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Number Thoery

100

Find the GCD of 84 and 126.

42

200

What is the smallest positive integer that leaves a remainder of 2 when divided by 3, 4, and 5?

62

300

Find the last digit of 3¹²³

7

400

Find the smallest positive integer n such that

gcd⁡(n,72)=18 

lcm(n,72)=360

90

500

Find the largest power of 2 that divides

100!

2⁹⁷

Calculus

100

Differentiate 

y=5x³

15x²

200

Integrate 

2x-3

x² -3x+c

300

Differentiate:

y=x²ln⁡x

2x lnx+x

400

Find the equation of the tangent to

y=x³ -3x at x=1

y=-2

500

Find the area enclosed between the curves

y=x² and y=2x  

4/3

Algebra

100

Solve for x

x²-5x+6=0

x=2,3

200

l 2x-5 l=3

x=4,1

300

Solve for x

x⁴-5x²+4=0

1,-1

2,-2

400

x+y=6

xy=5

find x²+y²

26

500

a+b=10

a²+b²=52

find ab

24

Trignometry

100

If sin⁡x=3/5 and x is in the first quadrant, find cos⁡x

4/5

200

Simplify 

1−2sin⁡²30

1/2

300

Simplify in terms of sin

sin45cos30+cos45sin30

sin75

400

Simplify 

cos⁴30−sin⁴30

1/2 or cos60

500

Given

sin⁡x+cos⁡x=1

Find the exact value of

sin⁡³x+cos³⁡x

1