Evaluate 12 – 22 + 32 – 42 + 52 – 62 + … + 1992.
Set 13
Cube Root, Numbers
What is the cube root of 415 + 69211 + 61037 + 324?
Multiply and Factor
Find the smallest root of the equation (x + 5)(x + 3) – (x + 5)(2x + 7) = 0
Non-Obvious Quadratic
If the points (1, y1) and (-1, y2) lie on the graph of
y = ax2 + bx + c, and the two points are such that y1 – y2 = -6, then b equals:
- -3
- 0
- 3
- ac
- a + c/2
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?
Waterbed Weight
Sammy wants to buy a waterbed. It’ll put a lot of strain on the floor of her room. The bed she wants is 4 feet wide by 6 feet long by 8 inches deep. The casing weighs 3 pounds. A cubic foot of water weighs 62.4 pounds. What will the whole thing weigh when it’s full?