Math Jeopardy (Better think properly)

Algebra

100

Solve the equation, 3(x - 3) = 30.9

10.3

200

In a class, 40% are girls. Soon, 2 girls leave and 2 boys arrive. Now, 30% of the class are girls. How Many girls were there originally

8

300

let u₁ = 5, and u_{n + 1} - u_n = 3 + 4(n - 1), for positive values of n. The sum of coefficients in the nth term is

5

400

Solve the equation x⁴−6x³+15x²−18x+10 = 0

1 + i, 1 - i, 2 + i, 2 - i

500

The sum of the first 2011 terms of a sequence is 200. The sum of the first 4022 terms is 380. Find the sum of the first 6033 terms

542

Geometry

100

In a right triangle, sides are 25 and 30. Calculate the 3rd side (no calculators)

sqrt 305

200

A square of area 40, is inscribed in a semicircle. Calculate the area of the semicircle

25 * pi

300

A right triangle has perimeter 32 and area 20. What is the length of the hypotenuese

59/4

400

Points a,b,c,d,e and f lie in a line in that order, dividing it into 5 segments of length 1. Point G is bot on line AF, Point H lies on GD, Point J lies on GF. GF, HC, JE, and AF are parallel. Find HC/JE

5/3

500

Calculate sin 7a

7sin(x) - 56sin³(x) + 112sin⁵(x) - 64sin⁷(x)

Statistics

100

2 fair die are rolled. calculate the probability of the most possible outcome

1/6

200

Calculate the mean, 1,2,3,4,5,6,7,8,9,9,10,10,11,11,13. 

7.267

300

A coin is flipped 3 times and another coin is flipped 4 times. What is the probability that the number of heads obtained is same.

35/128

400

Jacob writes a sequence of numbers. The first term is 6, to generate each succeding term, he flips a coin. If it comes heads, double the previous term and subtracts 1. If it comes tails, Half the previous term and subtract 1. What is the probability the 4th term is an integer

5/8

500

Charles has 2 die. one is fair, one is biased so it comes 6 with probability 2/3, and other 5 sides 1/15. Charles chooses 1 of them, and rolls it 3 times. Given that the first 2 rolls are sixes, the probability that the third roll will also be a 6 is p/q, where p and q are relatively prime. find p + q

167

Pre calculus

100

what is i^123456789

i

200

Differntiate x² - 6x + 5

2x - 6

300

Differntiate sin (x + y)

cos (x + y)/ 1 - cos(x + y)

400

Find the area under the curve x² - 4 = y

-10.67

500

integrate sin² x

x/2 - sin(x)/4 + c

Number theory

100

Prime factorize 1234567. 

127 x 9721

200

What is the units digit of (13¹⁵⁰⁶⁷ - 9⁴⁵) * 16¹²⁹⁶⁷

6

300

For how many positive integers does 1 + 2 + 3 .... + n evenly divide 6n

5

400

How many perfect squares are divisors of 1! * 2! * 3! * 4! * 5! * 6! * 7! * 8! * 9!

672

500

How many positive integers have exactly 3 proper divisors, each less than 50 (excluding the number itself)

109