AP Calc Review Game
Curve C is described by the equation 0.25x² + y2 = 9. Determine the y coordinates of the points on curve C whose tangent lines have slope equal to 1.
-3 sqrt(5) / 5 , 3 sqrt(5) / 5
Let P(x) = 2 x3 + K x + 1. Find K if the remainder of the division of P(x) by x - 2 is equal to 10
-7/2
What is the derivative of cotx?
-csc^2x
What is the derivative of cscx?
-cscxcotx
What is the derivative of cosx?
-sinx
An ice sculpture in the form of a sphere melts in such a way that it maintains its spherical shape. The volume of the sphere is decreasing at a constant rate of 2pi cubic meters per hour. At what rate, in square meters per hour, is the surface area of the sphere decreasing at the moment when the radius is 5 meters?
4pi/5
How many feet are in a mile?
5280
find dy/dx of 2x³sin(x)+(1/x)tan(x)+sec(x)+2
6x2 sin(x) + 2x3 cos(x) - (1/x2)tan(x) + (1/x) sec2(x)) + sec(x) + x sin(x) sec2(x)
There are 100 pairs of dogs in a zoo; a pair of babies are born for each dog. Unfortunately, 23 of the dogs have not survived. How many dogs are left in total?
977
A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top?
99 days
The expression (3x − 4y²)(3x + 4y²) is equivalent to:
9x² − 16y⁴
A group of students were standing in the blazing sun facing due west on a march past event. The leader shouted at them: Right turn! About turn! Left turn! At the end of these commands, which direction are the students facing now?
East
Extreme Value Theorem
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.
When you rotate a shape to create a solid around the y axis using the cylindrical shell method what do you put the equations in terms of?
In terms of "x"
If the number of scones Mary can make in a day is equal to the value of f'(32.16932) and f(x)= cos(tan(3x²+2x)) how many scones can Mary make in a day?
She eats 1751 scones
If Mary can make ∫f''(x) number of scones in a day from 2 to 15,000 and f(x) = (2x² + 13x - 13)/(4.05x³). How many scones can she make in a day?
She eats 2.1786523x10⁻¹⁰ scones
If Mary can make ∫sin(3x³) from 35.2 to 312.0005 in a day, how many scones can Mary make in a day?
She eats 38459 scones
If the number of scones Mary can make in a day is equal to MRAM of -2x⁶+9x⁵-x²+135.24 with the intervals of (2,3)(3,7)(7,23.5)(23.5,23.6).
She eats 568591319 scones
If the number of scones Mary can make in a day is equal to the difference between the values of the local maximum and minimum of the equation 2x³+5x²-6x+10. How many scones can Mary make?
She makes 12 scones
If the number of scones Mary can make in a day is equal to the volume of the shape made by the lines x³-2x+8 and 2x+4 from -2 to 3 when rotated around the line y=-1 how many scones can Mary make in a day?
She makes 1706 scones
If Mary can make f'(15.2) number of scones in a day and f(x) = 23x^5 + 4x^3 - 2x^2 how many scones can Mary make in a day?
She makes 6141352 scones
The temperature of a room, in degrees Fahrenheit, is modeled by H, a differentiable function of the number of minutes after the thermostat is adjusted. What is the best interpretation of H'(5)=2 ?
The temperature of the room is increasing at a rate of 2 degrees Fahrenheit per minute, 5 minutes after the thermostat is adjusted.
Washer Method
V = π∫([R(x)]²-[r(x)]²)dx
Disk Method
V = π∫[R(x)]² on x=a to x=b
What theorem is the instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
What theorem is the instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
Which of the following defines a function f for which f ( -x)=-f( x)?
Which of the following defines a function f for which f ( -x)=-f( x)?
x³+y³+z³=42
X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.
What is the acceleration at t=1 given v(t) = 3t^2-8t+4
a = -2
local maximum
f'(x) goes from + to -
local minimum
f'(x) goes from - to +
Average Value of a Function
f(c) = (1/b-a)∫f(x)dx on a to b
A derivative does not exist when there is a
hole, jump, vertical asymptote, sharp turn, vertical tangent
What is the Definition of Derivative?
lim h->0 f(x+h)-f(x)/h
∫ 2x / (x² - 1)
ln(x+1) + ln(x-1) + C
A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?
never
The graph of function g defined by g(x)= (x³+2x²-3x)/(x²+2x-3) will have vertical asymptotes at...
no real value of x
d/dx(xⁿ)
nxⁿ⁻¹
What is the derivative of tanx?
sec^2x
What is the derivative of secx?
secxtanx
Product rule: d/dx(uv)
u'v + uv'
Find the solution to the differential equation dy/dx = cos(x) / y2 , where y(π/2) = 0.
y = (3 sin(x) - 3)^(1/3)
The set of all points (ln(t - 2) , 3t), where t is a real number greater than 2, is the graph of...
y = 3(e^x+ 2)
average velocity
∆x/∆t
Fundamental Theorem of Calculus
∫f(x)dx from a to b = F(a) - F(b)[where F'(x) = f(x)]
A cellphone and a phone case cost $110 in total. The cell phone costs $100 more than the phone case. How much was the cellphone?
$105
The day before yesterday I was 25. The next year I will be 28. This is true only one day in a year. What day is my Birthday?
December 31
If Dylan has 73 5 oz chocolate bars and he eats 72 of them what does Dylan have now?
