Algebra Cumulative Exam

A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is -16 ft/s2, approximately how many seconds after the launch will the toy rocket reach the ground? h(t) = at2 + vt + h0

3.80 s

Which phrase best describes the translation from the graph y = 2x2 to the graph of y = 2x2 + 5?

5 units up

Which table shows a linear function?

B look at picture

For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?

B- 7/4

Which value must be added to the expression x2 - 3x to make it a perfect-square trinomial?

B- 9/4

What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.

C

What is the product of ?

C

What is the quotient?

C

Which equation is the inverse of y = x2 + 16?

C

Which two functions are inverses of each other?

C

Using the quadratic formula to solve 2x2 = 4x - 7, what are the values of x?

C look at photo

For which pair of functions is ?

C) f(a) = 5 + a2 and g (a) = StartRoot a minus 5 EndRoot minus 2

If f(x) = -x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

D

If is the inverse of and , what is ?

D

The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff, x, working on the project. Which rational function best models the data in the table?

D

Which equation represents a linear function?

y - 2 = -5(x - 2)

Which expression is equivalent to ? Assume .

A

Which expression is equivalent to ?

A look at photo

What property is used in the second step of solving the inequality below?

Addition Property

If a polynomial function f(x) has roots mc005-1.jpg and -6, what must be a factor of f(x)?

B

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10?

B

What is the difference?

B

Which expression is equivalent to the following complex fraction?

B

What is the domain of the square root function graphed below?

D

Which graph represents the function f (x) = StartFraction 2 x minus 1 Over x minus 1 EndFraction?

D

What is the binomial expansion of (x + 2y)7?

D) x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7

If f(x) is an odd function, which statement about the graph of f(x) must be true?

It has rotational symmetry about the origin.

Which statement best describes the effect on the graph of y = (x - 9)2 if the equation is changed to y = (x + 9)2?

The graph moves left 18 units.

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = (x3 - 3x + 1)2

6 roots

If f(x) = x2 - 1 and g(x) = 2x - 3, what is the domain of ?

A

The graph of f(x) = 4x3 - 13x2 + 9x + 2 is shown below. On a coordinate plane, a function is shown. The function starts from the bottom of quadrant 3 and goes up through the x-axis at (0, negative 0.25) and then through the y-axis at (0, 2). It then starts to curve down at (0.5, 4) until it reaches (1.75, negative 0.5). It then curves up and crosses the x-axis at (2, 0) and goes up approaching x = 3. How many roots of f(x) are rational numbers?

3

The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the roots of f(x)?

3, 4, 5, 6

Alice's backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2. What is the approximate width of her backyard? A = lw

22.4 m

Which expression is equivalent to ?

2a

The polynomial equation has complex roots . What is the other root? Use a graphing calculator and a system of equations.

-1

The values in the table represent the graph of a continuous function. Which interval must contain an x-intercept?

-2.3 < x < -1.9

Sandra graphed the system of equations that can be used to solve What are the roots of the polynomial equation?

-3, 4

What is the value of (-3 + 3i) + (-2 + 3i)?

-5 + 6i

What is the third term in the binomial expansion of (3x + y3)4?

18x2y6

Which expression is equivalent to -8?

2-3

What is the approximate value of a local maximum for the polynomial?

2.5

The graph below shows the function .Which statement is true?

There is a hole at x = 3 and an asymptote at x = -1.

What is the solution of ?

c = 0 and c = 3

For which interval is the average rate of change of f(x) negative?

from x = 0 to x = 2.5

Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?

look at pic

What substitution should be used to rewrite x8 - 3x4 + 2 = 0 as a quadratic equation?

u = x4

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

x + 2

One root of is x = -10. What are all the roots of the function? Use the Remainder Theorem.

x = -10, x = -5, or x = 5

Solve for x in the equation x squared minus 14 x + 31 = 63.

x = -2 or x = 16

The quotient of (x4 - 3x2 + 4x - 3) and (x2 + x - 3) is a polynomial. What is the quotient?

x2 - x + 1