Calculus
Find f ' (2) for f(x) = x2 - ln (5 - x)
13/3
The amount of total minutes late per student for classes during year 12 are normally distributed with a mean of 68 minutes and a Standard deviation of 24 minutes. Zander was a total of 140 minutes late during year 12. What is the probability that a student was late more often than Zander?
0.15%
Solve sin x = 0.75 for 0 < x < 2π , leave your answer to 3 decimal places.
0.848, 2.294
It is given that f(x)=5x-8 and g(x)=x2+x.
Find f(f(3)) + g(f(-1))
183
A geometric progression has a common ratio of 2.2 and a first term of 0.22. Find the 22nd term.
3, 414, 278.774
Differentiate y = x3 e2x
y ' = 3x2e2x + 2x3e2x
It is known at the beginning of winter in a large population, 15% of the people in the population will be infected with a particular virus. Four people are selected at random, find the probability that at least one of them has the virus. Give your answer to 3 decimals.
0.478
Three towns, A, Band C form a triangle. Town A is 80km from Town B and Town C is 40km from Town A.
The bearing of Town B from Town A is 130 degrees.
The bearing of Town C from Town A is 240 degrees.
Find the distance between Town B and Town C, to the nearest km.
101 km
Solve 3|2x + 1| = 21
x = -4 and x = 3
Find the sum of the first 12 terms of the series
2 + 11 + 20 + 29 + ...
618
Integrate cos x between the bounds of pi/4 and pi/3, leaving your answer to 2dp
0.16
P (X = 1) = 0.6
P (X = 2) = 0.11
P (X = 3) = 0.08
P (X = 4) = 0.2
P (X = 5) = 0.01
Find P(X>=4|X>2)
0.525
Solve 2cos2x - 3cosx - 2 = 0 for 0 < x < 180 degrees
120 degrees.
State the coordinates of the image of A after the following transformations:
- dilation, scale factor of 2 in the y-direction
- reflection in the x- axis
- translation 5 units to the left in the x-direction
(-6, - 6)
Find the value(s) of m given that m, 3m, m2+20 are consecutive terms of a G.P.
m = 4 and m = 5
The curve g(x) passes through (-2, 3) and has a gradient function of g'(x)=3x5 - 4x + 1. Find g(6)
23 243
100 students are in Year 12. They are asked whether they do Cross Fit or Swimming. 48 students do neither sports, while 37 swim and 21 do Cross Fit.
Find the probability that a student swims, given that they do not do Cross Fit.
31/79
cot x = - 0.4, with x being an obtuse angle.
Find the value of sec x.
- sqrt (29) / 2
For what values does kx2 - 2x + 2 = 0 have no real roots?
k > 1/2
What is the value of:
ln 2 + ln 4 + ln 8 + ... + ln 22n
n(2n + 1) ln 2
A swimming pool is to be emptied for maintenance. The quantity of water, Q in litres, remaining in the pool at a time, t minutes is given by:
Q(t) = 2000(25 - t)2 for 0<=t<=25
The pool begins to be emptied at 9:47am.
Find the time when the rate of flow of water is 20kL/min.
10:07am
A pdf is defined as f(x) = ke-x in the domain [0, 3].
Find the median value of the pdf.
0.645
The hours of screen time a student spends in a fortnight can be modelled by h(t) = a sin (π t/7) + b.
t is time in days and 0<=t<=14. The hours of screen time reaches a max of 5 hours halfway through day 3 and a min of 1 hour halfway through day 10.
How many days will the screen time be 2 hours or below?
4 2/3 days
A curve has an equation y = x3 - 12x2 + 36x with a domain of 0 <=x<=9.
Find the maximum value of the curve within this domain.
81
A sapling with a heigh of 50cm is planted in the ground. After 1 week of being planted, it grows 20% of its height. Each week thereafter, it grows 20% of the previous week's growth. Find the maximum height of the tree.
62.5cm