Search our library of Maths A Level questions

Top answers

Maths

A Level

Given that 3^(-3/2) = a* 3^(1/2), find the exact value of a.

3^(3/2) = a * 3^(1/2)
3^(1/2) * 3^(-2) = 3^(3/2)Therefore a must be equal to 3^(-2)a = 1/9

Answered by Oliver W. • Maths tutor

3316 Views

A curve with equation y = f(x) passes through the point (4,25). Given that f'(x) = (3/8)*x^2 - 10x^(-1/2) + 1, find f(x).

f'(x) = (3/8)x^2 - 10x^(-1/2) + 1Each term must be integrated (increase the power by 1 and divide by the new power), remembering to include + c.f(x) = (3/8)(x/3)^3 - 10*(2x)^(1/2) + x + cf(x) = (...

Answered by Oliver W. • Maths tutor

7458 Views

Use the substitution u=1+e^x to find the Integral of e^(3x) / (1 + e^x)

e^x=u-1 so e^3x=(u-1)³ and du/dx = e^x so rearranging gives dx=e^-x du Substituting all that information in the integral we get Integral ( (u-1)^...

Answered by Ismet P. • Maths tutor

9569 Views

The gradient of the curve at point (x,y) is given by dy/dx = [7 sqrt(x^5)] -4. where x>0. Find the equation of the curve given that the curve passes through the point 1,3.

I like this question because it can be broken down into parts, each which contain an important reminder/lesson for an A level/GCE maths student. I would start the lesson by running through the rules of in...

Answered by Michael S. • Maths tutor

3828 Views

Find the turning points of the curve (x^3)/3 + x^2 -8x + 5

Step one, we need to assess what the question is asking us to do, in this case, find the turning points.The turning points on the graph are where the gradient is equal to zero, so in order to find the tur...

Answered by Ellie M. • Maths tutor

2759 Views