Unit Five Test Review

Words Problems

100

You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft above you. The height of the grappling hook you throw is given by the function h(t) = – 16t2 + 32t + 5 . What is the maximum height of the grappling hook?

21 feet

200

Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t2 + 16t + 480 , where t is the time in seconds and h is the height in feet.

How long did it take for Jason to reach his maximum height?

0.5 seconds

300

The Vertical height, in feet, of a section of a roller coaster track is modeled by the equation given below, where x represents the horizontal distance, feet. 

f(x)=-0.14x²+2.8x+6 

What is the maximum height, in feet, of the section of the roller coaster? 

20 feet

400

The shape of the supporting arch under a bridge can be seen by graphing the function below, where t is the horizontal distance between the arch in meters. 

b(t)=-0.14t²=1.4t

What is the vertex of the function? 

(5,3.5)

500

You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t) = -16t2 + 12t . What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?

2.25 feet. No. 

GCF & Diff. of Squares

100

x²-9

(x-3)(x+3)

200

6m-24

6(m-4)

300

25-b²

(5+b)(5-b)

400

(4x²-16)

(2x-4)(2x+4)

500

12x²-28x+20

4(3x²-7x+5)

'Drop it Drop it" and "Rainbow Method" Factoring

100

x²+7x+12

(x+4)(x+3)

200

Factor: 

x²-5x+4

(x-1)(x-4)

300

find the zeros of the following function

f(x)=x²+5x-36

x=-9,4

400

3x²+13x+4

(x+4)(3x+1)

500

4x²+12x+9

(2x+3)(2x+3)

Function Notation & Consecutive Integers

100

h(x) - c(x) 

3x²-x-9

200

h(x) x g(x)

40x²-34-28

300

c(x) - f(x)

-7x²+13x-7

400

Find three consecutive integers whose sum is 51.

16, 17, 18

500

The product of two consecutive integers is 182. Find all possible Paris of numbers. 

-14,-13 & 13,14

Mixed

100

(4x²+5xy-3y²)+(6x²+8xy+9y²)

8x²+13xy+6y²

200

Find the zeros of the following function: 

f(x)= x(x-4)-21

x=-3, 7

300

3x²-27

3(x+3)(x-3)

400

Find three consecutive integers whose sum is -78

-27,-26,-25

500

What is the factored form of the following expression? 

25x²-130x+169

(5x-13)²