Jeopardy

Exponents and Percentages

100

2^2x+3 = 1/128

x = -5

200

John has $2500 in his savings account. He adds $400 to it in January. Calculate the percentage change in the value of his savings account in January.

16%

300

32^x-3 = 1/16^x+1

x = 11/9

400

3²¹⁰⁶ - 3²¹⁰⁵ = 6n. Find n.

n = 3²¹⁰⁴

500

The list price for a pair of shoes I want is $200. Luckily, I can apply 3 coupons of 40% off, 30% off, and 20% off. What is my total discount as a percentage?

66.4%

Misc

100

Rationalize

1/(√9 + √8)

3 - 2√2

200

Rationalize:

1/(√32 + √50 + √72) 

√2 / 30

300

Rationalize:

2/(√2 - √5 + √7)

(-2√5 + 5√2 + √70)/10

400

If the roots of the equation x² + 3x + 2 = 0 are p and q, find p² + q²

5

500

In (x³ + 2x² + 3x + 7)(x² + 7x + 1) what is the coefficient of x⁴

9

Special Factorizations

100

If a²+ab+b²=9 and c²+2cd+d²=25, what is the least possible sum of a+b+c+d?

-8

200

If a + b = 6 and ab = 1, what is a² + b²?

34

300

What does p³ - q³ factor into?

(p-q)(p² + pq + q²)

400

What is the expanded form of

(a - b)⁵

a⁵ - 5a⁴b + 10a³b² - 10a²b³ + 5ab⁴ - b⁵

500

If a + b = 4, and ab = 2, what is a³ + b³?

40

Quadratics

100

Solve for x:

x² - 7x + 12 = 0

x = 3,4

200

Solve for x:

2x² + 9x + 9 = 0

x = -3, -1.5

300

Factorize:

10x² + 33x + 9

(10x + 3)(x + 3)

400

Solve for x:

x² + 4x - 2 = 0

x = -2 ± √6

500

What is the quadratic formula and how do we derive it?

completing the square

More Misc

100

Solve for x:

18x² + 37x + 15 = 0

x = -3/2, -5/9

200

Evaluate the sum 21 + 28 + 34 + ... + 105

819

300

Find all real numbers x such that

[x/(x-1)] + [1/(x-2)] = 3

x = 2 ± √2/2

400

Let ab = 1 and a² + b² = 2. Find a⁴ + b⁴

2

500

For how many positive integers n does 1 + 2 + ... + n evenly divide 6n?

5