Superscript 6
Negative 8 x Superscript 4 Baseline y Superscript 6
StartFraction 4 x Superscript 4 Baseline Over y Superscript 6 EndFraction
StartFraction 8 x Superscript 4 Baseline Over y Superscript 6 Baseline EndFraction




Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction




What is the product?

(x + 3)(2 x minus 1)

2 x squared minus 3
2 x squared + 6 x
2 x squared + 5 x minus 3
2 x squared + 6 x minus 3




What is the product?

(5r − 4)(r2 − 6r + 4)

5r3 − 34r2 + 44r − 16
5r3 − 4r2 + 14r − 16
5r3 − 6r − 16
5r3 + 10r − 16

Answer 1

Here are the answers (with brief work):

1) Value after 4.5 years: V = 25000(0.8)^4.5 ≈ 25000(0.3660) ≈ $9,159. (Second choice)

2) Perimeter = 2(2x^2 −16 + (−x^2 +4x +1)) = 2x^2 +8x −30. If x=3, perimeter = 12 ft. (Fourth choice)

3) Profit = Revenue − Cost = (2x^3+30x−130) − (2x^3−3x−520) = 33x + 390. (Fourth choice)

4) (4x^2 + 14x − 9) ÷ (x + 5) gives quotient 4x − 6 with remainder 21 → 4x − 6 + 21/(x+5). (Choice: "4x − 6 +")

5) Difference = 6x^6 − 4x^5y − 3x^3y^4 − 10xy^5 → 4 terms, degree 7. (Fourth choice)

6) 3y^2 + (y+7)^2 − 15 = 4y^2 + 14y + 34. (Third choice)

7) T^2 = A^3 ⇒ T ∝ A^(3/2). If A increases by factor k, T increases by k^(3/2). (Fourth choice)

8) (7y^2 + 6xy) − (−2xy + 3) = 7y^2 + 8xy − 3. (Second choice)

9) (−2m + 5n)^2 = 4m^2 − 20mn + 25n^2, a perfect-square trinomial. (Third choice)

10) (16 x^8 y^(−12))^(1/2) = 4x^4 / y^6. (Third choice)

11) (x^(1/2) y^(−1/4) z)^(−2) = y^(1/2) / (x z^2). (Third choice)

12) (x+3)(2x−1) = 2x^2 + 5x − 3. (Third choice)

13) (5r − 4)(r^2 − 6r + 4) = 5r^3 − 34r^2 + 44r − 16. (First choice)