AI SL: Sequences and Series
The 10th term of a geometric sequence that has first term 3 and common ratio -2.
What is u_10=-1536
The amplitude of y=-12sin0.5x
What is 12?
(Nope, the amplitude is NOT negative!)
The number of hearts that an octopus has.
What is 3 ?
Using function notation, the gradient of the curve f(x) when x=-3 , if
f(x)=2x^3+2
What is f'(-3)= 54
The amount of money in the account after 5 years, when an initial sum of $4000 is deposited into an account paying 6% annual interest compounded quarterly.
What is $5387.42
The sum of the first 10 terms of an arithmetic sequence that has first term 5 and common difference -2.
What is -40?
The period of
y=4sin3x
What is 120?
The mean of the data set: (6,3,6,9,2,22,-15)
[3 significant figures]
What is 4.71
The number of eyes that a bee has.
What is 5?
The capital city of Turkey
What is Ankara?
The number of dots on a standard pair of dice.
What is 42 dots?
The capital city of Peru
What is Lima?
The probability that a flight departs on time is P(D)=0.83 , arrives on time is P(A)=0.92., arrives and departs on time is P(AnnD)=0.78
What is the probability that a flight arrives on time, given that it departed on time?
What is 0.940?
Using function notation, the derivative of
f(x)=(x^2+1)(3x-2)
What is
f'(x)=9x^2-4x+3
The amount of money in the account after 3 years, given an initial deposit of $10,000 into an account that pays 8.5% interest per year, compounded quarterly.
What is $12,870.19
The sum of the first 20 terms of the sequence 60, 57, 54,...
What is S_20=630 ?
The y-intercept, expressed as a coordinate point, of the function
y=10(3^-x)+2
What is (0, 12) ?
The first term u1 and the common difference d for an arithmetic sequence where the third term is 10 and the 15th term is 46.
What is u1 = 4 and d = 3?
The anti-derivative with respect to x
int(x+200)/x^4dx
What is
The monthly repayment required when you borrow $1000 at an annual interest rate of 8% compounded monthly and promise to pay it back within 6 months. Answer to 2 d.p.
What is $170.58
The number of terms in the finite arithmetic sequence -3, 5, ..., 1189.
What is n = 150?
The period of y=-12sin0.5x
What is 720?
The period is
360/0.5
Given f'(x)=x^2-x-6 , find the x- coordinates of all stationary points (turning points, local extrema) and identify them as a local maximum or a local minimum.
What is
local maximum at x=-2
local minimum at x=3