Evaluate 1^{2} – 2^{2} + 3^{2} – 4^{2} + 5^{2} – 6^{2} + … + 199^{2}.

## Set 13

## Cube Root, Numbers

What is the cube root of 4^{15} + 6^{9}2^{11} + 6^{10}3^{7} + 3^{24}?

## Non-Obvious Quadratic

If the points (1, *y*_{1}) and (-1, *y*_{2}) lie on the graph of

*y* = *ax*^{2} + *bx* + *c*, and the two points are such that *y*_{1} – *y*_{2} = -6, then *b* equals:

- -3
- 0
- 3
*ac**a*+*c*/2

## Multiply and Factor

Find the smallest root of the equation (x + 5)(x + 3) – (x + 5)(2x + 7) = 0

## Guernsey Holstein

Three Guernsey cows and two Holstein cows give as much milk in four days as two Guernseys and four Holsteins give in three days. Which breed produces more milk, Guernsey or Holstein?

## Horrendous Radical = N

Given this rather horrendous equation, can you find *N* in simplest form?

(Friendly observation: there’s a reason why it’s called *N*.)

## Fraction Not in Lowest Terms

For certain values of the whole number *x*, the fraction

9x + 7 |

6x + 9 |

will not be in lowest terms (simplest form). Explain and give examples.

## Babysitting Awake/Asleep

Holly used to get $2.00 per hour babysitting one child if it was awake and $1.50 per hour if it was asleep. Each additional child was another dollar per hour, awake or asleep. If she took care of *n* children for *x* hours before bedtime and *y* hours after bedtime, how much money did she earn? (The answer is a formula.)

## Baseball Cards

Jared and Willie are always trading baseball cards during their 6th grade math class. When their teacher decided she wasn’t having it any more and confiscated the cards, the other students wailed, in chorus, “That’s not fair; you should give them back.” The teacher, Mrs. Bibble, said, “Well, maybe, but you have to do some thinking first. Try this scenario. On Monday these two come in with their cards. On Tuesday, Jared gives Willie as many cards as Willie already has. On Wednesday, Willie then gives Jared back as many as Jared has left. On Thursday, Jared gives Willie back as many cards as Willie has left. Now here it is, Friday, and Willie has 80 cards altogether, but poor Jared has none. If you can tell me how many cards each of them had on Monday, then I will return the cards. But no more trading in class.” Can you help the boys get their cards back?

## Barbecue Bricks Weight

Stella’s student Jasper is building a barbecue out of bricks. Each brick measures 9 inches by 2 inches by 4 inches. He will use 1200 bricks to do the job. A cubic foot of bricks weighs 95 pounds. What will the bricks for Jasper’s barbecue weigh?