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Further Mathematics

GCSE

Why is it that when 'transformation A' is followed by 'transformation B', that the combined transformation is BA and not AB?

Remember that with matrix multiplication, "A times B" does not usually equal "B times A". If we take our 'matrix X' and transform it by 'matrix A'. We perform this transformation by ca...

Answered by JOE D. • Further Mathematics tutor

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Find the gradient of the line x^2 + 3x - 6 at the point (5,34)

Differentiate: 2x + 3.Substitute for x=5: 2(5) + 3Answer =13.

Answered by Dan D. • Further Mathematics tutor

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In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]

There are x boys and y girls. So x = boys, y = girls. Ten boys join so x + 10 = boys, one girl joins so y + 1 = girls. These values are said to be equal, so we construct an equation with x and y. x + 10 =...

Answered by Betsy L. • Further Mathematics tutor

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Use the factor theorem to show that (x-1) is a factor of x^3 - 3x^2 -13x + 15

If (x-1) is a factor of x³ - 3x² -13x + 15 then one of the solutions for x must be x = 1.(This is because, if (x-1) is a factor of this equation then it is true that x-1=0, because t...

Answered by James B. • Further Mathematics tutor

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A=(1,a;0,1/2) B=(1,-1;0,2) AB=I, calculate the value of a.

First notice I is the 2x2 identity matrix (1,0;0,1) now we can form an equation to solve for a, look for an entry where a is involved the (1,2) entry of I is 0 and calculated by 1(-1)+2a=0 now solving giv...

Answered by Dylan S. • Further Mathematics tutor

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