Math topics

Algebra

100

(2x²y)/4xy² * 8x/y

4

200

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

find x

x=6; -1 

x not equal +-2

300

If f(x)=x²−4x+7, find the value of f(2a−1).

4a²−12a+12

400

Solve the quadratic equation: 2x²−5x−3=0

x=3

x=-1/2

500

x²+y²=25

x+y=1 

Solve the system of equations using substitution or elimination

x= 4; -3

y=-3; 4

Geometry

100

Find the area of triangle with vertices A(0,0),B(4,0),C(0,3)

Area =1/2⋅4⋅3=6

200

A circle has radius 10. Find the arc length and sector area for a central angle 60.

Convert 60=π/3 rad. Arc length =rθ=10⋅π/3=10π/3.

Sector area =1/2r²θ=1/2⋅100⋅π/3=50π/3

300

Triangle ABC is right-angled at C. Hypotenuse AB=13, leg AC=5. Find BC

12

400

In triangle, two sides are 7 and 9 with included angle 60∘. Find the third side.

c= root of 67

500

Triangle with side lengths 13,14,15. Find its circumradius R.

8.125

Trigonometry

100

sin⁡30∘+cos⁡60∘

1

200

tan⁡45∘⋅cos⁡90∘+sin⁡260∘

3/4

300

sinx=(3^1/2)/2

x=60,120

400

 2sin⁡²x−3sin⁡x+1=0,   0∘≤x≤360∘

x= 30,90,150

500

sinx+cosx=2^1/2

x=pi/4

Logic

100

Alexa's mother has 4 children: Alex, Ceasar, Oscar and who is the fourth one?

Alexa

200

What you can't eat to breakfast?

Dinner

300

Emily has 5 brothers and each brother has 1 sister. How many people in this family?

6

400

There is a round lake. We have an rounded ice at center of lake which freezes the lake 2 times everyday. Ice covers the lake at 14 days. How many days it take to ice cover the half of the lake?

13th

500

Why polar bears do not eat penguins?

Polar bears live in Arctica,  while Penguins live in Antarctica