MHF 4UG Review Units 1-5

Unit 1 ~ Polynomial Functions

100

What is the degree of the polynomial function

f(x) = x² (x - 2)² 

4

200

The x-intercept(s) of

 f(x) = - (2x + 1)³ (x - 3) are...

(-0.5, 0) and (3, 0)

300

State the end behavior of the polynomial equation 

y = 4x³ - 5x² - 6x + 1

3 --> 1

400

Is f(x) = -3x³ + x odd, even, or neither?

Odd

500

A soccer ball was kicked into the air such that its height, h, in meters, after t seconds can be modeled by the function h(t) = -4.9t² + 14t +1. Determine the AROC of the height of the ball for the time interval [0, 0.5] if h(0) = 1m and h(0.5) = 6.775m. State your final answer in a complete sentence.

AROC = 6.775 - 1/ 0.5 - 0

AROC = 11.55m

Therefore, the height is increasing at an average rate of 11.55m/s

Unit 2 ~ Polynomial Equations and Inequalities

100

Solve x³ - x² - 2x = 0

x= 0, 2, -1

200

Solve 2 - 4x > 5x + 20

-2 > x

300

Divide (5x³ + 7x² - 8x - 4) by (x-2) using synthetic division. Conclude with a multiplication statement.

(5x³ + 7x² - 8x - 4) = (5x² + 17x + 26) (x - 2) + 48

400

The remainder theorem is if ___ is divided by ___ then the remainder equals ___.

Fill in the blanks using the variables P(x), P(a) and x-a

The remainder theorem is if P(x) is divided by x-a then the remainder equals P(a)

500

Solve (x + 3) (x - 5) > 0

-3 < x < 5

Unit 3 ~ Rational Functions

100

Determine the y-intercept of the equation

 y = x - 1 / x + 2

(0, -0.5)

200

Determine the x-intercept of the equation

y = 7 / x + 2

Undefined / No x-intercept

300

Determine the vertical, horizontal (or oblique) asymptotes of the equation y = 3 / x + 5

V.A. is x = -5

H.A is y = 0

400

Simplify and solve for x.

4 / 3x - 5 = 4

x = 2

500

Determine the inverse of the function 

f(x) = x + 5 / x - 1

f^-1(x) = x + 5 / x - 1

Unit 4 ~ Trig Functions

100

The reciprocal of sec x is...

1 / cos x

200

Convert 150 degrees into radians.

5 (3.14) / 6 rad

300

Convert 2.4 radians into degrees.

137.5 degrees

400

Determine the exact value for sec 7(3.14) / 6

sec x = -2 / √3

500

Determine the exact value of sin²3.14/4 + cos²3.14/4

1

Unit 5 ~ Trig Equations

100

Determine the co-function identity that is equivalent to sin 3.14 / 5

cos 3(3.14) / 10

200

What expression is equivalent to sin 5(3.14) / 4. Solve using the related acute angles. 

-sin 3.14 / 4

300

Simplify sin x sec x

tan x

400

Simplify sin x cos x cot x

cos² x

500

Simplify (tan x) + (1 / tan x) 

(tan² x + 1) / (tan x)