Math

functions

250

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.

500

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

750

For what value of c is the line y = 3x +c a tangent to the parabola with equation y = x² —5x+7?

c=-9

1000

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

1250

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 (x_p−x_q)² in terms of m.(Hint: Use Quadratic formula)  

1. discriminant greater than 0.

2. m²+76.

trig

250

Solve for x on the domain 0≤x≤2pi

tanx=1/sqr3

x= pi/6, 7pi/6

500

solve: 2sinx-1=0,   0≤x≤2pi

x= pi/6, 5pi/6

750

solve:cos2x+1=0,   0≤x≤4pi

x= pi/2, 3pi/2. 5pi/2, 7pi/2

1000

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

1250

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

log

250

solve: lnx=2

x=e²

500

DOUBLE POINTS QUESTION

Solve for x: log₂(x+1) +log₂(x-3)=3

x= 1+2sqr3

750

differentiate: y=ln(3x+1)

dy/dx=3/(3x+1)

1000

find lim x to infinity for lnx/x

0

1250

solve: ln(x+2)<1

-2<x<e-2

statistics

250

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

500

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

750

a fair die is rolled 3 times. Find the probability of getting exactly two 6's

5/72

1000

a class has 7 boys and 5 girls. 3 students are chosen randomly. Find the probability exactly 2 are girls. 

7/22

1250

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

calc

250

differentiate: y=4x²

8x

500

find integral of (3x+2)dx

3/2x²+2x+C

750

find the gradient of y=x²+3x, when x=2

7

1000

Find the stationary point of y=x²-8x+5

(4,-11)

1250

find the equation of the tangent to y=x²-3x at x=-1

y=-5x-1