Edexcel A Level Further Maths Core Pure EXAM QUESTIONS WITH SOLVED ANSWERS

Edexcel A Level Further Maths
Core Pure EXAM QUESTIONS
WITH SOLVED ANSWERS.

|z1 x z2| - CORRECT ANSWER✅✅|z1| x |z2|

|z1/z2| - CORRECT ANSWER✅✅|z1|/|z2|

∫1/(a^2 + x^2) - CORRECT ANSWER✅✅1/a arctan(x/a) + C

∫1/√(a^2-x^2)dx - CORRECT ANSWER✅✅arcsin(x/a)+C

1/α + 1/β + 1/γ + 1/δ = - CORRECT ANSWER✅✅(αβγ + αγδ + βγδ + αβδ) / αβγδ

1/α + 1/β + 1/γ = - CORRECT ANSWER✅✅(αβ+αγ+βγ)/αβγ

1/α + 1/β = - CORRECT ANSWER✅✅α+β/αβ

angle between plane r.n1 = k1 and r.n2 = k2 - CORRECT ANSWER✅✅cosθ = | n1.n2 /
|n1| |n2| |

angle between the line r = a + λb and plane r.n = k - CORRECT ANSWER✅✅sinθ =
|b.n/ |b| |n| |

area of a sector (polar coordinates) - CORRECT ANSWER✅✅1/2 ∫r^2 dθ

arg(z1 x z2) - CORRECT ANSWER✅✅arg(z1) + arg(z2)

arg(z1/z2) - CORRECT ANSWER✅✅arg(z1) - arg(z2)

complimentary function with 1 real root - CORRECT ANSWER✅✅y = (A + Bx) e^αx

complimentary function with 2 imaginary roots, p +/- qi - CORRECT ANSWER✅✅y =
e^px(Acosqx + Bsinqx)

complimentary function with 2 real roots - CORRECT ANSWER✅✅y = Ae^αx + Be^βx

cosh graph - CORRECT ANSWER✅✅

, cosh(A + B) - CORRECT ANSWER✅✅coshAcoshB + sinhAsinhB

cosh^2A - sinh^2A = ? - CORRECT ANSWER✅✅1

damped harmonic motion - CORRECT ANSWER✅✅d^2x/ dt^2 + kdx/dt + w^2x = 0

differentiate arccosx - CORRECT ANSWER✅✅-1/√1 - x^2

differentiate arcoshx = 1/√x^2 - 1 - CORRECT ANSWER✅✅

differentiate arcsinhx - CORRECT ANSWER✅✅1/ √x^2 + 1

differentiate arcsinx - CORRECT ANSWER✅✅1/ √1-x^2

differentiate arctan x - CORRECT ANSWER✅✅1/1+x^2

differentiate artanh x - CORRECT ANSWER✅✅1/ 1-x^2

differentiate cosh x - CORRECT ANSWER✅✅sinh x

differentiate sinh x - CORRECT ANSWER✅✅coshx

differentiate tanhx - CORRECT ANSWER✅✅sech^2x

Equation of a line (using normal) - CORRECT ANSWER✅✅r . n = a . n
where a is a point on the plane

forced harmonic motion - CORRECT ANSWER✅✅d^2x/ dt^2 + kdx/dt + w^2x = f(t)

how are cos and sin curves symmetrical (polar co-ordinates) - CORRECT
ANSWER✅✅cos curves symmetrical about the x axis
sin curves symmetrical about the y axis

how are polar co-ordinates written - CORRECT ANSWER✅✅(r, θ) where r is the
distance from the pole and θ is the angle from the initial line

how can you represent a linear transformation ? - CORRECT ANSWER✅✅using a
matrix

How can you write a complex number with modulus r and argument θ - CORRECT
ANSWER✅✅z = r(cosθ = isinθ)