Algebra 2 Test #1

Reviewing Algebra

100

What is the formula for slope

(y_2-y_1)/(x_2-x_1)

200

What is the value of x in the equation:
3(x−4)+8=17

x = 7

300

Solve for x with variables on both sides:
5x−2=4(x+4)+2x

x = -18

400

A line passes through the points (3, -5) and (7, 2). Calculate the slope.

m = 7/4

500

A line passing through points (1,4) and (x,8) has a slope of 2. This is the value of x.

x = 3

Simplifying Radicals

100

What is the number inside the radical called?

The radicand

200

Simplify 

sqrt90

3 sqrt 10

300

Simplify 

sqrt(72n^3)

Answer = 

6n sqrt2n

400

Simplify

4 root(4)(32n^4)

Answer = 

2n root(4)(2)

500

Simplify 

root(6)(512m^2n^6p^12)

Answer = 

2np^2 root(6)(8m^2)

Adding and Subtracting Radicals

100

Simplify 

40 sqrt2 +30 sqrt2

70 sqrt2

200

If the length of one side of a square is represented by  

sqrt50

and another side is represented by

2 sqrt2

, what is the sum of these two lengths expressed in simplest radical form?

sqrt 50+ 2 sqrt2

5 sqrt2 + 2 sqrt2

7 sqrt2

300

Simplify 

-3 sqrt6 -3 sqrt20 - 3sqrt45

-3 sqrt6-15sqrt5

400

Simplify

3 root(3)(24)+ 2 root(3)(81)+2 root(3)(135)

Answer = 

12 root(3)(3)+ 6 root(3)(5)

500

Simplify 

3 root(3)(27)- sqrt3 + 3 sqrt24-sqrt24

Answer = 

9 - sqrt 3+4sqrt6

Multiplying Radicals

100

When you multiply a radical by itself what is the answer.

The radicand. (The number inside the radical)

200

Simplify

3(sqrt5 + 2sqrt6)

Answer = 

3 sqrt5 +6 sqrt6

300

Simplify

2sqrt(5n)(5sqrt(5n)+sqrt(2n)

Answer = 

50n+2nsqrt10

400

Simplify

(3+sqrt5)(4+5sqrt5)

Answer = 

37 + 19 sqrt5

500

Simplify 

(3sqrt2+sqrt(3m))(sqrt2+sqrt(3m))

Answer =

6 +4sqrt(6m) +3m

Dividing Radicals

100

What is the biggest rule when dividing radicals?

There can not be a radical in the BOTTOM (denominator)

200

What is the conjugate use to rationalize the denominator in

(5 +2 sqrt3)/(-6-6 sqrt6)

-6 + 6 sqrt6

300

Simplify 

sqrt6/(5sqrt3)

Answer =

sqrt2/5

400

Simplify

(5 +sqrt5)/sqrt16

Answer = 

(5 +sqrt5)/4

500

Simplify

(3sqrt(3x^3)-4sqrt(x^2))/(5sqrt(5x)-5sqrt(3x^3)

Answer =

(3xsqrt15+9x^2-4sqrt(5x)-4xsqrt(3x))/(25-15x^2)

FINAL JEOPARDY

500

Two trains are traveling on separate routes. The first train covers a distance of the square root of 400 kilometers per hour, while the second train covers the square root of 100 kilometers per hour. After 3 hours, both trains have stopped, and the total distance traveled by both trains combined is needed. What is the total distance traveled by both trains in simplest radical form?

Travel Time = 90 Kilometers