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Probability
Speed and acceleration
Trigonometry
Algebra
General
100
If you flip 2 coins, what is the probability of getting two heads?
1/4 (0.25)
100
If the velocity of the object is presented by the formula 4x^2+3x+1 find the equation of acceleration.
8x+3
100
Simplfiy 2(sinxcosx+cos^2x)-1
sin2x+cos2x
100
2x+y=13 2y=17 Find the value of y and x
y=8.5 x=2.25
100
Write 73 in binary system
１００１００１
200
If you roll 2 dices (six sides), what is the probability of getting sum of the numbers lower than 5? (Including 5)
5/18
200
The equation of the velocity is 4t^3+7t^2+6, find the acceleration when time(t) is equal to 4 second.
220
200
In triangle LMN, LM=5.3cm, MN=7.9cm, angle M=127 degrees. Find LN.
11.9 cm
200
Factorize 9x^2+36
9(x+2)(x-2)
200
Prove why x=(-b±√b^2-4ac)/2a works
ax^2+bx+c=0 x^2+(b/a)x+(c/a)=0 x^2+(b/a)x=-(c/a) {x+(b/2a)}^2-(b/2a)^2=-(c/a) {x+(b/2a)}^2=-(c/a)+(b/2a)^2 {x+(b/2a)}^2=-(4ac/4a^2)+(b^2/4a^2) {x+(b/2a)}^2=(b^2-4ac)/4a^2 x+(b/2a)=±√{(b^2-4ac)/4a^2} x+(b/2a)=±√(b^2-4ac)/2a x={±√(b^2-4ac)/2a}-(b/2a) x={-b±√(b^2-4ac)}/2a
300
There is 12 red ball and 5 blue balls in a bag. Draw two ball randomly. What is the probability of getting one ball each color?
15/34
300
The displacement of the object is t^5+5t^3+3t^2+16. Find the acceleration when t=2
226
300
Find sin45cos60tan30 with out using calculator.
√3/6√2
300
a+b=6 ab=2 Find a^2+b^2
32
300
You are going to a fruit shop and buy some fruits. There are apples, oranges and grapes. You are going to buy 5 fruits, but you have to buy at least one of each. You are going to put the fruits in a rectangle box. For example, you will put the fruits like ( A A O O G ) in the box. How many ways are there to put the fruits in the box?
180. 5C2=10 10*3!=60 60*3=180
400
There is a cat in a box with a chemical which may or may not be released. If the chemical is released, the cat will die. The chemical have a 50% chance of releasing. What is the status of the cat in the box?
The cat is both dead and alive
400
The displacement of the object is 13 at t=3. The equation is v=11t^2+2t+3. Find the displacement at t=1.
-(289/3)
400
Find d/dx(sin^2(x)+cos^2(x)+sin2x)
2sin2x
400
123456789X=987654321y X=123456789 Find the value to y^4
5.67*10^28
400
There is a regular tetrahedron with 4cm side. Inside the regular tetrahedron, there is a ball touching all the surface. What is the radius of this ball?
√6/3
500
There are two students playing a game. There are two cards. One card has both side with Red colour, and the other one has one side Red and one side Blue. These cards are in a bag and one student will pick up (without looking). If they saw Red colour on the card, they will guess which colour is the back side. Student A said that back side Red and Student B said it's Blue. What is the probability of student A winning?
２／３ Σ（ｋ＝１０～１９）{１９Ｃｋ×（１／３）＾ｋ　×（２／３）＾（１９－ｋ）}＝０．０６４７６６１７２８
500
The acceleration of the particle is represented by the equation 6t+4. The velocity is 40 when t=5. The displacement is 2 when t=6 find the displacement when t=4
-80
500
find the value of cosecX*cotX*secX
1/cosec^2X
500
Find the results of d/dx(x^4+1/x+1/x^2+3)
3x^3-1/x^2-2/x^3
500
Prove why 0!=1
n! = n.(n-1)(n-2)....3.2.1 i.e. n! = n.(n-1)! i.e. (n!/n) = (n-1)! now substituting n =1 in the above equation (1!/1) = (1-1)! i.e. 1 = 0!