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Solve algebraically the simultaneous equations: x^2 + y^2 = 25 and y - 3x = 13

Firstly we should look at the question and notice that the two possible methods are substitution or elimination. We should then notice that since one equation is a quadratic and the other linear, then the...

Answered by Aviv S. • Maths tutor

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A curve has equation 2(x^2)+3x+10. What is the gradient of the curve at x=3

Answered by Tom E. • Maths tutor

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A curve has equations: x=2sin(t) and y=1-cos(2t). Find dy/dx at the point where t=pi/6

Since this question concerns parametric's, one may move to eliminate t from the equation to calculate dy/dx directly. However, in this case it is much easier to use the chain rule and realise that dy/dx=d...

Answered by Cameron H. • Maths tutor

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There are 5 red balls and 7 green balls in a bag. A ball is taken from the bag at random and not replaced. Then a second ball is taken from the bag. What is the probability that the 2 balls are the same colour?

Initially, there are 12 balls in the bag. Therefore the chance of the first ball being red is 5/12 and green is 7/12. The probabilities of the second ball are dependent on the first ball, as it is removed...

Answered by Stanley L. • Maths tutor

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Functions: If f(x)=3x^2 - 4 and g(x) = x + 3, 1) Evaluate f(3), 2) Find the inverse of f(x) (f^-1(x)), 3)Find fg(x).

in this case x=3 so you substitute it into f(x) to get f(3) = 3(3)² - 4 = 3*9 -4 = 27 - 4 = 232) There are 2 methods to this question, a logical method, and a more mathematical method. Th...

Answered by Jason P. • Maths tutor

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