NUMBERS AND STUFF

Rational Expressions

100

4/r+3/2+3/2r

11+3r/2r

200

(xy/z²)/(xz/y)

y²/z³

300

(x²-4/x+3)÷(x²-5x+6/x²-9)

x+2

400

(2x/x²+5x-36)-(10/x+9)

(-8x+40)/(x²+5x-36)

500

(x²-13x+36/x²-x-72)+(x²-3x-54/x²+14x+48)

(2x-13)/(x+8)

Polynomials

100

Simplify: (5x⁴- 3x³+4x)-(2x⁴-x³+2x)

3x⁴-2x³+2x

200

Expand:(2x-5)²

4x²-20x+25

300

Factor: -2x³+4x²+286x

-2x(x+11)(x-13)

400

Simplify: (14x³-8x²+3x)÷2x

7x²-4x+3/2

500

Simplify: (18x⁵-29x⁴+39x²+11x-12)÷(2×-1)

9x⁴-10x³-5x²+17x+14+2/(2x-1)

Speed and Distance Problems

100

A giraffe ran for 1 hour. A mouse ran the same distance in 4 hours. Find the speeds of the mouse and the giraffe, if the speed of the mouse was 39 kilometers per hour less than the speed of the giraffe.

Mouse: 13km/h

Giraffe: 52km/h

200

Jim went from the farm to the service garage at a speed of 18 mph. He then took his motor bike home on the same route at 36 mph. What was the distance between the farm and the garage,  if the whole trip took 30 minutes?

6 miles

300

A plane left the airport at 7 am and flew eastward. A quarter of an hour later, the second plane left the airport in the opposite direction. The planes flew at the same speed and were 1400 kilometers apart at 8 am. Find the speed of the planes.

800km/h

400

A train left San Antonio at 3 am heading for El Paso, which is 600 miles away. 10 hours later, another train leaves El Paso heading for San Antonio at the same speed. If the trains meet at 2 PM, what is the speed of the trains?

50 mph

500

Ship A sails from the Seaforth dock toward the Hornby dock in Liverpool. At the same time, ship B sails from the Hornby dock towards the Seaforth dock on the same route. Ship B sails 12 mph faster than ship A. They pass each other 15 minutes after departure.

a. What is the speed of the ships, if they are 5 miles apart?

b. How far did each ship sail before they met?

a. A= 4 mph        B= 16 mph

 b. A=1 mile         B= 4 miles

Questions Bentley Got Wrong

100

Find four consecutive even integers such that three times the sum of the first and third integers is four greater than the opposite of the fourth integer.

-2,0,2,4

200

| 7-3³|÷2-[(5²+7)÷8]+(1/3^-2)

15

300

Factor:  -5x²y²+5a²b²

5(ab-xy)(ab+xy)

400

Simplify: (x²-5x-6/x²-4x-21)×(x³+3x²/x³-6x²)

x+1/x-7

500

Solve the system of equations. Express your answer as an ordered pair.

-3x+2y=-4

2y+x=4

(2,1)

GOOD LUCK!!!

100

What are the first 25 digits of Pi?

3.141592653589793238462643

200

What is the least known country?

+200 for correct capital.

Tuvalu

Funafuti

300

What is the distance between the Sun and Pluto?

3.67 billion miles

400

Exactly how many episodes of "The Simpsons" are there?

787 episodes 

500

When was algebra created? Span of 400 years.

2000-1600 BC