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Maths
A Level

OCR C2 2015 Question 8: (a) Use logarithms to solve the equation 2^(n-3) = 18,000 , giving your answer correct to 3 significant figures. (b) Solve the simultaneous equations log2(x) + log2(y) = 8 & log2(x^2/y) = 7.

(a)This question actually tells us what to do. It is very hard to miss "use logarithms to solve...". So our first step is going to be to use logs (espec...

Answered by Jonathan H. Maths tutor
6500 Views

How do you integrate sin(3x)cos(5x)?

STEP 1 Cannot integrate directly in this form, therefore use a trigonometric identity. Identity: sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2) STEP 2 (A+B)/2 = 3x             A + B = 6x   (1) (A-B)/2 = 5x  ...

Answered by Catherine F. Maths tutor
6900 Views

Why does the constant disappear when differentiating a function?

We can think of the constant term in a function in terms of x, for example in x^2 + 3x + 2 as 2 being multiplied by x^0. Anything to the power of 0 is equal to one, so in our example we would have 2 * x^ ...

Answered by Abdullah P. Maths tutor
9474 Views

Can you show me why the integral of 1/x is the natural log of x?

We can break this down into steps, going deeper each time. First we might just say: well, since integration is fundamentally the inverse process of differentiation and we know that the derivative of ln(x)...

Answered by James L. Maths tutor
7224 Views

(C3 question). Find an expression for all stationary points on the curve y=sin(x)cos(x). How many such points are there and why?

Stationary points are points at which the gradient of the curve is zero. The gradient is given by dy/dx so we start by computing this using product rule to give us dy/dx=-sin2x+cos2x...

Answered by Tristan G. Maths tutor
4737 Views

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