High school math

algebra

100

 Solve the system of equations for x and y:

2x+3y=7

4x−y=5 

x= 2 and y=1/3

200

x^2-2x-24

x==6,-4

300

e^x=e^4x

x=0

400

If log⁡5(2x+3)=2 find x.

x=11

500

Solve for x given that x^2−4x+7=0 Express your answer in the form a±bi

x=2+-i

calc/stats

100

Derivative of x^2

2x

200

Express cos(2x) in terms of cos(x) and sin(x)

cos^2(x)- sin^2(x)

300

lim_x->3(x²-9)/(x-3)

6

400

derive x^3+6x^2-4x+2

3x^2+12x-4

500

 sin(arctan(x)) in terms of x

X/(sqrt(1+x^2))

geometry

100

If sin⁡(x)=3/5 and x is in the first quadrant, find cos⁡(2x)

-7/25

200

Triangle ABC has an area of 40 units^2 . Point D is on side AC, and AD:DC = 3:1. What is the area of triangle BDC?

10

300

A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone’s volume lies inside the cylinder? Express your answer as a common fraction.

4/9

400

A sector of a circle has a central angle of 120∘ and an area of 24 square units. Find the radius of the circle.

4

500

Find the equation of the line that is the perpendicular bisector of the line segment joining the points (1,2)and (7,−4)

y+1=1/3(x-4) or y=1/3x-7/3

logic puzzles

100

4, 16, 256,

find the next term

65536

200

find the general formula for the following geometric sequence

5,10,20,40, 80

5(2)^(n-1)

300

find the 6th term of the following sequence given the a2=6

a4=3

0

400

You have 9 balls that look identical but one of them is slightly heavier or lighter than the others. You have a balance scale and can only use it twice. How can you determine which ball is the odd one out and whether it is heavier or lighter?

• Divide the 9 balls into three groups of 3 balls each: Let’s label them as Group 1, Group 2, and Group 3.

• Weigh Group 1 against Group 2:

  • Case 1: If they balance, then all balls in Group 1 and Group 2 are normal. The odd ball is in Group 3.
    • Weigh two balls from Group 3 against each other.
      • If they balance, the ball not weighed is the odd one, and you can determine if it’s heavier or lighter by comparing it to one of the normal balls.
      • If they don’t balance, you will know which one is odd and whether it’s heavier or lighter by seeing which side is heavier or lighter.
  • Case 2: If they do not balance, then the odd ball is in either Group 1 or Group 2, and you know which group has the odd ball.
    • Weigh two balls from the heavier side of the imbalance against each other.
      • If they balance, the odd ball is in the remaining group of 3 balls not weighed, and you can find it as described in Case 1.
      • If they don’t balance, you will know which ball is the odd one and whether it’s heavier or lighter based on the balance.

500

A sequence of numbers follows a certain pattern: 1, 11, 21, 1211, 111221. What comes next in the sequence?

312211

random trivia

100

What is the absolute difference between the mean and median of the first 100 positive integers?

0

200

10!

3628800

300

What is the limit definition of a derivative. 

lim_x->0(f(x+h)-f(x))/h

400

10c2

45

500

What is the 40th positive odd integer?

79