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There are two possible outcomes in which all beads are the same colour: they may be all green, or all black. We need to work out the probability of each outcome to start with. This is done by multiplying ...
(a) The curve is defined by y=(2x-3)^5. To find x=w when y=-32, we must substitute these values into the equation C and re-arrange to find w. -32=(2w-3)^5. First we must remove the power of 5 by doing pow...
The equation of a straight line is usually given in the form y = mx + c. To prove that two lines are parallel we will need to show that both lines have the same gradient. The gradient of a line is the slo...
This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = piint_{a}^{b} y2dx to find the expression V =...
Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +......
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