AB
BC
Riddles
SAT
Random
100
d/dx (2x)
ln(2) x 2x
100
What is the sum of the following geometric series?
5 - 5/2 + 5/4 - 5/8 + 5/16 - ...
10/3
S = a/(1-r)
100
Using only addition, add eight 8s to get the number 1,000.
888 + 88 + 8 + 8 + 8 = 1,000
100
3x = 12
−3x +y = −6
The solution to the given system of equations is (x,y). What is the value of y?
A) −3
B) 6
C) 18
D) 30
B) 6
100
What classes did Ms. Jung teach last year?
(Name at least two)
Algebra 2 and Calculus AB
200
A function f is defined by f(x)=|x+4|. For what values of x is the graph of f not differentiable?
A: x = -4
B: x = 0
C: x = 4
D: The function is differentiable over its entire domain.
Correct Answer - A
Explanation:
If a graph has a sharp point, the function can't be differentiated at that point because the slopes just before and after the point are different. For example, an absolute value function has a sharp point at its vertex. The graph of 𝑓(𝑥)=∣𝑥+4∣ is just the standard absolute value function, y=∣x∣, moved 4 units to the left. This means its vertex is at (-4, 0), so the function isn't differentiable at 𝑥=−4.
200
integral of (1/(x2-7x-18))dx
(1/11)[ln(x-9)-ln(x+2)]
200
I add six to eleven, and get five. Why is this correct?
Time on a clock
200
Which expression is equivalent to a(11/12), where a>0?
A) a(132/12)
B) a(132/144)
C) a(132/121)
D) a(132/11)
B) a(132/144)
200
How much does it cost to dream?
(hint: look around)
Dreaming is free
300
If a function f is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in the open interval (a,b) such that f'(c) = (f(b)-f(a))/(b-a). What theorem is this?
Mean Value Theorem (MVT)
300
A particle moves in the xy-plane according to the parametric equations x(t) = tan(4t) and y(t) = cos(2t). Find the acceleration vector at t = pi/2.
<0, 4>
Find second derivatives for x(t) and y(t) and plug into vector
300
If a hen and a half lay an egg and a half in a day and a half, how many eggs will half a dozen hens lay in half a dozen days?
24
300
If (ax+2)(bx+7)=15x2+ cx+14 for all values of x, and a+b=8, what are the two possible values for c?
A) 3 and 5
B) 6 and 35
C) 10 and 21
D) 31 and 41
D) 31 and 41
300
In what room does Ms. Jung hold her SGI?
Room 103
400
limx->pi (cos(x) + sin(2x) + 1)/(x2 - pi2)
A) 1/(2pi)
B) 1/pi
C) 1
D) DNE
Answer: B
Explanation:
L'Hopital's Rule
400
The population P(t) of a species satisfies the logistic differential equation dP/dt P(500-(p/4)), where the initial population P(0) = 100 and t is the time in years. What is limit of P(t) as t approached infinity?
A. 19
B. 500
C. 1900
D. 2000
E. 38000
D. 2000
For logistic differential equations, dP/dt goes to zero as t goes to infinity. So, the only solution of P to make dP/dt zero is 2000.
400
One brother says to his younger brother: “Two years ago, I was three times as old as my brother was. In three years time, I will be twice as old as my brother.” How old are they each now?
7 and 17
400
For the exponential function f, the value of f(1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?
A) f(x) = 50(1.6)(x+1)
B) f(x) = 80(1.6)x
C) f(x) = 128(1.6)(x−1)
D) f(x) = 204.8(1.6)(x−2)
B) f(x) = 80(1.6)x
400
What college does Ms. Jung teach?
Hunter College
500
Answer: D
Explanation:
FTC and Chain Rule
500
Answer: C
Explanation:
First, if the integral converges, then the series has to converge too. So, choice D is wrong.
Next, since the graph of g is given and we know it's positive and decreasing, the sum of the series must be greater than the value of the integral. The value of the integral has to be lower than the sum of the series.
500
What is the smallest whole number that is equal to seven times the sum of its digits?
Answer: 21
Explanation:
For a two-digit number 𝑎𝑏, it stands for 10𝑎+𝑏 since the first digit is in the tens place and the second is in the units place. If 10𝑎+𝑏=7(𝑎+𝑏), then 10𝑎+𝑏=7𝑎+7𝑏. Simplifying this, we get 3𝑎=6𝑏, or 𝑎=2𝑏. This means the second digit is twice the first.
500
If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m?
A) m+6
B) m+7
C) 2m + 14
D) 3m + 21
B) m+7
500
Which math teacher was taught by another currently working math teacher at BxSci? (Name Both)
Mr. Weng was taught by Mr. Perna