Search our library of Maths A Level questions

Top answers

Maths

A Level

Express the equation cosecθ(3 cos 2θ+7)+11=0 in the form asin^2(θ) + bsin(θ) + c = 0, where a, b and c are constants.

We must first use the identity cosecθ = 1/sinθ. Now the equation becomes (1/sinθ)(3 cos 2θ+7)+11=0. Since we know that the question is asking for the answer in the form of asin²θ + bsinθ + c = ...

Answered by George L. • Maths tutor

5545 Views

Explain why for any constant a, if y = a^x then dy/dx = a^x(ln(a))

So let's start with taking the natural log on both sides of y=a^x, giving us ln(y) = ln(a^x). Using the laws of logarithms we can write this as ln(y) = xln(a).Next, we differentiate bo...

Answered by James M. • Maths tutor

9869 Views

How does one find the equation of a line passing through 2 points of a graph?

The general equation for a line on a graph is: y = mx + b ,where a is called the slope of the graph and b is the y-intercept(or the point where the line crosses the y axis). Let's assume the 2 points have...

Answered by Dimitar D. • Maths tutor

4233 Views

f(x) = x^3 - 13x^2 + 55x - 75 , find the gradient of the tangent at x=3

f(x) = yy= x³- 13x² + 55x - 751) find f'(x) [=dy/dx] Differentiation is (1) multiplying the coefficient by the original power --> 2) reducing the original power by 1dy/dx = 3x

Answered by Kiitan O. • Maths tutor

3145 Views

Solve 2sin2θ = 1 + cos2θ for 0° ≤ θ ≤ 180°

sin2θ = 2sinθcosθ (double angle formula for sine)cos2θ = cos²θ - sin²θ (double angle formula for cosine) = 2cos²θ - 1 (utilising the trignometric identit...

Answered by Samuel N. • Maths tutor

11446 Views