Math 3 EOC Review

Graphs

100

If f(x) = k(x - 2)⁴, where k is positive and real, what is the effect on the graph of f(x) as k increases? 

The graph of f(x) is stretched vertically.

200

What is a sine function with an amplitude of 2 and a period of 4pi?

y = 2sin(x/2)

300

The graph of the function f(x) = 2x + 5 is stretched horizontally by a factor of 6. What is the function that corresponds to the resulting graph?

f(x) = 12x + 5

400

The function f(x) has (x – 7) and (x + 4i) as factors and f(x) = 2x⁵ – 13x⁴ + 22x³ – 187x² – 160x + 336. What is the total number of real zeros of f(x)?

3

500

The graph of p(x) has 3 distinct zeros:  x = -2 has multiplicity one. x = 1 has multiplicity two. x = 3 has a multiplicity one. p(x) passes through the point (0, -12). What function represents p(x)?

p(x) = 2x⁴ - 6x³ - 6x² + 22x - 12

Exponents and Logarithms

100

Simplify:  (2s⁵)(4s)

8s⁶

200

(3^x)(3^x)(3^x) =

(3^3x) or (27^x)

300

What is the value of log₅(25)?

2

400

log₇(1/49)

-2

500

log₁₆(0.25)

-1/2

Circles

100

What equation describes the circle with center (5, -1) and radius 7?

(x - 5)² + (y + 1)² = 49

200

The equation of a circle is x² + y² - 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle? 

center = (3, -1) and radius = 4

300

The diameter of a circle is 8 centimeters. A central angle of the circle intercepts an arc of 12 centimeters. What is the measure of the central angle in radians?

3 radians

400

Find the center and radius of the circle represented by the equation x² + y² - 4x - 20y + 23 = 0.

Center = (2, 10) and Radius = 9

500

What is an equation to a circle that has center (-2, 3) and passes through (-1, 1)?

(x + 2)² + (y - 3)² = 5

Equivalent Expressions

100

Find the quotient of 8y⁴ + 20y³ divided by −4y²

-2y² - 5y

200

Factor completely by grouping:  16x³ + 12x² - 36x - 27.

(2x + 3)(2x - 3)(4x + 3) (in any order, since order is commutative for multiplication)

300

Factor completely: 27x³ + 125

(3x + 5)(9x² - 15x + 25)

400

Divide the polynomial x³ - 3x² - 6x + 15 by (x - 2)

x² - x - 8 - (1/(x-2))

500

Given f(x) = 2x³ + kx + 14, and (x - 2) is a factor of f(x), then what is the value of k?

k = -1

Equations

100

Solve for x:  -14(log₈(x)) + 19 = 5

x = 8

200

Write a sine function that has an amplitude of 2, a midline of y = 5, and a period of 2/3.

f(x) = 2sin(3(pi)(x)) + 5, or f(x) = -2sin(3(pi)(x)) + 5

300

Solve for x in the following equation:  8(2^{x + 3}) = 48 

x = -3 + log₂6

400

Rewrite the logarithmic equation as an exponential equation and solve for x:  log(x - 6) = 3

10³ = x - 6 and x = 1006

500

Solve for x:  log₈(x) = (5/3)

x = 32