functions
Is it possible to bend a 20 cm length of wire into a rectangle with area 30 cm2? why?
no, because a 20 cm perimeter can only make a maximum area of 25cm2.
Solve for x on the domain 0≤x≤2pi
tanx=1/sqr3
x= pi/6, 7pi/6
solve: lnx=2
x=e2
a bag contains 5 red and 3 blue marbles. if you pick only 2 marbles out, what is the probability that you pick 1 of each.
15/28
differentiate: y=4x2
8x
Find the maximum or minimum value of y = —2x2 +4x + 3, and the value of x at which this occurs.
Maximum value is 5 and it occurs at x=1
solve: 2sinx-1=0, 0≤x≤2pi
x= pi/6, 5pi/6
DOUBLE POINTS QUESTION
Solve for x: log2(x+1) +log2(x-3)=3
x= 1+2sqr3
A bag contains 6 red, 4 blue, and 2 green marbles. Two marbles are chosen without replacement. Find the probability both are different colors.
2/3
find integral of (3x+2)dx
3/2x2+2x+C
For what value of c is the line y = 3x +c a tangent to the parabola with equation y = x2 —5x+7?
c=-9
solve:cos2x+1=0, 0≤x≤4pi
x= pi/2, 3pi/2. 5pi/2, 7pi/2
differentiate: y=ln(3x+1)
dy/dx=3/(3x+1)
a fair die is rolled 3 times. Find the probability of getting exactly two 6's
5/72
find the gradient of y=x2+3x, when x=2
7
Let f(x)=(4x+2)/(2x−1), for x ≠ 1/2.
1. find the y-intercept of f
2. Write down lim x→∞ (4x+2)/(2x-1)
1. y-intercept of is (0,-2)
2. 2
Barry is at the top of an 80m cliff looking at two yachts at sea, "Seaview" and "Nauti Buoy." Seaview is at an angle of depression of 25, and Nauti Buoy is at an angle of depression of 35∘The angle between the lines of sight to the two yachts is 70∘Find the direct distance between the two yachts to 3 significant figures.
193m
find lim x to infinity for lnx/x
0
a class has 7 boys and 5 girls. 3 students are chosen randomly. Find the probability exactly 2 are girls.
7/22
Find the stationary point of y=x2-8x+5
(4,-11)
A line through A(−4,3) with gradient m intersects y=x2+8x at points P and Q. The distance PQ=11
1.Given that x2+(8−m)x+(−4m−3)=0, determine the condition on m for two distinct intersections.
2. Find (xp−xq)2 in terms of m.(Hint: Use Quadratic formula)
1. discriminant greater than 0.
2. m2+76.
In triangle ABC, side a=4 and side b=5cm. Let θ be the angle between these two given sides, and suppose the triangle has an area of 5cm2
1. find the exact value of sin(θ)
2. Hence determine the two possible values of θ in radians
1. 1/2
2. pi/6, 5pi/6
solve: ln(x+2)<1
-2<x<e-2
a biased coin lands heads with probability 0.65. it is flipped 5 times. find the probability of getting at least 4 heads.
0.4284
find the equation of the tangent to y=x2-3x at x=-1
y=-5x-1