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How do you simplify something of the form Acos(x) + Bsin(x) ?

This sort of question is quite common, and a little bit complicated, so the explanation is quite long! But it's a great one to understand. There are a few tricks you need to know to be able to do it. The fir...
JM
Answered by Jack M. • Maths tutor
15807 Views

How do you complete the square?

Say you start with a general equation of x 2 +ax+b=0. (If the x 2 has a coefficient the you will need to divide by that first.) You need to move to the equation (x+a/2) 2 -(a/2) 2 +b=0. Then put all of the c...
BC
Answered by Bryony C. • Maths tutor
3392 Views

How do you factorise?

Factorising is just simplyfying into brackets. To do this you need to find common terms on all the parts of the question. For example: fully factorise 3a 3 b+12a 2 b 2 +9a 5 b 3 the answer to the is 3a 2 b(a...
EW
Answered by Elizabeth W. • Maths tutor
7597 Views

Given f(x)=(x^3-7)*(x+4)^5, find the term x^3 of f(x).

Before starting to solve this problem, student should acknowledge that there are more than a variable, which satisfies the condition x^3. There are two ways to obtain this answer: (1) x^3 in the first multip...
AH
Answered by Amina H. • Maths tutor
1610 Views

f(x) = (4x + 1)/(x - 2) with x > 2. Find a value for 'x' such that f'(x) (first derivative of f(x) with respect to x) is equal to -1.

Re-write f(x) using indicies, so that the use of the product rule becomes more clear => f(x) = (4x + 1) *(x - 2)^-1 where ^ means 'raised to the power of' and * means 'multiplied by'. use the product rule...
ZS
Answered by Zak S. • Maths tutor
5257 Views