Logarithms
Applied Differentiation
Probability
Calculus
True or False
100
5x-4=25x-6
8
100
Use the Incremental formula to estimate, to 3dp, the value of:
sqrt(38)
sqrt38approx6.167
100
The amount of homework Joe does in minutes, for Methods is uniformly distributed over the interval [2, 14].
Find the expected value and standard deviation
mu = 8, sigma = 3.46
100
Find the gradient to the line when x = 3:
y=3sin((4pix)/3)
4pi
100
The sun is yellow
False, it is white
200
This can be written as a single logarithm:
What is 
200
Find the second derivative of
f(x)=ln(sin(x))
-1/sin^2x
200
A normal distribution has a mean of 100 and a standard deviation of 10. The percentage of data values that fall between the values of 70 and 90 is this.
15.85%
200
Find the acceleration after 4 seconds if the velocity of a robotic engine moving on a monorail is given by
v=3t^2 - 12t +9
12m/s2
200
People with blue eyes have better night vision
True: They believe this may be why the evolved in high latitude regions
300
log5(2x-7)=log5(3x-9)
no solution
300
Find the two non-negative numbers whose sum is 1 and whose sum of squares is as large as possible.
(0,1) and (1,0)
300
Flour from a mill is poured into bags with a weight normally distributed with a mean of 1005g and a standard deviation of 4g.
What is the weight that is exceeded by only 10% of the bags
1010.13 grams
300
The area bound by the parabola y=6x2-6x, the x axis and the lines x=1 and x=c, (c>1), is equal to 1 unit2.Find the value of the constant
c = 1.5
300
Apples and pears are a part of the rose family.
True
400
Solve for x:
2log(x)=log(3x+4)
x=4
400
Construct a window in the shape of a semi-circle over a rectangle. If the distance around the outside of the window is 12m, what dimensions will result in the rectangle having largest possible area?
x=approx 2.33m and y=3m
then A =approx 6.99m2 is the largest possible area of the rectangle.
400
Suppose that 15% of students at Comet Bay play sports. If there are 32 students in 1st period, what is the probability that less than 4 students in 1st period play sports?
0.2721
400
Evaluate the following Calc free:
d/dx int_4^(x^2) 2/(3t^3-1)dt
(4x)/(3x^6-1)
400
The Caesar salad was invented in Mexico
True
500
Solve exactly:
3^(x+1)=5^(x−4)
x=log_(5/3) (3×5^4 )
500
We want to construct a cylindrical can with a bottom but no top that will have a volume of 30 cm3. Determine the dimensions of the can that will minimize the amount of material needed to construct the can.
r=2.1216 and h=2.1215?
500
Find the expected value and variance of the probability distribution of given by:
f(x) = {(2(1-x)\ \ \ 0<x<1),(0\ \ \ elsewhere):}
E(X)=1/3
Var(X) = 1/18
500
Find the derivative of the first function and use it to solve the second function
e^(e^x )
int_0^1 e^((e^x)+x)dx
e^e-e^1
500
Studies have found that a moderate intake of alcohol is healthier then completely abstaining from alcohol
False, No alcohol is good for you