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Further Mathematics

GCSE

A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

^dy/_dx = 9x^2 + 2ax + b

x = 2, ^dy/_dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, ^dy/_dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

Answered by Alistair R. • Further Mathematics tutor

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How can you divide an algebraic expression by another algebraic expression?

I would begin the session with checking a basic understanding of the methods of long division, as these will not have been taught very recently. Many students will have been using short division, as it is...

Answered by Jane H. • Further Mathematics tutor

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Show that (n^2) + (n+1)^2 + (n+2)^2 = 3n^2 + 6n + 5, Hence show that the sum of 3 consecutive square numbers is always 2 away from a multiple of 3.

Expanding out the Brackets: (n²)+ (n² + n + n + 1) + (n² + 2n + 2n +4) = (n²) + (n²+2n+1) + (n²+4n+4) =3n² + 6n +5 Using this r...

Answered by James C. • Further Mathematics tutor

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Consider the Matrix M (below). Find the determiannt of the matrix M by using; (a) cofactor expansion along the first row, (b) cofactor expansion along the second column

Matrix M is

-2 1 -4

1 -1 5

3 0 2

Let A be a square nxn matrix. Then, for each entry Aij (where 1 </= i < n, 1 </= j < n), the minor of Aij is A(^i;^j), the deter...

Answered by Evi T. • Further Mathematics tutor

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Can you explain induction and go through an example?

Induction is a method that can be used to prove that a mathematical statement holds for possitive integers, n. It usually consists of four steps, as follows: 1) Basis: Show that the statement to be prove...

Answered by Adamos S. • Further Mathematics tutor

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