Number and Algebra
The first 4 terms of an Arithmetic Sequence is:
4, 7, 10, and 13
Find the 100th Term
301
If a problem says, "Show that two functions intersect at the point (3,2)," will you receive credit for plugging (3,2) into both functions?
No, you need to solve for the intersection point of the functions. Likely the problem is giving you the answer so you can use it in the next part of the problem.
A sphere's volume is roughly 8,580cm3.
What is the radius of the sphere?
12.7cm
At a school, 70% of students play a sport and 20%of the students are involved in band. 18% of the students do neither activity.
Find the probability that a random student plays a sport and is involved in band.
8%
Differentiate the function:
f(x)=x4+2x3-4x2+7x-2
f'(x)=4x3+6x2-8x+7
Why can't I simplify x2 / (x-2) to x / (1-2)?
That's a partial cancellation. I need to be able to cancel an x from both terms in the denominator.
Find the vertex for the function: h(t)=-2t2+20t+8
If this function modeled a ball being thrown, what does the vertex and positive x intercept represent?
(5,58)
The highest Point.
When the ball hit the ground.
A pizza with 8 slices and a diameter of 12 inches has one slice missing. The angle of the missing slice's sector is 45o.
What is the area of the remaining pizza?
99.0 in2
The following table shows how many hours a certain number of students spend exercising each week:
Time Excersising #of Students
2hours 5
3hours 1
4hours 4
5hours 3
6hours 7
Find the standard deviation.
1.56
Consider the function f(x)=x2
Find the equation of the tangent to f(x) when x=2
y=4x-4
Slove for x in terms of e2 when:
2 ln x = ln 9 + 4
x=3e2
A bird watcher modeled the migration of birds using the function P(t)=1350+400(1.25)-t where (P) represents Population and (t) represents time.
Calculate when the bird population will decrease below 1400.
9.32 days
Work as fast as you can answering only problems you feel confident on. Skip the rest and come back to them later.
The following table shows the probability of a weighted tetrahedral die rolling on each given value:
Roll: 1 2 3 4
P(X=x) k2 7k+2 -2k 3k2
Find the value of k.
(-1/4)
What is f'(x) if for the function f(x)=x2 - (k/x)
2x - (k/x2)
A geometric sequences common ratio (r) is 2
The sum of the first 5 terms in the sequence is 31.
What is the 1st term in the sequence?
1
The height of a single point on a spoked wheel is modeled by the function h(t)=10cos(2𝜋t) where h is height inches and t is time in seconds.
How long does it take a single spoke of the wheel to make a full rotation? How far has the outside edge of the spoke traveled?
1 second
20pi or 62.8 inches
The lenghts of two sides of Triangle ABC are: AB=6 and AC=8, and the cosA=(5/6)
What is the area of the triangle?
13.3 units2
A and B are events such that P(A) = 0.5, P(B) = 0.4 and P(AUB) = 0.6
Find P(A|B)
.75
When does the integral of xn involve a natural log?
When n=-1. That's it, that's the only time. Otherwise, use the power rule.
I take out a $100,000 30 year loan to buy a home. The bank gives ma an intrest rate of 6% compunded annually. What is my monthly payment?
$599.55
A quadratic function has a vertex of (-2,10) and an x intercept of (2,0).
What is the other x intercept?
(-6,0)
Solve: sin(2x) + cos(2x) - 1 + cos(x) - sin(x) = 0 |for all solutions between 0 and 2pi.
7pi/6
11pi/6
pi/4
5pi/4
How many days is Fiona expected to arrive at school on time?
151 days
A curve passing through the following points:
(0,2) (2,5) (4,7) (6,3) (8,3) (10,10)
Given that the curve is a cubic function, find the area under the curve betwen the x axis and x=0 through 10.
48.2