OCR GCE AS Level Further Maths B (MEI) Core Pure June 2022 question paper Y410

Hence solve the equations.

Show that the vector i + 4 j + 2 k is parallel to the plane 2 x + y - 3 z = 10.

Determine the acute angle between the planes 2 x + y - 3 z = 10 and x - y - 3 z = 3.

The complex number z satisfies the equation 5 (z - i) = (- 1 + 2 i) z *.

Determine z, giving your answer in the form a + b i, where a and b are real.

In this question you must show detailed reasoning.

Determine the roots in exact form.

An Argand diagram is shown below. The circle has centre at the point representing 1 + 3i, and the half line intersects the circle at the origin and at the point representing 4 + 4i.

State the two conditions that define the set of complex numbers represented by points in the

shaded segment, including its boundaries.

Use induction to prove the result in part (a).

On an Argand diagram, the point A represents the complex number z with modulus 2 and argument . The point B represents

Sketch an Argand diagram showing the origin O and the points A and B.

The point C is such that OACB is a parallelogram. C represents the complex number w.

Determine each of the following.

• The modulus of w, giving your answer in exact form.

• The argument of w, giving your answer correct to 3 significant figures.

Show that T leaves areas unchanged for all values of θ.

Find MN^-1.

Hence describe fully a sequence of two transformations of the plane that is equivalent

to T.