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This is a common question asked by young students and adults, which demotivates them to study and prevents passion from being the driving force during the tougher chapters. Mathematics is used in every in...

Firstly, we note that a 'root' is simply a solution of the equation (at least, in this case). Let's start from what we've been told: x = 1/2 is a root of the equation. Since it's a solution, let's sub it ...

a) ask student: purpose of differentiation (i), how to perform differentiation (ii) (i) to find the gradient of a curve (ii) multiply the coefficient of x by its indice then minus one from the indici perf...

Recall that ∫uv'=uv- ∫u'v Set u=sin²(x), v'=1 Therefore u'=2sin(x)cos(x) and v=x which gives us the following:

∫sin²(x)dx = xsin²(x) - ∫2xsin(x)cos(x)dx

The second integral in the above expr...

we start  y factoring and solving for each equation:

cos(x) (2cos(x) - 1) = 0 

this means: 

cos(x) = 0 and cos(x) = 1/2

from the first equation we get:   x = 90

and from...