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Further Mathematics

GCSE

Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.

Factorising denominator of fraction:x^2 + 10x + 21 = (x+3)(x+7)2) Partial fractions:f(x) = 12/(x+3)(x+7); let f(x) = A/(x+3) + B/(x+7)then equating the nomi...

Answered by Camilla Giulia B. • Further Mathematics tutor

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Why does tanx = sinx/cosx ?

This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse side...

Answered by Shehan R. • Further Mathematics tutor

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A straight line passes trough the points A(-4;7); B(6;-5); C(8;t). Use an algebraic method to work out the value of t.

We can write the equation of a straight line like y=ax+b, where a and b are constants. If a point is on the line, the equation will be true for the x,y of the point.Now start with point A: 7 = (-4)a + b. ...

Answered by Márk F. • Further Mathematics tutor

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(x+4)((x^2) - kx - 5) is expanded and simplified. The coefficient of the x^2 term twice the coefficient of the x term. Work out the value of k.

(x + 4) (x² - kx - 5) = x³- kx² - 5x + 4x² - 4kx - 20 = x³ + (4-k)x² + (-5-4k)x - 20.The coefficients are: (4-k) of x² and (-...

Answered by Márk F. • Further Mathematics tutor

9371 Views

Find the coordinates of the stationary points on the curve y=x^5 -15x^3

dy/dx = 5x⁴-45x²by multiplying each term by the power and then decreasing the power by oneAt stationary points, dy/dx=0 since the function is neither increasing nor decreasing at a ...

Answered by Shavon D. • Further Mathematics tutor

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