Math competition

Function

100

y = x+4

x=2

y=?

y=6

200

5y/18 = -2x/5 + 4/9

x=15

y= -20

300

x⁴y⁵ + 8x³y² = 18

Find the biggest degree.

9

400

x+y = 6

x² +3y = 22

x,y = ?

x₁=-1   x₂=4

y₁=7   y₂=2

500

BONUS

+500

Combination, Permutation

100

(8-3)!

120

200

P(10, 4)

5040

300

C(9, 5)

96096

400

How many different eight-letter permutations are there of the letters in the word HUMANITY?

40320

500

There are 10 players in a list. A debate coach will choose 6 players from the list for a school team. In how many ways can the coach from the team?

210

Basic identities

100

2021²-2015²

24216

200

101³-99³

60002

300

87²-2*87*67+67²

400

400

(32²-17²)/(70²-35²)

1/5

500

(3a+7)²-(3a-1)²

48a+48

Sequences

100

-3, 2, 7, 12, 17, ... Is it arithmetic sequence or not?

Yes, it is arithmetic sequence

200

-4, 3, 10... are the first three terms of an arithmetic sequence. Find the eleventh term

66

300

a₄=5 and a₉=30. Find the common difference

5

400

b₅=16, q=-1/2. Find b_12.

-1/8

500

q=2, b₁=7, and S_n=889. Find n.

7

Trigononetry

100

sin 60

sqrt3/2

200

2*sin45 + 3*cos60

sqrt2 + 3/2

300

Find the range of the function: y=2*sinx+1

[-1, 3]

400

sin(π /2 - a) + cos (π + a)

0

500

tan195

2- sqrt3