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Jeopardy

Jeopardy. Differentiation 10. Integration 10. Vectors 10. Probability 10. Probability 2 0. Differentiation 2 0. Integration 2 0. Vectors 2 0. Probability 3 0. Differentiation 3 0. Integration 3 0. Vectors 3 0. Vectors - 10. Back to Menu.

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Jeopardy

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  1. Jeopardy Differentiation 10 Integration 10 Vectors 10 Probability 10 Probability 20 Differentiation 20 Integration 20 Vectors 20 Probability 30 Differentiation 30 Integration 30 Vectors 30

  2. Vectors - 10 Back to Menu 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)?

  3. Vectors - 20 Back to Menu x = 4i – 3j + 2z and y = 5i +4j -7z. Find the cosine of the angle between the two vectors x and y.

  4. Vectors - 30 Back to Menu Find the point of intersection of the linesbelow. r = + sand r = + t

  5. Differentiation - 10 Back to Menu If f(x) = 3cos(2x-1) and g(x) = log(2x) • Find f ’(x) • Find g ’(x)

  6. Differentiation - 20 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 metresper 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.

  7. Differentiation - 30 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 ofthecurve 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.

  8. Integration - 10 Back to Menu Find ∫dx

  9. Integration - 20 Back to Menu Find the volume of revolution formed when y = sin(x) + 2 is turned through 360 degrees about thex-axis between0 and2π.

  10. Integration - 30 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.

  11. Probability - 10 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?

  12. Probability - 20 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?

  13. Probability - 30 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?

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