Diabetes
If the powers in the numerator and the denominator are the same
Divide them to get the horizontal asymptote
The graph of f(x) and that of f(x + 2) are the same
False
What can you put between a seven and an eight so that the result is greater than a seven but less than an eight?
a decimal
What is the derivative of sinx?
cosx
velocity
d/dt(position)
acceleration
d/dt(velocity)
d/dx(lnn)
(1/n)(dn/dx)
d/dx [arcsin(u/a)]
(1/√a²-u²)(du/dx)
When is the particle moving left given v(t) = 3t^2-8t+4
(2/3, 2)
d/dx[arctan(u/a)]
(a/a²+u²)(du/dx)
d/dx[arcsec(u/a)]
(a/|u|√u²-a²)(du/dx)
d/dx(aⁿ)
(aⁿ)(lna)(dn/dx)
d/dx(eⁿ)
(eⁿ)(dn/dx)
Quotient rule: d/dx(u/v)
(u'v - uv')/v²
point of inflection
- concavity changes - f''(x) goes from - to + or + to -
d/dx[arccotx]
-1/1 + x²
d/dx[arccscx]
-1/|x|√x²-1
d/dx[arccosx]
-1/√1-x²
d/dx(log₀x)
1/xln0
(x-2)<0 if and only if
2<x<3
2+2
3+1
When Miguel was 6 years old, his little sister, Leila, was half his age. If Miguel is 40 years old today, how old is Leila?
37
There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket?
4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it.
f and g are functions such that f'(x) = g(x) and g'(x) = f(x). The second derivative of (f . g)(x) is equal to
4 g(x) f(x)
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother times her age?
41 years ago
There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
42.5
Two girls were born to the same mother, at the same time, on the same day, in the same month and the same year and yet somehow they're not twins. Why not?
Because there was a third girl, which makes them triplets!
You have a 3-litre bottle and a 5-litre bottle. How can you measure 4 litres of water by using 3L and 5L bottles?
First, fill 3Lt bottle and pour 3 litres into 5Lt bottle. Again fill the 3Lt bottle. Now pour 2 litres into the 5Lt bottle until it becomes full. Now empty 5Lt bottle. Pour remaining 1 litre in 3Lt bottle into 5Lt bottle. Now again fill 3Lt bottle and pour 3 litres into 5Lt bottle. Now you have 4 litres in the 5Lt bottle. That's it.
If the highest power of x is on the bottom
Horizontal asymptote is y=0
What is the Intermediate Value Theorem?
If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k
Tardigrade
Is a bear
Rolle's Theorem
Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).
If 3x²+2xy+y²=2 then the value of dy/dx at x=1 is
Not defined
What is the capital of kazakhstan
Nur-Sultan
Dylan's favorite color
Pink
What math questions are on the ACT?
The ACT Math Test usually breaks down into 6 questions types: pre-algebra, elementary algebra, and intermediate algebra questions; plane geometry and coordinate geometry questions; and some trigonometry questions.
3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. The shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop. Now, the effective amount paid by each person is Rs.9 and the amount given to the beggar is Rs.2. So, the total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30?
The logic is payments should be equal to receipts. We cannot add the amount paid by persons and the amount given to the beggar and compare it to Rs.30.The total amount paid is ₹27. So, from ₹27, the shop owner received 25 rupees and beggar received ₹ 2. Thus, payments are equal to receipts.
The average rate of change of the function f defined by f(x) = sin(x) + x on the closed interval [0 , pi] is equal to
1
Robert and David played several golf matches against each other in a week. They played for a pizza at each match, but no pizzas were purchased until the end of the week. If Robert and David had the same number of wins at any time, those pizzas were canceled. Robert won four matches (but no pizzas), and David won three pizzas. How many rounds of golf were played?
11
Functions f, g and h are defined as follow: g(x) = f(x2), f(x) = h(x3 + 1) and h'(x) = 2x + 1. g'(x) =
12 x¹¹ + 18 x⁵
What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?
14.5
There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
141
A race car is traveling on a straight track at a velocity of 80 meters per second when the brakes are applied at time t=0 seconds. From time t=0 to the moment the race car stops, the acceleration of the race car is given by a(t)= -6t²-t meters per second per second. During this time period, how far does the race car travel.
198.766 m
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?
2 dozen
∫ x - 8x² + 2x - 8
2 ln(x+4) - ln(x-2) + C
A 300 ft. train is traveling 300 ft. per minute must travel through a 300 ft. long tunnel. How long will it take the train to travel through the tunnel?
2 minutes
Tom was asked to paint numbers outside 100 apartments, which means he will have to paint numbers one through 100. How many times will he have to paint the number eight?
20 times
What do the graphs, y=0{-2≤x≤2}, y=sqrt(-x²+4) {-2≤x≤(-6/4)}, y=sqrt(-(x+0.09)²+2) +1.12 {(-6/4)≤x≤-1.1}, y=sqrt(-(x+0.8)²+6)-.3 {-1.1≤x≤.99}, y=sqrt(-(x+0.8)²+9)-1 {1≤x≤2}, (y-1)²+(x+1)²=0.0001, (y-(1/2))²+(x-1)²=0.0001 create the shape of?
A blueberry scone
What is the street corner at the coordinates (1.05838678437 = 12^(1/x)), (0.96030639525 = 35^(1/x))?
CTH J and CTH Y
Chain rule: d/dx[f(u)]
f'(u)(du/dx)
Critical Point
f'(x) = 0 or undefined (and endpoints on closed interval)
