JeopardyProbability

10 Probability

20

Probability

30

Differentiation

10 Differentiation

20 Differentiation

30

Integration

10

Integration

20

Integration

30

Vectors

10

Vectors

20

Vectors

30

1. Given that a = i + 2j + k and b = 4i – 3j + 2k

a) Evaluate a.b

b) What can you conclude from your answer to a)?

Vectors - 10 Back to Menu

x = 4i – 3j + 2z and y = 5i +4j -7z.Find the cosine of the angle between the two

vectors xand y.

Vectors - 20 Back to Menu

Find the point of intersection of the lines below.

r = + s and r = + t

Vectors - 30 Back to Menu

If f(x) = 3cos(2x-1) and g(x) = log(2x)

a) Find f ’(x)

b) Find g ’(x)

Differentiation - 10 Back to Menu

A particle is moving in a straight line with velocity given by, v(t) = -t² + t + 5, where t is time in seconds and v is metres per second.a) Find the particle’s maximum velocity, and confirm by using calculus that this value is a maximum.

b) Find the acceleration at 5 seconds.

Differentiation - 20 Back to Menu

An equation of a curve is given as y = x³ + 2x² + 3x + 1.

a) Find the gradient function,, and hence find the gradient ofthe curve at the point where x=2.

b) Find the equation of the normal to the curve at the point where x=2, giving your answer in the form ax + by + c = 0.

Differentiation - 30 Back to Menu

Find ∫ dx

Integration - 10 Back to Menu

Find the volume of revolution formed when y = sin(x) +

2 is turned through 360 degrees about the x-axis

between 0 and 2π.

Integration - 20 Back to Menu

f(x) = and g(x) = where 5 .Find the area created between the two functions, shown in the diagram as the shaded region.

Integration - 30 Back to Menu

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement.(a) The first two apples are green. What is the probability that the third apple is red?

(b) What is the probability that exactly two of the three apples are red?

Probability - 10 Back to Menu

A box contains 35 red discs and 5 black discs. A disc is selected at random and its colour noted. The disc is then replaced in the box.(a) In eight such selections, what is the probability that a black disc is selected(i) exactly once?

(ii) at least once?

Probability - 20 Back to Menu

Intelligence Quotient (IQ) in a certain population is normally distributed with a mean of 100 and a standard deviation of 15.a) What percentage of the population has an IQ between 90 and 125?

(b) If two persons are chosen at random from the population, what is the probability that both have an IQ greater than 125?

Probability - 30 Back to Menu