Number Theory 1
How many unique prime numbers does 1260 have?
(20s is the goal)
4
2, 3, 5, 7
Let a(n)=5n+1 be a sequence where a(4) = 12.
What is a(7)?
(20s)
1531
What is the value of S if S = 5 + 16+27+....148?
(20s)
1071
14/2(1+148)
What is (2cis(30))^5?
Write your answer in both polar form and rectangular form.
(40s)
32cis(150) = 32cos(150)+32isin(150)
=-16sqrt(3) +16i
What is the exact value of sin(60+A)
(30s)
sqrt(3)/2*cos(A)+1/2sin(A)
How many numbers under 100 are both a Fibonacci number and a Sophie Germain Prime?
(20 seconds)
4
2, 3, 5, and 89
In a geometric sequence, a(5) = 3072 and a(8) = 196608. What is a(2)?
(30s)
48
What is the value of the following infinite series?
400*(.2)^(n-1)
500
z^3 = i. What is the answer in the 2nd quadrant of the complex plane? Write your answer polar form and rectangular form.
(30s)
cis(150) = -sqrt(3)/2 + 1/2i
What is the exact value of tan(135+A)?
(-1 +tan(A))/(1+tan(A))
The area of a rectangle is 14017. The sides are safe primes. What is the perimeter?
(30s)
476
Safe Primes = 107 & 131
If the first two values of a Fibonacci Sequence are A and 3B, what is the expression of the 8th term of the sequence?
(30s)
8A + 36B
A, 3B, A+3B, 2A+6B,....
What is the exact value of the following infinite series?
(3pi/8) - (3pi/8)^3 / 6 + (3pi/8)^5 /120 - (3pi/8)^7 / 5050+.....
(30s)
sqrt(2 +sqrt(2))/2
(30s)
1/2
If sin(2A) = 2cos(A), then what is the value of A?
(20s)
90 or pi/2
How many sophie germain prime numbers does the prime factorization of 1350 have?
3
2, 3, & 5
The 28th Fibonacci number is 317,811 and the 29th Fibonacci number is 514,229.
What is the 26th Fibonacci Number?
(30s)
121393
F(29) - F(28) = F(27)
F(28)-F(27) = F(26)
A machine is changing the length (L) of a rectangle by doubling and it's width (W) is shrinking by a 3rd. This change happens every minute and the area of each shape is added together. What is the total area combined if the machine continues to work forever?
(40s)
3LW or 3 times the original
If z^4 = 81cis(44), then what could be the value of z^3?
(30s)
27cis(33)
If f(x) = cos(x) + sin(7x), what is the exact value of f(15)?
40s
(sqrt(2)+sqrt(6))/2
Every Prime Number Greater Than 3 is either one more or one less than a multiple of 6. Which of the following huge numbers are prime?
a) 7749
b) 7741
c) 7501
d) 7683
(30s)
b
7741 -1 = 7740/6 = 1290
As n keeps getting larger and larger in F(n) = the Fibonacci Sequence, what value does F(n)/F(n-1) get closer and closer to?
a) 1.718
b) 1.618
c) 1.688
d) 1.554
(20s)
b
What is the value of z?
z = sum(n=1, 30, 2n+1)/sum(n=1, inf, 400*(1/4)^n-1
3/5
What is the exact value of 4cis(105) written in rectangular form?
(30s)
2sqrt(2)
If f(x) = sin(x), which statements are true?
A) f(50) = cos(25)-sin(25)
B) f(28) = 2sin(14)cos(14)
C) f(40) = sin(20)cos(20)
D) f(100) = 2sin(200)cos(200)
B