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1.1 Counting


(a) Where in the world do we find some early evidence that people counted? (1)


(b) Approximately to what year does this evidence date back? (1)


(c) Give detail of how counting was done in the example which you chose. (2)


(c) Where in CAPS is this type of counting covered as a topic? (1)

The arithmetic signs of qrev denote the loss heat by the of system and the gain of heat by the surrounding. since Tsys > Tsun in this case the the entropy change for the surroundings will be greater than that will give a por so the sum ASsys and ASsun OF positive value For ∆SunivThe arithmetic signs of qrev denote the loss heat by the of system and the gain of heat by the surrounding. since Tsys > Tsun in this case the the entropy change for the surroundings will be greater than that will give a por so the sum ASsys and ASsun OF positive value For ∆Suniv

24. The demand curve and supply curve for one-year discount

bonds with a face value of $1,000 are represented by the

following equations:

Bd : Price = -0.8 * Quantity + 1100

Bs : Price = Quantity + 680

a. What is the expected equilibrium price and quantity

of bonds in this market?

b. Given your answer to part (a), what is the expected

interest rate in this market?


Write an if-else statement for the following:

If userTickets is not equal to 6, execute awardPoints = 10. Else, execute awardPoints = userTickets.

Ex: If userTickets is 14, then awardPoints = 10.


Given that a = 3i - 5j, determine the angle vector a makes with the positive x-axis b. Given that c = 5i + 3j, d = 3i – 2j. Find the magnitude of (i) c + d (ii) c – d

Find the direction cosine (l, m, n) of vector r = 3i -2j + 6k b. Given that p = -12 and q = 1. Find a unit vector u such that │u│= 35 and u is the direction of p-3q 5 -1

A genetics research group has determined the sequence of a rat gene thought to be

involved in controlling the fertilising ability of rat sperm. They believe a similar gene may

control fertility in humans. Describe how what is known about the rat gene can be applied

in PCR to clone the complementary human gene. You should explain the experimental

approach taken and how it could confirm that the human gene in question does indeed

correspond to the rat gene.


Find the probanility of getting.

a.fewer than 4 head.

b.exactly 4 head.

C.not more than 4 head.

d.two or more heads.


5 Test the following numbers for divisibility by 6, 9 and 11. (Do not divide or factorise.)


a) 6 798 340


b) 54 786 978

How many different committees of 5people can be chosen from 10 people

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