Euler
What is sin of 3π/4?
sin(3π/4)=1/√2
The derivative of .5x2
x
What is a way of arranging objects or values where order does not matter? (combination or permutation)
combination
What is cosine of 2π/3?
cos(2π/3)= −1/2
log3 9
2
Solve for x log2x+log2(x-2)=3
x = 4
List the transformations in order for the quadratic equation y=2(x+1)2-7
left 1, vertical dilation by a factor of 2, down 7
225° in radians
5π/4
What is the remainder of the following polynomial: (2x2 + 2x) / (x+1)
What is the general equation for a difference of squares?
a2-b2=(a+b)(a-b)
Factor the polynomial:
x3+7x2+10x
x(x+5)(x+2)
Find the inverse of the equation y=4x^2-3
y=sqrt((x+3)/4)
There are 2 green marbles, 3 blue marbles, and 1 red marble. The probability of getting a green marble on the first pick and a red marble on the second with replacement
1/18
n!/(n-r)!r! is the formula for
Combinations
Find the domain and range. f(x)=(2x2)/(x4)+1
Range: (1,infinity)
Domain: R\{0}
Divide the polynomial by long division.
(3x2+7x-20) / (x+4)
3x-5
Twenty athletes compete in an olympic event. Write down how you would calculate the number of permutations for each one winning gold, silver, and bronze.
20 x 19 x 18
You have six pizza toppings. You create as many 3-topping pizzas as possible. How many different pizzas can you make?
20 different pizzas
Given the solutions x = -9 and x = 1/3, what would be the factors that would represent the quadratic?
(x+9)(3x-1)
What is the range, amplitude and period of y=3sin(2x)+3?
Range: [0,6]
Amplitude=3
Period= π
limx→3 (x2-x-12)/(x+3)
-1
Integrate
∫10/x2 dx
−10/x+C
Complete the square to find the coordiantes of the turning point: 2x^2 + 6x + 2
(-3/2, -5/2)
Write down the binomial probability formula
P(Event)=nCr(pr)(1-p)(n-r)
The speed a bike is travelling in metres per second after t seconds is given by the function
f:[0, 4] → R, f(t) = t2
Given that the bike is 10 m away after 3 seconds, what is the displacement of the bike?
The distance travelled in the first 4 seconds is
x(4) − x(0) = 64/3 meters